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  </channel><item rdf:about="https://arxiv.org/abs/2601.15500">
    <title>[2601.15500] Low-Dimensional Adaptation of Rectified Flow: A Diffusion and Stochastic Localization Perspective</title>
    <dc:date>2026-02-17T15:59:02+00:00</dc:date>
    <link>https://arxiv.org/abs/2601.15500</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In recent years, Rectified flow (RF) has gained considerable popularity largely due to its generation efficiency and state-of-the-art performance. In this paper, we investigate the degree to which RF automatically adapts to the intrinsic low dimensionality of the support of the target distribution to accelerate sampling. We show that, using a carefully designed choice of the time-discretization scheme and with sufficiently accurate drift estimates, the RF sampler enjoys an iteration complexity of order O(k/ε) (up to log factors), where ε is the precision in total variation distance and k is the intrinsic dimension of the target distribution. In addition, we show that the denoising diffusion probabilistic model (DDPM) procedure is equivalent to a stochastic version of RF by establishing a novel connection between these processes and stochastic localization. Building on this connection, we further design a stochastic RF sampler that also adapts to the low-dimensionality of the target distribution under milder requirements on the accuracy of the drift estimates, and also with a specific time schedule. We illustrate with simulations on the synthetic data and text-to-image data experiments the improved performance of the proposed samplers implementing the newly designed time-discretization schedules."]]></description>
<dc:subject>to:NB density_estimation computational_statistics rinaldo.alessandro monte_carlo</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3c3e3819ffd2/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:rinaldo.alessandro"/>
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<item rdf:about="https://openreview.net/forum?id=ib0aV2hphN">
    <title>High-Order Flow Matching: Unified Framework and Sharp Statistical Rates | OpenReview</title>
    <dc:date>2026-01-30T12:12:17+00:00</dc:date>
    <link>https://openreview.net/forum?id=ib0aV2hphN</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Flow matching is an emerging generative modeling framework that learns continuous-time dynamics to map noise into data. To enhance expressiveness and sampling efficiency, recent works have explored incorporating high-order trajectory information. Despite the empirical success, a holistic theoretical foundation is still lacking. We present a unified framework for standard and high-order flow matching that incorporates trajectory derivatives up to an arbitrary order $K$. Our key innovation is establishing the marginalization technique that converts the intractable $K$-order loss into a simple conditional regression with exact gradients and identifying the consistency constraint. We establish sharp statistical rates of the $K$-order flow matching implemented with transformer networks. With 
$n$ samples, flow matching estimates nonparametric distributions at a rate , matching minimax lower bounds up to logarithmic factors."]]></description>
<dc:subject>to:NB density_estimation neural_networks nonparametrics liu.han</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5033f0d08de2/</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:density_estimation"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:liu.han"/>
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<item rdf:about="https://arxiv.org/abs/2510.03994">
    <title>[2510.03994] Optimal estimation of a factorizable density using diffusion models with ReLU neural networks</title>
    <dc:date>2026-01-30T12:08:15+00:00</dc:date>
    <link>https://arxiv.org/abs/2510.03994</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper investigates the score-based diffusion models for density estimation when the target density admits a factorizable low-dimensional nonparametric structure. To be specific, we show that when the log density admits a d∗-way interaction model with β-smooth components, the vanilla diffusion model, which uses a fully connected ReLU neural network for score matching, can attain optimal n−β/(2β+d∗) statistical rate of convergence in total variation distance. This is, to the best of our knowledge, the first in the literature showing that diffusion models with standard configurations can adapt to the low-dimensional factorizable structures. The main challenge is that the low-dimensional factorizable structure no longer holds for most of the diffused timesteps, and it is very challenging to show that these diffused score functions can be well approximated without a significant increase in the number of network parameters. Our key insight is to demonstrate that the diffused score functions can be decomposed into a composition of either super-smooth or low-dimensional components, leading to a new approximation error analysis of ReLU neural networks with respect to the diffused score function. The rate of convergence under the 1-Wasserstein distance is also derived with a slight modification of the method."]]></description>
<dc:subject>to:NB factor_analysis density_estimation generative_diffusion_models fan.jianqing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:894249e6215f/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:fan.jianqing"/>
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<item rdf:about="https://arxiv.org/abs/1503.03585">
    <title>[1503.03585] Deep Unsupervised Learning using Nonequilibrium Thermodynamics</title>
    <dc:date>2025-04-10T18:40:59+00:00</dc:date>
    <link>https://arxiv.org/abs/1503.03585</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally tractable. Here, we develop an approach that simultaneously achieves both flexibility and tractability. The essential idea, inspired by non-equilibrium statistical physics, is to systematically and slowly destroy structure in a data distribution through an iterative forward diffusion process. We then learn a reverse diffusion process that restores structure in data, yielding a highly flexible and tractable generative model of the data. This approach allows us to rapidly learn, sample from, and evaluate probabilities in deep generative models with thousands of layers or time steps, as well as to compute conditional and posterior probabilities under the learned model. We additionally release an open source reference implementation of the algorithm."]]></description>
<dc:subject>density_estimation stochastic_processes generative_diffusion_models in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:053e927a1129/</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:stochastic_processes"/>
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<item rdf:about="https://projecteuclid.org/journals/annals-of-statistics/volume-38/issue-5/Kernel-density-estimation-via-diffusion/10.1214/10-AOS799.full">
    <title>Kernel density estimation via diffusion</title>
    <dc:date>2025-04-10T18:38:48+00:00</dc:date>
    <link>https://projecteuclid.org/journals/annals-of-statistics/volume-38/issue-5/Kernel-density-estimation-via-diffusion/10.1214/10-AOS799.full</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we propose a new plug-in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods. We present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability."

--- Ungated: https://arxiv.org/abs/1011.2602]]></description>
<dc:subject>density_estimation generative_diffusion_models in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:557950fb7241/</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:generative_diffusion_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
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</item>
<item rdf:about="https://arxiv.org/abs/2408.05807">
    <title>[2408.05807] Kernel Density Estimators in Large Dimensions</title>
    <dc:date>2025-04-10T18:37:32+00:00</dc:date>
    <link>https://arxiv.org/abs/2408.05807</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper studies Kernel Density Estimation for a high-dimensional distribution ρ(x). Traditional approaches have focused on the limit of large number of data points n and fixed dimension d. We analyze instead the regime where both the number n of data points yi and their dimensionality d grow with a fixed ratio α=(logn)/d. Our study reveals three distinct statistical regimes for the kernel-based estimate of the density ρ̂ h(x)=1nhd∑ni=1K(x−yih), depending on the bandwidth h: a classical regime for large bandwidth where the Central Limit Theorem (CLT) holds, which is akin to the one found in traditional approaches. Below a certain value of the bandwidth, hCLT(α), we find that the CLT breaks down. The statistics of ρ̂ h(x) for a fixed x drawn from ρ(x) is given by a heavy-tailed distribution (an alpha-stable distribution). In particular below a value hG(α), we find that ρ̂ h(x) is governed by extreme value statistics: only a few points in the database matter and give the dominant contribution to the density estimator. We provide a detailed analysis for high-dimensional multivariate Gaussian data. We show that the optimal bandwidth threshold based on Kullback-Leibler divergence lies in the new statistical regime identified in this paper. As known by practitioners, when decreasing the bandwidth a Kernel-estimated estimated changes from a smooth curve to a collections of peaks centred on the data points. Our findings reveal that this general phenomenon is related to sharp transitions between phases characterized by different statistical properties, and offer new insights for Kernel density estimation in high-dimensional settings."]]></description>
<dc:subject>density_estimation high-dimensional_statistics mezard.marc in_NB kernel_smoothing of_course_its_really_a_spin_glass have_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0591313c3f4a/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_smoothing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:of_course_its_really_a_spin_glass"/>
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</item>
<item rdf:about="https://link.springer.com/article/10.1007/s10472-024-09943-9">
    <title>Deep data density estimation through Donsker-Varadhan representation | Annals of Mathematics and Artificial Intelligence</title>
    <dc:date>2025-03-29T14:34:34+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10472-024-09943-9</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Estimating the data density is one of the challenging problem topics in the deep learning society. In this paper, we present a simple yet effective methodology for estimating the data density using the Donsker-Varadhan variational lower bound on the KL divergence and the modeling based on the deep neural network. We demonstrate that the optimal critic function associated with the Donsker-Varadhan representation on the KL divergence between the data and the uniform distribution can estimate the data density. Also, we present the deep neural network-based modeling and its stochastic learning procedure. The experimental results and possible applications of the proposed method demonstrate that it is competitive with the previous methods for data density estimation and has a lot of possibilities for various applications."

--- Not sure what to make of this, from the abstract and a quick scan.  Maybe worth going over in my copious spare time?]]></description>
<dc:subject>density_estimation information_theory optimization neural_networks in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f7f2b2cd009b/</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:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:optimization"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://openreview.net/forum?id=UvmDCdSPDOW">
    <title>Information-Theoretic Diffusion | OpenReview</title>
    <dc:date>2025-03-10T14:39:50+00:00</dc:date>
    <link>https://openreview.net/forum?id=UvmDCdSPDOW</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Denoising diffusion models have spurred significant gains in density modeling and image generation, precipitating an industrial revolution in text-guided AI art generation.  We introduce a new mathematical foundation for diffusion models inspired by classic results in information theory that connect Information with Minimum Mean Square Error regression, the so-called I-MMSE relations. We generalize the I-MMSE relations to \emph{exactly} relate the data distribution to an optimal denoising regression problem, leading to an elegant refinement of existing diffusion bounds.  This new insight leads to several improvements for probability distribution estimation, including a theoretical justification for diffusion model ensembling. Remarkably, our framework shows how continuous and discrete probabilities can be learned with the same regression objective, avoiding domain-specific generative models used in variational methods."]]></description>
<dc:subject>density_estimation information_theory neural_networks ver_steeg.greg tab_closure generative_diffusion_models in_NB have_read to_teach:statistics_and_generative_ai</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9889cc2216d2/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_networks"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:generative_diffusion_models"/>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
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</item>
<item rdf:about="https://projecteuclid.org/journals/annals-of-statistics/volume-51/issue-2/Minimax-rates-for-conditional-density-estimation-via-empirical-entropy/10.1214/23-AOS2270.short">
    <title>Minimax rates for conditional density estimation via empirical entropy</title>
    <dc:date>2024-03-05T14:57:19+00:00</dc:date>
    <link>https://projecteuclid.org/journals/annals-of-statistics/volume-51/issue-2/Minimax-rates-for-conditional-density-estimation-via-empirical-entropy/10.1214/23-AOS2270.short</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider the task of estimating a conditional density using i.i.d. samples from a joint distribution, which is a fundamental problem with applications in both classification and uncertainty quantification for regression. For joint density estimation, minimax rates have been characterized for general density classes in terms of uniform (metric) entropy, a well-studied notion of statistical capacity. When applying these results to conditional density estimation, the use of uniform entropy—which is infinite when the covariate space is unbounded and suffers from the curse of dimensionality—can lead to suboptimal rates. Consequently, minimax rates for conditional density estimation cannot be characterized using these classical results.
