The Annals of Statistics

Fixed points of the EM algorithm and nonnegative rank boundaries

Kaie Kubjas, Elina Robeva, and Bernd Sturmfels

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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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Ann. Statist., Volume 43, Number 1 (2015), 422-461.

First available in Project Euclid: 6 February 2015

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Primary: 62F10: Point estimation 13P25: Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)

Maximum likelihood EM algorithm mixture model nonnegative rank


Kubjas, Kaie; Robeva, Elina; Sturmfels, Bernd. Fixed points of the EM algorithm and nonnegative rank boundaries. Ann. Statist. 43 (2015), no. 1, 422--461. doi:10.1214/14-AOS1282.

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