Constraint-Based Inference in Probabilistic Logic Programs

Abstract

Probabilistic Logic Programs (PLPs) generalize traditional logic programs and allow the encoding of models combining logical structure and uncertainty. In PLP, inference is performed by summarizing the possible worlds which entail the query in a suitable data structure, and using this data structure to compute the answer probability. Systems such as ProbLog, PITA, etc., use propositional data structures like explanation graphs, BDDs, SDDs, etc., to represent the possible worlds. While this approach saves inference time due to substructure sharing, there are a number of problems where a more compact data structure is possible. We propose a data structure called Ordered Symbolic Derivation Diagram (OSDD) which captures the possible worlds by means of constraint formulas. We describe a program transformation technique to construct OSDDs via query evaluation, and give procedures to perform exact and approximate inference over OSDDs. Our approach has two key properties. Firstly, the exact inference procedure is a generalization of traditional inference, and results in speedup over the latter in certain settings. Secondly, the approximate technique is a generalization of likelihood weighting in Bayesian Networks, and allows us to perform sampling-based inference with lower rejection rate and variance. We evaluate the effectiveness of the proposed techniques through experiments on several problems.

A Comparison of MCMC Sampling for Probabilistic Logic Programming

“…In Metropolis Hastings sampling, a Markov chain is built by taking an initial sample and, starting from this sample, by generating successors samples. Here we consider the algorithm developed in [9] and implemented in cplint [14]. Algorithm 3 goes as follows: 1) it samples random choices so that the evidence is true to build an initial sample.…”

cplint on SWISH: Probabilistic Logical Inference with a Web Browser

“…In rejection sampling [VN51], you first query the evidence and, if the query is successful, query the goal in the same sample, otherwise the sample is discarded. In Metropolis-Hastings MCMC [NR14], a Markov chain is built by taking an initial sample and by generating successor samples.…”

“…You can ask conditional queries with rejection sampling or with Metropolis-Hastings MCMC, too. In the first case, the available predicate is: In the second case, mcintyre follows the algorithm proposed in [NR14] (the non adaptive version). The initial sample is built with a backtracking meta-interpreter that starts with the goal and randomizes the order in which clauses are selected during the search so that the initial sample is unbiased.…”

“…In [NR14] the lag is always 1. However, in [NR14], the proof that the acceptance probability (which is min{1, N0…”

“…The example kalman filter.pl (adapted from [NR14]) encodes a Kalman filter, i.e., a Hidden Markov model with a real value as state and a real value as output. The next state is given by the current state plus Gaussian noise (with mean 0 and variance 2 in this example) and the output is given by the current state plus Gaussian noise (with mean 0 and variance 1 in this example).…”