"We resolve this problem for well-specified models, obtaining matching (within logarithmic factors) upper and lower bounds on the minimax Kullback–Leibler risk in terms of the empirical Hellinger entropy for the conditional density class. The use of empirical entropy allows us to appeal to concentration arguments based on local Rademacher complexity, which—in contrast to uniform entropy—leads to matching rates for large, potentially nonparametric classes and captures the correct dependence on the complexity of the covariate space. Our results require only that the conditional densities are bounded above, and do not require that they are bounded below or otherwise satisfy any tail conditions."

--- Ungated: [https://arxiv.org/abs/2109.10461]]]></description>
<dc:subject>in_NB density_estimation learning_theory via:mraginsky</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:0416eeb58e24/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:mraginsky"/>
</rdf:Bag></taxo:topics>
</item>
<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"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2110.04227">
    <title>[2110.04227] Universal Joint Approximation of Manifolds and Densities by Simple Injective Flows</title>
    <dc:date>2022-10-07T19:51:20+00:00</dc:date>
    <link>https://arxiv.org/abs/2110.04227</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study approximation of probability measures supported on n-dimensional manifolds embedded in ℝm by injective flows -- neural networks composed of invertible flows and injective layers. We show that in general, injective flows between ℝn and ℝm universally approximate measures supported on images of extendable embeddings, which are a subset of standard embeddings: when the embedding dimension m is small, topological obstructions may preclude certain manifolds as admissible targets. When the embedding dimension is sufficiently large, m≥3n+1, we use an argument from algebraic topology known as the clean trick to prove that the topological obstructions vanish and injective flows universally approximate any differentiable embedding. Along the way we show that the studied injective flows admit efficient projections on the range, and that their optimality can be established "in reverse," resolving a conjecture made in Brehmer and Cranmer 2020."]]></description>
<dc:subject>to:NB neural_networks manifold_learning density_estimation re:codename:catherine_wheel via:mraginsky</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f108585bf0eb/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:manifold_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:codename:catherine_wheel"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:mraginsky"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.nber.org/papers/w5093">
    <title>Labor Market Institutions and the Distribution of Wages, 1973-1992: A Semiparametric Approach | NBER</title>
    <dc:date>2022-07-09T19:00:12+00:00</dc:date>
    <link>https://www.nber.org/papers/w5093</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper presents a semiparametric procedure to analyze the effects of institutional and labor market factors on recent changes in the U.S. distribution of wages. The effects of these factors are estimated by applying kernel density methods to appropriately 'reweighted' samples. The procedure provides a visually clear representation of where in the density of wages these various factors exert the greatest impact. Using data from the Current Population Survey, we find, as in previous research, that de-unionization and supply and demand shocks were important factors in explaining the rise in wage inequality from 1979 to 1988. We find also compelling visual and quantitative evidence that the decline in the real value of the minimum wage explains a substantial proportion of this increase in wage inequality, particularly for women. We conclude that labor market institutions are as important as supply and demand considerations in explaining changes in the U.S. distribution of wages from 1979 to 1988."]]></description>
<dc:subject>to:NB density_estimation inequality class_struggles_in_america via:donsker_class to_teach:statistics_of_inequality_and_discrimination</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:113ebd1f78bd/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:inequality"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:class_struggles_in_america"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:donsker_class"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:statistics_of_inequality_and_discrimination"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://onlinelibrary.wiley.com/doi/abs/10.3982/ECTA10582?casa_token=RYQGxAm5NPsAAAAA:Gjw9Whp2sT1TTcF-EurC9U-K98m8jQ6Z1Tl6-PTOVvOZYU9vgik8XniEBql7ru0bqZ7U8aepTqF3">
    <title>Inference on Counterfactual Distributions - Chernozhukov - 2013 - Econometrica - Wiley Online Library</title>
    <dc:date>2022-07-09T18:58:01+00:00</dc:date>
    <link>https://onlinelibrary.wiley.com/doi/abs/10.3982/ECTA10582?casa_token=RYQGxAm5NPsAAAAA:Gjw9Whp2sT1TTcF-EurC9U-K98m8jQ6Z1Tl6-PTOVvOZYU9vgik8XniEBql7ru0bqZ7U8aepTqF3</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Counterfactual distributions are important ingredients for policy analysis and decomposition analysis in empirical economics. In this article, we develop modeling and inference tools for counterfactual distributions based on regression methods. The counterfactual scenarios that we consider consist of ceteris paribus changes in either the distribution of covariates related to the outcome of interest or the conditional distribution of the outcome given covariates. For either of these scenarios, we derive joint functional central limit theorems and bootstrap validity results for regression-based estimators of the status quo and counterfactual outcome distributions. These results allow us to construct simultaneous confidence sets for function-valued effects of the counterfactual changes, including the effects on the entire distribution and quantile functions of the outcome as well as on related functionals. These confidence sets can be used to test functional hypotheses such as no-effect, positive effect, or stochastic dominance. Our theory applies to general counterfactual changes and covers the main regression methods including classical, quantile, duration, and distribution regressions. We illustrate the results with an empirical application to wage decompositions using data for the United States.
"As a part of developing the main results, we introduce distribution regression as a comprehensive and flexible tool for modeling and estimating the entire conditional distribution. We show that distribution regression encompasses the Cox duration regression and represents a useful alternative to quantile regression. We establish functional central limit theorems and bootstrap validity results for the empirical distribution regression process and various related functionals."]]></description>
<dc:subject>to:NB density_estimation regression causal_inference inequality via:donsker_class to_teach:statistics_of_inequality_and_discrimination</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4147b5ca4a38/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causal_inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:inequality"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:donsker_class"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:statistics_of_inequality_and_discrimination"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1811.11603">
    <title>[1811.11603] Distribution Regression with Sample Selection, with an Application to Wage Decompositions in the UK</title>
    <dc:date>2022-07-09T18:57:08+00:00</dc:date>
    <link>https://arxiv.org/abs/1811.11603</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We develop a distribution regression model under endogenous sample selection. This model is a semiparametric generalization of the Heckman selection model that accommodates much richer patterns of heterogeneity in the selection process and effect of the covariates. The model applies to continuous, discrete and mixed outcomes. We study the identification of the model, and develop a computationally attractive two-step method to estimate the model parameters, where the first step is a probit regression for the selection equation and the second step consists of multiple distribution regressions with selection corrections for the outcome equation. We construct estimators of functionals of interest such as actual and counterfactual distributions of latent and observed outcomes via plug-in rule. We derive functional central limit theorems for all the estimators and show the validity of multiplier bootstrap to carry out functional inference. We apply the methods to wage decompositions in the UK using new data. Here we decompose the difference between the male and female wage distributions into four effects: composition, wage structure, selection structure and selection sorting. After controlling for endogenous employment selection, we still find substantial gender wage gap -- ranging from 21% to 40% throughout the (latent) offered wage distribution that is not explained by observable labor market characteristics. We also uncover positive sorting for single men and negative sorting for married women that accounts for a substantive fraction of the gender wage gap at the top of the distribution. These findings can be interpreted as evidence of assortative matching in the marriage market and glass-ceiling in the labor market."

--- Last tag is "I should know this stuff", not "I should teach it to sophomores and juniors".]]></description>
<dc:subject>to:NB statistics density_estimation regression causal_inference inequality via:donsker_class to_teach:statistics_of_inequality_and_discrimination</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:a84c4133e283/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:causal_inference"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:inequality"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:donsker_class"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:statistics_of_inequality_and_discrimination"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://proceedings.mlr.press/v54/mcdonald17a.html">
    <title>Minimax Density Estimation for Growing Dimension</title>
    <dc:date>2021-11-09T03:13:44+00:00</dc:date>
    <link>http://proceedings.mlr.press/v54/mcdonald17a.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper presents minimax rates for density estimation when the data dimension 𝑑d is allowed to grow with the number of observations 𝑛n rather than remaining fixed as in previous analyses. We prove a non-asymptotic lower bound which gives the worst-case rate over standard classes of smooth densities, and we show that kernel density estimators achieve this rate. We also give oracle choices for the bandwidth and derive the fastest rate 𝑑d can grow with 𝑛n to maintain estimation consistency."

--- Have I really never bookmarked this before?
