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Titel:

Maximum Likelihood Estimates for Gaussian Mixtures Are Transcendental

Dokumenttyp:
Buchbeitrag
Autor(en):
Améndola, Carlos; Drton, Mathias; Sturmfels, Bernd
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.
Seitenangaben Beitrag:
579-590
Stichworte:
Algebraic statistics, Expectation maximization, Maximum likelihood, Mixture model, Normal distribution, Transcendence theory
Dewey-Dezimalklassifikation:
510 Mathematik
Buchtitel:
Mathematical Aspects of Computer and Information Sciences
Titelzusatz:
6th International Conference, MACIS 2015, Berlin, Germany, November 11-13, 2015, Revised Selected Papers
Verlag / Institution:
Springer International Publishing
Publikationsdatum:
16.04.2016
Jahr:
2016
Quartal:
2. Quartal
Jahr / Monat:
2016-04
Monat:
Apr
Seiten/Umfang:
579-590
Print-ISBN:
97833193285849783319328591
Sprache:
en
DOI:
doi:10.1007/978-3-319-32859-1_49
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