Probabilistic Logic Programming with Beta-Distributed Random Variables

TL;DR

This paper extends aProbLog to incorporate Beta-distributed random variables, enabling more accurate reasoning under uncertain probabilities, which is crucial for decision-making in complex relational domains with sparse data.

Contribution

It introduces a probabilistic logic programming framework that models uncertain probabilities as Beta distributions, maintaining performance while enhancing flexibility and accuracy.

Findings

Achieves state-of-the-art performance in specified domains

Effectively models probability uncertainty with Beta distributions

Supports complex relational reasoning under uncertainty

Abstract

We enable aProbLog---a probabilistic logical programming approach---to reason in presence of uncertain probabilities represented as Beta-distributed random variables. We achieve the same performance of state-of-the-art algorithms for highly specified and engineered domains, while simultaneously we maintain the flexibility offered by aProbLog in handling complex relational domains. Our motivation is that faithfully capturing the distribution of probabilities is necessary to compute an expected utility for effective decision making under uncertainty: unfortunately, these probability distributions can be highly uncertain due to sparse data. To understand and accurately manipulate such probability distributions we need a well-defined theoretical framework that is provided by the Beta distribution, which specifies a distribution of probabilities representing all the possible values of a probability when the exact value is unknown.