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    <title>Pinboard (cshalizi)</title>
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    <description>recent bookmarks from cshalizi</description>
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      <rdf:Seq>	<rdf:li rdf:resource="https://arxiv.org/abs/2306.01129"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2110.05518"/>
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	<rdf:li rdf:resource="https://projecteuclid.org/journals/annals-of-statistics/volume-49/issue-3/On-cross-validated-Lasso-in-high-dimensions/10.1214/20-AOS2000.short"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2006.11908"/>
	<rdf:li rdf:resource="https://psyarxiv.com/kjh2f"/>
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	<rdf:li rdf:resource="https://arxiv.org/abs/2105.02071"/>
	<rdf:li rdf:resource="https://www.tandfonline.com/doi/full/10.1080/01621459.2021.1895175"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2103.03191"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1802.08667"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1908.04904"/>
	<rdf:li rdf:resource="https://journals.aps.org/pre/abstract/10.1103/PhysRevE.103.042310"/>
	<rdf:li rdf:resource="https://www.jneurosci.org/content/41/5/1019"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/2101.03093"/>
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	<rdf:li rdf:resource="https://arxiv.org/abs/2012.04556"/>
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	<rdf:li rdf:resource="https://arxiv.org/abs/2011.04018"/>
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	<rdf:li rdf:resource="https://arxiv.org/abs/1909.13189"/>
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	<rdf:li rdf:resource="https://ieeexplore.ieee.org/document/8700269"/>
	<rdf:li rdf:resource="https://arxiv.org/abs/1806.03120"/>
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	<rdf:li rdf:resource="https://arxiv.org/abs/1712.05630"/>
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	<rdf:li rdf:resource="http://onlinelibrary.wiley.com/doi/10.1111/jtsa.12221/abstract"/>
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	<rdf:li rdf:resource="http://www.springer.com/us/book/9783319327730"/>
	<rdf:li rdf:resource="http://www.oneweirdkerneltrick.com/catbasis.pdf"/>
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	<rdf:li rdf:resource="http://cambridge.org/9781107058545"/>
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	<rdf:li rdf:resource="http://arxiv.org/abs/1205.0953"/>
	<rdf:li rdf:resource="http://ganguli-gang.stanford.edu/pdf/12.CompSense.pdf"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1401.6978"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1312.1706"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1311.6238"/>
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	<rdf:li rdf:resource="http://arxiv.org/abs/1311.4175"/>
	<rdf:li rdf:resource="http://www.tandfonline.com/doi/abs/10.1080/01621459.2013.803972#.Ukmy-hbPUlM"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1309.6702"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1308.2408"/>
	<rdf:li rdf:resource="http://arxiv.org/abs/1309.2895"/>
	<rdf:li rdf:resource="http://jmlr.org/papers/v14/rosasco13a.html"/>
	<rdf:li rdf:resource="http://normaldeviate.wordpress.com/2013/07/27/the-steep-price-of-sparsity/"/>
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  </channel><item rdf:about="https://arxiv.org/abs/2306.01129">
    <title>[2306.01129] White-Box Transformers via Sparse Rate Reduction</title>
    <dc:date>2023-06-05T15:12:58+00:00</dc:date>
    <link>https://arxiv.org/abs/2306.01129</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we contend that the objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a mixture of low-dimensional Gaussian distributions supported on incoherent subspaces. The quality of the final representation can be measured by a unified objective function called sparse rate reduction. From this perspective, popular deep networks such as transformers can be naturally viewed as realizing iterative schemes to optimize this objective incrementally. Particularly, we show that the standard transformer block can be derived from alternating optimization on complementary parts of this objective: the multi-head self-attention operator can be viewed as a gradient descent step to compress the token sets by minimizing their lossy coding rate, and the subsequent multi-layer perceptron can be viewed as attempting to sparsify the representation of the tokens. This leads to a family of white-box transformer-like deep network architectures which are mathematically fully interpretable. Despite their simplicity, experiments show that these networks indeed learn to optimize the designed objective: they compress and sparsify representations of large-scale real-world vision datasets such as ImageNet, and achieve performance very close to thoroughly engineered transformers such as ViT. "]]></description>
<dc:subject>in_NB large_language_models_(so_called) neural_networks sparsity re:large_language_models_in_statistical_perspective</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9a2c882b1b03/</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:large_language_models_(so_called)"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:large_language_models_in_statistical_perspective"/>
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</item>
<item rdf:about="https://arxiv.org/abs/2110.05518">
    <title>[2110.05518] Global Optimality Beyond Two Layers: Training Deep ReLU Networks via Convex Programs</title>
    <dc:date>2023-05-27T16:28:22+00:00</dc:date>
    <link>https://arxiv.org/abs/2110.05518</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Understanding the fundamental mechanism behind the success of deep neural networks is one of the key challenges in the modern machine learning literature. Despite numerous attempts, a solid theoretical analysis is yet to be developed. In this paper, we develop a novel unified framework to reveal a hidden regularization mechanism through the lens of convex optimization. We first show that the training of multiple three-layer ReLU sub-networks with weight decay regularization can be equivalently cast as a convex optimization problem in a higher dimensional space, where sparsity is enforced via a group ℓ1-norm regularization. Consequently, ReLU networks can be interpreted as high dimensional feature selection methods. More importantly, we then prove that the equivalent convex problem can be globally optimized by a standard convex optimization solver with a polynomial-time complexity with respect to the number of samples and data dimension when the width of the network is fixed. Finally, we numerically validate our theoretical results via experiments involving both synthetic and real datasets."]]></description>
<dc:subject>neural_networks sparsity convexity optimization in_NB have_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2c84a4be8565/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:convexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
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<item rdf:about="https://joss.theoj.org/papers/10.21105/joss.04522">
    <title>Journal of Open Source Software: haldensify: Highly adaptive lasso conditional density estimation in R</title>
    <dc:date>2022-12-09T20:04:28+00:00</dc:date>
    <link>https://joss.theoj.org/papers/10.21105/joss.04522</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The haldensify R package serves as a toolbox for nonparametric conditional density estimation
based on the highly adaptive lasso, a flexible nonparametric algorithm for the estimation of
functional statistical parameters (e.g., conditional mean, hazard, density). Building upon an
earlier proposal (Dı́az & van der Laan, 2011), haldensify leverages the relationship between
the hazard and density functions to estimate the latter by applying pooled hazard regression to
a synthetic repeated measures dataset created from the input data, relying upon the framework
of cross-validated loss-based estimation to yield an optimal estimator (Dudoit & van der Laan,
2005; van der Laan et al., 2004). While conditional density estimation is a fundamental problem
in statistics, arising naturally in a variety of applications (including machine learning), it plays
a critical role in estimating the causal effects of continuous- or ordinal-valued treatments. In
such settings this covariate-conditional treatment density has been termed the generalized
propensity score (Hirano & Imbens, 2004; Imai & Van Dyk, 2004), and, like its analog for
binary treatments (Rosenbaum & Rubin, 1983), serves as a key ingredient in developing both
inverse probability weighted and doubly robust estimators of causal effects (Dı́az & van der
Laan, 2012, 2018; Haneuse & Rotnitzky, 2013; Hejazi et al., 2022)"]]></description>
<dc:subject>density_estimation R lasso sparsity van_der_laan.mark in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d6b76808e7da/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:R"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lasso"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:van_der_laan.mark"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
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<item rdf:about="https://projecteuclid.org/journals/annals-of-statistics/volume-49/issue-3/LASSO-driven-inference-in-time-and-space/10.1214/20-AOS2019.short">
    <title>LASSO-driven inference in time and space</title>
    <dc:date>2021-08-10T14:07:16+00:00</dc:date>
    <link>https://projecteuclid.org/journals/annals-of-statistics/volume-49/issue-3/LASSO-driven-inference-in-time-and-space/10.1214/20-AOS2019.short</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider the estimation and inference in a system of high-dimensional regression equations allowing for temporal and cross-sectional dependency in covariates and error processes, covering rather general forms of weak temporal dependence. A sequence of regressions with many regressors using LASSO (Least Absolute Shrinkage and Selection Operator) is applied for variable selection purpose, and an overall penalty level is carefully chosen by a block multiplier bootstrap procedure to account for multiplicity of the equations and dependencies in the data. Correspondingly, oracle properties with a jointly selected tuning parameter are derived. We further provide high-quality de-biased simultaneous inference on the many target parameters of the system. We provide bootstrap consistency results of the test procedure, which are based on a general Bahadur representation for the Z-estimators with dependent data. Simulations demonstrate good performance of the proposed inference procedure. Finally, we apply the method to quantify spillover effects of textual sentiment indices in a financial market and to test the connectedness among sectors."]]></description>
<dc:subject>to:NB lasso sparsity regression time_series spatial_statistics variable_selection statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:86f9e897007b/</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:lasso"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spatial_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variable_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
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</item>
<item rdf:about="https://projecteuclid.org/journals/annals-of-statistics/volume-49/issue-3/On-cross-validated-Lasso-in-high-dimensions/10.1214/20-AOS2000.short">
    <title>On cross-validated Lasso in high dimensions</title>
    <dc:date>2021-08-09T16:26:22+00:00</dc:date>
    <link>https://projecteuclid.org/journals/annals-of-statistics/volume-49/issue-3/On-cross-validated-Lasso-in-high-dimensions/10.1214/20-AOS2000.short</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we derive nonasymptotic error bounds for the Lasso estimator when the penalty parameter for the estimator is chosen using K-fold cross-validation. Our bounds imply that the cross-validated Lasso estimator has nearly optimal rates of convergence in the prediction, L2 and L1 norms. For example, we show that in the model with the Gaussian noise and under fairly general assumptions on the candidate set of values of the penalty parameter, the estimation error of the cross-validated Lasso estimator converges to zero in the prediction norm with the √slogp/n×√log(pn) rate, where n is the sample size of available data, p is the number of covariates and s is the number of nonzero coefficients in the model. Thus, the cross-validated Lasso estimator achieves the fastest possible rate of convergence in the prediction norm up to a small logarithmic factor √log(pn), and similar conclusions apply for the convergence rate both in L2 and in L1 norms. Importantly, our results cover the case when p is (potentially much) larger than n and also allow for the case of non-Gaussian noise. Our paper therefore serves as a justification for the widely spread practice of using cross-validation as a method to choose the penalty parameter for the Lasso estimator."]]></description>
<dc:subject>to:NB cross-validation lasso sparsity high-dimensional_statistics statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:25ec0744b249/</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:cross-validation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lasso"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
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</item>
<item rdf:about="https://arxiv.org/abs/2006.11908">
    <title>[2006.11908] Decoupling Shrinkage and Selection in Gaussian Linear Factor Analysis</title>
    <dc:date>2021-07-27T12:34:42+00:00</dc:date>
    <link>https://arxiv.org/abs/2006.11908</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Factor Analysis is a popular method for modeling dependence in multivariate data. However, determining the number of factors and obtaining a sparse orientation of the loadings are still major challenges. In this paper, we propose a decision-theoretic approach that brings to light the relation between a sparse representation of the loadings and factor dimension. This relation is done through a summary from information contained in the multivariate posterior. To construct such summary, we introduce a three-step approach. In the first step, the model is fitted with a conservative factor dimension. In the second step, a series of sparse point-estimates, with a decreasing number of factors, is obtained by minimizing an expected predictive loss function. In step three, the degradation in utility in relation to the sparse loadings and factor dimensions is displayed in the posterior summary. The findings are illustrated with applications in classical data from the Factor Analysis literature. We used different prior choices and factor dimensions to demonstrate the flexibility of the proposed method."]]></description>
<dc:subject>to:NB factor_analysis sparsity model_selection carvalho.carlos_m. statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5efda0efeedf/</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:factor_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:model_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:carvalho.carlos_m."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://psyarxiv.com/kjh2f">
    <title>PsyArXiv Preprints | The Confidence Interval that Wasn’t: Bootstrapped “Confidence Intervals” in L1-Regularized Partial Correlation Networks</title>
    <dc:date>2021-07-19T13:52:15+00:00</dc:date>
    <link>https://psyarxiv.com/kjh2f</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["I shed much needed light upon the default measure of parameter uncertainty in network psychometrics; that is, ``confidence intervals'' (CI) computed from bootstrapping $\ell_1$-regularized partial correlations. Due to the nature of the $\ell_1$-penalty, however, bootstrapping does not provide an accurate sampling distribution. Although this has long been known in the statistical literature, I set out to determine whether the intervals can at least be considered \emph{approximate}. In multiple regression, I first describe the fundamental tension between model selection and estimation consistency inherent to the $\ell_1$-penalty---in the pursuit of sparsity, the sampling distribution of the non-zero coefficients is necessarily compromised which translates into coverage far below nominal levels.
