Optimal Concentration of Information Content For Log-Concave Densities
Matthieu Fradelizi, Mokshay Madiman, Liyao Wang
TL;DR
This paper provides elementary proofs of sharp bounds on varentropy and information content deviations for log-concave densities, improving previous bounds and enhancing understanding of their concentration properties.
Contribution
It introduces simpler proofs of optimal bounds for varentropy and information content deviations in log-concave densities, surpassing earlier results.
Findings
Sharp bounds for varentropy of log-concave densities
Improved bounds for deviations of information content
Elementary proof techniques for concentration inequalities
Abstract
An elementary proof is provided of sharp bounds for the varentropy of random vectors with log-concave densities, as well as for deviations of the information content from its mean. These bounds significantly improve on the bounds obtained by Bobkov and Madiman ({\it Ann. Probab.}, 39(4):1528--1543, 2011).
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Taxonomy
TopicsWireless Communication Security Techniques · Stochastic Gradient Optimization Techniques · Sparse and Compressive Sensing Techniques