English
Related papers

Related papers: Informational Divergence Approximations to Product…

200 papers

Given a pair of predictor variables and a response variable, how much information do the predictors have about the response, and how is this information distributed between unique, redundant, and synergistic components? Recent work has…

Information Theory · Computer Science 2018-10-29 Pradeep Kr. Banerjee , Johannes Rauh , Guido Montúfar

Information functionals allow to quantify the degree of randomness of a given probability distribution, either absolutely (through min/max entropy principles) or relative to a prescribed reference one. Our primary aim is to analyze the…

Quantum Physics · Physics 2007-11-22 Piotr Garbaczewski

Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible $N$--point correlation is measured by a decrease…

Biological Physics · Physics 2016-09-08 Elad Schneidman , Susanne Still , Michael J. Berry , William Bialek

Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…

Numerical Analysis · Mathematics 2015-03-19 Kamaljit Chowdhary , Paul Dupuis

We prove lower bounds on the error of any estimator for the mean of a real probability distribution under the knowledge that the distribution belongs to a given set. We apply these lower bounds both to parametric and nonparametric…

Statistics Theory · Mathematics 2024-03-05 Rémy Degenne , Timothée Mathieu

By employing various empirical estimators for the Mutual Information (MI) measure, we calculate and compare the estimates and their confidence intervals for both normal and non-normal bivariate data samples. We find that certain nonlinear…

Information Theory · Computer Science 2024-10-10 Theo Grigorenko , Leo Grigorenko

Finite precision approximations of discrete probability distributions are considered, applicable for distribution synthesis, e.g., probabilistic shaping. Two algorithms are presented that find the optimal $M$-type approximation $Q$ of a…

Information Theory · Computer Science 2017-05-08 Georg Böcherer , Bernhard C. Geiger

For a setting in which a large number of asymmetrically informed agents are randomly matched into groups over time, exchanging their information with each other when matched, we provide an explicit solution for the dynamics of the…

Probability · Mathematics 2008-11-20 Darrell Duffie , Gaston Giroux , Gustavo Manso

We study the problem of data integration from sources that contain probabilistic uncertain information. Data is modeled by possible-worlds with probability distribution, compactly represented in the probabilistic relation model. Integration…

Databases · Computer Science 2016-07-20 Fereidoon Sadri , Gayatri Tallur

The problem of how to properly quantify redundant information is an open question that has been the subject of much recent research. Redundant information refers to information about a target variable S that is common to two or more…

Information Theory · Computer Science 2017-07-14 Robin A. A. Ince

By combining a bound on the absolute value of the difference of mutual information between two joint probablity distributions with a fixed variational distance, and a bound on the probability of a maximal deviation in variational distance…

Information Theory · Computer Science 2013-01-29 A. G. Stefani , J. B. Huber , C. Jardin , H. Sticht

Notwithstanding various attempts to construct a Partial Information Decomposition (PID) for multiple variables by defining synergistic, redundant, and unique information, there is no consensus on how one ought to precisely define either of…

Data Analysis, Statistics and Probability · Physics 2023-06-07 Steven J. van Enk

The average uncertainty associated with words is an information-theoretic concept at the heart of quantitative and computational linguistics. The entropy has been established as a measure of this average uncertainty - also called average…

Computation and Language · Computer Science 2016-06-23 Christian Bentz , Dimitrios Alikaniotis

R\'enyi divergence is related to R\'enyi entropy much like information divergence (also called Kullback-Leibler divergence or relative entropy) is related to Shannon's entropy, and comes up in many settings. It was introduced by R\'enyi as…

Information Theory · Computer Science 2010-05-28 Tim van Erven , Peter Harremoës

The entropy production is commonly interpreted as measuring the distance from equilibrium. However, this explanation lacks a rigorous description due to the absence of a natural equilibrium measure. The present analysis formalizes this…

Statistical Mechanics · Physics 2025-10-23 David Andrieux

An information-theoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Let $P_{S_n}$ be the distribution of a sum $S_n=\Sumn Y_i$ of…

Probability · Mathematics 2019-06-05 A. D. Barbour , Oliver Johnson , Ioannis Kontoyiannis , Mokshay Madiman

Wyner's common information was originally defined for a pair of dependent discrete random variables. Its significance is largely reflected in, hence also confined to, several existing interpretations in various source coding problems. This…

Information Theory · Computer Science 2013-01-11 Ge Xu , Wei Liu , Biao Chen

This paper proposes a unifying variational approach for proving and extending some fundamental information theoretic inequalities. Fundamental information theory results such as maximization of differential entropy, minimization of Fisher…

Information Theory · Computer Science 2016-02-05 Sangwoo Park , Erchin Serpedin , Khalid Qaraqe

We establish the first known upper bound on the exact and Wyner's common information of $n$ continuous random variables in terms of the dual total correlation between them (which is a generalization of mutual information). In particular, we…

Information Theory · Computer Science 2018-12-11 Cheuk Ting Li , Abbas El Gamal

Information theory provides a mathematical foundation to measure uncertainty in belief. Belief is represented by a probability distribution that captures our understanding of an outcome's plausibility. Information measures based on…

Information Theory · Computer Science 2020-01-17 Jed A. Duersch , Thomas A. Catanach