BLT : Exact Bayesian Inference with Distribution Transformers

This paper presents a static analysis for solving the Bayesian inference problem for finite-state probabilistic programs featuring categorical random variables and looping control flow. The results of the analysis are transformations on state distributions, which efficiently compute output distributions from input distributions. The inference algorithm generates and composes probability transformations, and translates them to a system of constraints solvable by a combination of linear algebra and linear programming. To improve the efficiency of inference queries on output distributions, a dataflow analysis computes, for each program fragment, the relevant variables for an inference query. The inference is exact and proved to be sound with respect to a denotational semantics. The analysis has been implemented in the tool BLT, which successfully infers output distributions for probabilistic programs with possibly non-terminating loops. An experimental evaluation with existing and new benchmarks like Bayesian networks shows that BLT’s performance is comparable to state-of-the-art solvers for exact inference.