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February 2015 Fixed points of the EM algorithm and nonnegative rank boundaries
Kaie Kubjas, Elina Robeva, Bernd Sturmfels
Ann. Statist. 43(1): 422-461 (February 2015). DOI: 10.1214/14-AOS1282


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.


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Kaie Kubjas. Elina Robeva. Bernd Sturmfels. "Fixed points of the EM algorithm and nonnegative rank boundaries." Ann. Statist. 43 (1) 422 - 461, February 2015.


Published: February 2015
First available in Project Euclid: 6 February 2015

zbMATH: 1308.62035
MathSciNet: MR3311865
Digital Object Identifier: 10.1214/14-AOS1282

Primary: 13P25 , 62F10

Keywords: EM algorithm , maximum likelihood , mixture model , nonnegative rank

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.43 • No. 1 • February 2015
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