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For a parametric model of distributions, the closest distribution in the model to the true distribution located outside the model is considered. Measuring the closeness between two distributions with the Kullback-Leibler (K-L) divergence,…

Statistics Theory · Mathematics 2025-10-14 Yo Sheena

Given a set of points $P$ and axis-aligned rectangles $\mathcal{R}$ in the plane, a point $p \in P$ is called \emph{exposed} if it lies outside all rectangles in $\mathcal{R}$. In the \emph{max-exposure problem}, given an integer parameter…

Computational Geometry · Computer Science 2021-02-09 Neeraj Kumar , Stavros Sintos , Subhash Suri

In the present work, we present numerical results for an iterative method for solving an optimal control problem with inequality contraints. The method is based on generalized Bregman distances. Under a combination of a source condition and…

Optimization and Control · Mathematics 2016-06-07 Frank Pörner

The link with exponential families has allowed $k$-means clustering to be generalized to a wide variety of data generating distributions in exponential families and clustering distortions among Bregman divergences. Getting the framework to…

Machine Learning · Computer Science 2022-11-08 Ehsan Amid , Richard Nock , Manfred Warmuth

For a skew normal random sequence, convergence rates of the distribution of its partial maximum to the Gumbel extreme value distribution are derived. The asymptotic expansion of the distribution of the normalized maximum is given under an…

Methodology · Statistics 2012-12-06 Xin Liao , Zuoxiang Peng , Saralees Nadarajah , Xiaoqian Wang

We investigate the sets of joint probability distributions that maximize the average multi-information over a collection of margins. These functionals serve as proxies for maximizing the multi-information of a set of variables or the mutual…

Information Theory · Computer Science 2019-06-14 Thomas Merkh , Guido Montúfar

Distances are fundamental primitives whose choice significantly impacts the performances of algorithms in machine learning and signal processing. However selecting the most appropriate distance for a given task is an endeavor. Instead of…

Machine Learning · Computer Science 2020-10-01 Frank Nielsen , Richard Nock

The goal of opinion maximization is to maximize the positive view towards a product, an ideology or any entity among the individuals in social networks. So far, opinion maximization is mainly studied as finding a set of influential nodes…

Social and Information Networks · Computer Science 2019-01-03 Anuj Nayak , Seyyedali Hosseinalipour , Huaiyu Dai

Using a trimming approach, we investigate a k-means type method based on Bregman divergences for clustering data possibly corrupted with clutter noise. The main interest of Bregman divergences is that the standard Lloyd algorithm adapts to…

Statistics Theory · Mathematics 2020-09-10 Aurélie Fischer , Clément Levrard , Claire Brécheteau

Randomness in scientific estimation is generally assumed to arise from unmeasured or uncontrolled factors. However, when combining subjective probability estimates, heterogeneity stemming from people's cognitive or information diversity is…

Methodology · Statistics 2015-05-28 Ville Satopää , Robin Pemantle , Lyle Ungar

Four problems related to information divergence measures defined on finite alphabets are considered. In three of the cases we consider, we illustrate a contrast which arises between the binary-alphabet and larger-alphabet settings. This is…

Information Theory · Computer Science 2016-11-17 Jiantao Jiao , Thomas Courtade , Albert No , Kartik Venkat , Tsachy Weissman

We consider the design of prediction market mechanisms known as automated market makers. We show that we can design these mechanisms via the mold of \emph{exponential family distributions}, a popular and well-studied probability…

Artificial Intelligence · Computer Science 2014-02-25 Jacob Abernethy , Sindhu Kutty , Sébastien Lahaie , Rahul Sami

Randomness in scientific estimation is generally assumed to arise from unmeasured or uncontrolled factors. However, when combining subjective probability estimates, heterogeneity stemming from people's cognitive or information diversity is…

Methodology · Statistics 2015-09-14 Ville A. Satopää , Robin Pemantle , Lyle H. Ungar

The versatility of exponential families, along with their attendant convexity properties, make them a popular and effective statistical model. A central issue is learning these models in high-dimensions, such as when there is some sparsity…

Machine Learning · Computer Science 2015-05-19 Sham M. Kakade , Ohad Shamir , Karthik Sridharan , Ambuj Tewari

Social connections are conduits through which individuals communicate, information propagates, and diseases spread. Identifying individuals who are more likely to adopt ideas and spread them is essential in order to develop effective…

Social and Information Networks · Computer Science 2024-10-31 Vedran Sekara , Ivan Dotu , Manuel Cebrian , Esteban Moro , Manuel Garcia-Herranz

$f$-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

There are many applications that benefit from computing the exact divergence between 2 discrete probability measures, including machine learning. Unfortunately, in the absence of any assumptions on the structure or independencies within…

Machine Learning · Computer Science 2023-10-16 Loong Kuan Lee , Nico Piatkowski , François Petitjean , Geoffrey I. Webb

Information and free-energy maximization are physics principles that provide general rules for an agent to optimize actions in line with specific goals and policies. These principles are the building blocks for designing decision-making…

Machine Learning · Computer Science 2025-03-21 Alex Barbier-Chebbah , Christian L. Vestergaard , Jean-Baptiste Masson

The paper proposes another extension of the extremal principle. A new extremality model involving collections of arbitrary families of sets is studied. It generalizes the conventional model based on linear translations of given sets as well…

Optimization and Control · Mathematics 2024-09-04 Nguyen Duy Cuong , Alexander Y. Kruger , Nguyen Hieu Thao

The paper explores a new extremality model involving collections of arbitrary families of sets. We demonstrate its applicability to set-valued optimization problems with general preferences, weakening the assumptions of the known results…

Optimization and Control · Mathematics 2025-06-23 Nguyen Duy Cuong , Alexander Y. Kruger , Nguyen Hieu Thao