Speaker: Tomohiro Hayase (Univ. Tokyo)
Title: On Cauchy noise loss in a stochastic parameter optimization of random matrices
Time/Date: 4:45-6:15pm, Monday, January 22, 2018.
Abstract: Motivated by engineering and statistics, we consider an inverse problem of random matrices (RM); how to estimate parameters of a RM from a single-shot observation? We focus on empirical eigenvalue distributions of RM because it can be approximated by deterministic equivalents (DE). Moreover, recent tools of free probability make it possible to compute DE numerically by iterating algorithms. Based on them, this talk introduces a stochastic optimization algorithm; minimizing "Cauchy noise loss" which is defined as empirical cross entropy of hyperfunction representation (imaginary part of Cauchy transform of DE). No knowledge on free probability, random matrices or stochastic optimization is assumed for the talk.