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  • 标题:Statistical convergence of the EM algorithm on Gaussian mixture models
  • 本地全文:下载
  • 作者:Ruofei Zhao ; Yuanzhi Li ; Yuekai Sun
  • 期刊名称:Electronic Journal of Statistics
  • 印刷版ISSN:1935-7524
  • 出版年度:2020
  • 卷号:14
  • 期号:1
  • 页码:632-660
  • DOI:10.1214/19-EJS1660
  • 语种:English
  • 出版社:Institute of Mathematical Statistics
  • 摘要:We study the convergence behavior of the Expectation Maximization (EM) algorithm on Gaussian mixture models with an arbitrary number of mixture components and mixing weights. We show that as long as the means of the components are separated by at least $\Omega (\sqrt{\min \{M,d\}})$, where $M$ is the number of components and $d$ is the dimension, the EM algorithm converges locally to the global optimum of the log-likelihood. Further, we show that the convergence rate is linear and characterize the size of the basin of attraction to the global optimum.
  • 关键词:EM algorithm; Gaussian mixture models
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