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SMEM Algorithm Is Not Fully Compatible with Maximum-Likelihood Framework

akihiro{at}eei.metro-u.ac.jp, Graduate School of Engineering, Tokyo Metropolitan University, Hachioji, Tokyo, 192-0397 Japan

Norio Tagawa

tagawa{at}eei.metro-u.ac.jp, Graduate School of Engineering, Tokyo Metropolitan University, Hachioji, Tokyo, 192-0397 Japan

Toshiyuki Tanaka

tanaka{at}eei.metro-u.ac.jp, Graduate School of Engineering, Tokyo Metropolitan University, Hachioji, Tokyo, 192-0397 Japan

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 likeli-hoods.