Fast Bootstrapping Nonparametric Maximum Likelihood for Latent Mixture Models
Abstract
Estimating the mixing density of a latent mixture model is an important task in signal processing. Nonparametric maximum likelihood estimation is one popular approach to this problem. If the latent variable distribution is assumed to be continuous, then bootstrapping can be used to approximate it. However, traditional bootstrapping requires repeated evaluations on resampled data and is not scalable. In this letter, we construct a generative process to rapidly produce nonparametric maximum likelihood bootstrap estimates. Our method requires only a single evaluation of a novel two-stage optimization algorithm. Simulations and real data analyses demonstrate that our procedure accurately estimates the mixing density with little computational cost even when there are a hundred thousand observations.
Cite
@article{arxiv.2402.18748,
title = {Fast Bootstrapping Nonparametric Maximum Likelihood for Latent Mixture Models},
author = {Shijie Wang and Minsuk Shin and Ray Bai},
journal= {arXiv preprint arXiv:2402.18748},
year = {2024}
}
Comments
6 pages (main article is 4 pages, one page of references, and one page Appendix). 5 figures and 4 tables. This paper supersedes a previously circulated technical report by S. Wang and M. Shin (arXiv:2006.00767v2.pdf)