Convergence Results for the EM Approach to Mixtures of Experts Architectures
MASSACHUSETTS INST OF TECH CAMBRIDGE ARTIFICIAL INTELLIGENCE LAB
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The Expectation-Maximization EM algorithm is an iterative approach to maximum likelihood parameter estimation. Jordan and Jacobs 1993 recently proposed an EM algorithm for the mixture of experts architecture of Jacobs, Jordan, Nowlan and Hinton 1991 and the hierarchical mixture of experts architecture of Jordan and Jacobs 1992. They showed empirically that the EM algorithm for these architectures yields significantly faster convergence than gradient ascent. In the current paper we provide a theoretical analysis of this algorithm. We show that the algorithm can be regarded as a variable metric algorithm with its searching direction having a positive projection on the gradient of the log likelihood. We also analyze the convergence of the algorithm and provide an explicit expression for the convergence rate. In addition, we describe an acceleration technique that yields a significant speedup in simulation experiments.
- Statistics and Probability