User: Guest  Login
Title:

Maximum Likelihood Estimates for Gaussian Mixtures Are Transcendental

Document type:
Buchbeitrag
Author(s):
Améndola, Carlos; Drton, Mathias; Sturmfels, Bernd
Pages contribution:
579-590
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.
Keywords:
Algebraic statistics, Expectation maximization, Maximum likelihood, Mixture model, Normal distribution, Transcendence theory
Dewey Decimal Classification:
510 Mathematik
Book title:
Mathematical Aspects of Computer and Information Sciences
Book subtitle:
6th International Conference, MACIS 2015, Berlin, Germany, November 11-13, 2015, Revised Selected Papers
Publisher:
Springer International Publishing
Date of publication:
16.04.2016
Year:
2016
Quarter:
2. Quartal
Year / month:
2016-04
Month:
Apr
Pages:
579-590
Print-ISBN:
97833193285849783319328591
Language:
en
DOI:
doi:10.1007/978-3-319-32859-1_49
 BibTeX