"With the foundation laid, I proceed to investigate coverage for non-zero relations in partial correlation networks. At best, average coverage was around 0.65 for 90\% CIs. With increasing sample sizes, average coverage decreased to 0.30, perhaps approaching 0 if larger sample sizes were explored. Further, coverage was heavily influenced by the mere position of an edge in the network, ranging from essentially 0 to 0.90, with an average of around 0.50. Meanwhile, for the same simulation conditions, simply bootstrapping the sample covariance matrix provided coverage at the nominal level. In light of the results, I then demonstrate how to judiciously use the bootstrap in both regularized and non-regularized networks: the former can provide a useful summary of data-mining, whereas the latter allows for making inference on network parameters. To ensure network researchers have the option of computing valid CIs, I implemented a non-regularized bootstrap for various types of partial correlations in the {\tt R} package \textbf{GGMnonreg}. "]]></description>
<dc:subject>to:NB sparsity model_selection graphical_models statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f65b9477b29f/</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:model_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:graphical_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
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</item>
<item rdf:about="https://arxiv.org/abs/2107.03975">
    <title>[2107.03975] Compressibility Analysis of Asymptotically Mean Stationary Processes</title>
    <dc:date>2021-07-11T05:55:06+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.03975</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This work provides new results for the analysis of random sequences in terms of ℓp-compressibility. The results characterize the degree in which a random sequence can be approximated by its best k-sparse version under different rates of significant coefficients (compressibility analysis). In particular, the notion of strong ℓp-characterization is introduced to denote a random sequence that has a well-defined asymptotic limit (sample-wise) of its best k-term approximation error when a fixed rate of significant coefficients is considered (fixed-rate analysis). The main theorem of this work shows that the rich family of asymptotically mean stationary (AMS) processes has a strong ℓp-characterization. Furthermore, we present results that characterize and analyze the ℓp-approximation error function for this family of processes. Adding ergodicity in the analysis of AMS processes, we introduce a theorem demonstrating that the approximation error function is constant and determined in closed-form by the stationary mean of the process. Our results and analyses contribute to the theory and understanding of discrete-time sparse processes and, on the technical side, confirm how instrumental the point-wise ergodic theorem is to determine the compressibility expression of discrete-time processes even when stationarity and ergodicity assumptions are relaxed."]]></description>
<dc:subject>to:NB stochastic_processes sparsity approximation ergodic_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:485fccb044e3/</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:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ergodic_theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2105.02071">
    <title>[2105.02071] The costs and benefits of uniformly valid causal inference with high-dimensional nuisance parameters</title>
    <dc:date>2021-05-06T13:50:57+00:00</dc:date>
    <link>https://arxiv.org/abs/2105.02071</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Important advances have recently been achieved in developing procedures yielding uniformly valid inference for a low dimensional causal parameter when high-dimensional nuisance models must be estimated. In this paper, we review the literature on uniformly valid causal inference and discuss the costs and benefits of using uniformly valid inference procedures. Naive estimation strategies based on regularisation, machine learning, or a preliminary model selection stage for the nuisance models have finite sample distributions which are badly approximated by their asymptotic distributions. To solve this serious problem, estimators which converge uniformly in distribution over a class of data generating mechanisms have been proposed in the literature. In order to obtain uniformly valid results in high-dimensional situations, sparsity conditions for the nuisance models need typically to be made, although a double robustness property holds, whereby if one of the nuisance model is more sparse, the other nuisance model is allowed to be less sparse. While uniformly valid inference is a highly desirable property, uniformly valid procedures pay a high price in terms of inflated variability. Our discussion of this dilemma is illustrated by the study of a double-selection outcome regression estimator, which we show is uniformly asymptotically unbiased, but is less variable than uniformly valid estimators in the numerical experiments conducted."]]></description>
<dc:subject>to:NB causal_inference model_selection sparsity</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c2156cc8eff6/</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:model_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.tandfonline.com/doi/full/10.1080/01621459.2021.1895175">
    <title>Consistent Sparse Deep Learning: Theory and Computation: Journal of the American Statistical Association: Vol 0, No 0</title>
    <dc:date>2021-04-21T16:09:37+00:00</dc:date>
    <link>https://www.tandfonline.com/doi/full/10.1080/01621459.2021.1895175</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training, prediction and interpretation. We propose a frequentist-like method for learning sparse DNNs and justify its consistency under the Bayesian framework: the proposed method could learn a sparse DNN with at most O(n/log(n))O(n/ log (n)) connections and nice theoretical guarantees such as posterior consistency, variable selection consistency and asymptotically optimal generalization bounds. In particular, we establish posterior consistency for the sparse DNN with a mixture Gaussian prior, show that the structure of the sparse DNN can be consistently determined using a Laplace approximation-based marginal posterior inclusion probability approach, and use Bayesian evidence to elicit sparse DNNs learned by an optimization method such as stochastic gradient descent in multiple runs with different initializations. The proposed method is computationally more efficient than standard Bayesian methods for large-scale sparse DNNs. The numerical results indicate that the proposed method can perform very well for large-scale network compression and high-dimensional nonlinear variable selection, both advancing interpretable machine learning."]]></description>
<dc:subject>neural_networks nonparametrics sparsity bayesian_consistency in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:eaf86c3cae34/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bayesian_consistency"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2103.03191">
    <title>[2103.03191] Generalization Bounds for Sparse Random Feature Expansions</title>
    <dc:date>2021-04-21T14:53:40+00:00</dc:date>
    <link>https://arxiv.org/abs/2103.03191</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent similar function spaces without a costly training phase. However, for accuracy, random feature methods require more measurements than trainable parameters, limiting their use for data-scarce applications or problems in scientific machine learning. This paper introduces the sparse random feature expansion to obtain parsimonious random feature models. Specifically, we leverage ideas from compressive sensing to generate random feature expansions with theoretical guarantees even in the data-scarce setting. In particular, we provide uniform bounds on the approximation error and generalization bounds for functions in a certain class (that is dense in a reproducing kernel Hilbert space) depending on the number of samples and the distribution of features. The error bounds improve with additional structural conditions, such as coordinate sparsity, compact clusters of the spectrum, or rapid spectral decay. In particular, by introducing sparse features, i.e. features with random sparse weights, we provide improved bounds for low order functions. We show that the sparse random feature expansions outperforms shallow networks in several scientific machine learning tasks."]]></description>
<dc:subject>sparsity random_features approximation learning_theory to_teach:childs_garden_of_statistical_learning_theory in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:dde4a10d084c/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_features"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:approximation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:childs_garden_of_statistical_learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1802.08667">
    <title>[1802.08667] De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers</title>
    <dc:date>2021-04-14T14:48:58+00:00</dc:date>
    <link>https://arxiv.org/abs/1802.08667</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We provide adaptive inference methods, based on ℓ1 regularization, for regular (semiparametric) and non-regular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include average treatment effects, policy effects, and derivatives. Examples of non-regular functionals include average treatment effects, policy effects, and derivatives conditional on a covariate subvector fixed at a point. We construct a Neyman orthogonal equation for the target parameter that is approximately invariant to small perturbations of the nuisance parameters. To achieve this property, we include the Riesz representer for the functional as an additional nuisance parameter. Our analysis yields weak "double sparsity robustness": either the approximation to the regression or the approximation to the representer can be "completely dense" as long as the other is sufficiently "sparse". Our main results are non-asymptotic and imply asymptotic uniform validity over large classes of models, translating into honest confidence bands for both global and local parameters."]]></description>
<dc:subject>to:NB causal_inference sparsity nonparametrics to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:56b3f2bb1d9f/</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:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1908.04904">
    <title>[1908.04904] Least Squares Approximation for a Distributed System</title>
    <dc:date>2021-04-14T14:47:32+00:00</dc:date>
    <link>https://arxiv.org/abs/1908.04904</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this work, we develop a distributed least squares approximation (DLSA) method that is able to solve a large family of regression problems (e.g., linear regression, logistic regression, and Cox's model) on a distributed system. By approximating the local objective function using a local quadratic form, we are able to obtain a combined estimator by taking a weighted average of local estimators. The resulting estimator is proved to be statistically as efficient as the global estimator. Moreover, it requires only one round of communication. We further conduct a shrinkage estimation based on the DLSA estimation using an adaptive Lasso approach. The solution can be easily obtained by using the LARS algorithm on the master node. It is theoretically shown that the resulting estimator possesses the oracle property and is selection consistent by using a newly designed distributed Bayesian information criterion (DBIC). The finite sample performance and computational efficiency are further illustrated by an extensive numerical study and an airline dataset. The airline dataset is 52 GB in size. The entire methodology has been implemented in Python for a {\it de-facto} standard Spark system. The proposed DLSA algorithm on the Spark system takes 26 minutes to obtain a logistic regression estimator, which is more efficient and memory friendly than conventional methods."]]></description>
<dc:subject>to:NB distributed_systems linear_regression sparsity</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:15c67296b489/</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:distributed_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:linear_regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://journals.aps.org/pre/abstract/10.1103/PhysRevE.103.042310">
    <title>Phys. Rev. E 103, 042310 (2021) - Learning physically consistent differential equation models from data using group sparsity</title>
    <dc:date>2021-04-14T14:43:26+00:00</dc:date>
    <link>https://journals.aps.org/pre/abstract/10.1103/PhysRevE.103.042310</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We propose a statistical learning framework based on group-sparse regression that can be used to (i) enforce conservation laws, (ii) ensure model equivalence, and (iii) guarantee symmetries when learning or inferring differential-equation models from data. Directly learning interpretable mathematical models from data has emerged as a valuable modeling approach. However, in areas such as biology, high noise levels, sensor-induced correlations, and strong intersystem variability can render data-driven models nonsensical or physically inconsistent without additional constraints on the model structure. Hence, it is important to leverage prior knowledge from physical principles to learn biologically plausible and physically consistent models rather than models that simply fit the data best. We present the group iterative hard thresholding algorithm and use stability selection to infer physically consistent models with minimal parameter tuning. We show several applications from systems biology that demonstrate the benefits of enforcing priors in data-driven modeling."]]></description>
<dc:subject>statistical_inference_for_stochastic_processes equations_of_motion_from_a_time_series sparsity in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e7bbb81e3bd3/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:equations_of_motion_from_a_time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.jneurosci.org/content/41/5/1019">
    <title>Finding Distributed Needles in Neural Haystacks | Journal of Neuroscience</title>
    <dc:date>2021-02-05T19:38:35+00:00</dc:date>
    <link>https://www.jneurosci.org/content/41/5/1019</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The human cortex encodes information in complex networks that can be anatomically dispersed and variable in their microstructure across individuals. Using simulations with neural network models, we show that contemporary statistical methods for functional brain imaging—including univariate contrast, searchlight multivariate pattern classification, and whole-brain decoding with L1 or L2 regularization—each have critical and complementary blind spots under these conditions. We then introduce the sparse-overlapping-sets (SOS) LASSO—a whole-brain multivariate approach that exploits structured sparsity to find network-distributed information—and show in simulation that it captures the advantages of other approaches while avoiding their limitations. When applied to fMRI data to find neural responses that discriminate visually presented faces from other visual stimuli, each method yields a different result, but existing approaches all support the canonical view that face perception engages localized areas in posterior occipital and temporal regions. In contrast, SOS LASSO uncovers a network spanning all four lobes of the brain. The result cannot reflect spurious selection of out-of-system areas because decoding accuracy remains exceedingly high even when canonical face and place systems are removed from the dataset. When used to discriminate visual scenes from other stimuli, the same approach reveals a localized signal consistent with other methods—illustrating that SOS LASSO can detect both widely distributed and localized representational structure. Thus, structured sparsity can provide an unbiased method for testing claims of functional localization. For faces and possibly other domains, such decoding may reveal representations more widely distributed than previously suspected."]]></description>
