<?xml version="1.0" encoding="UTF-8"?>
 <rdf:RDF xmlns="http://purl.org/rss/1.0/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:taxo="http://purl.org/rss/1.0/modules/taxonomy/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://web.resource.org/cc/" xmlns:syn="http://purl.org/rss/1.0/modules/syndication/" xmlns:admin="http://webns.net/mvcb/">
  <channel rdf:about="http://pinboard.in">
    <title>Pinboard (cshalizi)</title>
    <link>https://pinboard.in/u:cshalizi/public/</link>
    <description>recent bookmarks from cshalizi</description>
    <items>
      <rdf:Seq>	<rdf:li rdf:resource="https://arxiv.org/abs/2006.13948"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2303.04871"/>
	<rdf:li rdf:resource="https://nowpublishers.com/article/Details/MAL-090"/>
	<rdf:li rdf:resource="https://sociologicalscience.com/articles-v4-15-353/"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2105.02499"/>
	<rdf:li rdf:resource="https://www.annualreviews.org/doi/abs/10.1146/annurev-control-061820-083817"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1705.00395"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2103.06885"/>
	<rdf:li rdf:resource="https://www.tandfonline.com/doi/full/10.1080/01621459.2020.1841646"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1401.5226"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2101.01535"/>
	<rdf:li rdf:resource="https://www.cambridge.org/core/journals/proceedings-of-the-international-astronomical-union/article/potential-of-likelihoodfree-inference-of-cosmological-parameters-with-weak-lensing-data/0E1FEF317A0C09039B52C8791E63670D"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1706.06296"/>
	<rdf:li rdf:resource="https://www.cambridge.org/9781108477444"/>
	<rdf:li rdf:resource="https://www.tandfonline.com/doi/full/10.1080/01621459.2020.1775614"/>
	<rdf:li rdf:resource="https://projecteuclid.org/euclid.aos/1594972830"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2011.01379"/>
	<rdf:li rdf:resource="https://link.springer.com/article/10.1007/s11222-019-09905-w"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1909.12902"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1909.12898"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1909.05097"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1909.03093"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1908.06319"/>
	<rdf:li rdf:resource="https://onlinelibrary.wiley.com/doi/abs/10.1111/sjos.12405"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1905.09944"/>
	<rdf:li rdf:resource="https://link.springer.com/article/10.1007/s11203-018-9172-1"/>
	<rdf:li rdf:resource="http://dx.doi.org/10.1002/rsa.10073"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1802.03426"/>
	<rdf:li rdf:resource="http://www.pnas.org/content/115/4/E639"/>
	<rdf:li rdf:resource="https://www.mitpressjournals.org/doi/abs/10.1162/neco_a_01035"/>
	<rdf:li rdf:resource="http://papers.nips.cc/paper/7213-poincare-embeddings-for-learning-hierarchical-representations"/>
	<rdf:li rdf:resource="http://www.calvinmurdock.com/aca/"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1602.00531"/>
	<rdf:li rdf:resource="http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00759"/>
	<rdf:li rdf:resource="http://link.springer.com/article/10.1007/BF01200757"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1503.00173"/>
	<rdf:li rdf:resource="http://projecteuclid.org/euclid.aos/1392733185"/>
	<rdf:li rdf:resource="http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00684"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1211.3046"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1406.0873"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/0907.0199"/>
	<rdf:li rdf:resource="http://www.tandfonline.com/doi/abs/10.1080/01621459.2013.849199#.Uztl8tx_Tuc"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1402.0119"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1401.0267"/>
	<rdf:li rdf:resource="http://projecteuclid.org/euclid.aos/1388545673"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1401.6978"/>
	<rdf:li rdf:resource="http://eliassi.org/papers/gilpin-kdd2013.pdf"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1310.5089"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1306.1350"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1309.4054"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1309.2895"/>
	<rdf:li rdf:resource="http://www.pnas.org/content/110/31/12535.abstract"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1305.7255"/>
	<rdf:li rdf:resource="http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00465"/>
	<rdf:li rdf:resource="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.ss/1369147911"/>
	<rdf:li rdf:resource="http://biomet.oxfordjournals.org/content/100/2/371.short?rss=1"/>
	<rdf:li rdf:resource="http://jmlr.csail.mit.edu/papers/v14/chen13a.html"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1304.6487"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1304.6663"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1304.5802"/>
	<rdf:li rdf:resource="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aos/1364302741"/>
	<rdf:li rdf:resource="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aos/1364302742"/>
	<rdf:li rdf:resource="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.imsc/1362751182"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1302.2752"/>
	<rdf:li rdf:resource="http://biomet.oxfordjournals.org/content/100/1/75.short?rss=1"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1302.4881"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1002.4283"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1104.3472"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1205.6040"/>
	<rdf:li rdf:resource="http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00407"/>
      </rdf:Seq>
    </items>
  </channel><item rdf:about="https://arxiv.org/abs/2006.13948">
    <title>[2006.13948] Extracting the main trend in a dataset: the Sequencer algorithm</title>
    <dc:date>2023-03-21T15:25:36+00:00</dc:date>
    <link>https://arxiv.org/abs/2006.13948</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Scientists aim to extract simplicity from observations of the complex world. An important component of this process is the exploration of data in search of trends. In practice, however, this tends to be more of an art than a science. Among all trends existing in the natural world, one-dimensional trends, often called sequences, are of particular interest as they provide insights into simple phenomena. However, some are challenging to detect as they may be expressed in complex manners. We present the Sequencer, an algorithm designed to generically identify the main trend in a dataset. It does so by constructing graphs describing the similarities between pairs of observations, computed with a set of metrics and scales. Using the fact that continuous trends lead to more elongated graphs, the algorithm can identify which aspects of the data are relevant in establishing a global sequence. Such an approach can be used beyond the proposed algorithm and can optimize the parameters of any dimensionality reduction technique. We demonstrate the power of the Sequencer using real-world data from astronomy, geology as well as images from the natural world. We show that, in a number of cases, it outperforms the popular t-SNE and UMAP dimensionality reduction techniques. This approach to exploratory data analysis, which does not rely on training nor tuning of any parameter, has the potential to enable discoveries in a wide range of scientific domains."]]></description>
<dc:subject>to:NB dimension_reduction time_series</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c9fd387ee16a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2303.04871">
    <title>[2303.04871] Discovering a change point in a time series of organoid networks via the iso-mirror</title>
    <dc:date>2023-03-17T18:12:06+00:00</dc:date>
    <link>https://arxiv.org/abs/2303.04871</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Recent advancements have been made in the development of cell-based in-vitro neuronal networks, or organoids. In order to better understand the network structure of these organoids, [6] propose a method for inferring effective connectivity networks from multi-electrode array data. In this paper, a novel statistical method called spectral mirror estimation [2] is applied to a time series of inferred effective connectivity organoid networks. This method produces a one-dimensional iso-mirror representation of the dynamics of the time series of the networks. A classical change point algorithm is then applied to this representation, which successfully detects a neuroscientifically significant change point coinciding with the time inhibitory neurons start appearing and the percentage of astrocytes increases dramatically [9]. This finding demonstrates the potential utility of applying the iso-mirror dynamic structure discovery method to inferred effective connectivity time series of organoid networks."]]></description>
<dc:subject>to:NB neural_data_analysis network_data_analysis change-point_problem re:network_differences dimension_reduction</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5859e41f08a4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:change-point_problem"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:network_differences"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://nowpublishers.com/article/Details/MAL-090">
    <title>now publishers - Minimum-Distortion Embedding</title>
    <dc:date>2021-10-18T13:50:48+00:00</dc:date>
    <link>https://nowpublishers.com/article/Details/MAL-090</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider the vector embedding problem. We are given a finite set of items, with the goal of assigning a representative vector to each one, possibly under some constraints (such as the collection of vectors being standardized, i.e., having zero mean and unit covariance). We are given data indicating that some pairs of items are similar, and optionally, some other pairs are dissimilar. For pairs of similar items, we want the corresponding vectors to be near each other, and for dissimilar pairs, we want the vectors to not be near each other, measured in Euclidean distance. We formalize this by introducing distortion functions, defined for some pairs of items. Our goal is to choose an embedding that minimizes the total distortion, subject to the constraints. We call this the minimum-distortion embedding (MDE) problem.
"The MDE framework is simple but general. It includes a wide variety of specific embedding methods, such as spectral embedding, principal component analysis, multidimensional scaling, Euclidean distance problems, dimensionality reduction methods (like Isomap and UMAP), semi-supervised learning, sphere packing, force-directed layout, and others. It also includes new embeddings, and provides principled ways of validating or sanity-checking historical and new embeddings alike.
"In a few special cases, MDE problems can be solved exactly. For others, we develop a projected quasi-Newton method that approximately minimizes the distortion and scales to very large data sets, while placing few assumptions on the distortion functions and constraints. This monograph is accompanied by an open-source Python package, PyMDE, for approximately solving MDE problems. Users can select from a library of distortion functions and constraints or specify custom ones, making it easy to rapidly experiment with new embeddings. Because our algorithm is scalable, and because PyMDE can exploit GPUs, our software scales to problems with millions of items and tens of millions of distortion functions. Additionally, PyMDE is competitive in runtime with specialized implementations of specific embedding methods. To demonstrate our method, we compute embeddings for several real-world data sets, including images, an academic co-author network, US county demographic data, and single-cell mRNA transcriptomes."
]]></description>
<dc:subject>to:NB to_read dimension_reduction principal_components graph_embedding re:hyperbolic_networks</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:828ed2b065ef/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:graph_embedding"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:hyperbolic_networks"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://sociologicalscience.com/articles-v4-15-353/">
    <title>Improving the Measurement of Shared Cultural Schemas with Correlational Class Analysis: Theory and Method | Sociological Science</title>
    <dc:date>2021-06-27T18:49:19+00:00</dc:date>
    <link>https://sociologicalscience.com/articles-v4-15-353/</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Measurement of shared cultural schemas is a central methodological challenge for the sociology of culture. Relational Class Analysis (RCA) is a recently developed technique for identifying such schemas in survey data. However, existing work lacks a clear definition of such schemas, which leaves RCA’s accuracy largely unknown. Here, I build on the theoretical intuitions behind RCA to arrive at this definition. I demonstrate that shared schemas should result in linear dependencies between survey rows—the relationship usually measured with Pearson’s correlation. I thus modify RCA into a “Correlational Class Analysis” (CCA). When I compare the methods using a broad set of simulations, results show that CCA is reliably more accurate at detecting shared schemas than RCA, even in scenarios that substantially violate CCA’s assumptions. I find no evidence of theoretical settings where RCA is more accurate. I then revisit a previous RCA analysis of the 1993 General Social Survey musical tastes module. Whereas RCA partitioned these data into three schematic classes, CCA partitions them into four. I compare these results with a multiple-groups analysis in structural equation modeling and find that CCA’s partition yields greatly improved model fit over RCA. I conclude with a parsimonious framework for future work."]]></description>
<dc:subject>to:NB surveys dimension_reduction inference_to_latent_objects social_measurement sociology via:gabriel_rossman statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ef8371b87faf/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:surveys"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:inference_to_latent_objects"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:social_measurement"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sociology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:gabriel_rossman"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2105.02499">
    <title>[2105.02499] SDRcausal: an R package for causal inference based on sufficient dimension reduction</title>
    <dc:date>2021-05-13T05:24:55+00:00</dc:date>
    <link>https://arxiv.org/abs/2105.02499</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["SDRcausal is a package that implements sufficient dimension reduction methods for causal inference as proposed in Ghosh, Ma, and de Luna (2021). The package implements (augmented) inverse probability weighting and outcome regression (imputation) estimators of an average treatment effect (ATE) parameter. Nuisance models, both treatment assignment probability given the covariates (propensity score) and outcome regression models, are fitted by using semiparametric locally efficient dimension reduction estimators, thereby allowing for large sets of confounding covariates. Techniques including linear extrapolation, numerical differentiation, and truncation have been used to obtain a practicable implementation of the methods. Finding the suitable dimension reduction map (central mean subspace) requires solving an optimization problem, and several optimization algorithms are given as choices to the user. The package also provides estimators of the asymptotic variances of the causal effect estimators implemented. Plotting options are provided. The core of the methods are implemented in C language, and parallelization is allowed for. The user-friendly and freeware R language is used as interface. The package can be downloaded from Github repository: this https URL."]]></description>
<dc:subject>to:NB causal_inference dimension_reduction</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:100741ef7313/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causal_inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.annualreviews.org/doi/abs/10.1146/annurev-control-061820-083817">
    <title>Model Reduction Methods for Complex Network Systems | Annual Review of Control, Robotics, and Autonomous Systems</title>
    <dc:date>2021-05-06T13:48:38+00:00</dc:date>
    <link>https://www.annualreviews.org/doi/abs/10.1146/annurev-control-061820-083817</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Network systems consist of subsystems and their interconnections and provide a powerful framework for the analysis, modeling, and control of complex systems. However, subsystems may have high-dimensional dynamics and a large number of complex interconnections, and it is therefore relevant to study reduction methods for network systems. Here, we provide an overview of reduction methods for both the topological (interconnection) structure of a network and the dynamics of the nodes while preserving structural properties of the network. We first review topological complexity reduction methods based on graph clustering and aggregation, producing a reduced-order network model. Next, we consider reduction of the nodal dynamics using extensions of classical methods while preserving the stability and synchronization properties. Finally, we present a structure-preserving generalized balancing method for simultaneously simplifying the topological structure and the order of the nodal dynamics."]]></description>
<dc:subject>to:NB dynamical_systems networks dimension_reduction graph_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b03640a0c4ff/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:graph_theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1705.00395">
    <title>[1705.00395] Inverse Moment Methods for Sufficient Forecasting using High-Dimensional Predictors</title>
    <dc:date>2021-04-22T15:22:57+00:00</dc:date>
    <link>https://arxiv.org/abs/1705.00395</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider forecasting a single time series using a large number of predictors in the presence of a possible nonlinear forecast function. Assuming that the predictors affect the response through the latent factors, we propose to first conduct factor analysis and then apply sufficient dimension reduction on the estimated factors, to derive the reduced data for subsequent forecasting. Using directional regression and the inverse third-moment method in the stage of sufficient dimension reduction, the proposed methods can capture the non-monotone effect of factors on the response. We also allow a diverging number of factors and only impose general regularity conditions on the distribution of factors, avoiding the undesired time reversibility of the factors by the latter. These make the proposed methods fundamentally more applicable than the sufficient forecasting method in Fan et al. (2017). The proposed methods are demonstrated in both simulation studies and an empirical study of forecasting monthly macroeconomic data from 1959 to 2016. Also, our theory contributes to the literature of sufficient dimension reduction, as it includes an invariance result, a path to perform sufficient dimension reduction under the high-dimensional setting without assuming sparsity, and the corresponding order-determination procedure."]]></description>
<dc:subject>to:NB prediction time_series factor_analysis dimension_reduction to_read re:your_favorite_dsge_sucks</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:595aabfa2cb8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:factor_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:your_favorite_dsge_sucks"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2103.06885">
    <title>[2103.06885] Modern Dimension Reduction</title>
    <dc:date>2021-03-19T15:54:50+00:00</dc:date>
    <link>https://arxiv.org/abs/2103.06885</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more manageable. This Element offers readers a suite of modern unsupervised dimension reduction techniques along with hundreds of lines of R code, to efficiently represent the original high dimensional data space in a simplified, lower dimensional subspace. Launching from the earliest dimension reduction technique principal components analysis and using real social science data, I introduce and walk readers through application of the following techniques: locally linear embedding, t-distributed stochastic neighbor embedding (t-SNE), uniform manifold approximation and projection, self-organizing maps, and deep autoencoders. The result is a well-stocked toolbox of unsupervised algorithms for tackling the complexities of high dimensional data so common in modern society. All code is publicly accessible on Github."]]></description>
<dc:subject>to:NB dimension_reduction to_teach:data-mining via:?</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:caee90c5ef8e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:data-mining"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:?"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.tandfonline.com/doi/full/10.1080/01621459.2020.1841646">
    <title>Markov Neighborhood Regression for High-Dimensional Inference: Journal of the American Statistical Association: Vol 0, No 0</title>
    <dc:date>2021-01-27T03:40:38+00:00</dc:date>
    <link>https://www.tandfonline.com/doi/full/10.1080/01621459.2020.1841646</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This article proposes an innovative method for constructing confidence intervals and assessing p-values in statistical inference for high-dimensional linear models. The proposed method has successfully broken the high-dimensional inference problem into a series of low-dimensional inference problems: For each regression coefficient βi , the confidence interval and p-value are computed by regressing on a subset of variables selected according to the conditional independence relations between the corresponding variable Xi and other variables. Since the subset of variables forms a Markov neighborhood of Xi in the Markov network formed by all the variables  X 1 , X 2 , … , X p , the proposed method is coined as Markov neighborhood regression (MNR). The proposed method is tested on high-dimensional linear, logistic, and Cox regression. The numerical results indicate that the proposed method significantly outperforms the existing ones. Based on the MNR, a method of learning causal structures for high-dimensional linear models is proposed and applied to identification of drug sensitive genes and cancer driver genes. The idea of using conditional independence relations for dimension reduction is general and potentially can be extended to other high-dimensional or big data problems as well."

