Related papers: On $f$-Divergences: Integral Representations, Loca…
This paper considers derivation of $f$-divergence inequalities via the approach of functional domination. Bounds on an $f$-divergence based on one or several other $f$-divergences are introduced, dealing with pairs of probability measures…
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…
We unify f-divergences, Bregman divergences, surrogate loss bounds (regret bounds), proper scoring rules, matching losses, cost curves, ROC-curves and information. We do this by systematically studying integral and variational…
We consider the problem of parameter estimation in a Bayesian setting and propose a general lower-bound that includes part of the family of $f$-Divergences. The results are then applied to specific settings of interest and compared to other…
This book deals with functions allowing to express the dissimilarity (discrepancy) between two data fields or ''divergence functions'' with the aim of applications to linear inverse problems. Most of the divergences found in the litterature…
Difference-in-differences is one of the most used identification strategies in empirical work in economics. This chapter reviews a number of important, recent developments related to difference-in-differences. First, this chapter reviews…
Minimum divergence problems under integral constraints appear throughout statistics and probability, including sequential inference, bandit theory, and distributionally robust optimization. In many such settings, dual representations are…
A stream of algorithmic advances has steadily increased the popularity of the Bayesian approach as an inference paradigm, both from the theoretical and applied perspective. Even with apparent successes in numerous application fields, a…
The main purpose of this paper is to present new families of test statistics for studying the problem of goodness-of-fit of some data to a latent class model for binary data. The families of test statistics introduced are based on…
The estimation of an f-divergence between two probability distributions based on samples is a fundamental problem in statistics and machine learning. Most works study this problem under very weak assumptions, in which case it is provably…
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…
$f$-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…
We introduce several novel change of measure inequalities for two families of divergences: $f$-divergences and $\alpha$-divergences. We show how the variational representation for $f$-divergences leads to novel change of measure…
This work establishes computable bounds between f-divergences for probability measures within a generalized quasi-$\varepsilon_{(M,m)}$-neighborhood framework. We make the following key contributions. (1) a unified characterization of local…
As a continuation of the paper [20] on standard $f$-divergences, we make a systematic study of maximal $f$-divergences in general von Neumann algebras. For maximal $f$-divergences, apart from their definition based on Haagerup's…
We show that the variational representations for f-divergences currently used in the literature can be tightened. This has implications to a number of methods recently proposed based on this representation. As an example application we use…
A class of distortions termed functional Bregman divergences is defined, which includes squared error and relative entropy. A functional Bregman divergence acts on functions or distributions, and generalizes the standard Bregman divergence…
$f$-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…
Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only…
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…