FIXED POINTS EM ALGORITHM AND NONNEGATIVE RANK BOUNDARIES

被引：24

作者：

Kubjas, Kaie ^{[1
]}

Robeva, Elina ^{[2
]}

Sturmfels, Bernd ^{[2
]}

机构：

[1] Aalto Univ, Aalto Sci Inst, FI-00076 Aalto, Finland

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

来源：

ANNALS OF STATISTICS | 2015年 / 43卷 / 01期

基金：

美国国家科学基金会;

关键词：

Maximum likelihood; EM algorithm; mixture model; nonnegative rank; MAXIMUM-LIKELIHOOD; FACTORIZATIONS; MATRICES; MODELS;

D O I：

10.1214/14-AOS1282

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：422 / 461

页数：40

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