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SUMMARY:Convexity properties of information functionals for Gaussian mixtu
 res - Dr Lampros Gavalakis\, Gustave Eiffel University
DTSTART:20240117T140000Z
DTEND:20240117T150000Z
UID:TALK209251@talks.cam.ac.uk
CONTACT:Dr Varun Jog
DESCRIPTION:We consider the entropy and Fisher information of Gaussian mix
 tures\, that is centered Gaussians with randomly chosen variance. For the 
 entropy\, we will show that a concavity conjecture of  Ball\, Nayar and Tk
 ocz (2016) holds true for this class of random variables.  For the Fisher 
 information\, we will first present a simple upper bound. In order to exte
 nd this bound to higher dimensions\, we will show that the Fisher informat
 ion matrix is in general operator convex as a matrix-valued functional of 
 the density\, extending a result of Bobkov (2022). Finally\, as an applica
 tion\, we will discuss convergence rates for the Fisher information of wei
 ghted sums of Gaussian mixtures in the CLT.\n\nThis is joint work with Ale
 xandros Eskenazis (Sorbonne and Cambridge).
LOCATION:MR5\, CMS Pavilion A
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