--- I am sure this works because it has been folklore since I started learning about causal model discovery in the 1990s.  But learning the conditional independencies is hard!]]></description>
<dc:subject>to:NB linear_regression high-dimensional_statistics dimension_reduction causal_discovery wheels:reinvention_of</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:72d2cc24b1b7/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:linear_regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causal_discovery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:wheels:reinvention_of"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1401.5226">
    <title>[1401.5226] The Why and How of Nonnegative Matrix Factorization</title>
    <dc:date>2021-01-14T16:28:46+00:00</dc:date>
    <link>https://arxiv.org/abs/1401.5226</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of high-dimensional data as it automatically extracts sparse and meaningful features from a set of nonnegative data vectors. We first illustrate this property of NMF on three applications, in image processing, text mining and hyperspectral imaging --this is the why. Then we address the problem of solving NMF, which is NP-hard in general. We review some standard NMF algorithms, and also present a recent subclass of NMF problems, referred to as near-separable NMF, that can be solved efficiently (that is, in polynomial time), even in the presence of noise --this is the how. Finally, we briefly describe some problems in mathematics and computer science closely related to NMF via the nonnegative rank."]]></description>
<dc:subject>to:NB linear_algebra to_teach:data-mining dimension_reduction via:mraginsky</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3172cde1a9f8/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:linear_algebra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:data-mining"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:mraginsky"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2101.01535">
    <title>[2101.01535] An RKHS-Based Semiparametric Approach to Nonlinear Sufficient Dimension Reduction</title>
    <dc:date>2021-01-06T17:10:25+00:00</dc:date>
    <link>https://arxiv.org/abs/2101.01535</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Based on the theory of reproducing kernel Hilbert space (RKHS) and semiparametric method, we propose a new approach to nonlinear dimension reduction. The method extends the semiparametric method into a more generalized domain where both the interested parameters and nuisance parameters to be infinite dimensional. By casting the nonlinear dimensional reduction problem in a generalized semiparametric framework, we calculate the orthogonal complement space of generalized nuisance tangent space to derive the estimating equation. Solving the estimating equation by the theory of RKHS and regularization, we obtain the estimation of dimension reduction directions of the sufficient dimension reduction (SDR) subspace and also show the asymptotic property of estimator. Furthermore, the proposed method does not rely on the linearity condition and constant variance condition. Simulation and real data studies are conducted to demonstrate the finite sample performance of our method in comparison with several existing methods."]]></description>
<dc:subject>to:NB nonparametrics hilbert_space dimension_reduction statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4499fc48f267/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hilbert_space"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.cambridge.org/core/journals/proceedings-of-the-international-astronomical-union/article/potential-of-likelihoodfree-inference-of-cosmological-parameters-with-weak-lensing-data/0E1FEF317A0C09039B52C8791E63670D">
    <title>The potential of likelihood-free inference of cosmological parameters with weak lensing data | Proceedings of the International Astronomical Union | Cambridge Core</title>
    <dc:date>2020-12-13T23:58:29+00:00</dc:date>
    <link>https://www.cambridge.org/core/journals/proceedings-of-the-international-astronomical-union/article/potential-of-likelihoodfree-inference-of-cosmological-parameters-with-weak-lensing-data/0E1FEF317A0C09039B52C8791E63670D</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In the statistical framework of likelihood-free inference, the posterior distribution of model parameters is explored via simulation rather than direct evaluation of the likelihood function, permitting inference in situations where this function is analytically intractable. We consider the problem of estimating cosmological parameters using measurements of the weak gravitational lensing of galaxies; specifically, we propose the use a likelihood-free approach to investigate the posterior distribution of some parameters in the ΛCDM model upon observing a large number of sheared galaxies. The choice of summary statistic used when comparing observed data and simulated data in the likelihood-free inference framework is critical, so we work toward a principled method of choosing the summary statistic, aiming for dimension reduction while seeking a statistic that is as close as possible to being sufficient for the parameters of interest."]]></description>
<dc:subject>have_read heard_the_talk approved_the_thesis astronomy approximate_bayesian_computation sufficiency exponential_families dimension_reduction simulation-based_estimation statistics in_NB re:codename:catherine_wheel</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:af0f8495eafc/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:heard_the_talk"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:approved_the_thesis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:astronomy"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:approximate_bayesian_computation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sufficiency"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:simulation-based_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:codename:catherine_wheel"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1706.06296">
    <title>[1706.06296] Approximate Kernel PCA Using Random Features: Computational vs. Statistical Trade-off</title>
    <dc:date>2020-12-04T21:43:57+00:00</dc:date>
    <link>https://arxiv.org/abs/1706.06296</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Kernel methods are powerful learning methodologies that provide a simple way to construct nonlinear algorithms from linear ones. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature approximation, have been proposed to alleviate the problem. However, the statistical consistency of most of these approximate kernel methods is not well understood except for kernel ridge regression wherein it has been shown that the random feature approximation is not only computationally efficient but also statistically consistent with a minimax optimal rate of convergence. In this paper, we investigate the efficacy of random feature approximation in the context of kernel principal component analysis (KPCA) by studying the trade-off between computational and statistical behaviors of approximate KPCA. We show that the approximate KPCA is both computationally and statistically efficient compared to KPCA in terms of the error associated with reconstructing a kernel function based on its projection onto the corresponding eigenspaces. The analysis hinges on Bernstein-type inequalities for the operator and Hilbert-Schmidt norms of a self-adjoint Hilbert-Schmidt operator-valued U-statistics, which is of independent interest."]]></description>
<dc:subject>dimension_reduction kernel_methods random_features principal_components in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:36ef988d8d25/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_features"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.cambridge.org/9781108477444">
    <title>Small summaries for big data | Knowledge management, databases and data mining | Cambridge University Press</title>
    <dc:date>2020-11-30T17:32:10+00:00</dc:date>
    <link>https://www.cambridge.org/9781108477444</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The massive volume of data generated in modern applications can overwhelm our ability to conveniently transmit, store, and index it. For many scenarios, building a compact summary of a dataset that is vastly smaller enables flexibility and efficiency in a range of queries over the data, in exchange for some approximation. This comprehensive introduction to data summarization, aimed at practitioners and students, showcases the algorithms, their behavior, and the mathematical underpinnings of their operation. The coverage starts with simple sums and approximate counts, building to more advanced probabilistic structures such as the Bloom Filter, distinct value summaries, sketches, and quantile summaries. Summaries are described for specific types of data, such as geometric data, graphs, and vectors and matrices. The authors offer detailed descriptions of and pseudocode for key algorithms that have been incorporated in systems from companies such as Google, Apple, Microsoft, Netflix and Twitter."]]></description>
<dc:subject>to:NB books:noted random_projections locality-sensitive_hashing dimension_reduction clustering data_mining computational_statistics to_teach:data-mining books:in_library books:have_suggested_to_library downloaded re:codename:catherine_wheel</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8fb436ef1b8f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:noted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_projections"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:locality-sensitive_hashing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:clustering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:data_mining"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:data-mining"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:in_library"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:have_suggested_to_library"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:downloaded"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:codename:catherine_wheel"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.tandfonline.com/doi/full/10.1080/01621459.2020.1775614">
    <title>Embedding Learning: Journal of the American Statistical Association: Vol 0, No 0</title>
    <dc:date>2020-11-20T19:48:08+00:00</dc:date>
    <link>https://www.tandfonline.com/doi/full/10.1080/01621459.2020.1775614</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Numerical embedding has become one standard technique for processing and analyzing unstructured data that cannot be expressed in a predefined fashion. It stores the main characteristics of data by mapping it onto a numerical vector. An embedding is often unsupervised and constructed by transfer learning from large-scale unannotated data. Given an embedding, a downstream learning method, referred to as a two-stage method, is applicable to unstructured data. In this article, we introduce a novel framework of embedding learning to deliver a higher learning accuracy than the two-stage method while identifying an optimal learning-adaptive embedding. In particular, we propose a concept of U-minimal sufficient learning-adaptive embeddings, based on which we seek an optimal one to maximize the learning accuracy subject to an embedding constraint. Moreover, when specializing the general framework to classification, we derive a graph embedding classifier based on a hyperlink tensor representing multiple hypergraphs, directed or undirected, characterizing multi-way relations of unstructured data. Numerically, we design algorithms based on blockwise coordinate descent and projected gradient descent to implement linear and feed-forward neural network classifiers, respectively. Theoretically, we establish a learning theory to quantify the generalization error of the proposed method. Moreover, we show, in linear regression, that the one-hot encoder is more preferable among two-stage methods, yet its dimension restriction hinders its predictive performance. For a graph embedding classifier, the generalization error matches up to the standard fast rate or the parametric rate for linear or nonlinear classification. Finally, we demonstrate the utility of the classifiers on two benchmarks in grammatical classification and sentiment analysis. Supplementary materials for this article are available online."]]></description>
<dc:subject>to:NB dimension_reduction learning_theory prediction sufficiency</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b907e350efd0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sufficiency"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.aos/1594972830">
    <title>Kim , Li , Yu , Li : On post dimension reduction statistical inference</title>
    <dc:date>2020-11-18T22:42:02+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.aos/1594972830</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The methodologies of sufficient dimension reduction have undergone extensive developments in the past three decades. However, there has been a lack of systematic and rigorous development of post dimension reduction inference, which has seriously hindered its applications. The current common practice is to treat the estimated sufficient predictors as the true predictors and use them as the starting point of the downstream statistical inference. However, this naive inference approach would grossly overestimate the confidence level of an interval, or the power of a test, leading to the distorted results. In this paper, we develop a general and comprehensive framework of post dimension reduction inference, which can accommodate any dimension reduction method and model building method, as long as their corresponding influence functions are available. Within this general framework, we derive the influence functions and present the explicit post reduction formulas for the combinations of numerous dimension reduction and model building methods. We then develop post reduction inference methods for both confidence interval and hypothesis testing. We investigate the finite-sample performance of our procedures by simulations and a real data analysis."


