FIXED POINTS EM ALGORITHM AND NONNEGATIVE RANK BOUNDARIES

Mixtures of r independent distributions for two discrete random variables can be represented by matrices of nonnegative rank r. Likelihood inference for the model of such joint distributions leads to problems in real algebraic geometry that are addressed here for the first time. We characterize the...

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Bibliographic Details
Published in:The Annals of statistics 2015-02, Vol.43 (1), p.422-461
Main Authors: Kubjas, Kaie, Robeva, Elina, Sturmfels, Bernd
Format: Article
Language:English
Subjects:
13P25
62F10
EM algorithm
Maximum likelihood
mixture model
nonnegative rank
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Summary:Mixtures of r independent distributions for two discrete random variables can be represented by matrices of nonnegative rank r. Likelihood inference for the model of such joint distributions leads to problems in real algebraic geometry that are addressed here for the first time. We characterize the set of fixed points of the Expectation-Maximization algorithm, and we study the boundary of the space of matrices with nonnegative rank at most 3. Both of these sets correspond to algebraic varieties with many irreducible components.
ISSN:0090-5364
2168-8966
DOI:10.1214/14-AOS1282