Perturbation of matrices and non-negative rank with a view toward statistical models

Cristiano Bocci; Enrico Carlini; Fabio Rapallo

Perturbation of matrices and non-negative rank with a view toward statistical models

Combinatorics 2011-07-21 v3 Commutative Algebra Probability Statistics Theory Statistics Theory

Authors: Cristiano Bocci , Enrico Carlini , Fabio Rapallo

Abstract

In this paper we study how perturbing a matrix changes its non-negative rank. We prove that the non-negative rank is upper-semicontinuos and we describe some special families of perturbations. We show how our results relate to Statistics in terms of the study of Maximum Likelihood Estimation for mixture models.

Keywords

non-negative rank matrix perturbation upper-semicontinuity maximum likelihood estimation mixture models

Cite

@article{arxiv.1010.3566,
  title  = {Perturbation of matrices and non-negative rank with a view toward statistical models},
  author = {Cristiano Bocci and Enrico Carlini and Fabio Rapallo},
  journal= {arXiv preprint arXiv:1010.3566},
  year   = {2011}
}

Comments

13 pages, 3 figures. A theorem has been rewritten, and some improvements in the presentations have been implemented

Perturbation of matrices and non-negative rank with a view toward statistical models

Abstract

Keywords

Cite

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