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).

翻译：参数学习是统计关系人工智能领域的一项关键任务：给定一个概率逻辑程序以及一组以解释形式呈现的观测数据，其目标是学习程序中事实的概率，使得这些解释的概率最大化。本文在概率答案集编程的形式框架内，提出了两种算法来解决此类任务，这两种算法均基于提取表示解释概率的符号方程。第一种算法使用现成的约束优化求解器来完成任务，而第二种算法则基于期望最大化算法的实现。实验结果表明，在解的质量和执行时间方面，我们的方案通常优于基于投影答案集枚举的现有方法。本文已被ICLP2024会议接收，并正在《逻辑编程理论与实践》（TPLP）期刊审议中。