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We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on $\mathbb{R}^p$ and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and…

Statistics Theory · Mathematics 2019-03-15 Min Xu , Richard J. Samworth

This paper discusses predictive densities under the Kullback--Leibler loss for high-dimensional Poisson sequence models under sparsity constraints. Sparsity in count data implies zero-inflation. We present a class of Bayes predictive…

Statistics Theory · Mathematics 2020-09-08 Keisuke Yano , Ryoya Kaneko , Fumiyasu Komaki

This paper deals with the problem of estimating predictive densities of a matrix-variate normal distribution with known covariance matrix. Our main aim is to establish some Bayesian predictive densities related to matricial shrinkage…

Statistics Theory · Mathematics 2017-04-03 Hisayuki Tsukuma , Tatsuya Kubokawa

The aim of this paper is to introduce new statistical criterions for estimation, suitable for inference in models with common continuous support. This proposal is in the direct line of a renewed interest for divergence based inference tools…

Statistics Theory · Mathematics 2015-03-19 Michel Broniatowski , Aida Toma , Igor Vajda

We study the convergence properties, in Hellinger and related distances, of nonparametric density estimators based on measure transport. These estimators represent the measure of interest as the pushforward of a chosen reference…

Statistics Theory · Mathematics 2022-09-20 Sven Wang , Youssef Marzouk

Based on independently distributed $X_1 \sim N_p(\theta_1, \sigma^2_1 I_p)$ and $X_2 \sim N_p(\theta_2, \sigma^2_2 I_p)$, we consider the efficiency of various predictive density estimators for $Y_1 \sim N_p(\theta_1, \sigma^2_Y I_p)$, with…

Statistics Theory · Mathematics 2017-09-25 Éric Marchand , Abdolnasser Sadeghkhani

We study the sensitivity of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs) with respect to modeling uncertainties. In particular, we consider derivative-based sensitivity analysis of…

Numerical Analysis · Mathematics 2024-05-17 Abhijit Chowdhary , Shanyin Tong , Georg Stadler , Alen Alexanderian

This paper addresses the problem of approximating an unknown probability distribution with density $f$ -- which can only be evaluated up to an unknown scaling factor -- with the help of a sequential algorithm that produces at each iteration…

Statistics Theory · Mathematics 2024-09-23 Pascal Bianchi , Bernard Delyon , Victor Priser , François Portier

We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…

Statistics Theory · Mathematics 2024-01-05 Y. Baraud , H. Halconruy , G. Maillard

In this paper, we consider nonparametric multidimensional finite mixture models and we are interested in the semiparametric estimation of the population weights. Here, the i.i.d. observations are assumed to have at least three components…

Statistics Theory · Mathematics 2017-12-14 Elisabeth Gassiat , Judith Rousseau , Elodie Vernet

Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces…

Information Theory · Computer Science 2017-03-30 David J. Galas , T. Gregory Dewey , James Kunert-Graf , Nikita A. Sakhanenko

In this technical report, we consider conditional density estimation with a maximum likelihood approach. Under weak assumptions, we obtain a theoretical bound for a Kullback-Leibler type loss for a single model maximum likelihood estimate.…

Statistics Theory · Mathematics 2012-07-11 Serge Cohen , Erwan Le Pennec

The Kullback-Leibler (KL) divergence is frequently used in data science. For discrete distributions on large state spaces, approximations of probability vectors may result in a few small negative entries, rendering the KL divergence…

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…

Statistics Theory · Mathematics 2023-06-16 Blair Bilodeau , Dylan J. Foster , Daniel M. Roy

In this paper, we consider an infinite dimensional exponential family, $\mathcal{P}$ 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…

Statistics Theory · Mathematics 2017-05-29 Bharath Sriperumbudur , Kenji Fukumizu , Arthur Gretton , Aapo Hyvärinen , Revant Kumar

This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…

Statistics Theory · Mathematics 2025-08-06 Yichen Lyu , Pengkun Yang

We study empirical Bayes (EB) predictive density estimation in linear mixed models (LMMs) with large number of units, which induce a high dimensional random effects space. Focusing on Kullback Leibler (KL) risk minimization, we develop a…

Methodology · Statistics 2026-03-31 Abir Sarkar , Gourab Mukherjee , Keisuke Yano

Rank-based statistical metrics, such as the invariant statistical loss (ISL), have recently emerged as robust and practically effective tools for training implicit generative models. In this work, we introduce dual-ISL, a novel…

Machine Learning · Computer Science 2025-11-07 José Manuel de Frutos , Manuel A. Vázquez , Pablo M. Olmos , Joaquín Míguez

We study minimax convergence rates of nonparametric density estimation in the Huber contamination model, in which a proportion of the data comes from an unknown outlier distribution. We provide the first results for this problem under a…

Statistics Theory · Mathematics 2021-09-08 Ananya Uppal , Shashank Singh , Barnabas Poczos

We study predictive density estimation under Kullback-Leibler loss in $\ell_0$-sparse Gaussian sequence models. We propose proper Bayes predictive density estimates and establish asymptotic minimaxity in sparse models. A surprise is the…

Statistics Theory · Mathematics 2017-08-01 Gourab Mukherjee , Iain M. Johnstone