[Коллоквиум]: On robust mean estimation and k-means clustering

Никита Животовский In this talk we consider the robust algorithms for the k-means clustering problem where a quantizer is constructed based on N independent observations. We start with an overview of the methods of robust statistics. First, we discuss the median-of-means estimator. This simple estimator allows us to evaluate the mean of some heavy-tailed distribution as if this distribution was Gaussian. We discuss some extensions to the multivariate case. In the context of clustering, we present the media