Variational Bayes Inference for Logic-Based Probabilistic Models on BDDs

Statistical abduction is an attempt to define a probability distribution over explanations derived by abduction and to evaluate them using their probabilities. In statistical abduction, deterministic knowledge like rules and facts are described as logic formulas. However nondeterministic knowledge like preference and frequency seems difficult to represent as logic. Bayesian inference can reflect such knowledge on a prior and variational Bayes (VB) is known as an approximation method for it. In this paper, we propose VB for logic-based probabilistic models and show that our proposed method is efficient in evaluating abductive explanations about failure in a logic circuit and a metabolic pathway.