FIXED POINTS OF THE EM ALGORITHM AND NONNEGATIVE RANK BOUNDARIES

Kaie Kubjas*, Elina Robeva, Bernd Sturmfels

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

20 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)422-461
Number of pages40
JournalANNALS OF STATISTICS
Volume43
Issue number1
DOIs
Publication statusPublished - Feb 2015
MoE publication typeA1 Journal article-refereed

Keywords

  • Maximum likelihood
  • EM algorithm
  • mixture model
  • nonnegative rank
  • MATRIX FACTORIZATION
  • LIKELIHOOD
  • GEOMETRY
  • MODELS

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