<dc:subject>to:NB distributed_systems neural_data_analysis neural_coding_and_decoding sparsity lasso to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:bc3cdfc5f1e7/</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:distributed_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_coding_and_decoding"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lasso"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2101.03093">
    <title>[2101.03093] Learning non-Gaussian graphical models via Hessian scores and triangular transport</title>
    <dc:date>2021-01-11T16:32:41+00:00</dc:date>
    <link>https://arxiv.org/abs/2101.03093</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Undirected probabilistic graphical models represent the conditional dependencies, or Markov properties, of a collection of random variables. Knowing the sparsity of such a graphical model is valuable for modeling multivariate distributions and for efficiently performing inference. While the problem of learning graph structure from data has been studied extensively for certain parametric families of distributions, most existing methods fail to consistently recover the graph structure for non-Gaussian data. Here we propose an algorithm for learning the Markov structure of continuous and non-Gaussian distributions. To characterize conditional independence, we introduce a score based on integrated Hessian information from the joint log-density, and we prove that this score upper bounds the conditional mutual information for a general class of distributions. To compute the score, our algorithm SING estimates the density using a deterministic coupling, induced by a triangular transport map, and iteratively exploits sparse structure in the map to reveal sparsity in the graph. For certain non-Gaussian datasets, we show that our algorithm recovers the graph structure even with a biased approximation to the density. Among other examples, we apply sing to learn the dependencies between the states of a chaotic dynamical system with local interactions."]]></description>
<dc:subject>to:NB graphical_models sparsity statistics information_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:fb9eca8344a8/</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:graphical_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<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/2101.02776">
    <title>[2101.02776] The Nonconvex Geometry of Linear Inverse Problems</title>
    <dc:date>2021-01-11T16:31:53+00:00</dc:date>
    <link>https://arxiv.org/abs/2101.02776</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The gauge function, closely related to the atomic norm, measures the complexity of a statistical model, and has found broad applications in machine learning and statistical signal processing. In a high-dimensional learning problem, the gauge function attempts to safeguard against overfitting by promoting a sparse (concise) representation within the learning alphabet.
"In this work, within the context of linear inverse problems, we pinpoint the source of its success, but also argue that the applicability of the gauge function is inherently limited by its convexity, and showcase several learning problems where the classical gauge function theory fails. We then introduce a new notion of statistical complexity, gaugep function, which overcomes the limitations of the gauge function. The gaugep function is a simple generalization of the gauge function that can tightly control the sparsity of a statistical model within the learning alphabet and, perhaps surprisingly, draws further inspiration from the Burer-Monteiro factorization in computational mathematics.
"We also propose a new learning machine, with the building block of gaugep function, and arm this machine with a number of statistical guarantees. The potential of the proposed gaugep function theory is then studied for two stylized applications. Finally, we discuss the computational aspects and, in particular, suggest a tractable numerical algorithm for implementing the new learning machine."]]></description>
<dc:subject>to:NB inverse_problems sparsity statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c45d1367d99b/</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:inverse_problems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2012.04171">
    <title>[2012.04171] Sparse encoding for more-interpretable feature-selecting representations in probabilistic matrix factorization</title>
    <dc:date>2021-01-03T19:48:45+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.04171</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Dimensionality reduction methods for count data are critical to a wide range of applications in medical informatics and other fields where model interpretability is paramount. For such data, hierarchical Poisson matrix factorization (HPF) and other sparse probabilistic non-negative matrix factorization (NMF) methods are considered to be interpretable generative models. They consist of sparse transformations for decoding their learned representations into predictions. However, sparsity in representation decoding does not necessarily imply sparsity in the encoding of representations from the original data features. HPF is often incorrectly interpreted in the literature as if it possesses encoder sparsity. The distinction between decoder sparsity and encoder sparsity is subtle but important. Due to the lack of encoder sparsity, HPF does not possess the column-clustering property of classical NMF -- the factor loading matrix does not sufficiently define how each factor is formed from the original features. We address this deficiency by self-consistently enforcing encoder sparsity, using a generalized additive model (GAM), thereby allowing one to relate each representation coordinate to a subset of the original data features. In doing so, the method also gains the ability to perform feature selection. We demonstrate our method on simulated data and give an example of how encoder sparsity is of practical use in a concrete application of representing inpatient comorbidities in Medicare patients."]]></description>
<dc:subject>to:NB variable_selection sparsity factor_analysis additive_models statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c88603e68cdb/</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:variable_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:factor_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:additive_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2002.02250">
    <title>[2002.02250] Uncovering differential equations from data with hidden variables</title>
    <dc:date>2020-12-26T17:46:56+00:00</dc:date>
    <link>https://arxiv.org/abs/2002.02250</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["SINDy is a method for learning system of differential equations from data by solving a sparse linear regression optimization problem [Brunton et al., 2016]. In this article, we propose an extension of the SINDy method that learns systems of differential equations in cases where some of the variables are not observed. Our extension is based on regressing a higher order time derivative of a target variable onto a dictionary of functions that includes lower order time derivatives of the target variable. We evaluate our method by measuring the prediction accuracy of the learned dynamical systems on synthetic data and on a real data-set of temperature time series provided by the Réseau de Transport d'Électricité (RTE). Our method provides high quality short-term forecasts and it is orders of magnitude faster than competing methods for learning differential equations with latent variables."]]></description>
<dc:subject>equations_of_motion_from_a_time_series sparsity linear_regression dynamical_systems inference_to_latent_objects in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3ba9d3e1c481/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:equations_of_motion_from_a_time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:linear_regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dynamical_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:inference_to_latent_objects"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.aoas/1608346892">
    <title>Baker , Tang , Allen : Feature selection for data integration with mixed multiview data</title>
    <dc:date>2020-12-19T16:42:14+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.aoas/1608346892</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Data integration methods that analyze multiple sources of data simultaneously can often provide more holistic insights than can separate inquiries of each data source. Motivated by the advantages of data integration in the era of “big data,” we investigate feature selection for high-dimensional multiview data with mixed data types (e.g., continuous, binary, count-valued). This heterogeneity of multiview data poses numerous challenges for existing feature selection methods. However, after critically examining these issues through empirical and theoretically-guided lenses, we develop a practical solution, the Block Randomized Adaptive Iterative Lasso (B-RAIL) which combines the strengths of the randomized Lasso, adaptive weighting schemes and stability selection. B-RAIL serves as a versatile data integration method for sparse regression and graph selection, and we demonstrate the effectiveness of B-RAIL through extensive simulations and a case study to infer the ovarian cancer gene regulatory network. In this case study, B-RAIL successfully identifies well-known biomarkers associated with ovarian cancer and hints at novel candidates for future ovarian cancer research."]]></description>
<dc:subject>to:NB variable_selection lasso sparsity statistics allen.genevera_i.</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c18ec82da65c/</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:variable_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lasso"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:allen.genevera_i."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2005.14057">
    <title>[2005.14057] Machine Learning Time Series Regressions with an Application to Nowcasting</title>
    <dc:date>2020-12-15T12:59:51+00:00</dc:date>
    <link>https://arxiv.org/abs/2005.14057</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper introduces structured machine learning regressions for high-dimensional time series data potentially sampled at different frequencies. The sparse-group LASSO estimator can take advantage of such time series data structures and outperforms the unstructured LASSO. We establish oracle inequalities for the sparse-group LASSO estimator within a framework that allows for the mixing processes and recognizes that the financial and the macroeconomic data may have heavier than exponential tails. An empirical application to nowcasting US GDP growth indicates that the estimator performs favorably compared to other alternatives and that text data can be a useful addition to more traditional numerical data."]]></description>
<dc:subject>to:NB time_series lasso sparsity statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:6bfda85c2bca/</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:lasso"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2012.06391">
    <title>[2012.06391] Learning physically consistent mathematical models from data using group sparsity</title>
    <dc:date>2020-12-15T01:36:26+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.06391</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We propose a statistical learning framework based on group-sparse regression that can be used to 1) enforce conservation laws, 2) ensure model equivalence, and 3) guarantee symmetries when learning or inferring differential-equation models from measurement data. Directly learning interpretable mathematical models from data has emerged as a valuable modeling approach. However, in areas like biology, high noise levels, sensor-induced correlations, and strong inter-system variability can render data-driven models nonsensical or physically inconsistent without additional constraints on the model structure. Hence, it is important to leverage prior knowledge from physical principles to learn "biologically plausible and physically consistent" models rather than models that simply fit the data best. We present a novel group Iterative Hard Thresholding (gIHT) algorithm and use stability selection to infer physically consistent models with minimal parameter tuning. We show several applications from systems biology that demonstrate the benefits of enforcing priors in data-driven modeling."]]></description>
<dc:subject>to:NB dynamical_systems statistical_inference_for_stochastic_processes sparsity statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7760c0b795d9/</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:statistical_inference_for_stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2012.04556">
    <title>[2012.04556] Finding nonlinear system equations and complex network structures from data: a sparse optimization approach</title>
    <dc:date>2020-12-12T03:25:09+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.04556</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system equations and structure based solely on measured time series. Recently, methods based on sparse optimization have been developed. For example, the principle of exploiting sparse optimization such as compressive sensing to find the equations of nonlinear dynamical systems from data was articulated in 2011 by the Nonlinear Dynamics Group at Arizona State University. This article presents a brief review of the recent progress in this area. The basic idea is to expand the equations governing the dynamical evolution of the system into a power series or a Fourier series of a finite number of terms and then to determine the vector of the expansion coefficients based solely on data through sparse optimization. Examples discussed here include discovering the equations of stationary or nonstationary chaotic systems to enable prediction of dynamical events such as critical transition and system collapse, inferring the full topology of complex networks of dynamical oscillators and social networks hosting evolutionary game dynamics, and identifying partial differential equations for spatiotemporal dynamical systems. Situations where sparse optimization is effective and those in which the method fails are discussed. Comparisons with the traditional method of delay coordinate embedding in nonlinear time series analysis are given and the recent development of model-free, data driven prediction framework based on machine learning is briefly introduced."]]></description>
<dc:subject>to:NB dynamical_systems time_series sparsity statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2a830c8c26f9/</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:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2011.12215">
    <title>[2011.12215] Searching for Interactions: Why the Laplace Kernel is your Friend</title>
    <dc:date>2020-11-25T14:25:54+00:00</dc:date>
    <link>https://arxiv.org/abs/2011.12215</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We tackle the problem of nonparametric variable selection with a focus on discovering interactions between variables. With p variables there are O(ps) possible order-s interactions making exhaustive search infeasible. It is nonetheless possible to identify the variables involved in interactions with only linear computation cost, O(p). The trick is to maximize a class of parametrized nonparametric dependence measures which we call \emph{metric learning objectives}; the landscape of these nonconvex objective functions is sensitive to interactions but the objectives themselves do not explicitly model interactions. Three properties make metric learning objectives highly attractive:
"(a) The stationary points of the objective are automatically sparse (i.e. performs selection)---no explicit ℓ1 penalization is needed.
