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Document type:
Buchbeitrag 
Author(s):
Améndola, Carlos; Drton, Mathias; Sturmfels, Bernd 
Title:
Maximum Likelihood Estimates for Gaussian Mixtures Are Transcendental 
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