--- Why not just use sample splitting?]]></description>
<dc:subject>to:NB dimension_reduction statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c7934148d63d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2011.01379">
    <title>[2011.01379] Detecting direct causality in multivariate time series: A comparative study</title>
    <dc:date>2020-11-06T05:05:22+00:00</dc:date>
    <link>https://arxiv.org/abs/2011.01379</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The concept of Granger causality is increasingly being applied for the characterization of directional interactions in different applications. A multivariate framework for estimating Granger causality is essential in order to account for all the available information from multivariate time series. However, the inclusion of non-informative or non-significant variables creates estimation problems related to the 'curse of dimensionality'. To deal with this issue, direct causality measures using variable selection and dimension reduction techniques have been introduced. In this comparative work, the performance of an ensemble of bivariate and multivariate causality measures in the time domain is assessed, focusing on dimension reduction causality measures. In particular, different types of high-dimensional coupled discrete systems are used (involving up to 100 variables) and the robustness of the causality measures to time series length and different noise types is examined. The results of the simulation study highlight the superiority of the dimension reduction measures, especially for high-dimensional systems."]]></description>
<dc:subject>to:NB time_series prediction granger_causality dimension_reduction</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:114bfd04861d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:granger_causality"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/s11222-019-09905-w">
    <title>Local dimension reduction of summary statistics for likelihood-free inference | SpringerLink</title>
    <dc:date>2020-02-23T15:47:12+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s11222-019-09905-w</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Approximate Bayesian computation (ABC) and other likelihood-free inference methods have gained popularity in the last decade, as they allow rigorous statistical inference for complex models without analytically tractable likelihood functions. A key component for accurate inference with ABC is the choice of summary statistics, which summarize the information in the data, but at the same time should be low-dimensional for efficiency. Several dimension reduction techniques have been introduced to automatically construct informative and low-dimensional summaries from a possibly large pool of candidate summaries. Projection-based methods, which are based on learning simple functional relationships from the summaries to parameters, are widely used and usually perform well, but might fail when the assumptions behind the transformation are not satisfied. We introduce a localization strategy for any projection-based dimension reduction method, in which the transformation is estimated in the neighborhood of the observed data instead of the whole space. Localization strategies have been suggested before, but the performance of the transformed summaries outside the local neighborhood has not been guaranteed. In our localization approach the transformation is validated and optimized over validation datasets, ensuring reliable performance. We demonstrate the improvement in the estimation accuracy for localized versions of linear regression and partial least squares, for three different models of varying complexity."]]></description>
<dc:subject>to:NB approximate_bayesian_computation indirect_inference dimension_reduction sufficiency statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e1ae3a67e467/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:approximate_bayesian_computation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:indirect_inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sufficiency"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1909.12902">
    <title>[1909.12902] Interpreting Distortions in Dimensionality Reduction by Superimposing Neighbourhood Graphs</title>
    <dc:date>2019-10-01T17:36:07+00:00</dc:date>
    <link>https://arxiv.org/abs/1909.12902</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["To perform visual data exploration, many dimensionality reduction methods have been developed. These tools allow data analysts to represent multidimensional data in a 2D or 3D space, while preserving as much relevant information as possible. Yet, they cannot preserve all structures simultaneously and they induce some unavoidable distortions. Hence, many criteria have been introduced to evaluate a map's overall quality, mostly based on the preservation of neighbourhoods. Such global indicators are currently used to compare several maps, which helps to choose the most appropriate mapping method and its hyperparameters. However, those aggregated indicators tend to hide the local repartition of distortions. Thereby, they need to be supplemented by local evaluation to ensure correct interpretation of maps. In this paper, we describe a new method, called MING, for `Map Interpretation using Neighbourhood Graphs'. It offers a graphical interpretation of pairs of map quality indicators, as well as local evaluation of the distortions. This is done by displaying on the map the nearest neighbours graphs computed in the data space and in the embedding. Shared and unshared edges exhibit reliable and unreliable neighbourhood information conveyed by the mapping. By this mean, analysts may determine whether proximity (or remoteness) of points on the map faithfully represents similarity (or dissimilarity) of original data, within the meaning of a chosen map quality criteria. We apply this approach to two pairs of widespread indicators: precision/recall and trustworthiness/continuity, chosen for their wide use in the community, which will allow an easy handling by users."

--- Isn't this the "false nearest neighbors" method of the old geometry-from-a-time-series literature?]]></description>
<dc:subject>to:NB dimension_reduction visual_display_of_quantitative_information statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5414d42b3487/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:visual_display_of_quantitative_information"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1909.12898">
    <title>[1909.12898] Identifying Low-Dimensional Structures in Markov Chains: A Nonnegative Matrix Factorization Approach</title>
    <dc:date>2019-10-01T15:39:46+00:00</dc:date>
    <link>https://arxiv.org/abs/1909.12898</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A variety of queries about stochastic systems boil down to study of Markov chains and their properties. If the Markov chain is large, as is typically true for discretized continuous spaces, such analysis may be computationally intractable. Nevertheless, in many scenarios, Markov chains have underlying structural properties that allow them to admit a low-dimensional representation. For instance, the transition matrix associated with the model may be low-rank and hence, representable in a lower-dimensional space. We consider the problem of learning low-dimensional representations for large-scale Markov chains. To that end, we formulate the task of representation learning as that of mapping the state space of the model to a low-dimensional state space, referred to as the kernel space. The kernel space contains a set of meta states which are desired to be representative of only a small subset of original states. To promote this structural property, we constrain the number of nonzero entries of the mappings between the state space and the kernel space. By imposing the desired characteristics of the structured representation, we cast the problem as the task of nonnegative matrix factorization. To compute the solution, we propose an efficient block coordinate gradient descent and theoretically analyze its convergence properties. Our extensive simulation results demonstrate the efficacy of the proposed algorithm in terms of the quality of the low-dimensional representation as well as its computational cost."]]></description>
<dc:subject>to:NB markov_models dimension_reduction</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:14ad4038c7f7/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:markov_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1909.05097">
    <title>[1909.05097] Spectral Non-Convex Optimization for Dimension Reduction with Hilbert-Schmidt Independence Criterion</title>
    <dc:date>2019-09-15T17:23:02+00:00</dc:date>
    <link>https://arxiv.org/abs/1909.05097</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The Hilbert Schmidt Independence Criterion (HSIC) is a kernel dependence measure that has applications in various aspects of machine learning. Conveniently, the objectives of different dimensionality reduction applications using HSIC often reduce to the same optimization problem. However, the nonconvexity of the objective function arising from non-linear kernels poses a serious challenge to optimization efficiency and limits the potential of HSIC-based formulations. As a result, only linear kernels have been computationally tractable in practice. This paper proposes a spectral-based optimization algorithm that extends beyond the linear kernel. The algorithm identifies a family of suitable kernels and provides the first and second-order local guarantees when a fixed point is reached. Furthermore, we propose a principled initialization strategy, thereby removing the need to repeat the algorithm at random initialization points. Compared to state-of-the-art optimization algorithms, our empirical results on real data show a run-time improvement by as much as a factor of 10^5 while consistently achieving lower cost and classification/clustering errors. The implementation source code is publicly available on this https URL."]]></description>
<dc:subject>to:NB kernel_methods hilbert_space probability dimension_reduction statistics computational_statistics spectral_methods</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3de6f1991994/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hilbert_space"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spectral_methods"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1909.03093">
    <title>[1909.03093] Solving Interpretable Kernel Dimension Reduction</title>
    <dc:date>2019-09-11T15:16:43+00:00</dc:date>
    <link>https://arxiv.org/abs/1909.03093</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Kernel dimensionality reduction (KDR) algorithms find a low dimensional representation of the original data by optimizing kernel dependency measures that are capable of capturing nonlinear relationships. The standard strategy is to first map the data into a high dimensional feature space using kernels prior to a projection onto a low dimensional space. While KDR methods can be easily solved by keeping the most dominant eigenvectors of the kernel matrix, its features are no longer easy to interpret. Alternatively, Interpretable KDR (IKDR) is different in that it projects onto a subspace \textit{before} the kernel feature mapping, therefore, the projection matrix can indicate how the original features linearly combine to form the new features. Unfortunately, the IKDR objective requires a non-convex manifold optimization that is difficult to solve and can no longer be solved by eigendecomposition. Recently, an efficient iterative spectral (eigendecomposition) method (ISM) has been proposed for this objective in the context of alternative clustering. However, ISM only provides theoretical guarantees for the Gaussian kernel. This greatly constrains ISM's usage since any kernel method using ISM is now limited to a single kernel. This work extends the theoretical guarantees of ISM to an entire family of kernels, thereby empowering ISM to solve any kernel method of the same objective. In identifying this family, we prove that each kernel within the family has a surrogate Φ matrix and the optimal projection is formed by its most dominant eigenvectors. With this extension, we establish how a wide range of IKDR applications across different learning paradigms can be solved by ISM. To support reproducible results, the source code is made publicly available on \url{this https URL}."

