Global Convergence of the EM Algorithm for Unconstrained Latent Variable Models with Categorical Indicators

作     者：Weissman, Alexander 

作者机构：Law Sch Admiss Council Newtown PA 18940 USA 

出 版 物：《PSYCHOMETRIKA》 (心理测量学)

年 卷 期：2013年第78卷第1期

页      面：134-153页

核心收录：

学科分类：0402[教育学-心理学(可授教育学、理学学位）] 04[教育学] 0701[理学-数学] 

主　　题：EM algorithm latent variable models latent class models information theory Kullback-Leibler divergence relative entropy variational calculus convex optimization optimal bounds 

摘      要：Convergence of the expectation-maximization (EM) algorithm to a global optimum of the marginal log likelihood function for unconstrained latent variable models with categorical indicators is presented. The sufficient conditions under which global convergence of the EM algorithm is attainable are provided in an information-theoretic context by interpreting the EM algorithm as alternating minimization of the Kullback-Leibler divergence between two convex sets. It is shown that these conditions are satisfied by an unconstrained latent class model, yielding an optimal bound against which more highly constrained models may be compared.