In The EM Algorithm and Related Statistical Models (STATISTICS: A Dekker series of Textbooks and Monographs 170.), Ed. by Michiko Watanabe and Kazunori Yamaguchi, Chap. 8, pp. 95–126.

ISBM: 0824747011

New York, NY/Basel: Marcel Dekker, Inc.

Authors:

  • Noboru Murata
  • Shiro Ikeda

Abstract:

(From ``introduction’’) In this article, we first review the EM algorithm from the geometrical viewpoint based on the em algorithm proposed in [7]. This geometrical concept is important to interpret various learning rules in neural networks. Then we give some examples of neural network models in which the EM algorithm implicitly appears in the learning process. From the biological point of view, it is an important problem that the EM algorithm can be appropriately implemented on real biological systems. This is usually hard, and with a special model, the Helmholtz machine, we shortly discuss the tradeoff between statistical models and biological models. In the end, we show two models of neural networks in which the EM algorithm is adopted for learning explicitly. These models are proposed mainly for practical applications, not for biological modeling, and they are applied for complicated tasks such as controlling robots.