Belief Revision and the EM Algorithm

Abstract

This paper provides a natural interpretation of the EM algorithm as a succession of revision steps that try to find a probability distribution in a parametric family of models in agreement with frequentist observations over a partition of a domain. Each step of the algorithm corresponds to a revision operation that respects a form of minimal change. In particular, the so-called expectation step actually applies Jeffrey’s revision rule to the current best parametric model so as to respect the frequencies in the available data. We also indicate that in the presence of incomplete data, one must be careful in the definition of the likelihood function in the maximization step, which may differ according to whether one is interested by the precise modeling of the underlying random phenomenon together with the imperfect observation process, or by the modeling of the underlying random phenomenon alone, despite imprecision.