Convexity of mutual information along the heat flow
Information Theory
2018-05-09 v2 math.IT
Abstract
We study the convexity of mutual information along the evolution of the heat equation. We prove that if the initial distribution is log-concave, then mutual information is always a convex function of time. We also prove that if the initial distribution is either bounded, or has finite fourth moment and Fisher information, then mutual information is eventually convex, i.e., convex for all large time. Finally, we provide counterexamples to show that mutual information can be nonconvex at small time.
Cite
@article{arxiv.1801.06968,
title = {Convexity of mutual information along the heat flow},
author = {Andre Wibisono and Varun Jog},
journal= {arXiv preprint arXiv:1801.06968},
year = {2018}
}
Comments
10 pages, 1 figure. To appear at the IEEE International Symposium on Information Theory (ISIT), June 2018