English
Related papers

Related papers: On Sibson's $\alpha$-Mutual Information

200 papers

We explore a large class of correlation measures called the $\alpha-z$ R\'enyi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of R\'enyi entropies, the $\alpha-z$ RMIs are positive…

High Energy Physics - Theory · Physics 2024-08-27 Jonah Kudler-Flam , Laimei Nie , Akash Vijay

We define the information threshold as the point of maximum curvature in the prior vs. posterior Bayesian curve, both of which are described as a function of the true positive and negative rates of the classification system in question. The…

Machine Learning · Statistics 2022-06-07 Jacques Balayla

Inequality measures provide a valuable tool for the analysis, comparison, and optimization based on system models. This work studies the relation between attributes or features of an individual to understand how redundant, unique, and…

Information Theory · Computer Science 2024-07-08 Tobias Mages , Christian Rohner

The analogues of Arimoto's definition of conditional R\'enyi entropy and R\'enyi mutual information are explored for abstract alphabets. These quantities, although dependent on the reference measure, have some useful properties similar to…

Information Theory · Computer Science 2021-10-20 Gautam Aishwarya , Mokshay Madiman

R\'enyi divergence is related to R\'enyi entropy much like Kullback-Leibler divergence is related to Shannon's entropy, and comes up in many settings. It was introduced by R\'enyi as a measure of information that satisfies almost the same…

Information Theory · Computer Science 2014-04-25 Tim van Erven , Peter Harremoës

The inverse relation between mutual information (MI) and Bayesian error is sharpened by deriving finite sequences of upper and lower bounds on MI in terms of the minimum probability of error (MPE) and related Bayesian quantities. The well…

Information Theory · Computer Science 2014-09-24 Sudhakar Prasad

This paper considers derivation of $f$-divergence inequalities via the approach of functional domination. Bounds on an $f$-divergence based on one or several other $f$-divergences are introduced, dealing with pairs of probability measures…

Information Theory · Computer Science 2016-10-31 Igal Sason , Sergio Verdú

Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…

Artificial Intelligence · Computer Science 2008-06-26 Marco Zaffalon , Marcus Hutter

Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…

Artificial Intelligence · Computer Science 2014-08-08 Marco Zaffalon , Marcus Hutter

An information theoretic approach to bounds in superconformal field theories is proposed. It is proved that the supersymmetric R\'enyi entropy $\bar S_\alpha$ is a monotonically decreasing function of $\alpha$ and $(\alpha-1)\bar S_\alpha$…

High Energy Physics - Theory · Physics 2023-03-03 Yang Zhou

We present a variational characterization for the R\'{e}nyi divergence of order infinity. Our characterization is related to guessing: the objective functional is a ratio of maximal expected values of a gain function applied to the…

Information Theory · Computer Science 2022-05-03 Gowtham R. Kurri , Oliver Kosut , Lalitha Sankar

The R\'enyi information measures are characterized in terms of their Shannon counterparts, and properties of the former are recovered from first principle via the associated properties of the latter. Motivated by this characterization, a…

Information Theory · Computer Science 2016-03-14 Ofer Shayevitz

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

Information divergence functions play a critical role in statistics and information theory. In this paper we show that a non-parametric f-divergence measure can be used to provide improved bounds on the minimum binary classification…

Information Theory · Computer Science 2015-02-11 Visar Berisha , Alan Wisler , Alfred O. Hero , Andreas Spanias

Mutual information is fundamentally important for measuring statistical dependence between variables and for quantifying information transfer by signaling and communication mechanisms. It can, however, be challenging to evaluate for…

Information Theory · Computer Science 2014-07-29 Clive G. Bowsher , Margaritis Voliotis

Quantum information quantities, such as mutual information and entropies, are essential for characterizing quantum systems and protocols in quantum information science. In this contribution, we identify types of information measures based…

Quantum Physics · Physics 2025-10-21 Christopher Popp , Tobias C. Sutter , Beatrix C. Hiesmayr

We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tool are the information theory…

Statistical Mechanics · Physics 2009-11-13 Piotr Garbaczewski

Mutual information is commonly used as a measure of similarity between competing labelings of a given set of objects, for example to quantify performance in classification and community detection tasks. As argued recently, however, the…

Social and Information Networks · Computer Science 2025-07-17 Maximilian Jerdee , Alec Kirkley , M. E. J. Newman

Under the Bayesian brain hypothesis, behavioural variations can be attributed to different priors over generative model parameters. This provides a formal explanation for why individuals exhibit inconsistent behavioural preferences when…

Neurons and Cognition · Quantitative Biology 2021-07-13 Noor Sajid , Francesco Faccio , Lancelot Da Costa , Thomas Parr , Jürgen Schmidhuber , Karl Friston

We evaluate the asymptotics of equivocations, their exponents as well as their second-order coding rates under various R\'{e}nyi information measures. Specifically, we consider the effect of applying a hash function on a source and we…

Information Theory · Computer Science 2016-07-06 Masahito Hayashi , Vincent Y. F. Tan