Formula-Based Probabilistic Inference

TL;DR

This paper introduces two algorithms for probabilistic inference on logical formulas, including an exact method and an approximate importance sampling approach, leveraging formula structure for efficiency and demonstrating significant empirical improvements.

Contribution

The paper presents novel algorithms for formula-based probabilistic inference, including the first use of model counting for approximation, enhancing efficiency by exploiting formula structure.

Findings

Exact and approximate algorithms outperform existing methods

Importance sampling is the first application of model counting in this context

Algorithms leverage structural information for efficiency gains

Abstract

Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in the literature to date, particularly considering that it includes many standard inference problems as special cases. In this paper, we propose two algorithms for this problem: formula decomposition and conditioning, which is an exact method, and formula importance sampling, which is an approximate method. The latter is, to our knowledge, the first application of model counting to approximate probabilistic inference. Unlike conventional variable-based algorithms, our algorithms work in the dual realm of logical formulas. Theoretically, we show that our algorithms can greatly improve efficiency by exploiting the structural information in the formulas. Empirically, we show that they are indeed quite powerful, often achieving substantial performance gains over state-of-the-art schemes.