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Probability density estimation from observed data constitutes a central task in statistics. In this brief, we focus on the problem of estimating the copula density associated to any observed data, as it fully describes the dependence…

Machine Learning · Computer Science 2025-07-09 Nunzio A. Letizia , Nicola Novello , Andrea M. Tonello

We study the problem of estimating multiple discrete unimodal distributions, motivated by search behavior analysis on a real-world platform. To incorporate prior knowledge of precedence relations among distributions, we impose stochastic…

Optimization and Control · Mathematics 2026-03-13 Yasuhiro Yoshida , Noriyoshi Sukegawa , Jiro Iwanaga

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

Recent advances in statistical learning theory have revealed profound connections between mutual information (MI) bounds, PAC-Bayesian theory, and Bayesian nonparametrics. This work introduces a novel mutual information bound for…

Machine Learning · Statistics 2025-08-18 El Mahdi Khribch , Pierre Alquier

We study the generic scaling properties of the mutual information between two disjoint intervals, in a class of one-dimensional quantum critical systems described by the c=1 bosonic field theory. A numerical analysis of a spin-chain model…

Statistical Mechanics · Physics 2009-04-30 Shunsuke Furukawa , Vincent Pasquier , Jun'ichi Shiraishi

The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…

Information Theory · Computer Science 2021-11-29 Georg Pichler , Pablo Piantanida , Günther Koliander

We introduce a novel Mutual Information (MI) estimator that fundamentally reframes the discriminative approach. Instead of training a classifier to discriminate between joint and marginal distributions, we learn a normalizing flow that…

Machine Learning · Computer Science 2026-02-10 Ivan Butakov , Alexander Semenenko , Valeriya Kirova , Alexey Frolov , Ivan Oseledets

This work considers the problem of Distributed Mean Estimation (DME) over networks with intermittent connectivity, where the goal is to learn a global statistic over the data samples localized across distributed nodes with the help of a…

Information Theory · Computer Science 2023-03-02 Rajarshi Saha , Mohamed Seif , Michal Yemini , Andrea J. Goldsmith , H. Vincent Poor

We study the problem of community detection when there is covariate information about the node labels and one observes multiple correlated networks. We provide an asymptotic upper bound on the per-node mutual information as well as a…

Information Theory · Computer Science 2019-12-12 Vaishakhi Mayya , Galen Reeves

The concepts of conditional mutual information (CMI) and normalized conditional mutual information (NCMI) are introduced to measure the concentration and separation performance of a classification deep neural network (DNN) in the output…

Machine Learning · Computer Science 2023-09-19 En-Hui Yang , Shayan Mohajer Hamidi , Linfeng Ye , Renhao Tan , Beverly Yang

By a mixture density is meant a density of the form $\pi_{\mu}(\cdot)=\int\pi_{\theta}(\cdot)\times\mu(d\theta)$, where $(\pi_{\theta})_{\theta\in\Theta}$ is a family of probability densities and $\mu$ is a probability measure on $\Theta$.…

Statistics Theory · Mathematics 2016-08-16 François Roueff , Tobias Rydén

Text-to-image generation and image captioning are recently emerged as a new experimental paradigm to assess machine intelligence. They predict continuous quantity accompanied by their sampling techniques in the generation, making evaluation…

Computer Vision and Pattern Recognition · Computer Science 2022-05-27 Jin-Hwa Kim , Yunji Kim , Jiyoung Lee , Kang Min Yoo , Sang-Woo Lee

We present a method for hierarchical clustering of data called {\it mutual information clustering} (MIC) algorithm. It uses mutual information (MI) as a similarity measure and exploits its grouping property: The MI between three objects $X,…

Quantitative Methods · Quantitative Biology 2007-05-23 Alexander Kraskov , Harald Stoegbauer , Ralph G. Andrzejak , Peter Grassberger

The asymptotic mutual information (MI) analysis for multiple-input multiple-output (MIMO) systems over double-scattering channels has achieved engaging results, but the convergence rates of the mean, variance, and the distribution of the MI…

Information Theory · Computer Science 2023-01-18 Xin Zhang , Shenghui Song

Estimation of the $\phi$-divergence between two unknown probability distributions using empirical data is a fundamental problem in information theory and statistical learning. We consider a multi-variate generalization of the data dependent…

Probability · Mathematics 2018-01-04 Fengqiao Luo , Sanjay Mehrotra

In machine learning, the performance of a classifier depends on both the classifier model and the separability/complexity of datasets. To quantitatively measure the separability of datasets, we create an intrinsic measure -- the…

Machine Learning · Computer Science 2021-09-14 Shuyue Guan , Murray Loew

Estimating the Shannon entropy of a discrete distribution from which we have only observed a small sample is challenging. Estimating other information-theoretic metrics, such as the Kullback-Leibler divergence between two sparsely sampled…

Data Analysis, Statistics and Probability · Physics 2023-02-24 Angelo Piga , Lluc Font-Pomarol , Marta Sales-Pardo , Roger Guimerà

Differential privacy is a precise mathematical constraint meant to ensure privacy of individual pieces of information in a database even while queries are being answered about the aggregate. Intuitively, one must come to terms with what…

Information Theory · Computer Science 2016-08-15 Paul Cuff , Lanqing Yu

The pointwise mutual information profile, or simply profile, is the distribution of pointwise mutual information for a given pair of random variables. One of its important properties is that its expected value is precisely the mutual…

Machine Learning · Statistics 2024-05-30 Paweł Czyż , Frederic Grabowski , Julia E. Vogt , Niko Beerenwinkel , Alexander Marx

Estimating and optimizing Mutual Information (MI) is core to many problems in machine learning; however, bounding MI in high dimensions is challenging. To establish tractable and scalable objectives, recent work has turned to variational…

Machine Learning · Computer Science 2019-05-17 Ben Poole , Sherjil Ozair , Aaron van den Oord , Alexander A. Alemi , George Tucker