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We propose a logical/mathematical framework for statistical parameterlearning of parameterized logic programs, i.e. definite clause programscontaining probabilistic facts with a parameterized distribution. It extendsthe traditional least Herbrand model semantics in logic programming todistribution semantics, possible world semantics with a probabilitydistribution which is unconditionally applicable to arbitrary logic programsincluding ones for HMMs, PCFGs and Bayesian networks. We also propose a new EMalgorithm, the graphical EM algorithm, that runs for a class of parameterizedlogic programs representing sequential decision processes where each decisionis exclusive and independent. It runs on a new data structure called supportgraphs describing the logical relationship between observations and theirexplanations, and learns parameters by computing inside and outside probabilitygeneralized for logic programs. The complexity analysis shows that whencombined with OLDT search for all explanations for observations, the graphicalEM algorithm, despite its generality, has the same time complexity as existingEM algorithms, i.e. the Baum-Welch algorithm for HMMs, the Inside-Outsidealgorithm for PCFGs, and the one for singly connected Bayesian networks thathave been developed independently in each research field. Learning experimentswith PCFGs using two corpora of moderate size indicate that the graphical EMalgorithm can significantly outperform the Inside-Outside algorithm.

Parameter Learning of Logic Programs for Symbolic-Statistical Modeling