--- Last tag is dreamily aspirational.]]></description>
<dc:subject>to:NB kernel_methods dimension_reduction principal_components to_teach:data-mining</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3222a6b145d7/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:data-mining"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1908.06319">
    <title>[1908.06319] Locally Linear Embedding and fMRI feature selection in psychiatric classification</title>
    <dc:date>2019-08-20T14:19:42+00:00</dc:date>
    <link>https://arxiv.org/abs/1908.06319</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Background: Functional magnetic resonance imaging (fMRI) provides non-invasive measures of neuronal activity using an endogenous Blood Oxygenation-Level Dependent (BOLD) contrast. This article introduces a nonlinear dimensionality reduction (Locally Linear Embedding) to extract informative measures of the underlying neuronal activity from BOLD time-series. The method is validated using the Leave-One-Out-Cross-Validation (LOOCV) accuracy of classifying psychiatric diagnoses using resting-state and task-related fMRI. Methods: Locally Linear Embedding of BOLD time-series (into each voxel's respective tensor) was used to optimise feature selection. This uses Gauß' Principle of Least Constraint to conserve quantities over both space and time. This conservation was assessed using LOOCV to greedily select time points in an incremental fashion on training data that was categorised in terms of psychiatric diagnoses. Findings: The embedded fMRI gave highly diagnostic performances (> 80%) on eleven publicly-available datasets containing healthy controls and patients with either Schizophrenia, Attention-Deficit Hyperactivity Disorder (ADHD), or Autism Spectrum Disorder (ASD). Furthermore, unlike the original fMRI data before or after using Principal Component Analysis (PCA) for artefact reduction, the embedded fMRI furnished significantly better than chance classification (defined as the majority class proportion) on ten of eleven datasets. Interpretation: Locally Linear Embedding appears to be a useful feature extraction procedure that retains important information about patterns of brain activity distinguishing among psychiatric cohorts."

--- Last tag is because I plan to teach LLE and this might make a good example or assignment, if I like how it was actually done.

--- ETA: It's... not horrible (though the writing is bad and far too pretentious), but not very insightful, and too complicated to make a good teaching example.]]></description>
<dc:subject>to:NB locally_linear_embedding classifiers fmri dimension_reduction to_teach:data-mining have_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ac687c5e5458/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:locally_linear_embedding"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:classifiers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:fmri"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:data-mining"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://onlinelibrary.wiley.com/doi/abs/10.1111/sjos.12405">
    <title>Dimension reduction for the conditional mean and variance functions in time series - Park - - Scandinavian Journal of Statistics - Wiley Online Library</title>
    <dc:date>2019-08-07T17:25:18+00:00</dc:date>
    <link>https://onlinelibrary.wiley.com/doi/abs/10.1111/sjos.12405</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper deals with the nonparametric estimation of the mean and variance functions of univariate time series data. We propose a nonparametric dimension reduction technique for both mean and variance functions of time series. This method does not require any model specification and instead we seek directions in both the mean and variance functions such that the conditional distribution of the current observation given the vector of past observations is the same as that of the current observation given a few linear combinations of the past observations without loss of inferential information. The directions of the mean and variance functions are estimated by maximizing the Kullback‐Leibler distance function. The consistency of the proposed estimators is established. A computational procedure is introduced to detect lags of the conditional mean and variance functions in practice. Numerical examples and simulation studies are performed to illustrate and evaluate the performance of the proposed estimators."]]></description>
<dc:subject>to:NB prediction time_series dimension_reduction statistics information_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:04b9e80f3a87/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1905.09944">
    <title>[1905.09944] Unsupervised Discovery of Temporal Structure in Noisy Data with Dynamical Components Analysis</title>
    <dc:date>2019-05-27T15:01:50+00:00</dc:date>
    <link>https://arxiv.org/abs/1905.09944</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Linear dimensionality reduction methods are commonly used to extract low-dimensional structure from high-dimensional data. However, popular methods disregard temporal structure, rendering them prone to extracting noise rather than meaningful dynamics when applied to time series data. At the same time, many successful unsupervised learning methods for temporal, sequential and spatial data extract features which are predictive of their surrounding context. Combining these approaches, we introduce Dynamical Components Analysis (DCA), a linear dimensionality reduction method which discovers a subspace of high-dimensional time series data with maximal predictive information, defined as the mutual information between the past and future. We test DCA on synthetic examples and demonstrate its superior ability to extract dynamical structure compared to commonly used linear methods. We also apply DCA to several real-world datasets, showing that the dimensions extracted by DCA are more useful than those extracted by other methods for predicting future states and decoding auxiliary variables. Overall, DCA robustly extracts dynamical structure in noisy, high-dimensional data while retaining the computational efficiency and geometric interpretability of linear dimensionality reduction methods."

--- How do they measure predictive information though?

--- Ah: by assuming everything's Gaussian, so you can calculate everything from covariance matrices.  Verdict: nice try.]]></description>
<dc:subject>to:NB dimension_reduction time_series statistics information_theory my_initial_skeptical_coloration_became_on_examination_a_permanent_stain</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4964c3d7ceb4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:my_initial_skeptical_coloration_became_on_examination_a_permanent_stain"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/s11203-018-9172-1">
    <title>Optimal dimension reduction for high-dimensional and functional time series | SpringerLink</title>
    <dc:date>2018-07-13T02:43:55+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s11203-018-9172-1</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Dimension reduction techniques are at the core of the statistical analysis of high-dimensional and functional observations. Whether the data are vector- or function-valued, principal component techniques, in this context, play a central role. The success of principal components in the dimension reduction problem is explained by the fact that, for any   K≤pK≤p , the K first coefficients in the expansion of a p-dimensional random vector   XX  in terms of its principal components is providing the best linear K-dimensional summary of   XX  in the mean square sense. The same property holds true for a random function and its functional principal component expansion. This optimality feature, however, no longer holds true in a time series context: principal components and functional principal components, when the observations are serially dependent, are losing their optimal dimension reduction property to the so-called dynamic principal components introduced by Brillinger in 1981 in the vector case and, in the functional case, their functional extension proposed by Hörmann, Kidziński and Hallin in 2015."]]></description>
<dc:subject>to:NB dimension_reduction time_series statistics principal_components</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4d73961cf5ab/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://dx.doi.org/10.1002/rsa.10073">
    <title>An elementary proof of a theorem of Johnson and Lindenstrauss - Dasgupta - 2003 - Random Structures &amp;amp; Algorithms - Wiley Online Library</title>
    <dc:date>2018-05-31T18:39:43+00:00</dc:date>
    <link>http://dx.doi.org/10.1002/rsa.10073</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A result of Johnson and Lindenstrauss [13] shows that a set of n points in high dimensional Euclidean space can be mapped into an O(log n/ϵ2)‐dimensional Euclidean space such that the distance between any two points changes by only a factor of (1 ± ϵ). In this note, we prove this theorem using elementary probabilistic techniques."

Ungated: http://cseweb.ucsd.edu/~dasgupta/papers/jl.pdf]]></description>
<dc:subject>to:NB random_projections geometry dimension_reduction have_read re:ADAfaEPoV</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b91ed1e17030/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_projections"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:ADAfaEPoV"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1802.03426">
    <title>[1802.03426] UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction</title>
    <dc:date>2018-03-11T18:56:42+00:00</dc:date>
    <link>https://arxiv.org/abs/1802.03426</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a practical scalable algorithm that applies to real world data. The UMAP algorithm is competitive with t-SNE for visualization quality, and arguably preserves more of the global structure with superior run time performance. Furthermore, UMAP as described has no computational restrictions on embedding dimension, making it viable as a general purpose dimension reduction technique for machine learning"]]></description>
<dc:subject>to:NB via:vaguery manifold_learning dimension_reduction data_analysis data_mining to_teach:data-mining re:ADAfaEPoV</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b2108ad9d881/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:vaguery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:manifold_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:data_mining"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:data-mining"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:ADAfaEPoV"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.pnas.org/content/115/4/E639">
    <title>Predicting tipping points in mutualistic networks through dimension reduction</title>
    <dc:date>2018-01-24T23:31:48+00:00</dc:date>
    <link>http://www.pnas.org/content/115/4/E639</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Complex networked systems ranging from ecosystems and the climate to economic, social, and infrastructure systems can exhibit a tipping point (a “point of no return”) at which a total collapse of the system occurs. To understand the dynamical mechanism of a tipping point and to predict its occurrence as a system parameter varies are of uttermost importance, tasks that are hindered by the often extremely high dimensionality of the underlying system. Using complex mutualistic networks in ecology as a prototype class of systems, we carry out a dimension reduction process to arrive at an effective 2D system with the two dynamical variables corresponding to the average pollinator and plant abundances. We show, using 59 empirical mutualistic networks extracted from real data, that our 2D model can accurately predict the occurrence of a tipping point, even in the presence of stochastic disturbances. We also find that, because of the lack of sufficient randomness in the structure of the real networks, weighted averaging is necessary in the dimension reduction process. Our reduced model can serve as a paradigm for understanding and predicting the tipping point dynamics in real world mutualistic networks for safeguarding pollinators, and the general principle can be extended to a broad range of disciplines to address the issues of resilience and sustainability."