"(b) All stationary points of the objective exclude noise variables with high probability.
"(c) Guaranteed recovery of all signal variables without needing to reach the objective's global maxima or special stationary points.
"The second and third properties mean that all our theoretical results apply in the practical case where one uses gradient ascent to maximize the metric learning objective. While not all metric learning objectives enjoy good statistical power, we design an objective based on ℓ1 kernels that does exhibit favorable power: it recovers (i) main effects with n∼logp samples, (ii) hierarchical interactions with n∼logp samples and (iii) order-s pure interactions with n∼p2(s−1)logp samples."]]></description>
<dc:subject>to:NB sparsity nonparametrics statistics kernel_methods</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2c6e8e00596e/</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:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_methods"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2011.04018">
    <title>[2011.04018] Online Sparse Reinforcement Learning</title>
    <dc:date>2020-11-23T17:45:22+00:00</dc:date>
    <link>https://arxiv.org/abs/2011.04018</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We investigate the hardness of online reinforcement learning in fixed horizon, sparse linear Markov decision process (MDP), with a special focus on the high-dimensional regime where the ambient dimension is larger than the number of episodes. Our contribution is two-fold. First, we provide a lower bound showing that linear regret is generally unavoidable in this case, even if there exists a policy that collects well-conditioned data. The lower bound construction uses an MDP with a fixed number of states while the number of actions scales with the ambient dimension. Note that when the horizon is fixed to one, the case of linear stochastic bandits, the linear regret can be avoided. Second, we show that if the learner has oracle access to a policy that collects well-conditioned data then a variant of Lasso fitted Q-iteration enjoys a nearly dimension-free regret of Õ (s2/3N2/3) where N is the number of episodes and s is the sparsity level. This shows that in the large-action setting, the difficulty of learning can be attributed to the difficulty of finding a good exploratory policy."]]></description>
<dc:subject>to:NB sparsity reinforcement_learning learning_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:da676e4c2ce4/</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:reinforcement_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.annualreviews.org/doi/abs/10.1146/annurev-statistics-030718-105038">
    <title>A Survey of Tuning Parameter Selection for High-Dimensional Regression | Annual Review of Statistics and Its Application</title>
    <dc:date>2020-11-19T20:05:48+00:00</dc:date>
    <link>https://www.annualreviews.org/doi/abs/10.1146/annurev-statistics-030718-105038</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Penalized (or regularized) regression, as represented by lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of penalized regression relies crucially on the choice of the tuning parameter, which determines the amount of regularization and hence the sparsity level of the fitted model. The optimal choice of tuning parameter depends on both the structure of the design matrix and the unknown random error distribution (variance, tail behavior, etc.). This article reviews the current literature of tuning parameter selection for high-dimensional regression from both the theoretical and practical perspectives. We discuss various strategies that choose the tuning parameter to achieve prediction accuracy or support recovery. We also review several recently proposed methods for tuning-free high-dimensional regression."]]></description>
<dc:subject>to:NB regression sparsity high-dimensional_statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f1362e8d5eb2/</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:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2004.05387">
    <title>[2004.05387] Vintage Factor Analysis with Varimax Performs Statistical Inference</title>
    <dc:date>2020-04-17T15:52:39+00:00</dc:date>
    <link>https://arxiv.org/abs/2004.05387</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Psychologists developed Multiple Factor Analysis to decompose multivariate data into a small number of interpretable factors without any a priori knowledge about those factors. In this form of factor analysis, the Varimax "factor rotation" is a key step to make the factors interpretable. Charles Spearman and many others objected to factor rotations because the factors seem to be rotationally invariant. These objections are still reported in all contemporary multivariate statistics textbooks. This is an engima because this vintage form of factor analysis has survived and is widely popular because, empirically, the factor rotation often makes the factors easier to interpret. We argue that the rotation makes the factors easier to interpret because, in fact, the Varimax factor rotation performs statistical inference. We show that Principal Components Analysis (PCA) with the Varimax rotation provides a unified spectral estimation strategy for a broad class of modern factor models, including the Stochastic Blockmodel and a natural variation of Latent Dirichlet Allocation (i.e., "topic modeling"). In addition, we show that Thurstone's widely employed sparsity diagnostics implicitly assess a key "leptokurtic" condition that makes the rotation statistically identifiable in these models. Taken together, this shows that the know-how of Vintage Factor Analysis performs statistical inference, reversing nearly a century of statistical thinking on the topic. With a sparse eigensolver, PCA with Varimax is both fast and stable. Combined with Thurstone's straightforward diagnostics, this vintage approach is suitable for a wide array of modern applications."

--- My impulse is to say that unidentified is untestable, so any "solution" to the rotation problem has to smuggle in an assumption which just can't be checked.  But Karl is a smart guy so I really do mean it about a fair trial.
--- ETA after reading: this is, indeed, smuggling in an untestable assumption about the latent space, viz., that the distribution in the latent space has preferred coordinate axes, and that the distribution in the latent space clusters along those coordinate axes.  Having assumed this, it is not surprising to me that there is a way of estimating those preferred axes, nor indeed is it surprising that PCA is one such way.  But the fact remains that I can use any coordinate system I like in the latent space, and nothing _observable_ changes when I switch coordinate systems.
--- I do not think this reaction is just pique/amusement at finding that I am now old enough to be one of the stodgy voices of received wisdom in section 1, comeuppance to follow.]]></description>
<dc:subject>factor_analysis sparsity statistics rohe.karl re:g_paper have_read i_remain_unconvinced in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:018615c13937/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:factor_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:rohe.karl"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:g_paper"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:i_remain_unconvinced"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1603.07632">
    <title>[1603.07632] Statistical inference in sparse high-dimensional additive models</title>
    <dc:date>2019-10-22T13:49:54+00:00</dc:date>
    <link>https://arxiv.org/abs/1603.07632</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper we discuss the estimation of a nonparametric component f1 of a nonparametric additive model Y=f1(X1)+...+fq(Xq)+ϵ. We allow the number q of additive components to grow to infinity and we make sparsity assumptions about the number of nonzero additive components. We compare this estimation problem with that of estimating f1 in the oracle model Z=f1(X1)+ϵ, for which the additive components f2,…,fq are known. We construct a two-step presmoothing-and-resmoothing estimator of f1 and state finite-sample bounds for the difference between our estimator and some smoothing estimators f̂ (oracle)1 in the oracle model. In an asymptotic setting these bounds can be used to show asymptotic equivalence of our estimator and the oracle estimators; the paper thus shows that, asymptotically, under strong enough sparsity conditions, knowledge of f2,…,fq has no effect on estimation accuracy. Our first step is to estimate f1 with an undersmoothed estimator based on near-orthogonal projections with a group Lasso bias correction. We then construct pseudo responses Ŷ  by evaluating a debiased modification of our undersmoothed estimator of f1 at the design points. In the second step the smoothing method of the oracle estimator f̂ (oracle)1 is applied to a nonparametric regression problem with responses Ŷ  and covariates X1. Our mathematical exposition centers primarily on establishing properties of the presmoothing estimator. We present simulation results demonstrating close-to-oracle performance of our estimator in practical applications."

--- ETA: Journal version, https://doi.org/10.1214/20-AOS2011]]></description>
<dc:subject>additive_models statistics regression nonparametrics sparsity in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:254865861d99/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:additive_models"/>
	<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:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1905.13657">
    <title>[1905.13657] Approximate Cross-Validation in High Dimensions with Guarantees</title>
    <dc:date>2019-10-22T13:19:50+00:00</dc:date>
    <link>https://arxiv.org/abs/1905.13657</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Leave-one-out cross validation (LOOCV) can be particularly accurate among CV variants for estimating out-of-sample error. Unfortunately, LOOCV requires re-fitting a model N times for a dataset of size N. To avoid this prohibitive computational expense, a number of authors have proposed approximations to LOOCV. These approximations work well when the unknown parameter is of small, fixed dimension but suffer in high dimensions; they incur a running time roughly cubic in the dimension, and, in fact, we show their accuracy significantly deteriorates in high dimensions. We demonstrate that these difficulties can be surmounted in ℓ1-regularized generalized linear models when we assume that the unknown parameter, while high dimensional, has a small support. In particular, we show that, under interpretable conditions, the support of the recovered parameter does not change as each datapoint is left out. This result implies that the previously proposed heuristic of only approximating CV along the support of the recovered parameter has running time and error that scale with the (small) support size even when the full dimension is large. Experiments on synthetic and real data support the accuracy of our approximations."]]></description>
<dc:subject>to:NB cross-validation sparsity high-dimensional_statistics computational_statistics statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:6d0b824228ec/</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:cross-validation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1909.13189">
    <title>[1909.13189] Learning Sparse Nonparametric DAGs</title>
    <dc:date>2019-10-01T16:16:54+00:00</dc:date>
    <link>https://arxiv.org/abs/1909.13189</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We develop a framework for learning sparse nonparametric directed acyclic graphs (DAGs) from data. Our approach is based on a recent algebraic characterization of DAGs that led to the first fully continuous optimization for score-based learning of DAG models parametrized by a linear structural equation model (SEM). We extend this algebraic characterization to nonparametric SEM by leveraging nonparametric sparsity based on partial derivatives, resulting in a continuous optimization problem that can be applied to a variety of nonparametric and semiparametric models including GLMs, additive noise models, and index models as special cases. We also explore the use of neural networks and orthogonal basis expansions to model nonlinearities for general nonparametric models. Extensive empirical study confirms the necessity of nonlinear dependency and the advantage of continuous optimization for score-based learning."]]></description>
<dc:subject>causal_discovery graphical_models optimization statistics ravikumar.pradeep xing.eric sparsity to_read in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e6bdf1913768/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causal_discovery"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:graphical_models"/>
	<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:ravikumar.pradeep"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:xing.eric"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<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="https://amstat.tandfonline.com/doi/full/10.1080/10618600.2019.1637749">
    <title>Testing Sparsity-Inducing Penalties: Journal of Computational and Graphical Statistics: Vol 0, No 0</title>
    <dc:date>2019-08-20T16:07:38+00:00</dc:date>
    <link>https://amstat.tandfonline.com/doi/full/10.1080/10618600.2019.1637749</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Many penalized maximum likelihood estimators correspond to posterior mode estimators under specific prior distributions. Appropriateness of a particular class of penalty functions can therefore be interpreted as the appropriateness of a prior for the parameters. For example, the appropriateness of a lasso penalty for regression coefficients depends on the extent to which the empirical distribution of the regression coefficients resembles a Laplace distribution. We give a testing procedure of whether or not a Laplace prior is appropriate and accordingly, whether or not using a lasso penalized estimate is appropriate. This testing procedure is designed to have power against exponential power priors which correspond to ℓqℓq penalties. Via simulations, we show that this testing procedure achieves the desired level and has enough power to detect violations of the Laplace assumption when the numbers of observations and unknown regression coefficients are large. We then introduce an adaptive procedure that chooses a more appropriate prior and corresponding penalty from the class of exponential power priors when the null hypothesis is rejected. We show that this can improve estimation of the regression coefficients both when they are drawn from an exponential power distribution and when they are drawn from a spike-and-slab distribution. Supplementary materials for this article are available online."

