Local Glivenko-Cantelli: Estimating the Mean in Infinite Dimensions

Explore a 59-minute lecture on Local Glivenko-Cantelli theory and mean estimation in infinite dimensions, delivered by Professor Aryeh Kontorovich from Ben-Gurion University. Dive into the mathematical challenges of estimating means in the d-dimensional Boolean cube using empirical mean estimators, with a focus on establishing dimension-free estimates. Learn about the novel sub-Gamma-type maximal inequality for shifted Bernoullis and discover the necessary conditions for convergence in product measures. Understand the transition from Universal to Local Glivenko-Cantelli settings, where distribution-dependent bounds become necessary for infinite-dimensional cases. Benefit from the expertise of Prof. Kontorovich, a distinguished researcher in machine learning, probability, and statistics, who currently serves as the director of the Ben-Gurion University Data Science Research Center. Engage with cutting-edge research problems presented from his joint work with Doron Cohen, while gaining insights into this complex mathematical domain.