]]></description>
<dc:subject>statistics density_estimation high-dimensional_statistics mcdonald.daniel_j. kith_and_kin re:codename:catherine_wheel in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b8a2c6690f89/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:mcdonald.daniel_j."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:codename:catherine_wheel"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2107.04118">
    <title>[2107.04118] OCDE: Odds Conditional Density Estimator</title>
    <dc:date>2021-07-12T15:19:29+00:00</dc:date>
    <link>https://arxiv.org/abs/2107.04118</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Conditional density estimation (CDE) models can be useful for many statistical applications, especially because the full conditional density is estimated instead of traditional regression point estimates, revealing more information about the uncertainty of the random variable of interest. In this paper, we propose a new methodology called Odds Conditional Density Estimator (OCDE) to estimate conditional densities in a supervised learning scheme. The main idea is that it is very difficult to estimate px,y and px in order to estimate the conditional density py|x, but by introducing an instrumental distribution, we transform the CDE problem into a problem of odds estimation, or similarly, training a binary probabilistic classifier. We demonstrate how OCDE works using simulated data and then test its performance against other known state-of-the-art CDE methods in real data. Overall, OCDE is competitive compared with these methods in real datasets."]]></description>
<dc:subject>to:NB density_estimation statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:6910b7ae2a5b/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2007.06408">
    <title>[2007.06408] Strong Uniform Consistency with Rates for Kernel Density Estimators with General Kernels on Manifolds</title>
    <dc:date>2021-06-10T02:23:17+00:00</dc:date>
    <link>https://arxiv.org/abs/2007.06408</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["When analyzing modern machine learning algorithms, we may need to handle kernel density estimation (KDE) with intricate kernels that are not designed by the user and might even be irregular and asymmetric. To handle this emerging challenge, we provide a strong uniform consistency result with the L∞ convergence rate for KDE on Riemannian manifolds with Riemann integrable kernels (in the ambient Euclidean space). We also provide an L1 consistency result for kernel density estimation on Riemannian manifolds with Lebesgue integrable kernels. The isotropic kernels considered in this paper are different from the kernels in the Vapnik-Chervonenkis class that are frequently considered in statistics society. We illustrate the difference when we apply them to estimate the probability density function. Moreover, we elaborate the delicate difference when the kernel is designed on the intrinsic manifold and on the ambient Euclidian space, both might be encountered in practice. At last, we prove the necessary and sufficient condition for an isotropic kernel to be Riemann integrable on a submanifold in the Euclidean space."]]></description>
<dc:subject>to:NB density_estimation statistics_on_manifolds statistics kernel_smoothing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3b782998da81/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics_on_manifolds"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_smoothing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2105.13010">
    <title>[2105.13010] An error analysis of generative adversarial networks for learning distributions</title>
    <dc:date>2021-06-07T03:58:50+00:00</dc:date>
    <link>https://arxiv.org/abs/2105.13010</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results estimate the convergence rates of GANs under a collection of integral probability metrics defined through Hölder classes, including the Wasserstein distance as a special case. We also show that GANs are able to adaptively learn data distributions with low-dimensional structure or have Hölder densities, when the network architectures are chosen properly. In particular, for distributions concentrate around a low-dimensional set, it is proved that the learning rates of GANs do not depend on the high ambient dimension, but on the lower intrinsic dimension. Our analysis is based on a new oracle inequality decomposing the estimation error into generator and discriminator approximation error and statistical error, which may be of independent interest."]]></description>
<dc:subject>to:NB density_estimation your_favorite_deep_neural_network_sucks statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1e57947289bd/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:your_favorite_deep_neural_network_sucks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2005.14458">
    <title>[2005.14458] Distributional Random Forests: Heterogeneity Adjustment and Multivariate Distributional Regression</title>
    <dc:date>2021-06-01T17:33:18+00:00</dc:date>
    <link>https://arxiv.org/abs/2005.14458</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Random Forests (Breiman, 2001) is a successful and widely used regression and classification algorithm. Part of its appeal and reason for its versatility is its (implicit) construction of a kernel-type weighting function on training data, which can also be used for targets other than the original mean estimation. We propose a novel forest construction for multivariate responses based on their joint conditional distribution, independent of the estimation target and the data model. It uses a new splitting criterion based on the MMD distributional metric, which is suitable for detecting heterogeneity in multivariate distributions. The induced weights define an estimate of the full conditional distribution, which in turn can be used for arbitrary and potentially complicated targets of interest. The method is very versatile and convenient to use, as we illustrate on a wide range of examples. The code is available as Python and R packages drf."]]></description>
<dc:subject>to:NB density_estimation random_fields buhlmann.peter ensemble_methods statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:35774f99f672/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_fields"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:buhlmann.peter"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ensemble_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2101.11083">
    <title>[2101.11083] Tree boosting for learning probability measures</title>
    <dc:date>2021-05-30T21:09:35+00:00</dc:date>
    <link>https://arxiv.org/abs/2101.11083</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Learning probability measures based on an i.i.d. sample is a fundamental inference task, but is challenging when the sample space is high-dimensional. Inspired by the success of tree boosting in high-dimensional classification and regression, we propose a tree boosting method for learning high-dimensional probability distributions. We formulate concepts of "addition" and "residuals" on probability distributions in terms of compositions of a new, more general notion of multivariate cumulative distribution functions (CDFs) than classical CDFs. This then gives rise to a simple boosting algorithm based on forward-stagewise (FS) fitting of an additive ensemble of measures, which sequentially minimizes the entropy loss. The output of the FS algorithm allows analytic computation of the probability density function for the fitted distribution. It also provides an exact simulator for drawing independent Monte Carlo samples from the fitted measure. Typical considerations in applying boosting--namely choosing the number of trees, setting the appropriate level of shrinkage/regularization in the weak learner, and the evaluation of variable importance--can all be accomplished in an analogous fashion to traditional boosting in supervised learning. Numerical experiments confirm that boosting can substantially improve the fit to multivariate distributions compared to the state-of-the-art single-tree learner and is computationally efficient. We illustrate through an application to a data set from mass cytometry how the simulator can be used to investigate various aspects of the underlying distribution."]]></description>
<dc:subject>to:NB ensemble_methods density_estimation statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1d7502cf7e69/</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:ensemble_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2009.00503">
    <title>[2009.00503] Informative Goodness-of-Fit for Multivariate Distributions</title>
    <dc:date>2021-04-16T19:35:35+00:00</dc:date>
    <link>https://arxiv.org/abs/2009.00503</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This article introduces an informative goodness-of-fit (iGOF) approach to study multivariate distributions. When the null model is rejected, iGOF allows us to identify the underlying sources of mismodeling and naturally equips practitioners with additional insights on the nature of the deviations from the true distribution. The informative character of the procedure is achieved by exploiting smooth tests and random fields theory to facilitate the analysis of multivariate data. Simulation studies show that iGOF enjoys high power for different types of alternatives. The methods presented here directly address the problem of background mismodeling arising in physics and astronomy. It is in these areas that the motivation of this work is rooted."

--- From the abstract it sounds like this is using the fact that a Neyman smooth test involves characterizing the departure from the null, which is a basic observation about them but no doubt under-exploited.  (Cf. appendix on such tests in ADAfaEPoV.)]]></description>
<dc:subject>to:NB goodness-of-fit hypothesis_testing density_estimation neyman_smooth_tests model_checking re:ADAfaEPoV to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7de4c3ae2a11/</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:goodness-of-fit"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hypothesis_testing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neyman_smooth_tests"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:model_checking"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:ADAfaEPoV"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2102.00199">
    <title>[2102.00199] Rates of convergence for density estimation with GANs</title>
    <dc:date>2021-03-15T06:16:36+00:00</dc:date>
    <link>https://arxiv.org/abs/2102.00199</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We undertake a precise study of the non-asymptotic properties of vanilla generative adversarial networks (GANs) and derive theoretical guarantees in the problem of estimating an unknown d-dimensional density p∗ under a proper choice of the class of generators and discriminators. We prove that the resulting density estimate converges to p∗ in terms of Jensen-Shannon (JS) divergence at the rate (logn/n)2β/(2β+d) where n is the sample size and β determines the smoothness of p∗. This is the first result in the literature on density estimation using vanilla GANs with JS rates faster than n−1/2 in the regime β>d/2."]]></description>
<dc:subject>to:NB density_estimation neural_networks</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:f052477a36d3/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_networks"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/2012.14482">
    <title>[2012.14482] Multivariate Smoothing via the Fourier Integral Theorem and Fourier Kernel</title>
    <dc:date>2021-01-03T20:13:12+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.14482</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Starting with the Fourier integral theorem, we present natural Monte Carlo estimators of multivariate functions including densities, mixing densities, transition densities, regression functions, and the search for modes of multivariate density functions (modal regression). Rates of convergence are established and, in many cases, provide superior rates to current standard estimators such as those based on kernels, including kernel density estimators and kernel regression functions. Numerical illustrations are presented."]]></description>
<dc:subject>to:NB fourier_analysis smoothing computational_statistics density_estimation nonparametrics regression statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7b370340cb7a/</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:fourier_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:smoothing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<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="https://arxiv.org/abs/2012.02385">
    <title>[2012.02385] Approximations of conditional probability density functions in Lebesgue spaces via mixture of experts models</title>
    <dc:date>2020-12-07T14:49:20+00:00</dc:date>
    <link>https://arxiv.org/abs/2012.02385</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Mixture of experts (MoE) models are widely applied for conditional probability density estimation problems. We demonstrate the richness of the class of MoE models by proving denseness results in Lebesgue spaces, when inputs and outputs variables are both compactly supported. We further prove an almost uniform convergence result when the input is univariate. Auxiliary lemmas are proved regarding the richness of the soft-max gating function class, and their relationships to the class of Gaussian gating functions."

