Symbolic Parameter Learning in Probabilistic Answer Set Programming

TL;DR

This paper introduces two novel algorithms for parameter learning in Probabilistic Answer Set Programming, leveraging symbolic equations to improve solution quality and efficiency compared to existing methods.

Contribution

The paper presents two new algorithms for probabilistic parameter learning in ASP, utilizing symbolic equations and outperforming existing approaches in accuracy and speed.

Findings

Algorithms outperform existing methods in solution quality.

Methods are faster in execution time.

Empirical results validate effectiveness.

Abstract

Parameter learning is a crucial task in the field of Statistical Relational Artificial Intelligence: given a probabilistic logic program and a set of observations in the form of interpretations, the goal is to learn the probabilities of the facts in the program such that the probabilities of the interpretations are maximized. In this paper, we propose two algorithms to solve such a task within the formalism of Probabilistic Answer Set Programming, both based on the extraction of symbolic equations representing the probabilities of the interpretations. The first solves the task using an off-the-shelf constrained optimization solver while the second is based on an implementation of the Expectation Maximization algorithm. Empirical results show that our proposals often outperform existing approaches based on projected answer set enumeration in terms of quality of the solution and in terms of execution time. The paper has been accepted at the ICLP2024 conference and is under consideration in Theory and Practice of Logic Programming (TPLP).