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The organization of high-dimensional probability spaces is a fundamental problem at the intersection of statistical physics and information theory. Here, we analyze the distributions populating level surfaces of the probability simplex…

Statistical Mechanics · Physics 2026-05-12 Bautista Arenaza , Sebastián Risau-Gusman , Inés Samengo , Damián G. Hernández

This paper focuses on the extreme-value problem for Shannon entropy of the joint distribution with given marginals. It is proved that the minimum-entropy coupling must be of order-preserving, while the maximum-entropy coupling coincides…

Information Theory · Computer Science 2022-06-09 Ya-Jing Ma , Feng Wang , Xian-Yuan Wu , Kai-Yuan Cai

Max stable laws are limit laws of linearly normalized partial maxima of indepen- dent, identically distributed (iid) random variables (rvs). These are analogous to stable laws which are limit laws of normalized partial sums of iid rvs. In…

Statistics Theory · Mathematics 2016-11-25 Sreenivasan Ravi , Ali Saeb

Most entropy measures depend on the spread of the probability distribution over the sample space $\mathcal{X}$, and the maximum entropy achievable scales proportionately with the sample space cardinality $|\mathcal{X}|$. For a finite…

Machine Learning · Computer Science 2023-05-25 Rohan Ghosh , Mehul Motani

We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…

Probability · Mathematics 2018-12-31 Hadrien De March

The tube model is a central concept in polymer physics, and allows to reduce the complex many-filament problem of an entangled polymer solution to a single filament description. We investigate the probability distribution function of…

Soft Condensed Matter · Physics 2009-08-12 Hauke Hinsch , Erwin Frey

Traditionally, the Method of (Shannon-Kullback's) Relative Entropy Maximization (REM) is considered with linear moment constraints. In this work, the method is studied under frequency moment constraints which are non-linear in…

Data Analysis, Statistics and Probability · Physics 2012-08-27 M. Grendar, , M. Grendar

We consider an extension of the conditional min- and max-entropies to infinite-dimensional separable Hilbert spaces. We show that these satisfy characterizing properties known from the finite-dimensional case, and retain…

Quantum Physics · Physics 2011-09-20 Fabian Furrer , Johan Aberg , Renato Renner

Probabilistic reasoning systems combine different probabilistic rules and probabilistic facts to arrive at the desired probability values of consequences. In this paper we describe the MESA-algorithm (Maximum Entropy by Simulated Annealing)…

Artificial Intelligence · Computer Science 2013-03-25 Gerhard Paaß

We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…

Data Analysis, Statistics and Probability · Physics 2007-07-13 Sabbir Rahman , Mahbub Majumdar

Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…

Applications · Statistics 2014-12-31 Alexis Bienvenüe , Christian Y. Robert

In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…

Probability · Mathematics 2018-03-30 C. Soizea , R. Ghanem , C. Safta , X. Huan , Z. P. Vane , J. Oefelein , G. Lacaz , H. N. Najm , Q. Tang , X. Chen

Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a…

Statistical Mechanics · Physics 2009-11-11 E. V. Vakarin , J. P. Badiali

We investigate entropy minimization problems for quantum states subject to convex block-separable constraints. Our principal result is a quantitative stability theorem: under a natural confining (fixed-support) hypothesis, if a state has…

Quantum Physics · Physics 2026-01-21 Hassan Nasreddine

In ordinary statistical mechanics the Boltzmann-Shannon entropy is related to the Maxwell-Bolzmann distribution $p_i$ by means of a twofold link. The first link is differential and is offered by the Jaynes Maximum Entropy Principle. The…

Statistical Mechanics · Physics 2009-10-02 G. Kaniadakis

We show that the principle of maximum entropy, a variational method appearing in statistical inference, statistical physics, and the analysis of stochastic dynamical systems, admits a geometric description from gauge theory. Using the…

Mathematical Physics · Physics 2023-01-05 Dalton A R Sakthivadivel

The entropy maximum approach (Maxent) was developed as a minimization of the subjective uncertainty measured by the Boltzmann--Gibbs--Shannon entropy. Many new entropies have been invented in the second half of the 20th century. Now there…

Data Analysis, Statistics and Probability · Physics 2013-11-07 A. N. Gorban

We study the problem of synthesizing a policy that maximizes the entropy of a Markov decision process (MDP) subject to a temporal logic constraint. Such a policy minimizes the predictability of the paths it generates, or dually, maximizes…

Optimization and Control · Mathematics 2019-06-17 Yagiz Savas , Melkior Ornik , Murat Cubuktepe , Mustafa O. Karabag , Ufuk Topcu

Maximum entropy (maxEnt) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic dynamical systems, the effect of state space topology and path-dependent constraints on…

Statistical Mechanics · Physics 2015-10-28 Purushottam D. Dixit

Estimating the entropy of a discrete random variable is a fundamental problem in information theory and related fields. This problem has many applications in various domains, including machine learning, statistics and data compression. Over…

Information Theory · Computer Science 2020-12-22 Yuval Shalev , Amichai Painsky , Irad Ben-Gal