Morgane Austern- Columbia University
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Title: Limit theorems for random structures and functions of exchangeable structures.
Abstract: Limit theorems are the theoretical foundation of statistical inference. Motivated by applications in statistics and machine learning we extend those beyond classical settings. Firstly, we consider empirical averages on distributionally 鈥漵tructured鈥� random objects鈥� i.e random objects whose distribution is invariant under the action of an amenable group. We show, under mild moment and mixing conditions, a series of universal second and third order limit theorems: central-limit theorems, concentration inequalities and Berry-Esseen bounds. Beyond empirical averages, we consider general functions of exchangeable structures, for which we provide鈥攗nder mild stability conditions鈥� general central-limit theorems. The utility of these will be illustrated by a series of example in machine learning theory, network theory and information theory.
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