k-Optimal: A Novel Approximate Inference Algorithm for ProbLog

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. Furthermore a useful feature of the set of calculated proofs is that it is diverse. Our experiments show the utility of the proposed algorithm.

An OpenCL implementation of a forward sampling algorithm for CP-logic

“…For the k-best [7] and k-optimal [14] algorithms, we were unable to run the most recent version (in YAP 6.3.3) on our system, even after contacting the authors. We were able to run an older version of k-best (in YAP 6.2.2), but this does For Bloodtype, the sampling approaches perform quite poorly in general.…”

“…However, because the high computational complexity of this task can be problematic for real applications, several approximate algorithms have also been developed. One possibility [7,14] is to compute only a subset of all proofs of the query, as opposed to computing all proofs to produce an exact probability. An alternative is the Monte Carlo algorithm MCINTYRE [15], which repeatedly samples an SLD proof tree of the query.…”

Approximate Inference for Neural Probabilistic Logic Programming

“…This has inspired various approximate inference techniques for probabilistic logic programming. Especially relevant are the techniques that do not compute the full set of proofs but focus on a subset of the proofs (Renkens, Van den Broeck, and Nijssen, 2012;De Raedt, Kimmig, and Toivonen, 2007), e.g., the k-best proofs. If fewer proofs are used then compilation also becomes simplified and faster.…”

Event recognition under uncertainty and incomplete data

“…The set may contain highly redundant proofs and does not guarantee better approximation than any other set. The k-Optimal algorithm [Renkens et al, 2012] overcomes these issues and ensures that the set of k proofs is of provably good quality and that the set of proofs is diverse, i.e., less likely to select proofs that share similar facts, leading to better approximation of the success probability with fewer proofs.…”

“…Therefore, more efficient inference methods are needed for on-line inference in ProbLog−EC. Examples are the k-best of Kimmig et al [2011], k-optimal of Renkens et al [2012] or by performing MLN inference using the transformation of Fierens et al [2011].…”