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We study the minimax estimation of $\alpha$-divergences between discrete distributions for integer $\alpha\ge 1$, which include the Kullback--Leibler divergence and the $\chi^2$-divergences as special examples. Dropping the usual…

Information Theory · Computer Science 2021-03-04 Yanjun Han , Jiantao Jiao , Tsachy Weissman

The projection predictive variable selection is a decision-theoretically justified Bayesian variable selection approach achieving an outstanding trade-off between predictive performance and sparsity. Its projection problem is not easy to…

Methodology · Statistics 2024-06-11 Frank Weber , Änne Glass , Aki Vehtari

Conformal predictive systems allow forecasters to issue predictive distributions for real-valued future outcomes that have out-of-sample calibration guarantees. On a more abstract level, conformal prediction makes use of in-sample…

Methodology · Statistics 2025-03-07 Sam Allen , Georgios Gavrilopoulos , Alexander Henzi , Gian-Reto Kleger , Johanna Ziegel

We propose a robust and scalable variational Bayes (VB) framework designed to effectively handle contamination and outliers in dataset. Our approach partitions the data into $m$ disjoint subsets and formulates a joint optimization problem…

Methodology · Statistics 2025-12-16 Jiawei Yan , Ju Liu , Weidong Liu , Jiyuan Tu

In machine learning, it is common to optimize the parameters of a probabilistic model, modulated by an ad hoc regularization term that penalizes some values of the parameters. Regularization terms appear naturally in Variational Inference,…

Machine Learning · Computer Science 2024-02-08 Pierre Wolinski , Guillaume Charpiat , Yann Ollivier

Left-invariant optimal control problems on Lie groups form an important class of problems with big symmetry group. They are interesting from the theoretical point of view since they often can be completely studied, and general features can…

Optimization and Control · Mathematics 2021-05-18 Yuri Sachkov

\cite{tsagris2025a} proposed the generalized circular projected Cauchy (GCPC) distribution, whose special case is the wrapped Cauchy distribution. In this paper we first derive the relationship with the wrapped Cauchy distribution, and then…

Statistics Theory · Mathematics 2026-03-26 Omar Alzeley , Michail Tsagris

Modern applications of Bayesian inference involve models that are sufficiently complex that the corresponding posterior distributions are intractable and must be approximated. The most common approximation is based on Markov chain Monte…

Machine Learning · Statistics 2019-05-15 Yue Yang , Ryan Martin , Howard Bondell

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

In a given problem, the Bayesian statistical paradigm requires the specification of a prior distribution that quantifies relevant information about the unknowns of main interest external to the data. In cases where little such information…

Statistics Theory · Mathematics 2017-10-11 Alexander Terenin , David Draper

A well-known technique in estimating probabilities of rare events in general and in information theory in particular (used, e.g., in the sphere-packing bound), is that of finding a reference probability measure under which the event of…

Information Theory · Computer Science 2014-12-23 Rami Atar , Neri Merhav

Conformal prediction provides finite-sample, distribution-free coverage under exchangeability, but standard constructions may lack robustness in the presence of outliers or heavy tails. We propose a robust conformal method based on a…

Statistics Theory · Mathematics 2026-04-21 Alejandro Cholaquidis , Emilien Joly , Leonardo Moreno

Many statistical studies are concerned with the analysis of observations organized in a matrix form whose elements are count data. When these observations are assumed to follow a Poisson or a multinomial distribution, it is of interest to…

Statistics Theory · Mathematics 2022-01-04 Jérémie Bigot , Charles Deledalle

In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…

Optimization and Control · Mathematics 2021-11-30 Romain Guillaume , Adam Kasperski , Pawel Zielinski

Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…

Machine Learning · Statistics 2023-01-19 Ali Siahkoohi , Gabrio Rizzuti , Rafael Orozco , Felix J. Herrmann

We consider Bayesian linear inverse problems in infinite-dimensional separable Hilbert spaces, with a Gaussian prior measure and additive Gaussian noise model, and provide an extension of the concept of Bayesian D-optimality to the…

Statistics Theory · Mathematics 2014-09-04 Alen Alexanderian , Philip Gloor , Omar Ghattas

Recent work has attempted to directly approximate the `function-space' or predictive posterior distribution of Bayesian models, without approximating the posterior distribution over the parameters. This is appealing in e.g. Bayesian neural…

Machine Learning · Statistics 2020-11-19 David R. Burt , Sebastian W. Ober , Adrià Garriga-Alonso , Mark van der Wilk

For linear inverse problems with Gaussian priors and Gaussian observation noise, the posterior is Gaussian, with mean and covariance determined by the conditioning formula. The covariance is the central object for uncertainty…

Statistics Theory · Mathematics 2025-08-13 Giuseppe Carere , Han Cheng Lie

The practice of employing empirical likelihood (EL) components in place of parametric likelihood functions in the construction of Bayesian-type procedures has been well-addressed in the modern statistical literature. We rigorously derive…

Methodology · Statistics 2018-08-21 Albert Vexler , Li Zou , Alan D. Hutson

Current approaches in approximate inference for Bayesian neural networks minimise the Kullback-Leibler divergence to approximate the true posterior over the weights. However, this approximation is without knowledge of the final application,…

Machine Learning · Statistics 2018-05-11 Adam D. Cobb , Stephen J. Roberts , Yarin Gal