Global Convergence of Least Squares EM for Demixing Two Log-Concave Densities
Abstract
This work studies the location estimation problem for a mixture of two rotation invariant log-concave densities. We demonstrate that Least Squares EM, a variant of the EM algorithm, converges to the true location parameter from a randomly initialized point. Moreover, we establish the explicit convergence rates and sample complexity bounds, revealing their dependence on the signal-to-noise ratio and the tail property of the log-concave distributions. Our analysis generalizes previous techniques for proving the convergence results of Gaussian mixtures, and highlights that an angle-decreasing property is sufficient for establishing global convergence for Least Squares EM.
Cite
Text
Qian et al. "Global Convergence of Least Squares EM for Demixing Two Log-Concave Densities." Neural Information Processing Systems, 2019.Markdown
[Qian et al. "Global Convergence of Least Squares EM for Demixing Two Log-Concave Densities." Neural Information Processing Systems, 2019.](https://mlanthology.org/neurips/2019/qian2019neurips-global/)BibTeX
@inproceedings{qian2019neurips-global,
title = {{Global Convergence of Least Squares EM for Demixing Two Log-Concave Densities}},
author = {Qian, Wei and Zhang, Yuqian and Chen, Yudong},
booktitle = {Neural Information Processing Systems},
year = {2019},
pages = {4794-4802},
url = {https://mlanthology.org/neurips/2019/qian2019neurips-global/}
}