Some techniques in density estimation
This is an incremental review paper that synthesizes existing methods for researchers in statistics and machine learning working on density estimation problems.
The paper reviews techniques for bounding sample complexity in density estimation, focusing on mixtures of Gaussians and summarizing recent results that provide new sample complexity bounds for this class.
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.