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A brief discussion is given of the traditional version of the Maximum Entropy Method, including a review of some of the criticism that has been made in regard to its use in statistical inference. Motivated by these questions, a modified…

Data Analysis, Statistics and Probability · Physics 2007-09-12 Robert Kariotis

Entropic uncertainty relations for the position and momentum within the generalized uncertainty principle are examined. Studies of this principle are motivated by the existence of a minimal observable length. Then the position and momentum…

Quantum Physics · Physics 2017-06-09 Alexey E. Rastegin

Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…

Quantum Physics · Physics 2007-05-23 Adam Azarchs

A simplified climate model based on maximum entropy production, described by a variational principle, is revisited and an analytical solution to its Euler-Lagrange equation is found. Mindful of controversy about maximum or minimum entropy…

Atmospheric and Oceanic Physics · Physics 2020-10-22 Valerio Faraoni

We show that the conditional min-entropy Hmin(A|B) of a bipartite state rho_AB is directly related to the maximum achievable overlap with a maximally entangled state if only local actions on the B-part of rho_AB are allowed. In the special…

Quantum Physics · Physics 2015-11-24 Robert Koenig , Renato Renner , Christian Schaffner

The well known maximum-entropy principle due to Jaynes, which states that given mean parameters, the maximum entropy distribution matching them is in an exponential family, has been very popular in machine learning due to its "Occam's…

Machine Learning · Computer Science 2016-07-13 Yuanzhi Li , Andrej Risteski

This is a preliminary article stating and proving a new maximum entropy theorem. The entropies that we consider can be used as measures of biodiversity. In that context, the question is: for a given collection of species, which frequency…

Information Theory · Computer Science 2011-01-14 Tom Leinster

It is well known that the entropy $H(X)$ of a discrete random variable $X$ is always greater than or equal to the entropy $H(f(X))$ of a function $f$ of $X$, with equality if and only if $f$ is one-to-one. In this paper, we give tight…

Information Theory · Computer Science 2017-12-22 Ferdinando Cicalese , Luisa Gargano , Ugo Vaccaro

In this article, I give a definition of topological entropy for random dynamical systems associated to an infinite countable discrete amenable group action. I obtain a variational principle between the topological entropy and measurable…

Dynamical Systems · Mathematics 2024-03-13 Yuan Lian

In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies with determining which subsets of variables can take…

Methodology · Statistics 2022-07-19 Emma S. Simpson , Jennifer L. Wadsworth , Jonathan A. Tawn

The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a…

Machine Learning · Computer Science 2013-11-08 Moshe Dubiner , Matan Gavish , Yoram Singer

The product expansion of conditional probabilities for belief nets is not maximum entropy. This appears to deny a desirable kind of assurance for the model. However, a kind of guarantee that is almost as strong as maximum entropy can be…

Artificial Intelligence · Computer Science 2013-03-25 Norman C. Dalkey

Many biological systems perform close to their physical limits, but promoting this optimality to a general principle seems to require implausibly fine tuning of parameters. Using examples from a wide range of systems, we show that this…

We give a characterization of Maximum Entropy/Minimum Relative Entropy inference by providing two `strong entropy concentration' theorems. These theorems unify and generalize Jaynes' `concentration phenomenon' and Van Campenhout and Cover's…

Information Theory · Computer Science 2008-09-17 Peter Grunwald

We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is…

Data Analysis, Statistics and Probability · Physics 2007-10-24 Peter Sunehag

Calibration methods have been widely studied in survey sampling over the last decades. Viewing calibration as an inverse problem, we extend the calibration technique by using a maximum entropy method. Finding the optimal weights is achieved…

Methodology · Statistics 2009-09-23 Fabrice Gamboa , Jean-Michel Loubes , Paul Rochet

Various notions of fluctuations exist depending on the way one chooses to measure them. We discuss two extreme cases (continuous measurement versus long inter-measurement times) and we see their relation with entropy production and with…

Statistical Mechanics · Physics 2009-11-05 C. Maes , K. Netocny

The extremization of an appropriate entropic functional may yield to the probability distribution functions maximizing the respective entropic structure. This procedure is known in Statistical Mechanics and Information Theory as Jaynes'…

Statistical Mechanics · Physics 2015-05-13 Thomas Oikonomou , Ugur Tirnakli

The concept of Relative Divergence of one Grading Function from another is extended from totally ordered chains to power sets of finite event spaces. Shannon Entropy concept is extended to normalized grading functions on such power sets.…

Probability · Mathematics 2022-07-15 Alexander Dukhovny

This paper investigates a function of macroscopic variables known as the singular potential, building on previous work by Ball and Majumdar. The singular potential is a function of the admissible statistical averages of probability…

Analysis of PDEs · Mathematics 2016-07-18 Jamie M. Taylor