Some techniques in density estimation

Abstract

Density estimation is an interdisciplinary topic at the intersection of statistics, theoretical computer science and machine learning. We review some old and new techniques for bounding the sample complexity of estimating densities of continuous distributions, focusing on the class of mixtures of Gaussians and its subclasses. In particular, we review the main techniques used to prove the new sample complexity bounds for mixtures of Gaussians by Ashtiani, Ben-David, Harvey, Liaw, Mehrabian, and Plan arXiv:1710.05209.

18 pages; new version includes tight results on mixtures of general Gaussians