]]></description>
<dc:subject>to:NB ecology dimension_reduction</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e4b78f526679/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ecology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.mitpressjournals.org/doi/abs/10.1162/neco_a_01035">
    <title>Sufficient Dimension Reduction via Direct Estimation of the Gradients of Logarithmic Conditional Densities | Neural Computation | MIT Press Journals</title>
    <dc:date>2018-01-24T23:29:28+00:00</dc:date>
    <link>https://www.mitpressjournals.org/doi/abs/10.1162/neco_a_01035</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Sufficient dimension reduction (SDR) is aimed at obtaining the low-rank projection matrix in the input space such that information about output data is maximally preserved. Among various approaches to SDR, a promising method is based on the eigendecomposition of the outer product of the gradient of the conditional density of output given input. In this letter, we propose a novel estimator of the gradient of the logarithmic conditional density that directly fits a linear-in-parameter model to the true gradient under the squared loss. Thanks to this simple least-squares formulation, its solution can be computed efficiently in a closed form. Then we develop a new SDR method based on the proposed gradient estimator. We theoretically prove that the proposed gradient estimator, as well as the SDR solution obtained from it, achieves the optimal parametric convergence rate. Finally, we experimentally demonstrate that our SDR method compares favorably with existing approaches in both accuracy and computational efficiency on a variety of artificial and benchmark data sets."]]></description>
<dc:subject>to:NB dimension_reduction sufficiency density_estimation linear_regression statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:15bf571a5ee2/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sufficiency"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:linear_regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://papers.nips.cc/paper/7213-poincare-embeddings-for-learning-hierarchical-representations">
    <title>Poincaré Embeddings for Learning Hierarchical Representations</title>
    <dc:date>2017-11-24T18:34:20+00:00</dc:date>
    <link>http://papers.nips.cc/paper/7213-poincare-embeddings-for-learning-hierarchical-representations</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincaré ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincaré embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability."]]></description>
<dc:subject>to:NB hyperbolic_geometry dimension_reduction hierarchical_structure statistics data_analysis</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c2b04267ee36/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hyperbolic_geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hierarchical_structure"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:data_analysis"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.calvinmurdock.com/aca/">
    <title>Additive Component Analysis – Calvin Murdock</title>
    <dc:date>2017-08-08T22:11:50+00:00</dc:date>
    <link>http://www.calvinmurdock.com/aca/</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Principal component analysis (PCA) is one of the most versatile tools for unsupervised learning with applications ranging from dimensionality reduction to exploratory data analysis and visualization. While much effort has been devoted to encouraging meaningful representations through regularization (e.g. non-negativity or sparsity), underlying linearity assumptions can limit their effectiveness. To address this issue, we propose Additive Component Analysis (ACA), a novel nonlinear extension of PCA. Inspired by multivariate nonparametric regression with additive models, ACA fits a smooth manifold to data by learning an explicit mapping from a low-dimensional latent space to the input space, which trivially enables applications like denoising. Furthermore, ACA can be used as a drop-in replacement in many algorithms that use linear component analysis methods as a subroutine via the local tangent space of the learned manifold. Unlike many other nonlinear dimensionality reduction techniques, ACA can be efficiently applied to large datasets since it does not require computing pairwise similarities or storing training data during testing. Multiple ACA layers can also be composed and learned jointly with essentially the same procedure for improved representational power, demonstrating the encouraging potential of nonparametric deep learning. We evaluate ACA on a variety of datasets, showing improved robustness, reconstruction performance, and interpretability."]]></description>
<dc:subject>to:NB dimension_reduction manifold_learning additive_models principal_components statistics to_read re:ADAfaEPoV</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f0476aa38803/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:manifold_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:additive_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:ADAfaEPoV"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1602.00531">
    <title>[1602.00531] Adaptive non-parametric estimation in the presence of dependence</title>
    <dc:date>2016-02-08T21:30:35+00:00</dc:date>
    <link>http://arxiv.org/abs/1602.00531</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension reduction. The minimax optimal rate of convergence of the estimator is derived assuming a sufficiently weak dependence characterized by fast decreasing mixing coefficients. We illustrate these results by considering classical smoothness assumptions. However, the proposed estimator requires an optimal choice of a dimension parameter depending on certain characteristics of the function of interest, which are not known in practice. The main issue addressed in our work is an adaptive choice of this dimension parameter combining model selection and Lepski's method. It is inspired by the recent work of Goldenshluger and Lepski (2011). We show that this data-driven estimator can attain the lower risk bound up to a constant provided a fast decay of the mixing coefficients."]]></description>
<dc:subject>to:NB statistics regression nonparametrics learning_under_dependence density_estimation dimension_reduction</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b9b529946e46/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_under_dependence"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00759">
    <title>Extracting Low-Dimensional Latent Structure from Time Series in the Presence of Delays</title>
    <dc:date>2015-08-20T13:25:04+00:00</dc:date>
    <link>http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00759</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Noisy, high-dimensional time series observations can often be described by a set of low-dimensional latent variables. Commonly used methods to extract these latent variables typically assume instantaneous relationships between the latent and observed variables. In many physical systems, changes in the latent variables manifest as changes in the observed variables after time delays. Techniques that do not account for these delays can recover a larger number of latent variables than are present in the system, thereby making the latent representation more difficult to interpret. In this work, we introduce a novel probabilistic technique, time-delay gaussian-process factor analysis (TD-GPFA), that performs dimensionality reduction in the presence of a different time delay between each pair of latent and observed variables. We demonstrate how using a gaussian process to model the evolution of each latent variable allows us to tractably learn these delays over a continuous domain. Additionally, we show how TD-GPFA combines temporal smoothing and dimensionality reduction into a common probabilistic framework. We present an expectation/conditional maximization either (ECME) algorithm to learn the model parameters. Our simulations demonstrate that when time delays are present, TD-GPFA is able to correctly identify these delays and recover the latent space. We then applied TD-GPFA to the activity of tens of neurons recorded simultaneously in the macaque motor cortex during a reaching task. TD-GPFA is able to better describe the neural activity using a more parsimonious latent space than GPFA, a method that has been used to interpret motor cortex data but does not account for time delays. More broadly, TD-GPFA can help to unravel the mechanisms underlying high-dimensional time series data by taking into account physical delays in the system."]]></description>
<dc:subject>to:NB to_read inference_to_latent_objects dimension_reduction neural_data_analysis nonparametrics time_series yu.byron</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:6c01bbea454b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:inference_to_latent_objects"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:yu.byron"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://link.springer.com/article/10.1007/BF01200757">
    <title>The geometry of graphs and some of its algorithmic applications (Linial, London and Rabinovich, 1995)</title>
    <dc:date>2015-07-14T04:02:31+00:00</dc:date>
    <link>http://link.springer.com/article/10.1007/BF01200757</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper we explore some implications of viewing graphs asgeometric objects. This approach offers a new perspective on a number of graph-theoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that respect themetric of the (possibly weighted) graph. Given a graphG we map its vertices to a normed space in an attempt to (i) keep down the dimension of the host space, and (ii) guarantee a smalldistortion, i.e., make sure that distances between vertices inG closely match the distances between their geometric images.
"In this paper we develop efficient algorithms for embedding graphs low-dimensionally with a small distortion. Further algorithmic applications include:
"•A simple, unified approach to a number of problems on multicommodity flows, including the Leighton-Rao Theorem [37] and some of its extensions. We solve an open question in this area, showing that the max-flow vs. min-cut gap in thek-commodities problem isO(logk). Our new deterministic polynomial-time algorithm finds a (nearly tight) cut meeting this bound.
"•For graphs embeddable in low-dimensional spaces with a small distortion, we can find low-diameter decompositions (in the sense of [7] and [43]). The parameters of the decomposition depend only on the dimension and the distortion and not on the size of the graph.
"•In graphs embedded this way, small balancedseparators can be found efficiently.
"Given faithful low-dimensional representations of statistical data, it is possible to obtain meaningful and efficientclustering. This is one of the most basic tasks in pattern-recognition. For the (mostly heuristic) methods used in the practice of pattern-recognition, see [20], especially chapter 6.
"Our studies of multicommodity flows also imply that every embedding of (the metric of) ann-vertex, constant-degree expander into a Euclidean space (of any dimension) has distortion Ω(logn). This result is tight, and closes a gap left open by Bourgain [12]."

--- So why don't we think of communities in terms of low-diameter decompositions?]]></description>
<dc:subject>in_NB graph_theory dimension_reduction mathematics random_projections clustering have_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:bfbac4c36470/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:graph_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mathematics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_projections"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:clustering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1503.00173">
    <title>[1503.00173] Signal Processing on Graphs: Modeling (Causal) Relations in Big Data</title>
    <dc:date>2015-05-27T14:21:46+00:00</dc:date>
    <link>http://arxiv.org/abs/1503.00173</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Many big data applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences continuously measured by weather stations across the US. A first task in the analytics of these data is to derive a low dimensional representation, a graph or discrete manifold, that describes well the interrelations among the time series and their intrarelations across time. This paper presents a computationally tractable algorithm for estimating this graph structure from the available data. This graph is directed and weighted, possibly representing causation relations, not just correlations as in most existing approaches in the literature. The algorithm is demonstrated on random graph and real network time series datasets, and its performance is compared to that of related methods. The adjacency matrices estimated with the new method are close to the true graph in the simulated data and consistent with prior physical knowledge in the real dataset tested."]]></description>
<dc:subject>to:NB time_series causal_inference causal_discovery dimension_reduction statistics color_me_skeptical</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7408f6e854bc/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causal_inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causal_discovery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:color_me_skeptical"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.aos/1392733185">
    <title>Feng , He : Statistical inference based on robust low-rank data matrix approximation</title>
    <dc:date>2015-02-23T07:17:31+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.aos/1392733185</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The singular value decomposition is widely used to approximate data matrices with lower rank matrices. Feng and He [Ann. Appl. Stat. 3 (2009) 1634–1654] developed tests on dimensionality of the mean structure of a data matrix based on the singular value decomposition. However, the first singular values and vectors can be driven by a small number of outlying measurements. In this paper, we consider a robust alternative that moderates the effect of outliers in low-rank approximations. Under the assumption of random row effects, we provide the asymptotic representations of the robust low-rank approximation. These representations may be used in testing the adequacy of a low-rank approximation. We use oligonucleotide gene microarray data to demonstrate how robust singular value decomposition compares with the its traditional counterparts. Examples show that the robust methods often lead to a more meaningful assessment of the dimensionality of gene intensity data matrices."]]></description>
<dc:subject>to:NB dimension_reduction low-rank_approximation statistics re:g_paper</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9d7b6824a182/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:low-rank_approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:g_paper"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00684">
    <title>Spike Train SIMilarity Space (SSIMS): A Framework for Single Neuron and Ensemble Data Analysis</title>
    <dc:date>2014-12-29T02:03:46+00:00</dc:date>
    <link>http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00684</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Increased emphasis on circuit level activity in the brain makes it necessary to have methods to visualize and evaluate large-scale ensemble activity beyond that revealed by raster-histograms or pairwise correlations. We present a method to evaluate the relative similarity of neural spiking patterns by combining spike train distance metrics with dimensionality reduction. Spike train distance metrics provide an estimate of similarity between activity patterns at multiple temporal resolutions. Vectors of pair-wise distances are used to represent the intrinsic relationships between multiple activity patterns at the level of single units or neuronal ensembles. Dimensionality reduction is then used to project the data into concise representations suitable for clustering analysis as well as exploratory visualization. Algorithm performance and robustness are evaluated using multielectrode ensemble activity data recorded in behaving primates. We demonstrate how spike train SIMilarity space (SSIMS) analysis captures the relationship between goal directions for an eight-directional reaching task and successfully segregates grasp types in a 3D grasping task in the absence of kinematic information. The algorithm enables exploration of virtually any type of neural spiking (time series) data, providing similarity-based clustering of neural activity states with minimal assumptions about potential information encoding models."

