Mathematics Colloquia and Seminars

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Description

Distinguishing between two distributions based on observed data is a classical problem in statistics and machine learning. But what if we aim to go further—not just test, but actually estimate a distribution close to the true one in, say, Kullback-Leibler divergence? Can we do this knowing only that the true distribution lies in a known class, without structural assumptions on the individual densities? In this talk, I will review classical results and present recent developments on this question. The focus will be on high-probability error bounds that are optimal up to constants in this general setting.