k-Optimal: A Novel Approximate Inference Algorithm for ProbLog

Joris Renkens, Guy Van den Broeck, Siegfried Nijssen

Abstract: ProbLog is a probabilistic extension of Prolog. Given the complexity of exact inference under ProbLog’s semantics, in many applications in machine learning approximate inference is necessary. Current approximate inference algorithms for ProbLog however require either dealing with large numbers of proofs or do not guarantee a low approximation error. In this paper we introduce a new approximate inference algorithm which addresses these shortcomings. Given a user-specified parameter k, this algorithm approximates the success probability of a query based on at most k proofs and ensures that the calculated probability p is (1 − 1/e)p * ≤ p ≤ p *, where p * is the highest probability that can be calculated based on any set of k proofs.