Formula-Based Probabilistic Inference
This addresses a foundational problem in probabilistic inference for AI and logic, offering new methods that can improve efficiency in various applications, though it is incremental in extending logical inference to the probabilistic setting.
The paper tackles the problem of computing the probability of a logical formula given probabilities of other formulas, proposing two algorithms: an exact method based on decomposition and conditioning, and an approximate method using formula importance sampling, which is the first application of model counting to approximate probabilistic inference. Empirically, the algorithms achieve substantial performance gains over state-of-the-art schemes.
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.