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Convexity properties of information functionals for Gaussian mixtures

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If you have a question about this talk, please contact Dr Varun Jog.

We consider the entropy and Fisher information of Gaussian mixtures, that is centered Gaussians with randomly chosen variance. For the entropy, we will show that a concavity conjecture of Ball, Nayar and Tkocz (2016) holds true for this class of random variables. For the Fisher information, we will first present a simple upper bound. In order to extend this bound to higher dimensions, we will show that the Fisher information matrix is in general operator convex as a matrix-valued functional of the density, extending a result of Bobkov (2022). Finally, as an application, we will discuss convergence rates for the Fisher information of weighted sums of Gaussian mixtures in the CLT .

This is joint work with Alexandros Eskenazis (Sorbonne and Cambridge).

This talk is part of the Information Theory Seminar series.

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