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The mutual information is a core statistical quantity that has applications in all areas of machine learning, whether this is in training of density models over multiple data modalities, in maximising the efficiency of noisy transmission…

Machine Learning · Statistics 2015-09-30 Shakir Mohamed , Danilo Jimenez Rezende

We examine a class of deep learning models with a tractable method to compute information-theoretic quantities. Our contributions are three-fold: (i) We show how entropies and mutual informations can be derived from heuristic statistical…

Machine Learning · Computer Science 2020-01-22 Marylou Gabrié , Andre Manoel , Clément Luneau , Jean Barbier , Nicolas Macris , Florent Krzakala , Lenka Zdeborová

We study how the Shannon entropy of sequences produced by an information source converges to the source's entropy rate. We synthesize several phenomenological approaches to applying information theoretic measures of randomness and memory to…

Statistical Mechanics · Physics 2007-05-23 James P. Crutchfield , David P. Feldman

We propose a new framework for reasoning about information in complex systems. Our foundation is based on a variational extension of Shannon's information theory that takes into account the modeling power and computational constraints of…

Machine Learning · Computer Science 2020-02-26 Yilun Xu , Shengjia Zhao , Jiaming Song , Russell Stewart , Stefano Ermon

In network science, researchers often use mutual information to understand the difference between network partitions produced by community detection methods. Here we extend the use of mutual information to covers, that is, the cases where a…

Mathematical Physics · Physics 2012-02-03 Alcides Viamontes Esquivel , Martin Rosvall

We derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the…

Quantum Physics · Physics 2025-05-16 Wojciech Górecki , Xi Lu , Chiara Macchiavello , Lorenzo Maccone

This paper considers the problem of appearance indication of useful acoustic signal in the signal/noise mixture. Various information characteristics (information entropy, Jensen-Shannon divergence, spectral information divergence and…

Methodology · Statistics 2023-04-14 Leonid Berlin , Andrey Galyaev , Pavel Lysenko

The aim of this work is to provide bounds connecting two probability measures of the same event using R\'enyi $\alpha$-Divergences and Sibson's $\alpha$-Mutual Information, a generalization of respectively the Kullback-Leibler Divergence…

Information Theory · Computer Science 2020-01-20 Amedeo Roberto Esposito , Michael Gastpar , Ibrahim Issa

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

Machine Learning · Computer Science 2007-07-13 Marcus Hutter , Marco Zaffalon

We study some of the most commonly used mutual information estimators, based on histograms of fixed or adaptive bin size, $k$-nearest neighbors and kernels, and focus on optimal selection of their free parameters. We examine the consistency…

Data Analysis, Statistics and Probability · Physics 2015-05-13 Angeliki Papana , Dimitris Kugiumtzis

Applying perturbation theory to the path-integral representation for the mutual information of the nonlinear communication channel described by the nonlinear Shr\"{o}dinger equation (NLSE) with the additive Gaussian noise we analyze the…

Information Theory · Computer Science 2016-08-19 I. S. Terekhov , A. V. Reznichenko , S. K. Turitsyn

The problem of calculating the rate of mutual information between two coarse-grained variables that together specify a continuous time Markov process is addressed. As a main obstacle, the coarse-grained variables are in general…

Statistical Mechanics · Physics 2013-10-01 Andre Cardoso Barato , David Hartich , Udo Seifert

Among all data augmentation techniques proposed so far, linear interpolation of training samples, also called Mixup, has found to be effective for a large panel of applications. Along with improved predictive performance, Mixup is also a…

Machine Learning · Computer Science 2025-03-20 Quentin Bouniot , Pavlo Mozharovskyi , Florence d'Alché-Buc

We study the problem of identifying correlations in multivariate data, under information constraints: Either on the amount of memory that can be used by the algorithm, or the amount of communication when the data is distributed across…

Machine Learning · Computer Science 2018-06-07 Yuval Dagan , Ohad Shamir

The development of optimal and efficient machine learning-based communication systems is likely to be a key enabler of beyond 5G communication technologies. In this direction, physical layer design has been recently reformulated under a…

Information Theory · Computer Science 2021-11-16 Nunzio A. Letizia , Andrea M. Tonello

A mixture of experts models the conditional density of a response variable using a mixture of regression models with covariate-dependent mixture weights. We extend the finite mixture of experts model by allowing the parameters in both the…

Computation · Statistics 2022-10-14 Parfait Munezero , Mattias Villani , Robert Kohn

Ensemble learning combines several individual models to obtain a better generalization performance. In this work we present a practical method for estimating the joint power of several classifiers. It differs from existing approaches which…

Artificial Intelligence · Computer Science 2023-12-22 Simi Haber , Yonatan Wexler

In this study, the cumulative effect of the empirical probability distribution of a random variable is identified as a factor that amplifies the occurrence of extreme events in datasets. To quantify this observation, a corresponding…

Recommendations based on behavioral data may be faced with ambiguous statistical evidence. We consider the case of association rules, relevant e.g.~for query and product recommendations. For example: Suppose that a customer belongs to…

Databases · Computer Science 2015-01-12 Rasmus Pagh , Morten Stöckel

Heterogeneous data from multiple populations, sub-groups, or sources is often represented as a ``mixture model'' with a single latent class influencing all of the observed covariates. Heterogeneity can be resolved at multiple levels by…

Machine Learning · Computer Science 2024-12-16 Bijan Mazaheri , Chandler Squires , Caroline Uhler