--- I feel like I fundamentally disagree with this approach.  Those priors are merely (to quote Jamie Robins and Larry Wasserman) "frequentist pursuit", and have no bearing on whether (say) the Lasso will give a good sparse, linear approximation to the underlying regression function (see https://normaldeviate.wordpress.com/2013/09/11/consistency-sparsistency-and-presistency/).  All of which said, Hoff is always worth listening to, so the last tag applies with special force.]]></description>
<dc:subject>to:NB model_checking sparsity regression hypothesis_testing bayesianism re:phil-of-bayes_paper hoff.peter to_besh</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:aaba8d8a838f/</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:model_checking"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hypothesis_testing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bayesianism"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:phil-of-bayes_paper"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hoff.peter"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_besh"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://ieeexplore.ieee.org/document/8700269">
    <title>High-Dimensional Adaptive Minimax Sparse Estimation With Interactions - IEEE Journals &amp; Magazine</title>
    <dc:date>2019-08-20T15:51:54+00:00</dc:date>
    <link>https://ieeexplore.ieee.org/document/8700269</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["High-dimensional linear regression with interaction effects is broadly applied in research fields such as bioinformatics and social science. In this paper, first, we investigate the minimax rate of convergence for regression estimation in high-dimensional sparse linear models with two-way interactions. Here, we derive matching upper and lower bounds under three types of heredity conditions: strong heredity, weak heredity, and no heredity. From the results: 1) A stronger heredity condition may or may not drastically improve the minimax rate of convergence. In fact, in some situations, the minimax rates of convergence are the same under all three heredity conditions; 2) The minimax rate of convergence is determined by the maximum of the total price of estimating the main effects and that of estimating the interaction effects, which goes beyond purely comparing the order of the number of non-zero main effects r1 and non-zero interaction effects r2 ; and 3) Under any of the three heredity conditions, the estimation of the interaction terms may be the dominant part in determining the rate of convergence. This is due to either the dominant number of interaction effects over main effects or the higher interaction estimation price induced by a large ambient dimension. Second, we construct an adaptive estimator that achieves the minimax rate of convergence regardless of the true heredity condition and the sparsity indices r1,r2 ."]]></description>
<dc:subject>to:NB statistics high-dimensional_statistics regression sparsity variable_selection linear_regression</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e3bf750aafd7/</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:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variable_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:linear_regression"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1806.03120">
    <title>[1806.03120] Variational inference for sparse network reconstruction from count data</title>
    <dc:date>2019-05-16T20:14:11+00:00</dc:date>
    <link>https://arxiv.org/abs/1806.03120</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In multivariate statistics, the question of finding direct interactions can be formulated as a problem of network inference - or network reconstruction - for which the Gaussian graphical model (GGM) provides a canonical framework. Unfortunately, the Gaussian assumption does not apply to count data which are encountered in domains such as genomics, social sciences or ecology. 
"To circumvent this limitation, state-of-the-art approaches use two-step strategies that first transform counts to pseudo Gaussian observations and then apply a (partial) correlation-based approach from the abundant literature of GGM inference. We adopt a different stance by relying on a latent model where we directly model counts by means of Poisson distributions that are conditional to latent (hidden) Gaussian correlated variables. In this multivariate Poisson lognormal-model, the dependency structure is completely captured by the latent layer. This parametric model enables to account for the effects of covariates on the counts. 
"To perform network inference, we add a sparsity inducing constraint on the inverse covariance matrix of the latent Gaussian vector. Unlike the usual Gaussian setting, the penalized likelihood is generally not tractable, and we resort instead to a variational approach for approximate likelihood maximization. The corresponding optimization problem is solved by alternating a gradient ascent on the variational parameters and a graphical-Lasso step on the covariance matrix. 
"We show that our approach is highly competitive with the existing methods on simulation inspired from microbiological data. We then illustrate on three various data sets how accounting for sampling efforts via offsets and integrating external covariates (which is mostly never done in the existing literature) drastically changes the topology of the inferred network."]]></description>
<dc:subject>to:NB sparsity graphical_models statistics re:6dfb</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3adc36cf07f2/</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:graphical_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:6dfb"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1903.04641">
    <title>[1903.04641] Generalized Sparse Additive Models</title>
    <dc:date>2019-04-11T00:30:41+00:00</dc:date>
    <link>https://arxiv.org/abs/1903.04641</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We present a unified framework for estimation and analysis of generalized additive models in high dimensions. The framework defines a large class of penalized regression estimators, encompassing many existing methods. An efficient computational algorithm for this class is presented that easily scales to thousands of observations and features. We prove minimax optimal convergence bounds for this class under a weak compatibility condition. In addition, we characterize the rate of convergence when this compatibility condition is not met. Finally, we also show that the optimal penalty parameters for structure and sparsity penalties in our framework are linked, allowing cross-validation to be conducted over only a single tuning parameter. We complement our theoretical results with empirical studies comparing some existing methods within this framework."]]></description>
<dc:subject>to:NB sparsity regression additive_models high-dimensional_statistics statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b6127a6a59e0/</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:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:additive_models"/>
	<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="https://arxiv.org/abs/1712.05630">
    <title>[1712.05630] Sparse principal component analysis via random projections</title>
    <dc:date>2018-09-13T16:40:16+00:00</dc:date>
    <link>https://arxiv.org/abs/1712.05630</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected random projections of the sample covariance matrix. Unlike most alternative approaches, our algorithm is non-iterative, so is not vulnerable to a bad choice of initialisation. Our theory provides great detail on the statistical and computational trade-off in our procedure, revealing a subtle interplay between the effective sample size and the number of random projections that are required to achieve the minimax optimal rate. Numerical studies provide further insight into the procedure and confirm its highly competitive finite-sample performance."]]></description>
<dc:subject>to:NB principal_components sparsity random_projections statistics samworth.richard_j.</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:6c614249e1dd/</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:random_projections"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:samworth.richard_j."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.pnas.org/content/114/32/8592.abstract.html?etoc">
    <title>Large numbers of explanatory variables, a semi-descriptive analysis</title>
    <dc:date>2017-08-08T17:59:58+00:00</dc:date>
    <link>http://www.pnas.org/content/114/32/8592.abstract.html?etoc</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Data with a relatively small number of study individuals and a very large number of potential explanatory features arise particularly, but by no means only, in genomics. A powerful method of analysis, the lasso [Tibshirani R (1996) J Roy Stat Soc B 58:267–288], takes account of an assumed sparsity of effects, that is, that most of the features are nugatory. Standard criteria for model fitting, such as the method of least squares, are modified by imposing a penalty for each explanatory variable used. There results a single model, leaving open the possibility that other sparse choices of explanatory features fit virtually equally well. The method suggested in this paper aims to specify simple models that are essentially equally effective, leaving detailed interpretation to the specifics of the particular study. The method hinges on the ability to make initially a very large number of separate analyses, allowing each explanatory feature to be assessed in combination with many other such features. Further stages allow the assessment of more complex patterns such as nonlinear and interactive dependences. The method has formal similarities to so-called partially balanced incomplete block designs introduced 80 years ago [Yates F (1936) J Agric Sci 26:424–455] for the study of large-scale plant breeding trials. The emphasis in this paper is strongly on exploratory analysis; the more formal statistical properties obtained under idealized assumptions will be reported separately."

