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$f$-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler…

Statistics Theory · Mathematics 2013-10-16 Adityanand Guntuboyina , Sujayam Saha , Geoffrey Schiebinger

$f$-divergences, which quantify discrepancy between probability distributions, are ubiquitous in information theory, machine learning, and statistics. While there are numerous methods for estimating $f$-divergences from data, a limit…

Statistics Theory · Mathematics 2023-10-13 Sreejith Sreekumar , Ziv Goldfeld , Kengo Kato

The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…

Statistics Theory · Mathematics 2022-11-28 Junichiro Yoshida , Nakahiro Yoshida

Tight bounds for several symmetric divergence measures are introduced, given in terms of the total variation distance. Each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these bounds…

Information Theory · Computer Science 2016-11-15 Igal Sason

Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…

Statistics Theory · Mathematics 2022-03-03 Michel Broniatowski , Wolfgang Stummer

The families of $f$-divergences (e.g. the Kullback-Leibler divergence) and Integral Probability Metrics (e.g. total variation distance or maximum mean discrepancies) are widely used to quantify the similarity between probability…

Statistics Theory · Mathematics 2021-06-08 Rohit Agrawal , Thibaut Horel

The problem of f-divergence estimation is important in the fields of machine learning, information theory, and statistics. While several nonparametric divergence estimators exist, relatively few have known convergence properties. In…

Information Theory · Computer Science 2015-03-16 Kevin R. Moon , Alfred O. Hero

Discrimination in machine learning often arises along multiple dimensions (a.k.a. protected attributes); it is then desirable to ensure \emph{intersectional fairness} -- i.e., that no subgroup is discriminated against. It is known that…

Machine Learning · Statistics 2023-06-27 Mathieu Molina , Patrick Loiseau

We consider the problem of approximating a function in a general nonlinear subset of $L^2$, when only a weighted Monte Carlo estimate of the $L^2$-norm can be computed. Of particular interest in this setting is the concept of sample…

Numerical Analysis · Mathematics 2023-01-24 Philipp Trunschke

Information divergence functions play a critical role in statistics and information theory. In this paper we show that a non-parametric f-divergence measure can be used to provide improved bounds on the minimum binary classification…

Information Theory · Computer Science 2015-02-11 Visar Berisha , Alan Wisler , Alfred O. Hero , Andreas Spanias

In this paper, we develop a non-asymptotic local normal approximation for multinomial probabilities. First, we use it to find non-asymptotic total variation bounds between the measures induced by uniformly jittered multinomials and the…

Statistics Theory · Mathematics 2023-09-06 Eric Bax , Frédéric Ouimet

We study a general framework of distributional computational graphs: computational graphs whose inputs are probability distributions rather than point values. We analyze the discretization error that arises when these graphs are evaluated…

Machine Learning · Statistics 2026-02-13 Olof Hallqvist Elias , Michael Selby , Phillip Stanley-Marbell

This paper develops systematic approaches to obtain $f$-divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on…

Information Theory · Computer Science 2016-12-06 Igal Sason , Sergio Verdú

Nearest neighbor cells in $R^d,d\in\mathbb{N}$, are used to define coefficients of divergence ($\phi$-divergences) between continuous multivariate samples. For large sample sizes, such distances are shown to be asymptotically normal with a…

Probability · Mathematics 2009-03-06 Yu. Baryshnikov , Mathew D. Penrose , J. E. Yukich

In this paper we consider one parameter generalizations of some non - symmetric divergence measures. Measures are \textit{relative information}, $\chi ^2 - $\textit{divergence}, \textit{relative J-divergence}, \textit{relative…

Statistics Theory · Mathematics 2007-06-13 Inder Jeet Taneja , Pranesh Kumar

The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-04-01 Fabian Kuhn , Thomas Moscibroda , Roger Wattenhofer

We develop a rigorous and general framework for constructing information-theoretic divergences that subsume both $f$-divergences and integral probability metrics (IPMs), such as the $1$-Wasserstein distance. We prove under which assumptions…

Machine Learning · Statistics 2021-09-16 Jeremiah Birrell , Paul Dupuis , Markos A. Katsoulakis , Yannis Pantazis , Luc Rey-Bellet

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

Statistics Theory · Mathematics 2025-07-29 Karl Oskar Ekvall , Matteo Bottai

The $f$-divergence is a fundamental notion that measures the difference between two distributions. In this paper, we study the problem of approximating the $f$-divergence between two Ising models, which is a generalization of recent work on…

Data Structures and Algorithms · Computer Science 2025-09-08 Weiming Feng , Yucheng Fu

This paper addresses the statistical problem of estimating the infinite-norm deviation from the empirical mean to the distribution mean for high-dimensional distributions on $\{0,1\}^d$, potentially with $d=\infty$. Unlike traditional…

Statistics Theory · Mathematics 2024-02-21 Moïse Blanchard , Václav Voráček
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