ArticleEntropy (Basel, Switzerland)2022
Revisiting Chernoff Information with Likelihood Ratio Exponential Families.
Article in Entropy (Basel, Switzerland), 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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10 citing papers in PubMed.
- Weighted Chernoff Information and Optimal Loss Exponent in Context-Sensitive Hypothesis Testing.Entropy (Basel, Switzerland) · 2026Article
- Two Types of Geometric Jensen-Shannon Divergences.Entropy (Basel, Switzerland) · 2025Article
- Tight Bounds Between the Jensen-Shannon Divergence and the Minmax Divergence.Entropy (Basel, Switzerland) · 2025Article
- Fast Proxy Centers for the Jeffreys Centroid: The Jeffreys-Fisher-Rao Center and the Gauss-Bregman Inductive Center.Entropy (Basel, Switzerland) · 2024Article
- Joint Detection and Communication over Type-Sensitive Networks.Entropy (Basel, Switzerland) · 2023Article
- Information and Divergence Measures.Entropy (Basel, Switzerland) · 2023Article
- The Cauchy Distribution in Information Theory.Entropy (Basel, Switzerland) · 2023Article
- On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius.Entropy (Basel, Switzerland) · 2021Article
- An Elementary Introduction to Information Geometry.Entropy (Basel, Switzerland) · 2020Review
- Computational Information Geometry for Binary Classification of High-Dimensional Random Tensors.Entropy (Basel, Switzerland) · 2018Article
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Abstract
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 bounding the Bayes error in statistical hypothesis testing, the divergence found many other applications due to its empirical robustness property found in applications ranging from information fusion to quantum information. From the viewpoint of information theory, the Chernoff information can also be interpreted as a minmax symmetrization of the Kullback-Leibler divergence. In this paper, we first revisit the Chernoff information between two densities of a measurable Lebesgue space by considering the exponential families induced by their geometric mixtures: The so-called likelihood ratio exponential families. Second, we show how to (i) solve exactly the Chernoff information between any two univariate Gaussian distributions or get a closed-form formula using symbolic computing, (ii) report a closed-form formula of the Chernoff information of centered Gaussians with scaled covariance matrices and (iii) use a fast numerical scheme to approximate the Chernoff information between any two multivariate Gaussian distributions.
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