Analysis of Bayesian Networks via Prob-Solvable Loops
This work provides a method for automating analysis of Bayesian networks, which is incremental as it builds on existing Prob-solvable loop frameworks.
The paper tackles the problem of automating moment-based invariant generation for probabilistic programs by extending Prob-solvable loops to encode Bayesian networks, enabling automatic solution of tasks like exact inference and sensitivity analysis on various BN benchmarks.
Prob-solvable loops are probabilistic programs with polynomial assignments over random variables and parametrised distributions, for which the full automation of moment-based invariant generation is decidable. In this paper we extend Prob-solvable loops with new features essential for encoding Bayesian networks (BNs). We show that various BNs, such as discrete, Gaussian, conditional linear Gaussian and dynamic BNs, can be naturally encoded as Prob-solvable loops. Thanks to these encodings, we can automatically solve several BN related problems, including exact inference, sensitivity analysis, filtering and computing the expected number of rejecting samples in sampling-based procedures. We evaluate our work on a number of BN benchmarks, using automated invariant generation within Prob-solvable loop analysis.