--- Last tag is because isn't this basically the old Gershenfeld et al. cluster-weighted modeling idea [https://doi.org/10.1038/16873]?  Not that they proved anything remotely like this of course.]]></description>
<dc:subject>to:NB mixture_models density_estimation statistics conditional_density_estimation cluster-weighted_modeling</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3e191cdc089c/</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:mixture_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:conditional_density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:cluster-weighted_modeling"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://doi.org/10.1111/sjos.12495">
    <title>Parametric versus nonparametric: The fitness coefficient - Mazo - - Scandinavian Journal of Statistics - Wiley Online Library</title>
    <dc:date>2020-11-15T20:54:34+00:00</dc:date>
    <link>https://doi.org/10.1111/sjos.12495</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Olkin and Spiegelman introduced a semiparametric estimator of the density defined as a mixture between the maximum likelihood estimator and the kernel density estimator. Due to the absence of any leave‐one‐out strategy and the hardness of estimating the Kullback–Leibler loss of kernel density estimate, their approach produces unsatisfactory results. This article investigates an alternative approach in which only the kernel density estimate is modified. From a theoretical perspective, the estimated mixture parameter is shown to converge in probability to one if the parametric model is true and to zero otherwise. From a practical perspective, the utility of the approach is illustrated on real and simulated data sets."]]></description>
<dc:subject>to:NB density_estimation misspecification statistics re:ADAfaEPoV</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:302f5f93d218/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:misspecification"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:ADAfaEPoV"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1905.11255">
    <title>[1905.11255] Kernel Conditional Density Operators</title>
    <dc:date>2019-10-30T13:42:33+00:00</dc:date>
    <link>https://arxiv.org/abs/1905.11255</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We introduce a novel conditional density estimation model termed the conditional density operator (CDO). It naturally captures multivariate, multimodal output densities and shows performance that is competitive with recent neural conditional density models and Gaussian processes. The proposed model is based on a novel approach to the reconstruction of probability densities from their kernel mean embeddings by drawing connections to estimation of Radon-Nikodym derivatives in the reproducing kernel Hilbert space (RKHS). We prove finite sample bounds for the estimation error in a standard density reconstruction scenario, independent of problem dimensionality. Interestingly, when a kernel is used that is also a probability density, the CDO allows us to both evaluate and sample the output density efficiently. We demonstrate the versatility and performance of the proposed model on both synthetic and real-world data."]]></description>
<dc:subject>to:NB kernel_estimators hilbert_space density_estimation statistics to_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1e1457dd1023/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_estimators"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hilbert_space"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1906.01235">
    <title>[1906.01235] Universal Boosting Variational Inference</title>
    <dc:date>2019-10-29T02:18:39+00:00</dc:date>
    <link>https://arxiv.org/abs/1906.01235</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Boosting variational inference (BVI) approximates an intractable probability density by iteratively building up a mixture of simple component distributions one at a time, using techniques from sparse convex optimization to provide both computational scalability and approximation error guarantees. But the guarantees have strong conditions that do not often hold in practice, resulting in degenerate component optimization problems; and we show that the ad-hoc regularization used to prevent degeneracy in practice can cause BVI to fail in unintuitive ways. We thus develop universal boosting variational inference (UBVI), a BVI scheme that exploits the simple geometry of probability densities under the Hellinger metric to prevent the degeneracy of other gradient-based BVI methods, avoid difficult joint optimizations of both component and weight, and simplify fully-corrective weight optimizations. We show that for any target density and any mixture component family, the output of UBVI converges to the best possible approximation in the mixture family, even when the mixture family is misspecified. We develop a scalable implementation based on exponential family mixture components and standard stochastic optimization techniques. Finally, we discuss statistical benefits of the Hellinger distance as a variational objective through bounds on posterior probability, moment, and importance sampling errors. Experiments on multiple datasets and models show that UBVI provides reliable, accurate posterior approximations."]]></description>
<dc:subject>to:NB density_estimation probability ensemble_methods computational_statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:68d19002e973/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:ensemble_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1910.08477">
    <title>[1910.08477] Density estimation on an unknown submanifold</title>
    <dc:date>2019-10-21T15:51:21+00:00</dc:date>
    <link>https://arxiv.org/abs/1910.08477</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We investigate density estimation from a n-sample in the Euclidean space ℝD, when the data is supported by an unknown submanifold M of possibly unknown dimension d<D under a reach condition. We study nonparametric kernel methods for pointwise and integrated loss, with data-driven bandwidths that incorporate some learning of the geometry via a local dimension estimator. When f has Hölder smoothness β and M has regularity α in a sense to be defined, our estimator achieves the rate n−α∧β/(2α∧β+d) and does not depend on the ambient dimension D and is asymptotically minimax for α≥β. Following Lepski's principle, a bandwidth selection rule is shown to achieve smoothness adaptation. We also investigate the case α≤β: by estimating in some sense the underlying geometry of M, we establish in dimension d=1 that the minimax rate is n−β/(2β+1) proving in particular that it does not depend on the regularity of M. Finally, a numerical implementation is conducted on some case studies in order to confirm the practical feasibility of our estimators."]]></description>
<dc:subject>to:NB density_estimation statistics_on_manifolds statistics nonparametrics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5cf29a2b288f/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics_on_manifolds"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/rssb.12338?af=R">
    <title>Fused density estimation: theory and methods - Bassett - - Journal of the Royal Statistical Society: Series B (Statistical Methodology) - Wiley Online Library</title>
    <dc:date>2019-09-25T03:29:39+00:00</dc:date>
    <link>https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/rssb.12338?af=R</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We introduce a method for non‐parametric density estimation on geometric networks. We define fused density estimators as solutions to a total variation regularized maximum likelihood density estimation problem. We provide theoretical support for fused density estimation by proving that the squared Hellinger rate of convergence for the estimator achieves the minimax bound over univariate densities of log‐bounded variation. We reduce the original variational formulation to transform it into a tractable, finite dimensional quadratic program. Because random variables on geometric networks are simple generalizations of the univariate case, this method also provides a useful tool for univariate density estimation. Lastly, we apply this method and assess its performance on examples in the univariate and geometric network setting. We compare the performance of various optimization techniques to solve the problem and use these results to inform recommendations for the computation of fused density estimators."]]></description>
<dc:subject>to:NB density_estimation statistics sharpnack.james</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9baed568cb4d/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sharpnack.james"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1902.02408">
    <title>[1902.02408] Weak consistency of the 1-nearest neighbor measure with applications to missing data</title>
    <dc:date>2019-09-15T14:34:32+00:00</dc:date>
    <link>https://arxiv.org/abs/1902.02408</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["When data is partially missing at random, imputation and importance weighting are often used to estimate moments of the unobserved population. In this paper, we study 1-nearest neighbor (1NN) importance weighting, which estimates moments by replacing missing data with the complete data that is the nearest neighbor in the non-missing covariate space. We define an empirical measure, the 1NN measure, and show that it is weakly consistent for the measure of the missing data. The main idea behind this result is that the 1NN measure is performing inverse probability weighting in the limit. We study applications to missing data and mitigating the impact of covariate shift in prediction tasks."]]></description>
<dc:subject>to:NB missing_data density_estimation statistics sharpnack.james re:ADAfaEPoV</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1e183076dff4/</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:missing_data"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sharpnack.james"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:ADAfaEPoV"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1909.03681">
    <title>[1909.03681] Outlier Detection in High Dimensional Data</title>
    <dc:date>2019-09-15T14:24:42+00:00</dc:date>
    <link>https://arxiv.org/abs/1909.03681</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["High-dimensional data poses unique challenges in outlier detection process. Most of the existing algorithms fail to properly address the issues stemming from a large number of features. In particular, outlier detection algorithms perform poorly on data set of small size with a large number of features. In this paper, we propose a novel outlier detection algorithm based on principal component analysis and kernel density estimation. The proposed method is designed to address the challenges of dealing with high-dimensional data by projecting the original data onto a smaller space and using the innate structure of the data to calculate anomaly scores for each data point. Numerical experiments on synthetic and real-life data show that our method performs well on high-dimensional data. In particular, the proposed method outperforms the benchmark methods as measured by the F1-score. Our method also produces better-than-average execution times compared to the benchmark methods."

--- Seems OK but ad hoc.  Might make a decent extension to the eigendresses assignment for data mining.]]></description>
<dc:subject>to:NB anomaly_detection density_estimation principal_components high-dimensional_statistics statistics to_teach:data-mining</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c4ca0118845f/</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:anomaly_detection"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:principal_components"/>
	<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:to_teach:data-mining"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1909.02662">
    <title>[1909.02662] Block bootstrap optimality for density estimation with dependent data</title>
    <dc:date>2019-09-09T03:48:14+00:00</dc:date>
    <link>https://arxiv.org/abs/1909.02662</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Accurate approximation of the sampling distribution of nonparametric kernel density estimators is crucial for many statistical inference problems. Since these estimators have complex asymptotic distributions, bootstrap methods are often used for this purpose. With i.i.d. observations, a large literature exists concerning optimal bootstrap methods which achieve the fastest possible convergence rate of the bootstrap estimator of the sampling distribution of the kernel density estimator. With dependent data, such an optimality theory is an important open problem. We establish a general theory of optimality of the block bootstrap for kernel density estimation under weak dependence assumptions which are satisfied by many important time series models. We propose a unified framework for a theoretical study of a rich class of bootstrap methods which include as special cases subsampling, Kunsch's moving block bootstrap, Hall's under-smoothing (UNS) as well as approaches incorporating no (NBC) or explicit bias correction (EBC). Moreover, we consider their accuracy under a broad spectrum of choices of the bandwidth h, which include as an important special case the MSE-optimal choice, as well as other under-smoothed choices. Under each choice of h, we derive the optimal tuning parameters and compare optimal performances between the main subclasses (EBC, NBC, UNS) of the bootstrap methods."]]></description>
<dc:subject>to:NB bootstrap time_series density_estimation statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:3a0b7b2a417e/</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:bootstrap"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:time_series"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.ejs/1565748200">
    <title>Devroye , Reddad : Discrete minimax estimation with trees</title>
    <dc:date>2019-08-21T13:25:41+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.ejs/1565748200</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We propose a simple recursive data-based partitioning scheme which produces piecewise-constant or piecewise-linear density estimates on intervals, and show how this scheme can determine the optimal L1L1 minimax rate for some discrete nonparametric classes."]]></description>
<dc:subject>to:NB density_estimation devroye.luc minimax nonparametrics statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c8785a772707/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:devroye.luc"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:minimax"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1708.05254">
    <title>[1708.05254] Adaptive Clustering Using Kernel Density Estimators</title>
    <dc:date>2019-08-20T15:34:14+00:00</dc:date>
    <link>https://arxiv.org/abs/1708.05254</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it receives level set estimates from a kernel density estimator. In particular, we derive finite sample guarantees, consistency, rates of convergence, and an adaptive data-driven strategy for choosing the kernel bandwidth. For these results we do not need continuity assumptions on the density such as Hölder continuity, but only require intuitive geometric assumptions of non-parametric nature."]]></description>