- Sounds straightforward enough...]]></description>
<dc:subject>to:NB neural_data_analysis time_series dimension_reduction statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:812a98e48913/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1211.3046">
    <title>[1211.3046] Recovering the Optimal Solution by Dual Random Projection</title>
    <dc:date>2014-07-30T16:05:26+00:00</dc:date>
    <link>http://arxiv.org/abs/1211.3046</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Random projection has been widely used in data classification. It maps high-dimensional data into a low-dimensional subspace in order to reduce the computational cost in solving the related optimization problem. While previous studies are focused on analyzing the classification performance of using random projection, in this work, we consider the recovery problem, i.e., how to accurately recover the optimal solution to the original optimization problem in the high-dimensional space based on the solution learned from the subspace spanned by random projections. We present a simple algorithm, termed Dual Random Projection, that uses the dual solution of the low-dimensional optimization problem to recover the optimal solution to the original problem. Our theoretical analysis shows that with a high probability, the proposed algorithm is able to accurately recover the optimal solution to the original problem, provided that the data matrix is of low rank or can be well approximated by a low rank matrix."]]></description>
<dc:subject>to:NB optimization low-rank_approximation dimension_reduction random_projections</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:63b8be9dbcf0/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:low-rank_approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_projections"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1406.0873">
    <title>[1406.0873] Unifying linear dimensionality reduction</title>
    <dc:date>2014-07-12T00:26:03+00:00</dc:date>
    <link>http://arxiv.org/abs/1406.0873</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of interest, such as covariance, dynamical structure, correlation between data sets, input-output relationships, and margin between data classes. Methods have been developed with a variety of names and motivations in many fields, and perhaps as a result the deeper connections between all these methods have not been understood. Here we unify methods from this disparate literature as optimization programs over matrix manifolds. We discuss principal component analysis, factor analysis, linear multidimensional scaling, Fisher's linear discriminant analysis, canonical correlations analysis, maximum autocorrelation factors, slow feature analysis, undercomplete independent component analysis, linear regression, and more. This optimization framework helps elucidate some rarely discussed shortcomings of well-known methods, such as the suboptimality of certain eigenvector solutions. Modern techniques for optimization over matrix manifolds enable a generic linear dimensionality reduction solver, which accepts as input data and an objective to be optimized, and returns, as output, an optimal low-dimensional projection of the data. This optimization framework further allows rapid development of novel variants of classical methods, which we demonstrate here by creating an orthogonal-projection canonical correlations analysis. More broadly, we suggest that our generic linear dimensionality reduction solver can move linear dimensionality reduction toward becoming a blackbox, objective-agnostic numerical technology."]]></description>
<dc:subject>data_analysis principal_components factor_analysis optimization statistics dimension_reduction ghahramani.zoubin in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:6bae21f8af20/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:factor_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ghahramani.zoubin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/0907.0199">
    <title>[0907.0199] High-Dimensional Density Estimation via SCA: An Example in the Modelling of Hurricane Tracks</title>
    <dc:date>2014-04-22T15:55:22+00:00</dc:date>
    <link>http://arxiv.org/abs/0907.0199</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We present nonparametric techniques for constructing and verifying density estimates from high-dimensional data whose irregular dependence structure cannot be modelled by parametric multivariate distributions. A low-dimensional representation of the data is critical in such situations because of the curse of dimensionality. Our proposed methodology consists of three main parts: (1) data reparameterization via dimensionality reduction, wherein the data are mapped into a space where standard techniques can be used for density estimation and simulation; (2) inverse mapping, in which simulated points are mapped back to the high-dimensional input space; and (3) verification, in which the quality of the estimate is assessed by comparing simulated samples with the observed data. These approaches are illustrated via an exploration of the spatial variability of tropical cyclones in the North Atlantic; each datum in this case is an entire hurricane trajectory. We conclude the paper with a discussion of extending the methods to model the relationship between TC variability and climatic variables."]]></description>
<dc:subject>to_read heard_the_talk kith_and_kin dimension_reduction buchman.susan high-dimensional_statistics density_estimation meteorology hurricanes diffusion_maps entableted in_NB lee.ann_b.</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:feaeb1982195/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:heard_the_talk"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:buchman.susan"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:meteorology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hurricanes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:diffusion_maps"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entableted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lee.ann_b."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.tandfonline.com/doi/abs/10.1080/01621459.2013.849199#.Uztl8tx_Tuc">
    <title>Taylor &amp; Francis Online :: Principal Flows - Journal of the American Statistical Association - Volume 109, Issue 505</title>
    <dc:date>2014-04-02T01:54:34+00:00</dc:date>
    <link>http://www.tandfonline.com/doi/abs/10.1080/01621459.2013.849199#.Uztl8tx_Tuc</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We revisit the problem of extending the notion of principal component analysis (PCA) to multivariate datasets that satisfy nonlinear constraints, therefore lying on Riemannian manifolds. Our aim is to determine curves on the manifold that retain their canonical interpretability as principal components, while at the same time being flexible enough to capture nongeodesic forms of variation. We introduce the concept of a principal flow, a curve on the manifold passing through the mean of the data, and with the property that, at any point of the curve, the tangent velocity vector attempts to fit the first eigenvector of a tangent space PCA locally at that same point, subject to a smoothness constraint. That is, a particle flowing along the principal flow attempts to move along a path of maximal variation of the data, up to smoothness constraints. The rigorous definition of a principal flow is given by means of a Lagrangian variational problem, and its solution is reduced to an ODE problem via the Euler–Lagrange method. Conditions for existence and uniqueness are provided, and an algorithm is outlined for the numerical solution of the problem. Higher order principal flows are also defined. It is shown that global principal flows yield the usual principal components on a Euclidean space. By means of examples, it is illustrated that the principal flow is able to capture patterns of variation that can escape other manifold PCA methods."]]></description>
<dc:subject>to:NB dimension_reduction principal_components manifold_learning geometry statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ad0f6432b1db/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:manifold_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1402.0119">
    <title>[1402.0119] Randomized Nonlinear Component Analysis</title>
    <dc:date>2014-03-10T01:44:49+00:00</dc:date>
    <link>http://arxiv.org/abs/1402.0119</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Classical techniques such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques only reveal linear relationships in data. Although nonlinear variants of PCA and CCA have been proposed, they are computationally prohibitive in the large scale. 
"In a separate strand of recent research, randomized methods have been proposed to construct features that help reveal nonlinear patterns in data. For basic tasks such as regression or classification, random features exhibit little or no loss in performance, while achieving dramatic savings in computational requirements. 
"In this paper we leverage randomness to design scalable new variants of nonlinear PCA and CCA; our ideas also extend to key multivariate analysis tools such as spectral clustering or LDA. We demonstrate our algorithms through experiments on real-world data, on which we compare against the state-of-the-art. Code in R implementing our methods is provided in the Appendix."

--- This looks _awesome_.]]></description>
<dc:subject>to:NB to_read principal_components dimension_reduction statistics to_teach:undergrad-ADA random_features</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:79b245b38a8f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:undergrad-ADA"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_features"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1401.0267">
    <title>[1401.0267] Transformed sufficient dimension reduction</title>
    <dc:date>2014-03-08T21:45:09+00:00</dc:date>
    <link>http://arxiv.org/abs/1401.0267</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A novel general framework is proposed in this paper for dimension reduction in regression to fill the gap between linear and fully nonlinear dimension reduction. The main idea is to transform first each of the raw predictors monotonically, and then search for a low-dimensional projection in the space defined by the transformed variables. Both user-specified and data-driven transformations are suggested. In each case, the methodology is discussed first in a general manner, and a representative method, as an example, is then proposed and evaluated by simulation. The proposed methods are applied to a real data set for illustration."]]></description>
<dc:subject>dimension_reduction regression sufficiency statistics in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3874b310ccd7/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sufficiency"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.aos/1388545673">
    <title>Vu , Lei : Minimax sparse principal subspace estimation in high dimensions</title>
    <dc:date>2014-02-20T22:20:20+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.aos/1388545673</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study sparse principal components analysis in high dimensions, where p (the number of variables) can be much larger than n (the number of observations), and analyze the problem of estimating the subspace spanned by the principal eigenvectors of the population covariance matrix. We introduce two complementary notions of ℓq subspace sparsity: row sparsity and column sparsity. We prove nonasymptotic lower and upper bounds on the minimax subspace estimation error for 0≤q≤1. The bounds are optimal for row sparse subspaces and nearly optimal for column sparse subspaces, they apply to general classes of covariance matrices, and they show that ℓq constrained estimates can achieve optimal minimax rates without restrictive spiked covariance conditions. Interestingly, the form of the rates matches known results for sparse regression when the effective noise variance is defined appropriately. Our proof employs a novel variational sinΘ theorem that may be useful in other regularized spectral estimation problems."]]></description>
<dc:subject>to:NB principal_components sparsity dimension_reduction kith_and_kin vu.vincent statistics to_read minimax high-dimensional_statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ed0ddaddd49e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:vu.vincent"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:minimax"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1401.6978">
    <title>[1401.6978] Sparsistency and Agnostic Inference in Sparse PCA</title>
    <dc:date>2014-02-03T20:25:20+00:00</dc:date>
    <link>http://arxiv.org/abs/1401.6978</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The presence of a sparse "truth" has been a constant assumption in the theoretical analysis of sparse PCA and is often implicit in its methodological development. This naturally raises questions about the properties of sparse PCA methods and how they depend on the assumption of sparsity. Under what conditions can the relevant variables be selected consistently if the truth is assumed to be sparse? If the truth is not sparse, let alone unique, what can be said about the results of sparse PCA? We answer these questions by investigating the properties of the recently proposed Fantope projection and selection (FPS) method in the high dimensional setting. Our results provide general sufficient conditions for sparsistency of the FPS estimator. These conditions are weak and can hold in situations where other estimators are known to fail. On the other hand, without assuming sparsity or identifiability, we show that FPS provides a sparse, linear dimension-reducing transformation that is close to the best possible in terms of maximizing the predictive covariance."]]></description>
<dc:subject>to:NB principal_components sparsity dimension_reduction kith_and_kin statistics vu.vincent lei.jing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2a94c1eec2f6/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:vu.vincent"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lei.jing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://eliassi.org/papers/gilpin-kdd2013.pdf">
    <title>Guided Learning for Role Discovery (GLRD): Framework, Algorithms, and Applications</title>
    <dc:date>2014-01-08T18:21:50+00:00</dc:date>
    <link>http://eliassi.org/papers/gilpin-kdd2013.pdf</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Role discovery in graphs is an emerging area that allows analysis of complex graphs in an intuitive way. In contrast to community discovery, which finds groups of highly con- nected nodes, role discovery finds groups of nodes that share similar topological structure in the graph, and hence a com- mon role (or function) such as being a broker or a periphery node. However, existing work so far is completely unsuper- vised, which is undesirable for a number of reasons. We provide an alternating least squares framework that allows convex constraints to be placed on the role discovery prob- lem, which can provide useful supervision. In particular we explore supervision to enforce i) sparsity, ii) diversity, and iii) alternativeness in the roles. We illustrate the usefulness of this supervision on various data sets and applications."]]></description>
<dc:subject>to:NB to_read community_discovery network_data_analysis data_mining re:network_differences heard_the_talk matrix_and_tensor_factorization dimension_reduction eliassi-rad.tina</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1dad24d3ed94/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:community_discovery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:data_mining"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:network_differences"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:heard_the_talk"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:matrix_and_tensor_factorization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:eliassi-rad.tina"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1310.5089">
    <title>[1310.5089] Kernel Multivariate Analysis Framework for Supervised Subspace Learning: A Tutorial on Linear and Kernel Multivariate Methods</title>
    <dc:date>2013-10-23T14:25:13+00:00</dc:date>
    <link>http://arxiv.org/abs/1310.5089</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever higher resolution, and problems involving multimodal data sources become more common. A plethora of feature extraction methods are available in the literature collectively grouped under the field of Multivariate Analysis (MVA). This paper provides a uniform treatment of several methods: Principal Component Analysis (PCA), Partial Least Squares (PLS), Canonical Correlation Analysis (CCA) and Orthonormalized PLS (OPLS), as well as their non-linear extensions derived by means of the theory of reproducing kernel Hilbert spaces. We also review their connections to other methods for classification and statistical dependence estimation, and introduce some recent developments to deal with the extreme cases of large-scale and low-sized problems. To illustrate the wide applicability of these methods in both classification and regression problems, we analyze their performance in a benchmark of publicly available data sets, and pay special attention to specific real applications involving audio processing for music genre prediction and hyperspectral satellite images for Earth and climate monitoring."]]></description>
<dc:subject>to:NB signal_processing dimension_reduction regression principal_components kernel_methods statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a643506f78fb/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:signal_processing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1306.1350">
    <title>[1306.1350] Diffusion map for clustering fMRI spatial maps extracted by independent component analysis</title>
    <dc:date>2013-09-30T20:40:38+00:00</dc:date>
    <link>http://arxiv.org/abs/1306.1350</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Functional magnetic resonance imaging (fMRI) produces data about activity inside the brain, from which spatial maps can be extracted by independent component analysis (ICA). In datasets, there are n spatial maps that contain p voxels. The number of voxels is very high compared to the number of analyzed spatial maps. Clustering of the spatial maps is usually based on correlation matrices. This usually works well, although such a similarity matrix inherently can explain only a certain amount of the total variance contained in the high-dimensional data where n is relatively small but p is large. For high-dimensional space, it is reasonable to perform dimensionality reduction before clustering. In this research, we used the recently developed diffusion map for dimensionality reduction in conjunction with spectral clustering. This research revealed that the diffusion map based clustering worked as well as the more traditional methods, and produced more compact clusters when needed."]]></description>
<dc:subject>to:NB fmri dimension_reduction neuroscience diffusion_maps statistics independent_component_analysis</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8e53e7de3081/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:fmri"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neuroscience"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:diffusion_maps"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:independent_component_analysis"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1309.4054">
    <title>[1309.4054] Data-driven Algorithms for Dimension Reduction in Causal Inference: analyzing the effect of school achievements on acute complications of type 1 diabetes mellitus</title>
    <dc:date>2013-09-18T00:35:40+00:00</dc:date>
    <link>http://arxiv.org/abs/1309.4054</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In observational studies, the causal effect of a treatment may be confounded with variables that are related to both the treatment and the outcome of interest. In order to identify a causal effect, such studies often rely on the unconfoundedness assumption, i.e., that all confounding variables are observed. The choice of covariates to control for, which is primarily based on subject matter knowledge, may result in a large covariate vector in the attempt to ensure that unconfoundedness holds. However, including redundant covariates is suboptimal when the effect is estimated nonparametrically, e.g., due to the curse of dimensionality. In this paper, data-driven algorithms for the selection of sufficient covariate subsets are investigated. Under the assumption of unconfoundedness we search for minimal subsets of the covariate vector. Based on the framework of sufficient dimension reduction or kernel smoothing, the algorithms perform a backward elimination procedure testing the significance of each covariate. Their performance is evaluated in simulations and an application using data from the Swedish Childhood Diabetes Register is also presented."]]></description>
<dc:subject>to:NB dimension_reduction causal_inference nonparametrics statistics to_teach:undergrad-ADA</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:eb3e35141299/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causal_inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:undergrad-ADA"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1309.2895">
    <title>[1309.2895] Sparse and Functional Principal Components Analysis</title>
    <dc:date>2013-09-12T20:05:36+00:00</dc:date>
    <link>http://arxiv.org/abs/1309.2895</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Regularized principal components analysis, especially Sparse PCA and Functional PCA, has become widely used for dimension reduction in high-dimensional settings. Many examples of massive data, however, may benefit from estimating both sparse AND functional factors. These include neuroimaging data where there are discrete brain regions of activation (sparsity) but these regions tend to be smooth spatially (functional). Here, we introduce an optimization framework that can encourage both sparsity and smoothness of the row and/or column PCA factors. This framework generalizes many of the existing approaches to Sparse PCA, Functional PCA and two-way Sparse PCA and Functional PCA, as these are all special cases of our method. In particular, our method permits flexible combinations of sparsity and smoothness that lead to improvements in feature selection and signal recovery as well as more interpretable PCA factors. We demonstrate our method on simulated data and a neuroimaging example on EEG data. This work provides a unified framework for regularized PCA that can form the foundation for a cohesive approach to regularization in high-dimensional multivariate analysis."]]></description>
<dc:subject>to:NB sparsity functional_data_analysis principal_components statistics dimension_reduction allen.genevera_i.</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:def8a3768d6a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:functional_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:allen.genevera_i."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.pnas.org/content/110/31/12535.abstract">
    <title>Empirical intrinsic geometry for nonlinear modeling and time series filtering</title>
    <dc:date>2013-09-03T12:26:55+00:00</dc:date>
    <link>http://www.pnas.org/content/110/31/12535.abstract</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization."

