Probabilistic Inference for Datalog with Correlated Inputs

TL;DR

This paper presents Praline, a Datalog extension for probabilistic inference with correlated inputs, formulating the problem as a constrained optimization and proposing scalable algorithms with strong empirical results.

Contribution

Introduces Praline, a novel Datalog extension for probabilistic inference with input correlations, and develops scalable algorithms with proven tight probability bounds.

Findings

Praline effectively handles input correlations in probabilistic Datalog.

The $ ext{delta}$-exact inference algorithm scales to large programs.

Empirical results show tight probability bounds in real-world benchmarks.

Abstract

Probabilistic extensions of logic programming languages, such as ProbLog, integrate logical reasoning with probabilistic inference to evaluate probabilities of output relations; however, prior work does not account for potential statistical correlations among input facts. This paper introduces Praline, a new extension to Datalog designed for precise probabilistic inference in the presence of (partially known) input correlations. We formulate the inference task as a constrained optimization problem, where the solution yields sound and precise probability bounds for output facts. However, due to the complexity of the resulting optimization problem, this approach alone often does not scale to large programs. To address scalability, we propose a more efficient $\delta$-exact inference algorithm that leverages constraint solving, static analysis, and iterative refinement. Our empirical evaluation on challenging real-world benchmarks, including side-channel analysis, demonstrates that our method not only scales effectively but also delivers tight probability bounds.