<dc:subject>to:NB density_estimation clustering statistics kernel_smoothing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:360ad9210178/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:clustering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_smoothing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1908.06081">
    <title>[1908.06081] Analyzing the Fine Structure of Distributions</title>
    <dc:date>2019-08-20T15:29:50+00:00</dc:date>
    <link>https://arxiv.org/abs/1908.06081</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["One aim of data mining is the identification of interesting structures in data. Basic properties of the empirical distribution, such as skewness and an eventual clipping, i.e., hard limits in value ranges, need to be assessed. Of particular interest is the question, whether the data originates from one process, or contains subsets related to different states of the data producing process. Data visualization tools should deliver a sensitive picture of the univariate probability density distribution (PDF) for each feature. Visualization tools for PDFs are typically kernel density estimates and range from the classical histogram to modern tools like bean or violin plots. Conventional methods have difficulties in visualizing the pdf in case of uniform, multimodal, skewed and clipped data if density estimation parameters remain in a default setting. As a consequence, a new visualization tool called Mirrored Density plot (MD plot) is proposed which is particularly designed to discover interesting structures in continuous features. The MD plot does not require any adjustments of parameters of density estimation which makes the usage compelling for non-experts. The visualization tools are evaluated in comparison to statistical tests for the typical challenges of explorative distribution analysis. The results are presented on bimodal Gaussian and skewed distributions as well as several features with published pdfs. In exploratory data analysis of 12 features describing the quarterly financial statements, when statistical testing becomes a demanding task, only the MD plots can identify the structure of their pdfs. Overall, the MD plot can outperform the methods mentioned above."]]></description>
<dc:subject>to:NB visual_display_of_quantitative_information density_estimation statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8c6b9fda1aed/</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:visual_display_of_quantitative_information"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1907.13630">
    <title>[1907.13630] Kernel Density Estimation for Undirected Dyadic Data</title>
    <dc:date>2019-08-02T15:20:07+00:00</dc:date>
    <link>https://arxiv.org/abs/1907.13630</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We study nonparametric estimation of density functions for undirected dyadic random variables (i.e., random variables defined for all n\overset{def}{\equiv}\tbinom{N}{2} unordered pairs of agents/nodes in a weighted network of order N). These random variables satisfy a local dependence property: any random variables in the network that share one or two indices may be dependent, while those sharing no indices in common are independent. In this setting, we show that density functions may be estimated by an application of the kernel estimation method of Rosenblatt (1956) and Parzen (1962). We suggest an estimate of their asymptotic variances inspired by a combination of (i) Newey's (1994) method of variance estimation for kernel estimators in the "monadic" setting and (ii) a variance estimator for the (estimated) density of a simple network first suggested by Holland and Leinhardt (1976). More unusual are the rates of convergence and asymptotic (normal) distributions of our dyadic density estimates. Specifically, we show that they converge at the same rate as the (unconditional) dyadic sample mean: the square root of the number, N, of nodes. This differs from the results for nonparametric estimation of densities and regression functions for monadic data, which generally have a slower rate of convergence than their corresponding sample mean."]]></description>
<dc:subject>to:NB density_estimation network_data_analysis nonparametrics kernel_methods re:smoothing_adjacency_matrices</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:9f0623d7f460/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:network_data_analysis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:smoothing_adjacency_matrices"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.tandfonline.com/doi/full/10.1080/01621459.2019.1635481">
    <title>Nonparametric Estimation of Multivariate Mixtures: Journal of the American Statistical Association: Vol 0, No 0</title>
    <dc:date>2019-07-24T13:58:40+00:00</dc:date>
    <link>https://www.tandfonline.com/doi/full/10.1080/01621459.2019.1635481</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["A multivariate mixture model is determined by three elements: the number of components, the mixing proportions, and the component distributions. Assuming that the number of components is given and that each mixture component has independent marginal distributions, we propose a nonparametric method to estimate the component distributions. The basic idea is to convert the estimation of component density functions to a problem of estimating the coordinates of the component density functions with respect to a good set of basis functions. Specifically, we construct a set of basis functions by using conditional density functions and try to recover the coordinates of component density functions with respect to this set of basis functions. Furthermore, we show that our estimator for the component density functions is consistent. Numerical studies are used to compare our algorithm with other existing nonparametric methods of estimating component distributions under the assumption of conditionally independent marginals."]]></description>
<dc:subject>to:NB mixture_models density_estimation statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4b7ea0082b97/</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:mixture_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.ejs/1561687408">
    <title>Cheng , Chen : Nonparametric inference via bootstrapping the debiased estimator</title>
    <dc:date>2019-07-04T09:44:55+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.ejs/1561687408</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we propose to construct confidence bands by bootstrapping the debiased kernel density estimator (for density estimation) and the debiased local polynomial regression estimator (for regression analysis). The idea of using a debiased estimator was recently employed by Calonico et al. (2018b) to construct a confidence interval of the density function (and regression function) at a given point by explicitly estimating stochastic variations. We extend their ideas of using the debiased estimator and further propose a bootstrap approach for constructing simultaneous confidence bands. This modified method has an advantage that we can easily choose the smoothing bandwidth from conventional bandwidth selectors and the confidence band will be asymptotically valid. We prove the validity of the bootstrap confidence band and generalize it to density level sets and inverse regression problems. Simulation studies confirm the validity of the proposed confidence bands/sets. We apply our approach to an Astronomy dataset to show its applicability."]]></description>
<dc:subject>to:NB to_read statistics bootstrap confidence_sets regression density_estimation re:ADAfaEPoV</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:25365e040388/</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:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bootstrap"/>
	<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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:ADAfaEPoV"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1906.07177">
    <title>[1906.07177] (f)RFCDE: Random Forests for Conditional Density Estimation and Functional Data</title>
    <dc:date>2019-06-19T15:33:10+00:00</dc:date>
    <link>https://arxiv.org/abs/1906.07177</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Random forests is a common non-parametric regression technique which performs well for mixed-type unordered data and irrelevant features, while being robust to monotonic variable transformations. Standard random forests, however, do not efficiently handle functional data and runs into a curse-of dimensionality when presented with high-resolution curves and surfaces. Furthermore, in settings with heteroskedasticity or multimodality, a regression point estimate with standard errors do not fully capture the uncertainty in our predictions. A more informative quantity is the conditional density p(y | x) which describes the full extent of the uncertainty in the response y given covariates x. In this paper we show how random forests can be efficiently leveraged for conditional density estimation, functional covariates, and multiple responses without increasing computational complexity. We provide open-source software for all procedures with R and Python versions that call a common C++ library."]]></description>
<dc:subject>to:NB ensemble_methods regression density_estimation statistics kith_and_kin decision_trees lee.ann_b. random_forests</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:7a354f01b8c9/</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:ensemble_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:decision_trees"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lee.ann_b."/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:random_forests"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://arxiv.org/abs/1903.00954">
    <title>[1903.00954] Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks</title>
    <dc:date>2019-04-11T00:41:49+00:00</dc:date>
    <link>https://arxiv.org/abs/1903.00954</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Given a set of empirical observations, conditional density estimation aims to capture the statistical relationship between a conditional variable x and a dependent variable y by modeling their conditional probability p(y|x). The paper develops best practices for conditional density estimation for finance applications with neural networks, grounded on mathematical insights and empirical evaluations. In particular, we introduce a noise regularization and data normalization scheme, alleviating problems with over-fitting, initialization and hyper-parameter sensitivity of such estimators. We compare our proposed methodology with popular semi- and non-parametric density estimators, underpin its effectiveness in various benchmarks on simulated and Euro Stoxx 50 data and show its superior performance. Our methodology allows to obtain high-quality estimators for statistical expectations of higher moments, quantiles and non-linear return transformations, with very little assumptions about the return dynamic."]]></description>
<dc:subject>to:NB neural_networks density_estimation statistics nonparametrics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:60fc041c5678/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:neural_networks"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://onlinelibrary.wiley.com/doi/book/10.1002/9781118575574">
    <title>Multivariate Density Estimation | Wiley Series in Probability and Statistics</title>
    <dc:date>2019-01-07T17:29:39+00:00</dc:date>
    <link>https://onlinelibrary.wiley.com/doi/book/10.1002/9781118575574</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Featuring a thoroughly revised presentation, Multivariate Density Estimation: Theory, Practice, and Visualization, Second Edition maintains an intuitive approach to the underlying methodology and supporting theory of density estimation. Including new material and updated research in each chapter, the Second Edition presents additional clarification of theoretical opportunities, new algorithms, and up-to-date coverage of the unique challenges presented in the field of data analysis.
"The new edition focuses on the various density estimation techniques and methods that can be used in the field of big data. Defining optimal nonparametric estimators, the Second Edition demonstrates the density estimation tools to use when dealing with various multivariate structures in univariate, bivariate, trivariate, and quadrivariate data analysis. Continuing to illustrate the major concepts in the context of the classical histogram, Multivariate Density Estimation: Theory, Practice, and Visualization, Second Edition also features:
Over 150 updated figures to clarify theoretical results and to show analyses of real data sets
An updated presentation of graphic visualization using computer software such as R
A clear discussion of selections of important research during the past decade, including mixture estimation, robust parametric modeling algorithms, and clustering
More than 130 problems to help readers reinforce the main concepts and ideas presented
Boxed theorems and results allowing easy identification of crucial ideas
Figures in color in the digital versions of the book
A website with related data sets
"Multivariate Density Estimation: Theory, Practice, and Visualization, Second Edition is an ideal reference for theoretical and applied statisticians, practicing engineers, as well as readers interested in the theoretical aspects of nonparametric estimation and the application of these methods to multivariate data. The Second Edition is also useful as a textbook for introductory courses in kernel statistics, smoothing, advanced computational statistics, and general forms of statistical distributions."]]></description>
<dc:subject>to:NB books:noted downloaded smoothing density_estimation statistics nonparametrics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:273d88198929/</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:downloaded"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:smoothing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.aoms/1177704472">
    <title>Parzen : On Estimation of a Probability Density Function and Mode</title>
    <dc:date>2018-09-08T18:47:34+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.aoms/1177704472</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA[In which Parzen introduces kernel density estimation, three years after Rosenblatt introduced it _in the same journal_.]]></description>
<dc:subject>to:NB statistics density_estimation have_read parzen.emanuel re:ADAfaEPoV</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:c53e99585c16/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:parzen.emanuel"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:ADAfaEPoV"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://projecteuclid.org/euclid.aoms/1177728190#abstract">
    <title>Rosenblatt : Remarks on Some Nonparametric Estimates of a Density Function (1956)</title>
    <dc:date>2018-09-08T18:44:03+00:00</dc:date>
    <link>https://projecteuclid.org/euclid.aoms/1177728190#abstract</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This note discusses some aspects of the estimation of the density function of a univariate probability distribution. All estimates of the density function satisfying relatively mild conditions are shown to be biased. The asymptotic mean square error of a particular class of estimates is evaluated."

