MAP Inference for Probabilistic Logic Programming

TL;DR

This paper introduces a new algorithm for MAP and MPE inference in Probabilistic Logic Programming, using Binary Decision Diagrams, and demonstrates its superior performance over existing methods on synthetic datasets.

Contribution

The paper presents a novel algorithm integrated into the PITA reasoner for MAP and MPE inference using BDDs, improving efficiency over ProbLog.

Findings

PITA outperforms ProbLog in many synthetic dataset experiments.

The algorithm effectively handles MAP and MPE tasks in PLP.

Binary Decision Diagrams enable efficient dynamic programming for inference.

Abstract

In Probabilistic Logic Programming (PLP) the most commonly studied inference task is to compute the marginal probability of a query given a program. In this paper, we consider two other important tasks in the PLP setting: the Maximum-A-Posteriori (MAP) inference task, which determines the most likely values for a subset of the random variables given evidence on other variables, and the Most Probable Explanation (MPE) task, the instance of MAP where the query variables are the complement of the evidence variables. We present a novel algorithm, included in the PITA reasoner, which tackles these tasks by representing each problem as a Binary Decision Diagram and applying a dynamic programming procedure on it. We compare our algorithm with the version of ProbLog that admits annotated disjunctions and can perform MAP and MPE inference. Experiments on several synthetic datasets show that PITA outperforms ProbLog in many cases.