Summary
The 2018 International Symposium on Information Theory and Its Applications　(ISITA2018)
2018
Session Number:Mo-AM-1-3
Session:
Number:Mo-AM-1-3.3
Convexity of mutual information along the Ornstein-Uhlenbeck flow
Andre Wibisono, Varun Jog,
pp.55-59
Publication Date:2018/10/18
Online ISSN:2188-5079
DOI:10.34385/proc.55.Mo-AM-1-3.3
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Summary:
We study the convexity of mutual information as a function of time along the flow of the Ornstein-Uhlenbeck process. We prove that if the initial distribution is strongly log-concave, then mutual information is eventually convex, i.e., convex for all large time. In particular, if the initial distribution is sufficiently strongly log-concave compared to the target Gaussian measure, 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. Finally, we provide counterexamples to show that mutual information can be nonconvex at small time.