Strongly Convex Divergences

Abstract

We consider a sub-class of the $f$-divergences satisfying a stronger convexity property, which we refer to as strongly convex, or $\kappa$-convex divergences. We derive new and old relationships, based on convexity arguments, between popular $f$-divergences.

arXiv commentSubmitted to Entropy, special issue, Divergence Measures: Mathematical Foundations and Applications in Information-Theoretic and Statistical Problems, edited by Igal Sason

References in corpus (8)

• Rényi Divergence and Kullback-Leibler Divergence
• $f$-divergence Inequalities
• On a generalization of the Jensen-Shannon divergence
• On the Chi square and higher-order Chi distances for approximating f-divergences
• Quantum Skew Divergence
• Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasi-arithmetic means
• On Relations Between the Relative entropy and ${\chi }^2$-Divergence, Generalizations and Applications
• On Data-Processing and Majorization Inequalities for $f$-Divergences with Applications

Cited by in corpus (2)

• The Differential Entropy of Mixtures: New Bounds and Applications
• Improving the convergence of Markov chains via permutations and projections