Maximum Likelihood Estimates for Gaussian Mixtures Are Transcendental
Statistics Theory
2019-04-19 v2 Optimization and Control
Statistics Theory
Abstract
Gaussian mixture models are central to classical statistics, widely used in the information sciences, and have a rich mathematical structure. We examine their maximum likelihood estimates through the lens of algebraic statistics. The MLE is not an algebraic function of the data, so there is no notion of ML degree for these models. The critical points of the likelihood function are transcendental, and there is no bound on their number, even for mixtures of two univariate Gaussians.
Cite
@article{arxiv.1508.06958,
title = {Maximum Likelihood Estimates for Gaussian Mixtures Are Transcendental},
author = {Carlos Améndola and Mathias Drton and Bernd Sturmfels},
journal= {arXiv preprint arXiv:1508.06958},
year = {2019}
}
Comments
11 pages, 1 figure