Convexity of mutual information along the heat flow

Andre Wibisono; Varun Jog

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arXiv · 1801.06968

Convexity of mutual information along the heat flow

Andre Wibisono·Varun Jog

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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.

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Andre Wibisono, Varun Jog. 2018-01-22. Convexity of mutual information along the heat flow. https://arxiv.org/abs/1801.06968

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