Photo by ldxcreative from unsplash
Recently, Ledoux, Nair, and Wang proved that the Fisher information along the heat flow is log-convex in dimension one, that is d2dt2log(I(Xt))≥0 for n=1, where Xt is a random variable… Click to show full abstract
Recently, Ledoux, Nair, and Wang proved that the Fisher information along the heat flow is log-convex in dimension one, that is d2dt2log(I(Xt))≥0 for n=1, where Xt is a random variable with density function satisfying the heat equation. In this paper, we consider the high dimensional case and prove that the Fisher information is square root convex in dimension two, that is d2dt2IX≥0 for n=2. The proof is based on the semidefinite programming approach.
Keywords:
information;
information along;
along heat;
fisher information;
dimension
Journal Title: Entropy
Year Published: 2023
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Entropy
Year Published: 2023
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!