🤖 AI Summary
This work proposes the first semantically consistent sequential Monte Carlo (SMC) framework grounded in the Feynman–Kac formalism for efficient and provably correct inference in general-purpose probabilistic programs that support arbitrary measure sampling and conditional reweighting within unbounded loops. The approach employs probabilistic program graphs (PPGs) as an intermediate representation and leverages a finite-trace approximation theorem to rigorously establish the correspondence between the program’s expectation semantics and the Feynman–Kac model. Building on this foundation, the authors design a vectorized particle filtering algorithm (VPF) tailored to PPGs. Empirical evaluations demonstrate that VPF significantly outperforms existing state-of-the-art inference tools across multiple benchmarks, achieving a compelling combination of theoretical soundness, computational efficiency, and strong scalability.
📝 Abstract
We study provably correct and efficient instantiations of Sequential Monte Carlo (SMC) inference in the context of formal operational semantics of Probabilistic Programs (PPs). We focus on universal PPs featuring sampling from arbitrary measures and conditioning/reweighting in unbounded loops. We first equip Probabilistic Program Graphs (PPGs), an automata-theoretic description format of PPs, with an expectation-based semantics over infinite execution traces, which also incorporates trace weights. We then prove a finite approximation theorem that provides bounds to this semantics based on expectations taken over finite, fixed-length traces. This enables us to frame our semantics within a Feynman-Kac (FK) model, and ensures the consistency of the Particle Filtering (PF) algorithm, an instance of SMC, with respect to our semantics. Building on these results, we introduce VPF, a vectorized version of the PF algorithm tailored to PPGs and our semantics. Experiments conducted with a proof-of-concept implementation of VPF show very promising results compared to state-of-the-art PP inference tools.