--- In which Rosenblatt introduces kernel density estimation.]]></description>
<dc:subject>statistics density_estimation have_read rosenblatt.murray re:ADAfaEPoV in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:564688c73e60/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:rosenblatt.murray"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:ADAfaEPoV"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.jmlr.org/papers/v18/16-011.html">
    <title>Density Estimation in Infinite Dimensional Exponential Families</title>
    <dc:date>2018-07-23T16:10:55+00:00</dc:date>
    <link>http://www.jmlr.org/papers/v18/16-011.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we consider an infinite dimensional exponential family P of probability densities, which are parametrized by functions in a reproducing kernel Hilbert space H, and show it to be quite rich in the sense that a broad class of densities on ℝdRd can be approximated arbitrarily well in Kullback-Leibler (KL) divergence by elements in P. Motivated by this approximation property, the paper addresses the question of estimating an unknown density p0p0 through an element in P. Standard techniques like maximum likelihood estimation (MLE) or pseudo MLE (based on the method of sieves), which are based on minimizing the KL divergence between p0p0 and P, do not yield practically useful estimators because of their inability to efficiently handle the log-partition function. We propose an estimator p̂ np^n based on minimizing the Fisher divergence, J(p0‖p)J(p0‖p) between p0p0 and p∈p∈P, which involves solving a simple finite-dimensional linear system. When p0∈p0∈P, we show that the proposed estimator is consistent, and provide a convergence rate of n−min{23,2β+12β+2}n−min{23,2β+12β+2} in Fisher divergence under the smoothness assumption that logp0∈(Cβ)log⁡p0∈R(Cβ) for some β≥0β≥0, where CC is a certain Hilbert-Schmidt operator on H and (Cβ)R(Cβ) denotes the image of CβCβ. We also investigate the misspecified case of p0∉p0∉P and show that J(p0‖p̂ n)→infp∈J(p0‖p)J(p0‖p^n)→infp∈PJ(p0‖p) as n→∞n→∞, and provide a rate for this convergence under a similar smoothness condition as above. Through numerical simulations we demonstrate that the proposed estimator outperforms the non- parametric kernel density estimator, and that the advantage of the proposed estimator grows as dd increases."]]></description>
<dc:subject>density_estimation exponential_families statistics via:? in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:96131f032145/</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:exponential_families"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:via:?"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/article/10.1007/s10472-015-9465-7">
    <title>Boosting conditional probability estimators | SpringerLink</title>
    <dc:date>2018-05-23T13:08:22+00:00</dc:date>
    <link>https://link.springer.com/article/10.1007/s10472-015-9465-7</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In the standard agnostic multiclass model, <instance, label > pairs are sampled independently from some underlying distribution. This distribution induces a conditional probability over the labels given an instance, and our goal in this paper is to learn this conditional distribution. Since even unconditional densities are quite challenging to learn, we give our learner access to <instance, conditional distribution > pairs. Assuming a base learner oracle in this model, we might seek a boosting algorithm for constructing a strong learner. Unfortunately, without further assumptions, this is provably impossible. However, we give a new boosting algorithm that succeeds in the following sense: given a base learner guaranteed to achieve some average accuracy (i.e., risk), we efficiently construct a learner that achieves the same level of accuracy with arbitrarily high probability. We give generalization guarantees of several different kinds, including distribution-free accuracy and risk bounds. None of our estimates depend on the number of boosting rounds and some of them admit dimension-free formulations."]]></description>
<dc:subject>to:NB boosting density_estimation kith_and_kin kontorovich.aryeh statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:38c8f51c7430/</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:boosting"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kontorovich.aryeh"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://www.mitpressjournals.org/doi/abs/10.1162/neco_a_01035">
    <title>Sufficient Dimension Reduction via Direct Estimation of the Gradients of Logarithmic Conditional Densities | Neural Computation | MIT Press Journals</title>
    <dc:date>2018-01-24T23:29:28+00:00</dc:date>
    <link>https://www.mitpressjournals.org/doi/abs/10.1162/neco_a_01035</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Sufficient dimension reduction (SDR) is aimed at obtaining the low-rank projection matrix in the input space such that information about output data is maximally preserved. Among various approaches to SDR, a promising method is based on the eigendecomposition of the outer product of the gradient of the conditional density of output given input. In this letter, we propose a novel estimator of the gradient of the logarithmic conditional density that directly fits a linear-in-parameter model to the true gradient under the squared loss. Thanks to this simple least-squares formulation, its solution can be computed efficiently in a closed form. Then we develop a new SDR method based on the proposed gradient estimator. We theoretically prove that the proposed gradient estimator, as well as the SDR solution obtained from it, achieves the optimal parametric convergence rate. Finally, we experimentally demonstrate that our SDR method compares favorably with existing approaches in both accuracy and computational efficiency on a variety of artificial and benchmark data sets."]]></description>
<dc:subject>to:NB dimension_reduction sufficiency density_estimation linear_regression statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:15bf571a5ee2/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:sufficiency"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:linear_regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://papers.nips.cc/paper/7215-robust-conditional-probabilities">
    <title>Robust Conditional Probabilities</title>
    <dc:date>2017-11-24T18:33:30+00:00</dc:date>
    <link>http://papers.nips.cc/paper/7215-robust-conditional-probabilities</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Conditional probabilities are a core concept in machine learning. For example, optimal prediction of a label Y given an input X corresponds to maximizing the conditional probability of Y given X. A common approach to inference tasks is learning a model of conditional probabilities. However, these models are often based on strong assumptions (e.g., log-linear models), and hence their estimate of conditional probabilities is not robust and is highly dependent on the validity of their assumptions. Here we propose a framework for reasoning about conditional probabilities without assuming anything about the underlying distributions, except knowledge of their second order marginals, which can be estimated from data. We show how this setting leads to guaranteed bounds on conditional probabilities, which can be calculated efficiently in a variety of settings, including structured-prediction. Finally, we apply them to semi-supervised deep learning, obtaining results competitive with variational autoencoders."]]></description>
<dc:subject>to:NB statistics density_estimation probability</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b6545c819d4c/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:probability"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://papers.nips.cc/paper/7243-the-power-of-absolute-discounting-all-dimensional-distribution-estimation">
    <title>The power of absolute discounting: all-dimensional distribution estimation</title>
    <dc:date>2017-11-24T18:32:40+00:00</dc:date>
    <link>http://papers.nips.cc/paper/7243-the-power-of-absolute-discounting-all-dimensional-distribution-estimation</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Categorical models are the natural fit for many problems. When learning the distribution of categories from samples, high-dimensionality may dilute the data. Minimax optimality is too pessimistic to remedy this issue. A serendipitously discovered estimator, absolute discounting, corrects empirical frequencies by subtracting a constant from observed categories, which it then redistributes among the unobserved. It outperforms classical estimators empirically, and has been used extensively in natural language modeling. In this paper, we rigorously explain the prowess of this estimator using less pessimistic notions. We show (1) that absolute discounting recovers classical minimax KL-risk rates, (2) that it is \emph{adaptive} to an effective dimension rather than the true dimension, (3) that it is strongly related to the Good-Turing estimator and inherits its \emph{competitive} properties. We use power-law distributions as the corner stone of these results. We validate the theory via synthetic data and an application to the Global Terrorism Database."]]></description>
<dc:subject>to:NB to_read density_estimation statistics heavy_tails</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5b8bf70af9f2/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:heavy_tails"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="https://link.springer.com/book/10.1007%2F978-3-319-25388-6">
    <title>Lectures on the Nearest Neighbor Method | SpringerLink</title>
    <dc:date>2017-08-25T23:52:03+00:00</dc:date>
    <link>https://link.springer.com/book/10.1007%2F978-3-319-25388-6</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This text presents a wide-ranging and rigorous overview of nearest neighbor methods, one of the most important paradigms in machine learning. Now in one self-contained volume, this book systematically covers key statistical, probabilistic, combinatorial and geometric ideas for understanding, analyzing and developing nearest neighbor methods."]]></description>
<dc:subject>books:noted nearest-neighbors density_estimation regression classifiers statistics devroye.luc biau.gerard nonparametrics re:ADAfaEPoV entropy_estimation in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b3e8daedeae4/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:books:noted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nearest-neighbors"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:classifiers"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:devroye.luc"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:biau.gerard"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:ADAfaEPoV"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entropy_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00906">
    <title>Online Reinforcement Learning Using a Probability Density Estimation | Neural Computation | MIT Press Journals</title>
    <dc:date>2017-01-17T13:23:30+00:00</dc:date>
    <link>http://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00906</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Function approximation in online, incremental, reinforcement learning needs to deal with two fundamental problems: biased sampling and nonstationarity. In this kind of task, biased sampling occurs because samples are obtained from specific trajectories dictated by the dynamics of the environment and are usually concentrated in particular convergence regions, which in the long term tend to dominate the approximation in the less sampled regions. The nonstationarity comes from the recursive nature of the estimations typical of temporal difference methods. This nonstationarity has a local profile, varying not only along the learning process but also along different regions of the state space. We propose to deal with these problems using an estimation of the probability density of samples represented with a gaussian mixture model. To deal with the nonstationarity problem, we use the common approach of introducing a forgetting factor in the updating formula. However, instead of using the same forgetting factor for the whole domain, we make it dependent on the local density of samples, which we use to estimate the nonstationarity of the function at any given input point. To address the biased sampling problem, the forgetting factor applied to each mixture component is modulated according to the new information provided in the updating, rather than forgetting depending only on time, thus avoiding undesired distortions of the approximation in less sampled regions."]]></description>
<dc:subject>to:NB online_learning density_estimation statistics reinforcement_learning</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e05b3a828630/</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:online_learning"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:reinforcement_learning"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1602.00531">
    <title>[1602.00531] Adaptive non-parametric estimation in the presence of dependence</title>
    <dc:date>2016-02-08T21:30:35+00:00</dc:date>
    <link>http://arxiv.org/abs/1602.00531</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension reduction. The minimax optimal rate of convergence of the estimator is derived assuming a sufficiently weak dependence characterized by fast decreasing mixing coefficients. We illustrate these results by considering classical smoothness assumptions. However, the proposed estimator requires an optimal choice of a dimension parameter depending on certain characteristics of the function of interest, which are not known in practice. The main issue addressed in our work is an adaptive choice of this dimension parameter combining model selection and Lepski's method. It is inspired by the recent work of Goldenshluger and Lepski (2011). We show that this data-driven estimator can attain the lower risk bound up to a constant provided a fast decay of the mixing coefficients."]]></description>
<dc:subject>to:NB statistics regression nonparametrics learning_under_dependence density_estimation dimension_reduction</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b9b529946e46/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:learning_under_dependence"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1506.04513">
    <title>[1506.04513] Convex Risk Minimization and Conditional Probability Estimation</title>
    <dc:date>2015-07-14T09:40:20+00:00</dc:date>
    <link>http://arxiv.org/abs/1506.04513</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general enough to include cases in which no minimum exists, as occurs typically, for instance, with standard boosting algorithms. Concretely, we first show that any sequence of predictors minimizing convex risk over the source distribution will converge to this unique model when the class of predictors is linear (but potentially of infinite dimension). Secondly, we show the same result holds for \emph{empirical} risk minimization whenever this class of predictors is finite dimensional, where the essential technical contribution is a norm-free generalization bound."]]></description>
<dc:subject>to:NB learning_theory statistics density_estimation re:AoS_project to_teach:childs_garden_of_statistical_learning_theory</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:6897d617cff8/</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:learning_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:AoS_project"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:childs_garden_of_statistical_learning_theory"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.aos/1410440625">
    <title>Chernozhukov , Chetverikov , Kato : Anti-concentration and honest, adaptive confidence bands</title>
    <dc:date>2015-02-13T18:31:05+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.aos/1410440625</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Modern construction of uniform confidence bands for nonparametric densities (and other functions) often relies on the classical Smirnov–Bickel–Rosenblatt (SBR) condition; see, for example, Giné and Nickl [Probab. Theory Related Fields 143 (2009) 569–596]. This condition requires the existence of a limit distribution of an extreme value type for the supremum of a studentized empirical process (equivalently, for the supremum of a Gaussian process with the same covariance function as that of the studentized empirical process). The principal contribution of this paper is to remove the need for this classical condition. We show that a considerably weaker sufficient condition is derived from an anti-concentration property of the supremum of the approximating Gaussian process, and we derive an inequality leading to such a property for separable Gaussian processes. We refer to the new condition as a generalized SBR condition. Our new result shows that the supremum does not concentrate too fast around any value.
"We then apply this result to derive a Gaussian multiplier bootstrap procedure for constructing honest confidence bands for nonparametric density estimators (this result can be applied in other nonparametric problems as well). An essential advantage of our approach is that it applies generically even in those cases where the limit distribution of the supremum of the studentized empirical process does not exist (or is unknown). This is of particular importance in problems where resolution levels or other tuning parameters have been chosen in a data-driven fashion, which is needed for adaptive constructions of the confidence bands. Finally, of independent interest is our introduction of a new, practical version of Lepski’s method, which computes the optimal, nonconservative resolution levels via a Gaussian multiplier bootstrap method."

