Quantization of Probability Distributions

This lecture explores the quantization of probability distributions under minimal moment assumptions, focusing on statistical k-means clustering and mean estimation. It covers the distortion measure, empirical optimal quantizer, asymptotic normality, heavy-tailed distributions, and robust mean estimation. Landmark results, exponential inequalities, and robust clustering methods are discussed. The lecture delves into higher dimensions, multivariate cases, Voronoi diagrams, and main results related to quantization. Lower bounds and informal conclusions regarding robust statistical clustering are also presented, along with open questions for further research.