FIXED POINTS EM ALGORITHM AND NONNEGATIVE RANK BOUNDARIES

• 成果类型: Article
• 署名作者: Kubjas, Kaie; Robeva, Elina; Sturmfels, Bernd
• 署名单位: Aalto University; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1282
• 发表日期: 2015
• 页码: 422-461
• 关键词: maximum-likelihood; factorizations; matrices; models

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.