--- Ungated version: http://arxiv.org/abs/1303.7152]]></description>
<dc:subject>confidence_sets bootstrap density_estimation nonparametrics statistics regression to_read re:ADAfaEPoV in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:033f56a445d2/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:confidence_sets"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:bootstrap"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<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:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:re:ADAfaEPoV"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.aos/1176346710">
    <title>Silverman : Spline Smoothing: The Equivalent Variable Kernel Method</title>
    <dc:date>2015-02-13T17:31:01+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.aos/1176346710</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The spline smoothing approach to nonparametric regression and curve estimation is considered. It is shown that, in a certain sense, spline smoothing corresponds approximately to smoothing by a kernel method with bandwidth depending on the local density of design points. Some exact calculations demonstrate that the approximation is extremely close in practice. Consideration of kernel smoothing methods demonstrates that the way in which the effective local bandwidth behaves in spline smoothing has desirable properties. Finally, the main result of the paper is applied to the related topic of penalized maximum likelihood probability density estimates; a heuristic discussion shows that these estimates should adapt well in the tails of the distribution."]]></description>
<dc:subject>have_read splines nonparametrics regression density_estimation statistics in_NB silverman.bernard kernel_smoothing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:b14f5c1bbcbe/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:splines"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:regression"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:silverman.bernard"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_smoothing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/euclid.bj/1411134448">
    <title>Crisan , Míguez : Particle-kernel estimation of the filter density in state-space models</title>
    <dc:date>2015-01-24T14:11:26+00:00</dc:date>
    <link>http://projecteuclid.org/euclid.bj/1411134448</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Sequential Monte Carlo (SMC) methods, also known as particle filters, are simulation-based recursive algorithms for the approximation of the a posteriori probability measures generated by state-space dynamical models. At any given time t, a SMC method produces a set of samples over the state space of the system of interest (often termed “particles”) that is used to build a discrete and random approximation of the posterior probability distribution of the state variables, conditional on a sequence of available observations. One potential application of the methodology is the estimation of the densities associated to the sequence of a posteriori distributions. While practitioners have rather freely applied such density approximations in the past, the issue has received less attention from a theoretical perspective. In this paper, we address the problem of constructing kernel-based estimates of the posterior probability density function and its derivatives, and obtain asymptotic convergence results for the estimation errors. In particular, we find convergence rates for the approximation errors that hold uniformly on the state space and guarantee that the error vanishes almost surely as the number of particles in the filter grows. Based on this uniform convergence result, we first show how to build continuous measures that converge almost surely (with known rate) toward the posterior measure and then address a few applications. The latter include maximum a posteriori estimation of the system state using the approximate derivatives of the posterior density and the approximation of functionals of it, for example, Shannon’s entropy."]]></description>
<dc:subject>particle_filters density_estimation filtering state_estimation state-space_models statistics computational_statistics in_NB kernel_smoothing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:77a953685926/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:state-space_models"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_smoothing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1412.1716">
    <title>[1412.1716] Nonparametric Modal Regression</title>
    <dc:date>2015-01-19T23:59:14+00:00</dc:date>
    <link>http://arxiv.org/abs/1412.1716</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Modal regression estimates the local modes of the distribution of Y given X = x, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods. We study a simple nonparametric method for modal regression, based on a kernel density estimate (KDE) of the joint distribution of Y and X. We derive asymptotic error bounds for this method, and propose techniques for constructing confidence sets and prediction sets. The latter is used to select the smoothing bandwidth of the underlying KDE. The idea behind modal regression is connected to many others, such as mixture regression and density ridge estimation, and we discuss these ties as well."]]></description>
<dc:subject>to:NB regression density_estimation nonparametrics statistics kith_and_kin genovese.chris wasserman.larry tibshirani.ryan</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:8f1f692d6d42/</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:density_estimation"/>
	<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:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:genovese.chris"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:wasserman.larry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:tibshirani.ryan"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1411.4040">
    <title>[1411.4040] Kernel Density Estimation on Symmetric Spaces</title>
    <dc:date>2014-11-25T18:14:28+00:00</dc:date>
    <link>http://arxiv.org/abs/1411.4040</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We investigate a natural variant of kernel density estimation on a large class of symmetric spaces and prove a minimax rate of convergence as fast as the minimax rate on Euclidean space. We make neither compactness assumptions on the space nor Holder-class assumptions on the densities. A main tool used in proving the convergence rate is the Helgason-Fourier transform, a generalization of the Fourier transform for semisimple Lie groups modulo maximal compact subgroups. This paper obtains a simplified formula in the special case when the symmetric space is the 2-dimensional hyperboloid."]]></description>
<dc:subject>density_estimation statistics nonparametrics kith_and_kin asta.dena statistics_on_manifolds in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:1fc8ccff90b9/</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:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:asta.dena"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics_on_manifolds"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1307.7760">
    <title>[1307.7760] Geometric Inference on Kernel Density Estimates</title>
    <dc:date>2014-10-16T15:14:17+00:00</dc:date>
    <link>http://arxiv.org/abs/1307.7760</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate. This intermediate step results in the inference being statically robust to noise and allows for large computational gains and scalability (e.g. on 100 million points). In particular, by first creating a coreset for the kernel density estimate, the data representing the final geometric and topological structure has size depending only on the error tolerance, not on the size of the original point set or the complexity of the structure. To achieve this result, we study how to replace distance to a measure, as studied by Chazal, Cohen-Steiner, and Merigot, with the kernel distance. The kernel distance is monotonic with the kernel density estimate (sublevel sets of the kernel distance are superlevel sets of the kernel density estimate), thus allowing us to examine the kernel density estimate in this manner. We show it has several computational and stability advantages. Moreover, we provide an algorithm to estimate its topology using weighted Vietoris-Rips complexes."]]></description>
<dc:subject>to:NB geometry density_estimation statistics computational_statistics have_read kernel_smoothing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:e25e972c1a2d/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to:NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:geometry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_smoothing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://dl.acm.org/citation.cfm?id=2465319">
    <title>Quality and efficiency for kernel density estimates in large data</title>
    <dc:date>2014-10-16T15:10:26+00:00</dc:date>
    <link>http://dl.acm.org/citation.cfm?id=2465319</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Kernel density estimates are important for a broad variety of applications. Their construction has been well-studied, but existing techniques are expensive on massive datasets and/or only provide heuristic approximations without theoretical guarantees. We propose randomized and deterministic algorithms with quality guarantees which are orders of magnitude more efficient than previous algorithms. Our algorithms do not require knowledge of the kernel or its bandwidth parameter and are easily parallelizable. We demonstrate how to implement our ideas in a centralized setting and in MapReduce, although our algorithms are applicable to any large-scale data processing framework. Extensive experiments on large real datasets demonstrate the quality, efficiency, and scalability of our techniques."

--- Ungated version: http://www.cs.utah.edu/~lifeifei/papers/kernelsigmod13.pdf]]></description>
<dc:subject>computational_statistics statistics density_estimation to_teach:statcomp to_teach:undergrad-ADA have_read kernel_smoothing in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:72a4e0a4dfd5/</dc:identifier>
<taxo:topics><rdf:Bag>	<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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:statcomp"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_teach:undergrad-ADA"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_smoothing"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/0907.0199">
    <title>[0907.0199] High-Dimensional Density Estimation via SCA: An Example in the Modelling of Hurricane Tracks</title>
    <dc:date>2014-04-22T15:55:22+00:00</dc:date>
    <link>http://arxiv.org/abs/0907.0199</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We present nonparametric techniques for constructing and verifying density estimates from high-dimensional data whose irregular dependence structure cannot be modelled by parametric multivariate distributions. A low-dimensional representation of the data is critical in such situations because of the curse of dimensionality. Our proposed methodology consists of three main parts: (1) data reparameterization via dimensionality reduction, wherein the data are mapped into a space where standard techniques can be used for density estimation and simulation; (2) inverse mapping, in which simulated points are mapped back to the high-dimensional input space; and (3) verification, in which the quality of the estimate is assessed by comparing simulated samples with the observed data. These approaches are illustrated via an exploration of the spatial variability of tropical cyclones in the North Atlantic; each datum in this case is an entire hurricane trajectory. We conclude the paper with a discussion of extending the methods to model the relationship between TC variability and climatic variables."]]></description>
<dc:subject>to_read heard_the_talk kith_and_kin dimension_reduction buchman.susan high-dimensional_statistics density_estimation meteorology hurricanes diffusion_maps entableted in_NB lee.ann_b.</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:feaeb1982195/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:to_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:heard_the_talk"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:dimension_reduction"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:buchman.susan"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:meteorology"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hurricanes"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:diffusion_maps"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entableted"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lee.ann_b."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://jmlr.org/proceedings/papers/v33/izbicki14.html">
    <title>High-Dimensional Density Ratio Estimation with Extensions to Approximate Likelihood Computation | AISTATS 2014 | JMLR W&amp;CP</title>
    <dc:date>2014-04-20T17:52:35+00:00</dc:date>
    <link>http://jmlr.org/proceedings/papers/v33/izbicki14.html</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification. Recently, several estimators of this ratio have been proposed. Most of these methods fail if the sample space is high-dimensional, and hence require a dimension reduction step, the result of which can be a significant loss of information. Here we propose a simple-to-implement, fully nonparametric density ratio estimator that expands the ratio in terms of the eigenfunctions of a kernel-based operator; these functions reflect the underlying geometry of the data (e.g., submanifold structure), often leading to better estimates without an explicit dimension reduction step. We show how our general framework can be extended to address another important problem, the estimation of a likelihood function in situations where that function cannot be well-approximated by an analytical form. One is often faced with this situation when performing statistical inference with data from the sciences, due the complexity of the data and of the processes that generated those data. We emphasize applications where using existing likelihood-free methods of inference would be challenging due to the high dimensionality of the sample space, but where our spectral series method yields a reasonable estimate of the likelihood function. We provide theoretical guarantees and illustrate the effectiveness of our proposed method with numerical experiments."]]></description>
<dc:subject>density_estimation density_ratio_estimation likelihood spectral_methods high-dimensional_statistics kith_and_kin izbicki.rafael read_the_thesis in_NB lee.ann_b.</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:4b615eab616e/</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:density_ratio_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:likelihood"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:spectral_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:high-dimensional_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:izbicki.rafael"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:read_the_thesis"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:lee.ann_b."/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1402.3466">
