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
收藏
页码：422 / 461
页数：40
相关论文
共 50 条
  • [41] A NOTE ON NONNEGATIVE RANK FACTORIZATIONS
    JETER, MW
    PYE, WC
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1981, 38 (JUN) : 171 - 173
  • [42] Lower bounds on nonnegative rank via nonnegative nuclear norms
    Fawzi, Hamza
    Parrilo, Pablo A.
    [J]. MATHEMATICAL PROGRAMMING, 2015, 153 (01) : 41 - 66
  • [43] On reduced rank nonnegative matrix factorization for symmetric nonnegative matrices
    Catral, M
    Han, LX
    Neumann, M
    Plemmons, RJ
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 393 : 107 - 126
  • [44] A Fixed-Point EM Algorithm for Straight Line Detection
    Fang, Chonglun
    Ma, Jinwen
    [J]. ADVANCES IN NEURAL NETWORKS - ISNN 2011, PT II, 2011, 6676 : 136 - +
  • [45] A New Approximation Algorithm for Fixed Points of Nonexpansive Mappings
    Su, Y.
    Agarwal, R. P.
    [J]. MATHEMATICAL MODELLING AND ANALYSIS, 2010, 15 (02) : 257 - 264
  • [46] The iterative turbo decoding algorithm has fixed points
    Duan, L
    Rimoldi, B
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2001, 47 (07) : 2993 - 2995
  • [47] An Iterative Algorithm on Approximating Fixed Points of Pseudocontractive Mappings
    Yu, Youli
    [J]. JOURNAL OF APPLIED MATHEMATICS, 2012,
  • [48] Lower bounds on nonnegative rank via nonnegative nuclear norms
    Hamza Fawzi
    Pablo A. Parrilo
    [J]. Mathematical Programming, 2015, 153 : 41 - 66
  • [49] A monotone projection algorithm for fixed points of nonlinear operators
    Changqun Wu
    Lijuan Sun
    [J]. Fixed Point Theory and Applications, 2013
  • [50] A monotone projection algorithm for fixed points of nonlinear operators
    Wu, Changqun
    Sun, Lijuan
    [J]. FIXED POINT THEORY AND APPLICATIONS, 2013,
12345