- Contributed papers in PNAS are however always somewhat dubious.]]></description>
<dc:subject>time_series prediction manifold_learning dimension_reduction statistics machine_learning to_read filtering state_estimation information_geometry entableted in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5c5423af007e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:manifold_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:machine_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entableted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1305.7255">
    <title>[1305.7255] Non-linear dimensionality reduction: Riemannian metric estimation and the problem of geometric discovery</title>
    <dc:date>2013-06-06T17:09:06+00:00</dc:date>
    <link>http://arxiv.org/abs/1305.7255</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man ifold geometry using either local or global features of the data. 
"Building on the Laplacian Eigenmap and Diffusionmaps framework, we propose a new paradigm that offers a guarantee, under reasonable assumptions, that any manifo ld learning algorithm will preserve the geometry of a data set. Our approach is based on augmenting the output of embedding algorithms with geometric informatio n embodied in the Riemannian metric of the manifold. We provide an algorithm for estimating the Riemannian metric from data and demonstrate possible application s of our approach in a variety of examples."]]></description>
<dc:subject>manifold_learning statistics in_NB metric_learning dimension_reduction</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:59c1108de4e1/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:manifold_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:metric_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00465">
    <title>Identifying Functional Bases for Multidimensional Neural Computations</title>
    <dc:date>2013-06-01T16:46:41+00:00</dc:date>
    <link>http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00465</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Current dimensionality-reduction methods can identify relevant subspaces for neural computations but do not favor one basis over the other within the relevant subspace. Finding the appropriate basis can simplify the description of the nonlinear computation with respect to the relevant variables, making it easier to elucidate the underlying neural computation and make hypotheses about the neural circuitry, giving rise to the observed responses. Part of the problem is that although some of the dimensionality reduction methods can identify many of the relevant dimensions, it is usually difficult to map out or interpret the nonlinear transformation with respect to more than a few relevant dimensions simultaneously without some simplifying assumptions. While recent approaches make it possible to create predictive models based on many relevant dimensions simultaneously, there still remains the need to relate such predictive models to the mechanistic descriptions of the operation of underlying neural circuitry. Here we demonstrate that transforming to a basis within the relevant subspace where the neural computation is best described by a given nonlinear function often makes it easier to interpret the computation and describe it with a small number of parameters. We refer to the corresponding basis as the functional basis, and illustrate the utility of such transformation in the context of logical OR and logical AND functions. We show that although dimensionality-reduction methods such as spike-triggered covariance are able to find a relevant subspace, they often produce dimensions that are difficult to interpret and do not correspond to a functional basis. The functional features can be found using a maximum likelihood approach. The results are illustrated using simulated neurons and recordings from retinal ganglion cells. The resulting features are uniquely defined and nonorthogonal, and they make it easier to relate computational and mechanistic models to each other."]]></description>
<dc:subject>to:NB neural_networks neural_data_analysis dimension_reduction inverse_problems distributed_systems basis_selection</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a62ae8e915cf/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:inverse_problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:distributed_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:basis_selection"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.ss/1369147911">
    <title>Blum , Nunes , Prangle , Sisson : A Comparative Review of Dimension Reduction Methods in Approximate Bayesian Computation</title>
    <dc:date>2013-05-21T22:51:55+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.ss/1369147911</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets."]]></description>
<dc:subject>approximate_bayesian_computation statistics dimension_reduction information_criteria in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:55662e045598/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:approximate_bayesian_computation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_criteria"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://biomet.oxfordjournals.org/content/100/2/371.short?rss=1">
    <title>Efficiency loss and the linearity condition in dimension reduction</title>
    <dc:date>2013-05-11T16:32:17+00:00</dc:date>
    <link>http://biomet.oxfordjournals.org/content/100/2/371.short?rss=1</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Linearity, sometimes jointly with constant variance, is routinely assumed in the context of sufficient dimension reduction. It is well understood that, when these conditions do not hold, blindly using them may lead to inconsistency in estimating the central subspace and the central mean subspace. Surprisingly, we discover that even if these conditions do hold, using them will bring efficiency loss. This paradoxical phenomenon is illustrated through sliced inverse regression and principal Hessian directions. The efficiency loss also applies to other dimension reduction procedures. We explain this empirical discovery by theoretical investigation."]]></description>
<dc:subject>to:NB dimension_reduction regression statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:38a59016a2f7/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://jmlr.csail.mit.edu/papers/v14/chen13a.html">
    <title>Stress Functions for Nonlinear Dimension Reduction, Proximity Analysis, and Graph Drawing</title>
    <dc:date>2013-05-07T20:34:13+00:00</dc:date>
    <link>http://jmlr.csail.mit.edu/papers/v14/chen13a.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Multidimensional scaling (MDS) is the art of reconstructing pointsets (embeddings) from pairwise distance data, and as such it is at the basis of several approaches to nonlinear dimension reduction and manifold learning. At present, MDS lacks a unifying methodology as it consists of a discrete collection of proposals that differ in their optimization criteria, called ''stress functions''. To correct this situation we propose (1) to embed many of the extant stress functions in a parametric family of stress functions, and (2) to replace the ad hoc choice among discrete proposals with a principled parameter selection method. This methodology yields the following benefits and problem solutions: (a )It provides guidance in tailoring stress functions to a given data situation, responding to the fact that no single stress function dominates all others across all data situations; (b) the methodology enriches the supply of available stress functions; (c) it helps our understanding of stress functions by replacing the comparison of discrete proposals with a characterization of the effect of parameters on embeddings; (d) it builds a bridge to graph drawing, which is the related but not identical art of constructing embeddings from graphs."]]></description>
<dc:subject>manifold_learning dimension_reduction data_mining to_teach:data-mining visual_display_of_quantitative_information network_data_analysis in_NB network_visualization</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:82fe59f894b9/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:manifold_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:data_mining"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:data-mining"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:visual_display_of_quantitative_information"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_visualization"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1304.6487">
    <title>[1304.6487] Locally linear representation for subspace learning and clustering</title>
    <dc:date>2013-04-26T00:21:06+00:00</dc:date>
    <link>http://arxiv.org/abs/1304.6487</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular schemes to construct a similarity graph, i.e., pairwise distance based scheme and linear representation based scheme. Most existing works have only involved one of the above schemes and suffered from some limitations. Specifically, pairwise distance based methods are sensitive to the noises and outliers compared with linear representation based methods. On the other hand, there is the possibility that linear representation based algorithms wrongly select inter-subspaces points to represent a point, which will degrade the performance. In this paper, we propose an algorithm, called Locally Linear Representation (LLR), which integrates pairwise distance with linear representation together to address the problems. The proposed algorithm can automatically encode each data point over a set of points that not only could denote the objective point with less residual error, but also are close to the point in Euclidean space. The experimental results show that our approach is promising in subspace learning and subspace clustering."

