Some techniques in density estimation

TL;DR

This paper reviews various techniques for density estimation, focusing on sample complexity bounds for mixtures of Gaussians, highlighting recent advances and key methods in the field.

Contribution

It provides a comprehensive review of both old and new techniques for bounding sample complexity in density estimation, especially for Gaussian mixtures.

Findings

Summarizes key techniques for density estimation.

Highlights recent bounds for Gaussian mixtures.

Discusses interdisciplinary approaches across statistics, CS, and ML.

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.