--- Contributed, which is a bad sign, but by Cox, so...]]></description>
<dc:subject>to:NB statistics regression sparsity lasso high-dimensional_statistics cox.d.r.</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f64e83ba1977/</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:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lasso"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cox.d.r."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://onlinelibrary.wiley.com/doi/10.1111/jtsa.12221/abstract">
    <title>Oracle M-Estimation for Time Series Models - Giurcanu - 2016 - Journal of Time Series Analysis - Wiley Online Library</title>
    <dc:date>2017-04-04T13:16:54+00:00</dc:date>
    <link>http://onlinelibrary.wiley.com/doi/10.1111/jtsa.12221/abstract</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We propose a thresholding M-estimator for multivariate time series. Our proposed estimator has the oracle property that its large-sample properties are the same as of the classical M-estimator obtained under the a priori information that the zero parameters were known. We study the consistency of the standard block bootstrap, the centred block bootstrap and the empirical likelihood block bootstrap distributions of the proposed M-estimator. We develop automatic selection procedures for the thresholding parameter and for the block length of the bootstrap methods. We present the results of a simulation study of the proposed methods for a sparse vector autoregressive VAR(2) time series model. The analysis of two real-world data sets illustrate applications of the methods in practice."]]></description>
<dc:subject>bootstrap time_series statistics estimation in_NB sparsity variable_selection high-dimensional_statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7728d02c1d9a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bootstrap"/>
	<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:estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variable_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1311.5768">
    <title>[1311.5768] An RKHS Approach to Estimation with Sparsity Constraints</title>
    <dc:date>2016-12-04T21:30:35+00:00</dc:date>
    <link>https://arxiv.org/abs/1311.5768</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The investigation of the effects of sparsity or sparsity constraints in signal processing problems has received considerable attention recently. Sparsity constraints refer to the a priori information that the object or signal of interest can be represented by using only few elements of a predefined dictionary. Within this thesis, sparsity refers to the fact that a vector to be estimated has only few nonzero entries. One specific field concerned with sparsity constraints has become popular under the name Compressed Sensing (CS). Within CS, the sparsity is exploited in order to perform (nearly) lossless compression. Moreover, this compression is carried out jointly or simultaneously with the process of sensing a physical quantity. In contrast to CS, one can alternatively use sparsity to enhance signal processing methods. Obviously, sparsity constraints can only improve the obtainable estimation performance since the constraints can be interpreted as an additional prior information about the unknown parameter vector which is to be estimated. Our main focus will be on this aspect of sparsity, i.e., we analyze how much we can gain in estimation performance due to the sparsity constraints."]]></description>
<dc:subject>to:NB sparsity compressed_sensing hilbert_space estimation statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:bdb13f5deb4c/</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:compressed_sensing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hilbert_space"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1209.1508">
    <title>[1209.1508] Confidence sets in sparse regression</title>
    <dc:date>2016-11-30T02:04:08+00:00</dc:date>
    <link>https://arxiv.org/abs/1209.1508</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The problem of constructing confidence sets in the high-dimensional linear model with n response variables and p parameters, possibly p≥n, is considered. Full honest adaptive inference is possible if the rate of sparse estimation does not exceed n−1/4, otherwise sparse adaptive confidence sets exist only over strict subsets of the parameter spaces for which sparse estimators exist. Necessary and sufficient conditions for the existence of confidence sets that adapt to a fixed sparsity level of the parameter vector are given in terms of minimal ℓ2-separation conditions on the parameter space. The design conditions cover common coherence assumptions used in models for sparsity, including (possibly correlated) sub-Gaussian designs."]]></description>
<dc:subject>to:NB confidence_sets regression high-dimensional_statistics linear_regression statistics sparsity van_de_geer.sara nickl.richard</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:fa957ddc0986/</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:confidence_sets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:linear_regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:van_de_geer.sara"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nickl.richard"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.springer.com/us/book/9783319327730">
    <title>Estimation and Testing Under Sparsity | Sara van de Geer | Springer</title>
    <dc:date>2016-07-06T13:53:56+00:00</dc:date>
    <link>http://www.springer.com/us/book/9783319327730</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Taking the Lasso method as its starting point, this book describes the main ingredients needed to study general loss functions and sparsity-inducing regularizers. It also provides a semi-parametric approach to establishing confidence intervals and tests. Sparsity-inducing methods have proven to be very useful in the analysis of high-dimensional data. Examples include the Lasso and group Lasso methods, and the least squares method with other norm-penalties, such as the nuclear norm. The illustrations provided include generalized linear models, density estimation, matrix completion and sparse principal components. Each chapter ends with a problem section. The book can be used as a textbook for a graduate or PhD course."]]></description>
<dc:subject>to:NB books:noted statistics sparsity high-dimensional_statistics lasso hypothesis_testing confidence_sets van_de_geer.sara to_read empirical_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a21d87b7abc5/</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:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lasso"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hypothesis_testing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:confidence_sets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:van_de_geer.sara"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:empirical_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.oneweirdkerneltrick.com/catbasis.pdf">
    <title>Cat Basis Pursuit</title>
    <dc:date>2016-02-24T20:40:33+00:00</dc:date>
    <link>http://www.oneweirdkerneltrick.com/catbasis.pdf</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[Will the statistical machine learning reading group meet on 1 April?]]></description>
<dc:subject>machine_learning cats funny:geeky principal_components sparsity</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:031d454cc51b/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:machine_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cats"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:funny:geeky"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1602.00355">
    <title>[1602.00355] A Spectral Series Approach to High-Dimensional Nonparametric Regression</title>
    <dc:date>2016-02-06T19:50:57+00:00</dc:date>
    <link>http://arxiv.org/abs/1602.00355</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has been much interest in sparse techniques, current methods do not generalize well to data with nonlinear structure. In this work, we present an orthogonal series estimator for predictors that are complex aggregate objects, such as natural images, galaxy spectra, trajectories, and movies. Our series approach ties together ideas from kernel machine learning, and Fourier methods. We expand the unknown regression on the data in terms of the eigenfunctions of a kernel-based operator, and we take advantage of orthogonality of the basis with respect to the underlying data distribution, P, to speed up computations and tuning of parameters. If the kernel is appropriately chosen, then the eigenfunctions adapt to the intrinsic geometry and dimension of the data. We provide theoretical guarantees for a radial kernel with varying bandwidth, and we relate smoothness of the regression function with respect to P to sparsity in the eigenbasis. Finally, using simulated and real-world data, we systematically compare the performance of the spectral series approach with classical kernel smoothing, k-nearest neighbors regression, kernel ridge regression, and state-of-the-art manifold and local regression methods."]]></description>
<dc:subject>to:NB have_read statistics regression nonparametrics sparsity kernel_methods kith_and_kin lee.ann_b.</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d6f28b287ea4/</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:have_read"/>
	<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:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lee.ann_b."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://cambridge.org/9781107058545">
    <title>An Introduction to Sparse Stochastic Processes | Communications and Signal Processing | Cambridge University Press</title>
    <dc:date>2015-12-17T14:11:44+00:00</dc:date>
    <link>http://cambridge.org/9781107058545</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Providing a novel approach to sparsity, this comprehensive book presents the theory of stochastic processes that are ruled by linear stochastic differential equations, and that admit a parsimonious representation in a matched wavelet-like basis. Two key themes are the statistical property of infinite divisibility, which leads to two distinct types of behaviour - Gaussian and sparse - and the structural link between linear stochastic processes and spline functions, which is exploited to simplify the mathematical analysis. The core of the book is devoted to investigating sparse processes, including a complete description of their transform-domain statistics. The final part develops practical signal-processing algorithms that are based on these models, with special emphasis on biomedical image reconstruction. This is an ideal reference for graduate students and researchers with an interest in signal/image processing, compressed sensing, approximation theory, machine learning, or statistics."]]></description>
<dc:subject>to:NB books:noted sparsity stochastic_processes compressed_sensing splines statistics levy_processes</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ad6052f5838a/</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:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:stochastic_processes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:compressed_sensing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:splines"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:levy_processes"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1507.05185">
    <title>[1507.05185] Fast Sparse Least-Squares Regression with Non-Asymptotic Guarantees</title>
    <dc:date>2015-08-05T17:53:26+00:00</dc:date>
    <link>http://arxiv.org/abs/1507.05185</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we study a fast approximation method for {\it large-scale high-dimensional} sparse least-squares regression problem by exploiting the Johnson-Lindenstrauss (JL) transforms, which embed a set of high-dimensional vectors into a low-dimensional space. In particular, we propose to apply the JL transforms to the data matrix and the target vector and then to solve a sparse least-squares problem on the compressed data with a {\it slightly larger regularization parameter}. Theoretically, we establish the optimization error bound of the learned model for two different sparsity-inducing regularizers, i.e., the elastic net and the ℓ1 norm. Compared with previous relevant work, our analysis is {\it non-asymptotic and exhibits more insights} on the bound, the sample complexity and the regularization. As an illustration, we also provide an error bound of the {\it Dantzig selector} under JL transforms."]]></description>
<dc:subject>to:NB regression random_projections computational_statistics statistics sparsity</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c444206315c9/</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:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_projections"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1507.00280">
    <title>[1507.00280] Network Lasso: Clustering and Optimization in Large Graphs</title>
    <dc:date>2015-08-05T14:46:20+00:00</dc:date>
    <link>http://arxiv.org/abs/1507.00280</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and scalable solvers are often specialized to only work on a narrow class of problems. Therefore, there is a need for simple, scalable algorithms that can solve many common optimization problems. In this paper, we introduce the \emph{network lasso}, a generalization of the group lasso to a network setting that allows for simultaneous clustering and optimization on graphs. We develop an algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve this problem in a distributed and scalable manner, which allows for guaranteed global convergence even on large graphs. We also examine a non-convex extension of this approach. We then demonstrate that many types of problems can be expressed in our framework. We focus on three in particular - binary classification, predicting housing prices, and event detection in time series data - comparing the network lasso to baseline approaches and showing that it is both a fast and accurate method of solving large optimization problems."]]></description>
<dc:subject>to:NB optimization sparsity prediction regression networks</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8850e926060c/</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:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:prediction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:networks"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1506.03850">
    <title>[1506.03850] Generalized Additive Model Selection</title>
    <dc:date>2015-07-14T09:55:10+00:00</dc:date>
    <link>http://arxiv.org/abs/1506.03850</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We introduce GAMSEL (Generalized Additive Model Selection), a penalized likelihood approach for fitting sparse generalized additive models in high dimension. Our method interpolates between null, linear and additive models by allowing the effect of each variable to be estimated as being either zero, linear, or a low-complexity curve, as determined by the data. We present a blockwise coordinate descent procedure for efficiently optimizing the penalized likelihood objective over a dense grid of the tuning parameter, producing a regularization path of additive models. We demonstrate the performance of our method on both real and simulated data examples, and compare it with existing techniques for additive model selection."]]></description>
<dc:subject>to:NB statistics sparsity additive_models regression kith_and_kin chouldechova.alexandra hastie.trevor</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5d40f2b72122/</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:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:additive_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:chouldechova.alexandra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hastie.trevor"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.pnas.org/content/112/19/5950.abstract.html">
    <title>How a well-adapted immune system is organized</title>
    <dc:date>2015-05-18T01:18:42+00:00</dc:date>
    <link>http://www.pnas.org/content/112/19/5950.abstract.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The repertoire of lymphocyte receptors in the adaptive immune system protects organisms from diverse pathogens. A well-adapted repertoire should be tuned to the pathogenic environment to reduce the cost of infections. We develop a general framework for predicting the optimal repertoire that minimizes the cost of infections contracted from a given distribution of pathogens. The theory predicts that the immune system will have more receptors for rare antigens than expected from the frequency of encounters; individuals exposed to the same infections will have sparse repertoires that are largely different, but nevertheless exploit cross-reactivity to provide the same coverage of antigens; and the optimal repertoires can be reached via the dynamics of competitive binding of antigens by receptors and selective amplification of stimulated receptors. Our results follow from a tension between the statistics of pathogen detection, which favor a broader receptor distribution, and the effects of cross-reactivity, which tend to concentrate the optimal repertoire onto a few highly abundant clones. Our predictions can be tested in high-throughput surveys of receptor and pathogen diversity."]]></description>
<dc:subject>to:NB immunology distributed_systems adaptive_behavior sparsity</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1a79e6bd52cf/</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:immunology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:distributed_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:adaptive_behavior"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1405.5103">
    <title>[1405.5103] Estimation in high dimensions: a geometric perspective</title>
    <dc:date>2014-06-11T20:28:30+00:00</dc:date>
    <link>http://arxiv.org/abs/1405.5103</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This tutorial paper provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The paper develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation problems. The theory is illustrated with applications to sparse recovery, matrix completion, quantization, linear and logistic regression and generalized linear models."]]></description>
<dc:subject>to:NB statistics high-dimensional_statistics estimation sparsity convexity geometry compressed_sensing to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:ff1e079dc4ac/</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:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:convexity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:compressed_sensing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://jmlr.org/proceedings/papers/v33/aksoylar14.html">
    <title>Information-Theoretic Characterization of Sparse Recovery | AISTATS 2014 | JMLR W&amp;CP</title>
    <dc:date>2014-04-20T17:55:03+00:00</dc:date>
    <link>http://jmlr.org/proceedings/papers/v33/aksoylar14.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We formulate sparse support recovery as a salient set identification problem and use information-theoretic analyses to characterize the recovery performance and sample complexity. We consider a very general framework where we are not restricted to linear models or specific distributions. We state non-asymptotic bounds on recovery probability and a tight mutual information formula for sample complexity. We evaluate our bounds for applications such as sparse linear regression and explicitly characterize effects of correlation or noisy features on recovery performance. We show improvements upon previous work and identify gaps between the performance of recovery algorithms and fundamental information. This illustrates a trade-off between computational complexity and sample complexity, contrasting the recovery of the support as a discrete object with signal estimation approaches."]]></description>
<dc:subject>to:NB to_read information_theory statistics learning_theory sparsity compressed_sensing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2a48b09609b3/</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:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:compressed_sensing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://jmlr.org/proceedings/papers/v33/vats14a.html">
    <title>&lt;span&gt;Path Thresholding: Asymptotically Tuning-Free High-Dimensional Sparse Regression&lt;/span&gt; | AISTATS 2014 | JMLR W&amp;CP</title>
    <dc:date>2014-04-15T12:27:29+00:00</dc:date>
    <link>http://jmlr.org/proceedings/papers/v33/vats14a.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we address the challenging problem of selecting tuning parameters for high-dimensional sparse regression. We propose a simple and computationally efficient method, called path thresholding PaTh, that transforms any tuning parameter-dependent sparse regression algorithm into an asymptotically tuning-free sparse regression algorithm. More specifically, we prove that, as the problem size becomes large (in the number of variables and in the number of observations), PaTh performs accurate sparse regression, under appropriate conditions, without specifying a tuning parameter. In finite-dimensional settings, we demonstrate that PaTh can alleviate the computational burden of model selection algorithms by significantly reducing the search space of tuning parameters."]]></description>
<dc:subject>to:NB to_read regression sparsity high-dimensional_statistics statistics vats.divyanshu</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3b3fc0182134/</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:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<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:li rdf:resource="https://pinboard.in/u:cshalizi/t:vats.divyanshu"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6719502">
    <title>IEEE Xplore Abstract - Minimum Complexity Pursuit for Universal Compressed Sensing</title>
    <dc:date>2014-04-02T01:53:18+00:00</dc:date>
    <link>http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6719502</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The nascent field of compressed sensing is founded on the fact that high-dimensional signals with simple structure can be recovered accurately from just a small number of randomized samples. Several specific kinds of structures have been explored in the literature, from sparsity and group sparsity to low-rankness. However, two fundamental questions have been left unanswered. What are the general abstract meanings of structure and simplicity? Do there exist universal algorithms for recovering such simple structured objects from fewer samples than their ambient dimension? In this paper, we address these two questions. Using algorithmic information theory tools such as the Kolmogorov complexity, we provide a unified definition of structure and simplicity. Leveraging this new definition, we develop and analyze an abstract algorithm for signal recovery motivated by Occam's Razor. Minimum complexity pursuit (MCP) requires approximately 2κ randomized samples to recover a signal of complexity κ and ambient dimension n. We also discuss the performance of the MCP in the presence of measurement noise and with approximately simple signals."

