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Feature selection is one of the most fundamental problems in machine learning. An extensive body of work on information-theoretic feature selection exists which is based on maximizing mutual information between subsets of features and class…

Machine Learning · Statistics 2016-06-10 Shuyang Gao , Greg Ver Steeg , Aram Galstyan

We propose to interpret distribution model risk as sensitivity of expected loss to changes in the risk factor distribution, and to measure the distribution model risk of a portfolio by the maximum expected loss over a set of plausible…

Risk Management · Quantitative Finance 2013-01-22 Thomas Breuer , Imre Csiszar

This document describes concisely the ubiquitous class of exponential family distributions met in statistics. The first part recalls definitions and summarizes main properties and duality with Bregman divergences (all proofs are skipped).…

Machine Learning · Computer Science 2011-05-16 Frank Nielsen , Vincent Garcia

The Levenberg-Marquardt algorithm is a flexible iterative procedure used to solve non-linear least squares problems. In this work we study how a class of possible adaptations of this procedure can be used to solve maximum likelihood…

Computation · Statistics 2014-10-06 Marco Giordan , Federico Vaggi , Ron Wehrens

We study an iterative regularization method of optimal control problems with control constraints. The regularization method is based on generalized Bregman distances. We provide convergence results under a combination of a source condition…

Optimization and Control · Mathematics 2016-11-04 Frank Pörner , Daniel Wachsmuth

Generation of deviates from random graph models with non-trivial edge dependence is an increasingly important problem. Here, we introduce a method which allows perfect sampling from random graph models in exponential family form…

Computation · Statistics 2020-01-07 Carter T. Butts

The present paper investigates the update of an empirical probability distribution with the results of a new set of observations. The optimal update is obtained by minimizing either the Hellinger distance or the quadratic Bregman…

Statistics Theory · Mathematics 2022-01-03 Jan Naudts

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…

Information Theory · Computer Science 2022-05-19 Adrien Vandenbroucque , Amedeo Roberto Esposito , Michael Gastpar

The Chernoff information between two probability measures is a statistical divergence measuring their deviation defined as their maximally skewed Bhattacharyya distance. Although the Chernoff information was originally introduced for…

Information Theory · Computer Science 2022-10-04 Frank Nielsen

Score-based divergences have been widely used in machine learning and statistics applications. Despite their empirical success, a blindness problem has been observed when using these for multi-modal distributions. In this work, we discuss…

Machine Learning · Statistics 2025-11-25 Mingtian Zhang , Oscar Key , Peter Hayes , David Barber , Brooks Paige , François-Xavier Briol

When additional information sources are available in decision making problems that allow stochastic optimization formulations, an important question is how to optimally use the information the sources are capable of providing. A framework…

Data Analysis, Statistics and Probability · Physics 2013-02-04 Eugene Perevalov , David Grace

We generalize the generalized Arimoto-Blahut algorithm to a general function defined over Bregman-divergence system. In existing methods, when linear constraints are imposed, each iteration needs to solve a convex minimization. Exploiting…

Optimization and Control · Mathematics 2025-03-11 Masahito Hayashi

Best possible bounds are established for families without s pairwise disjoint members and the more general problem for several families. The results are shown to apply several classical results.

Combinatorics · Mathematics 2019-04-24 Peter Frankl

In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed, where the defining convex function has an exponential nature. These estimators avoid the necessity of using an intermediate kernel…

Methodology · Statistics 2019-11-25 Taranga Mukherjee , Abhijit Mandal , Ayanendranath Basu

The Bregman divergence have been the subject of several studies. We do not go to do an exhaustive study of its subclasses, but propose a proof that shows that the \b{eta}-divergence are subclasses of the Bregman divergences. It is in this…

Methodology · Statistics 2018-05-21 Macoumba Ndourand Mactar Ndaw , Papa Ngom

We consider the precise upper large deviations estimates for the maximal displacement of a branching random walk. In addition, we obtain a description of the extremal process of the branching random walk conditioned on this large deviations…

Probability · Mathematics 2025-02-04 Lianghui Luo

Interpretable and explainable machine learning has seen a recent surge of interest. We focus on safety as a key motivation behind the surge and make the relationship between interpretability and safety more quantitative. Toward assessing…

Machine Learning · Computer Science 2022-11-04 Dennis Wei , Rahul Nair , Amit Dhurandhar , Kush R. Varshney , Elizabeth M. Daly , Moninder Singh

In this paper we establish lower bounds on information divergence from a distribution to certain important classes of distributions as Gaussian, exponential, Gamma, Poisson, geometric, and binomial. These lower bounds are tight and for…

Information Theory · Computer Science 2011-02-15 Peter Harremoës , Christophe Vignat

The family of f-divergences is ubiquitously applied to generative modeling in order to adapt the distribution of the model to that of the data. Well-definedness of f-divergences, however, requires the distributions of the data and model to…

Machine Learning · Statistics 2019-06-04 Akash Srivastava , Kristjan Greenewald , Farzaneh Mirzazadeh

We present a method for learning max-weight matching predictors in bipartite graphs. The method consists of performing maximum a posteriori estimation in exponential families with sufficient statistics that encode permutations and data…

Machine Learning · Computer Science 2009-06-05 James Petterson , Tiberio Caetano , Julian McAuley , Jin Yu