    <title>[1402.3466] Kernel density estimates in particle filter</title>
    <dc:date>2014-03-08T22:39:09+00:00</dc:date>
    <link>http://arxiv.org/abs/1402.3466</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The paper deals with kernel estimates of densities of filtering distributions in the particle filter. The convergence of the estimates is investigated by means of Fourier analysis. It is shown that the estimates converge to theoretical filtering densities in the mean integrated squared error under a certain assumption on the Sobolev character of the filtering densities. A sufficient condition is presented for the persistence of this Sobolev character over time."]]></description>
<dc:subject>to:NB density_estimation particle_filters filtering statistics kernel_smoothing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:dfbfe8acfb74/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:particle_filters"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:filtering"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_smoothing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1402.2966">
    <title>[1402.2966] Nonparametric Estimation of Renyi Divergence and Friends</title>
    <dc:date>2014-02-13T18:22:38+00:00</dc:date>
    <link>http://arxiv.org/abs/1402.2966</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["We consider nonparametric estimation of L_2, Renyi-α and Tsallis-α divergences of continuous distributions. Our approach is to construct estimators for particular integral functionals of two densities and translate them into divergence estimators. For the integral functionals, our estimators are based on corrections of a preliminary plug-in estimator. We analyze the rates of convergence for our estimators and show that the parametric rate of n−1/2 is achievable when the densities' smoothness s are both at least d/4 where d is the dimension. We also derive minimax lower bounds for this problem which confirm that s>d/4 is necessary to achieve the n−1/2 rate of convergence. We confirm our theoretical guarantees with a number of simulations."]]></description>
<dc:subject>information_theory density_estimation divergence_estimation kith_and_kin entropy_estimation in_NB wasserman.larry poczos.barnabas</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:99cbe70c5261/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:information_theory"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:divergence_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kith_and_kin"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:entropy_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:wasserman.larry"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:poczos.barnabas"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1312.1099">
    <title>[1312.1099] Multiscale Dictionary Learning for Estimating Conditional Distributions</title>
    <dc:date>2014-01-02T17:57:15+00:00</dc:date>
    <link>http://arxiv.org/abs/1312.1099</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Nonparametric estimation of the conditional distribution of a response given high-dimensional features is a challenging problem. It is important to allow not only the mean but also the variance and shape of the response density to change flexibly with features, which are massive-dimensional. We propose a multiscale dictionary learning model, which expresses the conditional response density as a convex combination of dictionary densities, with the densities used and their weights dependent on the path through a tree decomposition of the feature space. A fast graph partitioning algorithm is applied to obtain the tree decomposition, with Bayesian methods then used to adaptively prune and average over different sub-trees in a soft probabilistic manner. The algorithm scales efficiently to approximately one million features. State of the art predictive performance is demonstrated for toy examples and two neuroscience applications including up to a million features."]]></description>
<dc:subject>to:NB density_estimation conditional_density_estimation nonparametrics statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:790d60c2999c/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:conditional_density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1311.4780">
    <title>[1311.4780] Asymptotically Exact, Embarrassingly Parallel MCMC</title>
    <dc:date>2013-12-18T15:17:41+00:00</dc:date>
    <link>http://arxiv.org/abs/1311.4780</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Communication costs, resulting from synchronization requirements during learning, can greatly slow down many parallel machine learning algorithms. In this paper, we present a parallel Markov chain Monte Carlo (MCMC) algorithm in which subsets of data are processed independently, with very little communication. First, we arbitrarily partition data onto multiple machines. Then, on each machine, any classical MCMC method (e.g., Gibbs sampling) may be used to draw samples from a posterior distribution given the data subset. Finally, the samples from each machine are combined to form samples from the full posterior. This embarrassingly parallel algorithm effectively allows each machine to act independently on a subset of the data (without communication) until the final combination stage. We prove that our algorithm generates asymptotically exact samples and empirically demonstrate its effectiveness on several large-scale synthetic and real datasets."]]></description>
<dc:subject>monte_carlo density_estimation distributed_systems computational_statistics xing.eric have_read in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:cb16d125c286/</dc:identifier>
<taxo:topics><rdf:Bag>	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:monte_carlo"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:distributed_systems"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:computational_statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:xing.eric"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1312.3516">
    <title>[1312.3516] Density Estimation in Infinite Dimensional Exponential Families</title>
    <dc:date>2013-12-16T01:53:04+00:00</dc:date>
    <link>http://arxiv.org/abs/1312.3516</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper, we consider the problem of estimating densities in an infinite dimensional exponential family indexed by functions in a reproducing kernel Hilbert space. Since standard techniques like maximum likelihood estimation (MLE) or pseudo MLE (based on the method of sieves) do not yield practically useful estimators because of their inability to handle the log-partition function efficiently, we propose an estimator based on the score matching method introduced by Hyv\"{a}rinen, which involves solving a simple linear system. We show that the proposed estimator is consistent, and provide convergence rates under smoothness assumptions. We also empirically demonstrate that the proposed method outperforms the standard non-parametric kernel density estimator."

--- The theory is interesting, but I think the (brief) empirical comparison to kernel density estimation is a bit of a cheat, because they seem to be using the objective function _their_ method optimizes!  Something like out-of-sample log-likelihood would have been much fairer.]]></description>
<dc:subject>to:NB density_estimation hilbert_space kernel_methods statistics nonparametrics have_read</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:5618c9fa60d6/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hilbert_space"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_methods"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://onlinelibrary.wiley.com/doi/10.1111/rssb.12041/abstract">
    <title>Preadjusted non-parametric estimation of a conditional distribution function - Veraverbeke - 2013 - Journal of the Royal Statistical Society: Series B (Statistical Methodology) - Wiley Online Library</title>
    <dc:date>2013-11-15T01:21:38+00:00</dc:date>
    <link>http://onlinelibrary.wiley.com/doi/10.1111/rssb.12041/abstract</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["The paper deals with non-parametric estimation of a conditional distribution function. We suggest a method of preadjusting the original observations non-parametrically through location and scale, to reduce the bias of the estimator. We derive the asymptotic properties of the estimator proposed. A simulation study investigating the finite sample performances of the estimators discussed is provided and reveals the gain that can be achieved. It is also shown how the idea of the preadjusting opens the path to improved estimators in other settings such as conditional quantile and density estimation, and conditional survival function estimation in the case of censored data."]]></description>
<dc:subject>to:NB density_estimation nonparametrics statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:098a3333cb1f/</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:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.ejs/1380719362">
    <title>Bott , Devroye , Kohler : Estimation of a distribution from data with small measurement errors</title>
    <dc:date>2013-10-03T16:51:24+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.ejs/1380719362</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["In this paper we study the problem of estimation of a distribution from data that contain small measurement errors. The only assumption on these errors is that the average absolute measurement error converges to zero for sample size tending to infinity with probability one. In particular we do not assume that the measurement errors are independent with expectation zero. Throughout the paper we assume that the distribution, which has to be estimated, has a density with respect to the Lebesgue-Borel measure.
"We show that the empirical measure based on the data with measurement error leads to an uniform consistent estimate of the distribution function. Furthermore, we show that in general no estimate is consistent in the total variation sense for all distributions under the above assumptions. However, in case that the average measurement error converges to zero faster than a properly chosen sequence of bandwidths, the total variation error of the distribution estimate corresponding to a kernel density estimate converges to zero for all distributions. In case of a general additive error model we show that this result even holds if only the average measurement error converges to zero. The results are applied in the context of estimation of the density of residuals in a random design regression model, where the residual error is not independent from the predictor."]]></description>
<dc:subject>to:NB density_estimation nonparametrics statistics error-in-variables kernel_smoothing</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:bd4e37a72179/</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:density_estimation"/>
	<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:error-in-variables"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:kernel_smoothing"/>
</rdf:Bag></taxo:topics>
</item>
<item rdf:about="http://arxiv.org/abs/1309.6906">
    <title>[1309.6906] Hellinger Distance and Bayesian Non-Parametrics: Hierarchical Models for Robust and Efficient Bayesian Inference</title>
    <dc:date>2013-09-27T16:42:10+00:00</dc:date>
    <link>http://arxiv.org/abs/1309.6906</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["This paper introduces a hierarchical framework to incorporate Hellinger distance methods into Bayesian analysis. We propose to modify a prior over non-parametric densities with the exponential of twice the Hellinger distance between a candidate and a parametric density. By incorporating a prior over the parameters of the second density, we arrive at a hierarchical model in which a non-parametric model is placed between parameters and the data. The parameters of the family can then be estimated as hyperparameters in the model. In frequentist estimation, minimizing the Hellinger distance between a kernel density estimate and a parametric family has been shown to produce estimators that are both robust to outliers and statistically efficient when the parametric model is correct. In this paper, we demonstrate that the same results are applicable when a non-parametric Bayes density estimate replaces the kernel density estimate. We then demonstrate that robustness and efficiency also hold for the proposed hierarchical model. The finite-sample behavior of the resulting estimates is investigated by simulation and on real world data."]]></description>
<dc:subject>to:NB density_estimation nonparametrics hooker.giles statistics</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:90902ad8e44f/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:density_estimation"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:nonparametrics"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:hooker.giles"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:statistics"/>
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</item>
<item rdf:about="http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aos/1378386242">
    <title>Hall , Horowitz : A simple bootstrap method for constructing nonparametric confidence bands for functions</title>
    <dc:date>2013-09-06T19:48:31+00:00</dc:date>
    <link>http://projecteuclid.org/DPubS?service=UI&amp;version=1.0&amp;verb=Display&amp;handle=euclid.aos/1378386242</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators. To overcome this problem it is common practice to either undersmooth, so as to reduce the impact of bias, or oversmooth, and thereby introduce an explicit or implicit bias estimator. However, these approaches, and others based on nonstandard smoothing methods, complicate the process of inference, for example, by requiring the choice of new, unconventional smoothing parameters and, in the case of undersmoothing, producing relatively wide bands. In this paper we suggest a new approach, which exploits to our advantage one of the difficulties that, in the past, has prevented an attractive solution to the problem—the fact that the standard bootstrap bias estimator suffers from relatively high-frequency stochastic error. The high frequency, together with a technique based on quantiles, can be exploited to dampen down the stochastic error term, leading to relatively narrow, simple-to-construct confidence bands."

--- Huh.  Need to see how hard this would really be to implement, and also what it really establishes.]]></description>
<dc:subject>statistics regression density_estimation bootstrap confidence_sets to_teach:undergrad-ADA have_read in_NB</dc:subject>
<dc:source>https://pinboard.in/</dc:source>
<dc:identifier>https://pinboard.in/u:cshalizi/b:dbe29df764e8/</dc:identifier>
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	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:have_read"/>
	<rdf:li rdf:resource="https://pinboard.in/u:cshalizi/t:in_NB"/>
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