Ungated version: http://arxiv.org/abs/1208.5814]]></description>
<dc:subject>compressed_sensing sparsity information_theory algorithmic_information_theory statistics in_NB color_me_skeptical</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:73d6beaa7dd5/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:compressed_sensing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:algorithmic_information_theory"/>
	<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:color_me_skeptical"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1403.7023">
    <title>[1403.7023] Worst possible sub-directions in high-dimensional models</title>
    <dc:date>2014-04-01T21:19:01+00:00</dc:date>
    <link>http://arxiv.org/abs/1403.7023</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We examine the rate of convergence of the Lasso estimator of lower dimensional components of the high-dimensional parameter. Under bounds on the ℓ1-norm on the worst possible sub-direction these rates are of order |J|logp/n‾‾‾‾‾‾‾‾‾√ where p is the total number of parameters, J⊂{1,…,p} represents a subset of the parameters and n is the number of observations. We also derive rates in sup-norm in terms of the rate of convergence in ℓ1-norm. The irrepresentable condition on a set J requires that the ℓ1-norm of the worst possible sub-direction is sufficiently smaller than one. In that case sharp oracle results can be obtained. Moreover, if the coefficients in J are small enough the Lasso will put these coefficients to zero. This extends known results which say that the irrepresentable condition on the inactive set (the set where coefficients are exactly zero) implies no false positives. We further show that by de-sparsifying one obtains fast rates in supremum norm without conditions on the worst possible sub-direction. The main assumption here is that approximate sparsity is of order o(n‾‾√/logp). The results are extended to M-estimation with ℓ1-penalty for generalized linear models and exponential families for example. For the graphical Lasso this leads to an extension of known results to the case where the precision matrix is only approximately sparse. The bounds we provide are non-asymptotic but we also present asymptotic formulations for ease of interpretation."]]></description>
<dc:subject>to:NB high-dimensional_statistics lasso sparsity variable_selection statistics van_de_geer.sara</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:d88ae59edb90/</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:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lasso"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variable_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:van_de_geer.sara"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://statweb.stanford.edu/~markad/publications/ddek-chapter1-2011.pdf">
    <title>Introduction to Compressed Sensing</title>
    <dc:date>2014-03-20T13:21:46+00:00</dc:date>
    <link>http://statweb.stanford.edu/~markad/publications/ddek-chapter1-2011.pdf</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In recent years, compressed sensing (CS) has attracted considerable attention in areas of applied mathematics, computer science, and electrical engineering by suggesting that it may be possible to surpass the traditional limits of sam- pling theory. CS builds upon the fundamental fact that we can represent many signals using only a few non-zero coefficients in a suitable basis or dictionary. Nonlinear optimization can then enable recovery of such signals from very few measurements. In this chapter, we provide an up-to-date review of the basic theory underlying CS. After a brief historical overview, we begin with a dis- cussion of sparsity and other low-dimensional signal models. We then treat the central question of how to accurately recover a high-dimensional signal from a small set of measurements and provide performance guarantees for a variety of sparse recovery algorithms. We conclude with a discussion of some extensions of the sparse recovery framework. In subsequent chapters of the book, we will see how the fundamentals presented in this chapter are extended in many excit- ing directions, including new models for describing structure in both analog and discrete-time signals, new sensing design techniques, more advanced recovery results, and emerging applications."]]></description>
<dc:subject>to:NB compressed_sensing sparsity estimation statistics linear_algebra re:network_differences entableted</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a18d78f2adc6/</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:compressed_sensing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:linear_algebra"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:network_differences"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entableted"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://jmlr.org/papers/v15/richard14a.html">
    <title>Link Prediction in Graphs with Autoregressive Features</title>
    <dc:date>2014-03-11T17:40:17+00:00</dc:date>
    <link>http://jmlr.org/papers/v15/richard14a.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In the paper, we consider the problem of link prediction in time-evolving graphs. We assume that certain graph features, such as the node degree, follow a vector autoregressive (VAR) model and we propose to use this information to improve the accuracy of prediction. Our strategy involves a joint optimization procedure over the space of adjacency matrices and VAR matrices. On the adjacency matrix it takes into account both sparsity and low rank properties and on the VAR it encodes the sparsity. The analysis involves oracle inequalities that illustrate the trade-offs in the choice of smoothing parameters when modeling the joint effect of sparsity and low rank. The estimate is computed efficiently using proximal methods, and evaluated through numerical experiments."]]></description>
<dc:subject>to:NB time_series network_data_analysis statistics sparsity low-rank_approximation</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9d4df08b858b/</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:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:low-rank_approximation"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1402.7349">
    <title>[1402.7349] Learning Graphical Models With Hubs</title>
    <dc:date>2014-03-08T22:04:25+00:00</dc:date>
    <link>http://arxiv.org/abs/1402.7349</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider the problem of learning a high-dimensional graphical model in which certain hub nodes are highly-connected to many other nodes. Many authors have studied the use of an l1 penalty in order to learn a sparse graph in high-dimensional setting. However, the l1 penalty implicitly assumes that each edge is equally likely and independent of all other edges. We propose a general framework to accommodate more realistic networks with hub nodes, using a convex formulation that involves a row-column overlap norm penalty. We apply this general framework to three widely-used probabilistic graphical models: the Gaussian graphical model, the covariance graph model, and the binary Ising model. An alternating direction method of multipliers algorithm is used to solve the corresponding convex optimization problems. On synthetic data, we demonstrate that our proposed framework outperforms competitors that do not explicitly model hub nodes. We illustrate our proposal on a webpage data set and a gene expression data set."]]></description>
<dc:subject>to:NB graphical_models statistics sparsity network_data_analysis re:6dfb</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:20460cffdec4/</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:graphical_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:6dfb"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.aos/1387313392">
    <title>Nickl , van de Geer : Confidence sets in sparse regression</title>
    <dc:date>2014-02-20T22:22:07+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.aos/1387313392</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The problem of constructing confidence sets in the high-dimensional linear model with n response variables and p parameters, possibly p≥n, is considered. Full honest adaptive inference is possible if the rate of sparse estimation does not exceed n−1/4, otherwise sparse adaptive confidence sets exist only over strict subsets of the parameter spaces for which sparse estimators exist. Necessary and sufficient conditions for the existence of confidence sets that adapt to a fixed sparsity level of the parameter vector are given in terms of minimal ℓ2-separation conditions on the parameter space. The design conditions cover common coherence assumptions used in models for sparsity, including (possibly correlated) sub-Gaussian designs."