--- Not clear to me from the abstract how this differs from locally linear embedding...]]></description>
<dc:subject>to:NB data_mining dimension_reduction</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e06f2a3f104c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:data_mining"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1304.6663">
    <title>[1304.6663] Low-rank optimization for distance matrix completion</title>
    <dc:date>2013-04-26T00:19:53+00:00</dc:date>
    <link>http://arxiv.org/abs/1304.6663</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the number of considered data points. The focus is on high-dimensional problems. We recast the considered problem into an optimization problem over the set of low-rank positive semidefinite matrices and propose two efficient algorithms for low-rank distance matrix completion. In addition, we propose a strategy to determine the dimension of the embedding space. The resulting algorithms scale to high-dimensional problems and monotonically converge to a global solution of the problem. Finally, numerical experiments illustrate the good performance of the proposed algorithms on benchmarks."]]></description>
<dc:subject>to:NB low-rank_approximation dimension_reduction dimension_estimation high-dimensional_statistics statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8487aa08d4fb/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:low-rank_approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1304.5802">
    <title>[1304.5802] Nonlinear Basis Pursuit</title>
    <dc:date>2013-04-23T18:00:10+00:00</dc:date>
    <link>http://arxiv.org/abs/1304.5802</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In compressive sensing, the basis pursuit algorithm aims to find the sparsest solution to an underdetermined linear equation system. In this paper, we generalize basis pursuit to finding the sparsest solution to higher order nonlinear systems of equations, called nonlinear basis pursuit. In contrast to the existing nonlinear compressive sensing methods, the new algorithm that solves the nonlinear basis pursuit problem is convex and not greedy. The novel algorithm enables the compressive sensing approach to be used for a broader range of applications where there are nonlinear relationships between the measurements and the unknowns."]]></description>
<dc:subject>to:NB sparsity dimension_reduction information_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:69d447e1a3a2/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aos/1364302741">
    <title>Lee , Li , Chiaromonte : A general theory for nonlinear sufficient dimension reduction: Formulation and estimation</title>
    <dc:date>2013-03-26T16:44:38+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aos/1364302741</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper we introduce a general theory for nonlinear sufficient dimension reduction, and explore its ramifications and scope. This theory subsumes recent work employing reproducing kernel Hilbert spaces, and reveals many parallels between linear and nonlinear sufficient dimension reduction. Using these parallels we analyze the properties of existing methods and develop new ones. We begin by characterizing dimension reduction at the general level of σ-fields and proceed to that of classes of functions, leading to the notions of sufficient, complete and central dimension reduction classes. We show that, when it exists, the complete and sufficient class coincides with the central class, and can be unbiasedly and exhaustively estimated by a generalized sliced inverse regression estimator (GSIR). When completeness does not hold, this estimator captures only part of the central class. However, in these cases we show that a generalized sliced average variance estimator (GSAVE) can capture a larger portion of the class. Both estimators require no numerical optimization because they can be computed by spectral decomposition of linear operators. Finally, we compare our estimators with existing methods by simulation and on actual data sets."

Open: http://arxiv.org/abs/1304.0580]]></description>
<dc:subject>sufficiency regression dimension_reduction to_read in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:42f9fd4fc82f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sufficiency"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aos/1364302742">
    <title>Ma , Zhu : Efficient estimation in sufficient dimension reduction</title>
    <dc:date>2013-03-26T16:43:50+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aos/1364302742</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite dimensional parameter in a semiparametric model. This conversion allows us to derive an efficient estimator which reaches the optimal semiparametric efficiency bound. The resulting efficient estimator can exhaustively estimate the central subspace without imposing any distributional assumptions. Our proposed efficient estimation also provides a possibility for making inference of parameters that uniquely identify the central subspace. We conduct simulation studies and a real data analysis to demonstrate the finite sample performance in comparison with several existing methods."

Open: http://arxiv.org/abs/1304.0593]]></description>
<dc:subject>statistics sufficiency dimension_reduction regression in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:6f8da75bf795/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sufficiency"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.imsc/1362751182">
    <title>Dümbgen, Del Conte-Zerial: On low-dimensional projections of high-dimensional distributions</title>
    <dc:date>2013-03-10T01:12:49+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.imsc/1362751182</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Let $P$ be a probability distribution on $q$-dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension $d\ll q$, most $d$-dimensional projections of $P$ look like a scale mixture of spherically symmetric Gaussian distributions. The present paper provides necessary and sufficient conditions for this phenomenon in a suitable asymptotic framework with increasing dimension $q$. It turns out that the conditions formulated by Diaconis and Freedman [Ann. Statist. 12 (1984) 793–815] are not only sufficient but necessary as well. Moreover, letting $\widehat{P}$ be the empirical distribution of $n$ independent random vectors with distribution $P$, we investigate the behavior of the empirical process $\sqrt{n}(\widehat{P}-P)$ under random projections, conditional on $\widehat{P}$."]]></description>
<dc:subject>to:NB dimension_reduction high-dimensional_probability probability random_projections</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1fade6af970c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_projections"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1302.2752">
    <title>[1302.2752] Adaptive Metric Dimensionality Reduction</title>
    <dc:date>2013-03-06T15:29:12+00:00</dc:date>
    <link>http://arxiv.org/abs/1302.2752</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We initiate the study of dimensionality reduction in general metric spaces in the context of supervised learning. Our statistical contribution consists of tight Rademacher bounds for Lipschitz functions in metric spaces that are doubling, or nearly doubling. As a by-product, we obtain a new theoretical explanation for the empirically reported improvements gained by pre-processing Euclidean data by PCA (Principal Components Analysis) prior to constructing a linear classifier. 
"On the algorithmic front, we describe an analogue of PCA for metric spaces, namely an efficient procedure that approximates the data's intrinsic dimension, which is often much lower than the ambient dimension. Thus, our approach can exploit the dual benefits of low dimensionality: (1) more efficient proximity search algorithms, and (2) more optimistic generalization bounds."]]></description>
<dc:subject>to:NB dimension_reduction principal_components machine_learning kith_and_kin kontorovich.aryeh</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5968ffe22d74/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:machine_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kontorovich.aryeh"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://biomet.oxfordjournals.org/content/100/1/75.short?rss=1">
    <title>Efficient Gaussian process regression for large datasets</title>
    <dc:date>2013-02-23T17:46:20+00:00</dc:date>
    <link>http://biomet.oxfordjournals.org/content/100/1/75.short?rss=1</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Gaussian processes are widely used in nonparametric regression, classification and spatiotemporal modelling, facilitated in part by a rich literature on their theoretical properties. However, one of their practical limitations is expensive computation, typically on the order of n3 where n is the number of data points, in performing the necessary matrix inversions. For large datasets, storage and processing also lead to computational bottlenecks, and numerical stability of the estimates and predicted values degrades with increasing n. Various methods have been proposed to address these problems, including predictive processes in spatial data analysis and the subset-of-regressors technique in machine learning. The idea underlying these approaches is to use a subset of the data, but this raises questions concerning sensitivity to the choice of subset and limitations in estimating fine-scale structure in regions that are not well covered by the subset. Motivated by the literature on compressive sensing, we propose an alternative approach that involves linear projection of all the data points onto a lower-dimensional subspace. We demonstrate the superiority of this approach from a theoretical perspective and through simulated and real data examples."]]></description>
<dc:subject>to:NB gaussian_processes regression nonparametrics statistics compressed_sensing dimension_reduction</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:49f5a0eb3f27/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:gaussian_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:compressed_sensing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1302.4881">
    <title>[1302.4881] Elliptical Insights: Understanding Statistical Methods through Elliptical Geometry</title>
    <dc:date>2013-02-21T23:40:01+00:00</dc:date>
    <link>http://arxiv.org/abs/1302.4881</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the virtues of the ellipse and her higher-dimensional cousins for both these purposes in a variety of contexts, including linear models, multivariate linear models and mixed-effect models. We emphasize the strong relationships among statistical methods, matrix-algebraic solutions and geometry that can often be easily understood in terms of ellipses."]]></description>
<dc:subject>to:NB geometry statistics visual_display_of_quantitative_information dimension_reduction data_analysis</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ef5149e48935/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:visual_display_of_quantitative_information"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:data_analysis"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1002.4283">
    <title>[1002.4283] Learning gradients on manifolds</title>
    <dc:date>2013-02-21T23:27:09+00:00</dc:date>
    <link>http://arxiv.org/abs/1002.4283</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on manifolds for dimension reduction for high-dimensional data with few observations. We obtain generalization error bounds for the gradient estimates and show that the convergence rate depends on the intrinsic dimension of the manifold and not on the dimension of the ambient space. We illustrate the efficacy of this approach empirically on simulated and real data and compare the method to other dimension reduction procedures."]]></description>
<dc:subject>dimension_reduction manifold_learning statistics in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4461aef9a54c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:manifold_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1104.3472">
    <title>[1104.3472] Principal arc analysis on direct product manifolds</title>
    <dc:date>2013-02-21T23:22:14+00:00</dc:date>
    <link>http://arxiv.org/abs/1104.3472</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We propose a new approach to analyze data that naturally lie on manifolds. We focus on a special class of manifolds, called direct product manifolds, whose intrinsic dimension could be very high. Our method finds a low-dimensional representation of the manifold that can be used to find and visualize the principal modes of variation of the data, as Principal Component Analysis (PCA) does in linear spaces. The proposed method improves upon earlier manifold extensions of PCA by more concisely capturing important nonlinear modes. For the special case of data on a sphere, variation following nongeodesic arcs is captured in a single mode, compared to the two modes needed by previous methods. Several computational and statistical challenges are resolved. The development on spheres forms the basis of principal arc analysis on more complicated manifolds. The benefits of the method are illustrated by a data example using medial representations in image analysis."]]></description>
<dc:subject>to:NB statistics dimension_reduction principal_components statistics_on_manifolds</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2bf4e5566e74/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics_on_manifolds"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1205.6040">
    <title>[1205.6040] Nonlinear manifold representations for functional data</title>
    <dc:date>2013-02-21T23:14:02+00:00</dc:date>
    <link>http://arxiv.org/abs/1205.6040</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute nonlinear representations of functional data that complement classical linear representations such as eigenfunctions and functional principal components. Our manifold learning procedures borrow ideas from existing nonlinear dimension reduction methods, which we modify to address functional data settings. In simulations and applications, we study examples of functional data which lie on a manifold and validate the superior behavior of manifold mean and functional manifold components over traditional cross-sectional mean and functional principal components. We also include consistency proofs for our estimators under certain assumptions."]]></description>
<dc:subject>manifold_learning statistics in_NB functional_data_analysis dimension_reduction</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f4cdb9c1ee4b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:manifold_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:functional_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00407">
    <title>Sufficient Dimension Reduction via Squared-Loss Mutual Information Estimation</title>
    <dc:date>2013-02-06T14:42:37+00:00</dc:date>
    <link>http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00407</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The goal of sufficient dimension reduction in supervised learning is to find the low-dimensional subspace of input features that contains all of the information about the output values that the input features possess. In this letter, we propose a novel sufficient dimension-reduction method using a squared-loss variant of mutual information as a dependency measure. We apply a density-ratio estimator for approximating squared-loss mutual information that is formulated as a minimum contrast estimator on parametric or nonparametric models. Since cross-validation is available for choosing an appropriate model, our method does not require any prespecified structure on the underlying distributions. We elucidate the asymptotic bias of our estimator on parametric models and the asymptotic convergence rate on nonparametric models. The convergence analysis utilizes the uniform tail-bound of a U-process, and the convergence rate is characterized by the bracketing entropy of the model. We then develop a natural gradient algorithm on the Grassmann manifold for sufficient subspace search. The analytic formula of our estimator allows us to compute the gradient efficiently. Numerical experiments show that the proposed method compares favorably with existing dimension-reduction approaches on artificial and benchmark data sets."]]></description>
<dc:subject>dimension_reduction regression nonparametrics information_theory sufficiency statistics machine_learning in_NB sugiyama.masashi</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:34bf4767419a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sufficiency"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:machine_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sugiyama.masashi"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>