EÆcient EM Learning with Tabulation for Parameterized Logic Programs

We have been developing a general symbolic-statistical modeling language [6, 19, 20] based on the logic programming framework that semantically uni es (and extends) major symbolic-statistical frameworks such as hidden Markov models (HMMs) [18], probabilistic contextfree grammars (PCFGs) [23] and Bayesian networks [16]. The language, PRISM, is intended to model complex symbolic phenomena governed by rules and probabilities based on the distributional semantics[19]. Programs contain statistical parameters and they are automatically learned from randomly sampled data by a specially derived EM algorithm, the graphical EM algorithm. It works on support graphs representing the shared structure of explanations for an observed goal. In this paper, we propose the use of tabulation technique to build support graphs, and show that as a result, the graphical EM algorithm attains the same time complexity as specilized EM algorithms for HMMs (the Baum-Welch algorithm [18]) and PCFGs (the Inside-Outside algorithm [1]).