Abstract:
Recently, it was shown that the Fisher information is log-convex along the heat flow. The main tools involved were the Cauchy-Schwarz inequality and clever observations o...Show MoreMetadata
Abstract:
Recently, it was shown that the Fisher information is log-convex along the heat flow. The main tools involved were the Cauchy-Schwarz inequality and clever observations on the sum of squares. In this work, we reformulate their method as a rank-one constrained semidefinite programming problem. Then we show that the rank-one matrix can be determined through investigating the first diagonal entry. We apply this new approach to recover existing results, as well as to obtain new results on the derivative of the negative Fisher information along the heat flow: the derivative is convex if it is raised to the power of three-eighths, and is log-convex if the input distribution is log-concave.
Published in: 2024 IEEE Information Theory Workshop (ITW)
Date of Conference: 24-28 November 2024
Date Added to IEEE Xplore: 30 December 2024
ISBN Information: