Hyper-EM for large recursive models of categorical variables

Abstract

When a recursive model is of a manageable size on a computing machine to use, whether it involves latent variables or not matters little. Application of an EM algorithm for the model is straightforward. But when the model is large enough to reach or exceed the storage space and contains latent variables, parameter estimation for the model looks almost infeasible. In this paper, a new EM approach is proposed for large recursive models and its convergence is proved. A key idea behind it is (1) that we partition a model into several submodels in such a way that the variables of submodel A, say, are conditionally independent of the other Variables in the model given that the values of the variables of submodel A which are involved in any other submodels are known and (2) that the likelihood function for the whole model is factorized by the submodels. (C) 2000 Elsevier Science B.V. All rights reserved.