--- Ungated version: http://arxiv.org/abs/1209.1508]]></description>
<dc:subject>high-dimensional_statistics sparsity confidence_sets regression statistics van_de_geer.sara nickl.richard lasso model_selection linear_regression in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:de2a3bc8882a/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:confidence_sets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:van_de_geer.sara"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nickl.richard"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lasso"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:model_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:linear_regression"/>
	<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/1205.0953">
    <title>[1205.0953] Non-negative least squares for high-dimensional linear models: consistency and sparse recovery without regularization</title>
    <dc:date>2014-02-13T18:23:16+00:00</dc:date>
    <link>http://arxiv.org/abs/1205.0953</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Least squares fitting is in general not useful for high-dimensional linear models, in which the number of predictors is of the same or even larger order of magnitude than the number of samples. Theory developed in recent years has coined a paradigm according to which sparsity-promoting regularization is regarded as a necessity in such setting. Deviating from this paradigm, we show that non-negativity constraints on the regression coefficients may be similarly effective as explicit regularization if the design matrix has additional properties, which are met in several applications of non-negative least squares (NNLS). We show that for these designs, the performance of NNLS with regard to prediction and estimation is comparable to that of the lasso. We argue further that in specific cases, NNLS may have a better ℓ∞-rate in estimation and hence also advantages with respect to support recovery when combined with thresholding. From a practical point of view, NNLS does not depend on a regularization parameter and is hence easier to use."]]></description>
<dc:subject>to:NB regression high-dimensional_statistics sparsity</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:2afa11779b41/</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:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://ganguli-gang.stanford.edu/pdf/12.CompSense.pdf">
    <title>Annu. Rev. Neurosci. 2012. 35:485–508 First published online as a Review in Advance on April 5, 2012 The Annual Review of Neuroscience is online at neuro.annualreviews.org This article’s doi: 10.1146/annurev-neuro-062111–150410 Copyright ⃝c 2012 b</title>
    <dc:date>2014-02-03T21:42:47+00:00</dc:date>
    <link>http://ganguli-gang.stanford.edu/pdf/12.CompSense.pdf</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The curse of dimensionality poses severe challenges to both techni- cal and conceptual progress in neuroscience. In particular, it plagues our ability to acquire, process, and model high-dimensional data sets. Moreover, neural systems must cope with the challenge of processing data in high dimensions to learn and operate successfully within a com- plex world. We review recent mathematical advances that provide ways to combat dimensionality in specific situations. These advances shed light on two dual questions in neuroscience. First, how can we as neu- roscientists rapidly acquire high-dimensional data from the brain and subsequently extract meaningful models from limited amounts of these data? And second, how do brains themselves process information in their intrinsically high-dimensional patterns of neural activity as well as learn meaningful, generalizable models of the external world from limited experience?"]]></description>
<dc:subject>to:NB high-dimensional_statistics neural_data_analysis neuroscience compressed_sensing sparsity</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0721ee839422/</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:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neuroscience"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:compressed_sensing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
</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://arxiv.org/abs/1312.1706">
    <title>[1312.1706] Swapping Variables for High-Dimensional Sparse Regression from Correlated Measurements</title>
    <dc:date>2014-01-02T18:27:15+00:00</dc:date>
    <link>http://arxiv.org/abs/1312.1706</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider the high-dimensional sparse linear regression problem of accurately estimating a sparse vector using a small number of linear measurements that are contaminated by noise. It is well known that standard computationally tractable sparse regression algorithms, such as the Lasso, OMP, and their various extensions, perform poorly when the measurement matrix contains highly correlated columns. We develop a simple greedy algorithm, called SWAP, that iteratively swaps variables until a desired loss function cannot be decreased any further. SWAP is surprisingly effective in handling measurement matrices with high correlations. In particular, we prove that (i) SWAP outputs the true support, the location of the non-zero entries in the sparse vector, when initialized with the true support, and (ii) SWAP outputs the true support under a relatively mild condition on the measurement matrix when initialized with a support other than the true support. These theoretical results motivate the use of SWAP as a wrapper around various sparse regression algorithms for improved performance. We empirically show the advantages of using SWAP in sparse regression problems by comparing SWAP to several state-of-the-art sparse regression algorithms."]]></description>
<dc:subject>to:NB high-dimensional_statistics lasso sparsity variable_selection statistics vats.divyanshu</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c1912ea2ab6c/</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:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lasso"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variable_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:vats.divyanshu"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1311.6238">
    <title>[1311.6238] Exact inference after model selection via the Lasso</title>
    <dc:date>2013-11-26T13:56:29+00:00</dc:date>
    <link>http://arxiv.org/abs/1311.6238</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We develop a framework for inference after model selection based on the Lasso. At the core of this framework is a result that characterizes the exact (non-asymptotic) distribution of a pivot computed from the Lasso solution. This pivot allows us to (i) devise a test statistic that has an exact (non-asymptotic) $\unif(0,1)$ distribution under the null hypothesis that all relevant variables have been included in the model, and (ii) construct valid confidence intervals for the selected coefficients that account for the selection procedure."]]></description>
<dc:subject>model_selection confidence_sets sparsity lasso hypothesis_testing regression statistics in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c32f98a9792e/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:model_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:confidence_sets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lasso"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hypothesis_testing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<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/1311.6425">
    <title>[1311.6425] Robust Multimodal Graph Matching: Sparse Coding Meets Graph Matching</title>
    <dc:date>2013-11-26T04:06:22+00:00</dc:date>
    <link>http://arxiv.org/abs/1311.6425</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in sparsity-related techniques. We cast the problem, resembling group or collaborative sparsity formulations, as a non-smooth convex optimization problem that can be efficiently solved using augmented Lagrangian techniques. The method can deal with weighted or unweighted graphs, as well as multimodal data, where different graphs represent different types of data. The proposed approach is also naturally integrated with collaborative graph inference techniques, solving general network inference problems where the observed variables, possibly coming from different modalities, are not in correspondence. The algorithm is tested and compared with state-of-the-art graph matching techniques in both synthetic and real graphs. We also present results on multimodal graphs and applications to collaborative inference of brain connectivity from alignment-free functional magnetic resonance imaging (fMRI) data. The code is publicly available."]]></description>
<dc:subject>to_read network_data_analysis optimization sparsity re:network_differences entableted in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:fa20cf1d019d/</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:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:network_differences"/>
	<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/1311.4175">
    <title>[1311.4175] Estimation in High-dimensional Vector Autoregressive Models</title>
    <dc:date>2013-11-21T17:41:27+00:00</dc:date>
    <link>http://arxiv.org/abs/1311.4175</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Vector Autoregression (VAR) is a widely used method for learning complex interrelationship among the components of multiple time series. Over the years it has gained popularity in the fields of control theory, statistics, economics, finance, genetics and neuroscience. We consider the problem of estimating stable VAR models in a high-dimensional setting, where both the number of time series and the VAR order are allowed to grow with sample size. In addition to the ``curse of dimensionality" introduced by a quadratically growing dimension of the parameter space, VAR estimation poses considerable challenges due to the temporal and cross-sectional dependence in the data. Under a sparsity assumption on the model transition matrices, we establish estimation and prediction consistency of ℓ1-penalized least squares and likelihood based methods. Exploiting spectral properties of stationary VAR processes, we develop novel theoretical techniques that provide deeper insight into the effect of dependence on the convergence rates of the estimates. We study the impact of error correlations on the estimation problem and develop fast, parallelizable algorithms for penalized likelihood based VAR estimates."]]></description>
<dc:subject>time_series sparsity statistics re:your_favorite_dsge_sucks in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:00527dc690c7/</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:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:your_favorite_dsge_sucks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.tandfonline.com/doi/abs/10.1080/01621459.2013.803972#.Ukmy-hbPUlM">
    <title>Taylor &amp; Francis Online :: Asymptotic Equivalence of Regularization Methods in Thresholded Parameter Space - Journal of the American Statistical Association - Volume 108, Issue 503</title>
    <dc:date>2013-09-30T17:45:15+00:00</dc:date>
    <link>http://www.tandfonline.com/doi/abs/10.1080/01621459.2013.803972#.Ukmy-hbPUlM</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["High-dimensional data analysis has motivated a spectrum of regularization methods for variable selection and sparse modeling, with two popular methods being convex and concave ones. A long debate has taken place on whether one class dominates the other, an important question both in theory and to practitioners. In this article, we characterize the asymptotic equivalence of regularization methods, with general penalty functions, in a thresholded parameter space under the generalized linear model setting, where the dimensionality can grow exponentially with the sample size. To assess their performance, we establish the oracle inequalities—as in Bickel, Ritov, and Tsybakov (2009)—of the global minimizer for these methods under various prediction and variable selection losses. These results reveal an interesting phase transition phenomenon. For polynomially growing dimensionality, the L 1-regularization method of Lasso and concave methods are asymptotically equivalent, having the same convergence rates in the oracle inequalities. For exponentially growing dimensionality, concave methods are asymptotically equivalent but have faster convergence rates than the Lasso. We also establish a stronger property of the oracle risk inequalities of the regularization methods, as well as the sampling properties of computable solutions. Our new theoretical results are illustrated and justified by simulation and real data examples."]]></description>
<dc:subject>to:NB lasso sparsity high-dimensional_statistics regression statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:11a674948a6d/</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:lasso"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
	<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://arxiv.org/abs/1309.6702">
    <title>[1309.6702] Statistical paleoclimate reconstructions via Markov random fields</title>
    <dc:date>2013-09-27T16:45:27+00:00</dc:date>
    <link>http://arxiv.org/abs/1309.6702</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Understanding centennial scale climate variability requires datasets that are accurate, long, continuous, and of broad spatial coverage. Since instrumental measurements are generally only available after 1850, temperature fields must be reconstructed using paleoclimate archives, known as proxies. Various climate field reconstructions (CFR) methods have been proposed to relate past temperature and multiproxy networks, most notably the regularized EM algorithm (RegEM). In this work, we propose a new CFR method, called GraphEM, based on Gaussian Markov random fields (GMRF) embedded within RegEM. GMRFs provide a natural and flexible framework for modeling the inherent spatial heterogeneities of high-dimensional spatial fields, which would in general be more difficult with standard parametric covariance models. At the same time, they provide the parameter reduction necessary for obtaining precise and well-conditioned estimates of the covariance structure of the field, even when the sample size is much smaller than the number of variables (as is typically the case in paleoclimate applications). We demonstrate how the graphical structure of the field can be estimated from the data via l1-penalization methods, and how the GraphEM algorithm can be used to reconstruct past climate variations. The performance of GraphEM is then compared to a popular CFR method (RegEM TTLS) using synthetic data. Our results show that GraphEM can yield significant improvements over existing methods, with gains uniformly over space, and far better risk properties. We proceed to demonstrate that the increase in performance is directly related to recovering the underlying sparsity in the covariance of the spatial field. In particular, we show that spatial points with fewer neighbors in the recovered graph tend to be the ones where there are higher improvements in the reconstructions."]]></description>
<dc:subject>to:NB climatology variance_estimation random_fields sparsity statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:77aa4d790174/</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:climatology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variance_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1308.2408">
    <title>[1308.2408] Group Lasso for generalized linear models in high dimension</title>
    <dc:date>2013-09-17T20:30:01+00:00</dc:date>
    <link>http://arxiv.org/abs/1308.2408</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good estimation of the regression parameter. This sparsity assumption as well as a block structuration of the covariates into groups with similar modes of behavior is for example quite natural in genomics. A huge amount of scientific literature exists for Gaussian linear models including the Lasso estimator and also the Group Lasso estimator which promotes group sparsity under an a priori knowledge of the groups. We extend this Group Lasso procedure to generalized linear models and we study the properties of this estimator for sparse high-dimensional generalized linear models to find convergence rates. We provide oracle inequalities for the prediction and estimation error under assumptions on the joint distribution of the pair observable covariables and under a condition on the design matrix. We show the ability of this estimator to recover good sparse approximation of the true model. At last we extend these results to the case of an Elastic net penalty and we apply them to the so-called Poisson regression case which has not been studied in this context contrary to the logistic regression."

--- Isn't this already done in Buhlmann and van de Geer's book?]]></description>
<dc:subject>to:NB linear_regression regression sparsity statistics high-dimensional_statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1d3e66a2dbc3/</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:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<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/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://jmlr.org/papers/v14/rosasco13a.html">
    <title>Nonparametric Sparsity and Regularization</title>
    <dc:date>2013-09-05T00:01:07+00:00</dc:date>
    <link>http://jmlr.org/papers/v14/rosasco13a.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric model, hence avoiding linear or additive models. The key idea is to measure the importance of each variable in the model by making use of partial derivatives. Based on this intuition we propose a new notion of nonparametric sparsity and a corresponding least squares regularization scheme. Using concepts and results from the theory of reproducing kernel Hilbert spaces and proximal methods, we show that the proposed learning algorithm corresponds to a minimization problem which can be provably solved by an iterative procedure. The consistency properties of the obtained estimator are studied both in terms of prediction and selection performance. An extensive empirical analysis shows that the proposed method performs favorably with respect to the state-of-the-art methods."]]></description>
<dc:subject>to:NB sparsity hilbert_space regression statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e7686e47d284/</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:hilbert_space"/>
	<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://normaldeviate.wordpress.com/2013/07/27/the-steep-price-of-sparsity/">
    <title>The Steep Price of Sparsity « Normal Deviate</title>
    <dc:date>2013-07-29T19:52:06+00:00</dc:date>
    <link>http://normaldeviate.wordpress.com/2013/07/27/the-steep-price-of-sparsity/</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>model_selection track_down_references statistics sparsity variable_selection</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1185172426ca/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:model_selection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:track_down_references"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sparsity"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:variable_selection"/>
</rdf:Bag></taxo:topics>
</item>
</rdf:RDF>