Convergence of a stochastic approximation version of the EM algorithm

• 成果类型: Article
• 署名作者: Delyon, B; Lavielle, V; Moulines, E
• 署名单位: Inria; Universite Paris Cite; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1999
• 页码: 94-128
• 关键词: carlo maximum-likelihood; ecm algorithm

摘要

The expectation-maximization (EM) algorithm isa powerful computational technique for locating maxima of functions. It is widely used in statistics for maximum likelihood or maximum a posteriori estimation in incomplete data models. In certain situations, however, this method is not applicable because the expectation step cannot be performed in closed form. To deal with these problems, a novel method is introduced, the stochastic approximation EM (SAEM), which replaces the expectation step of the EM algorithm by one iteration of a stochastic approximation procedure. The convergence of the SAEM algorithm is established under conditions that are applicable to many practical situations. Moreover,it is proved that, under mild additional conditions, the attractive stationary points of the SAEM algorithm correspond to the local maxima of the function. presented to support our findings.