SMEM algorithm is not fully compatible with maximum-likelihood framework

Authors:
Akihiro Minagawa;Norio Tagawa;Toshiyuki Tanaka
Affiliations:
Graduate School of Engineering, Tokyo Metropolitan University, Hachioji, Tokyo, 192-0397 Japan;Graduate School of Engineering, Tokyo Metropolitan University, Hachioji, Tokyo, 192-0397 Japan;Graduate School of Engineering, Tokyo Metropolitan University, Hachioji, Tokyo, 192-0397 Japan
Venue:
Neural Computation
Year:
2002

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Abstract

The expectation-maximization (EM) algorithm with split-and-merge operations (SMEM algorithm) proposed by Ueda, Nakano, Ghahramani, and Hinton (2000) is a nonlocal searching method, applicable to mixture models, for relaxing the local optimum property of the EM algorithm. In this article, we point out that the SMEM algorithm uses the acceptance-rejection evaluation method, which may pick up a distribution with smaller likelihood, and demonstrate that an increase in likelihood can then be guaranteed only by comparing log likelihoods.