Incremental Computation for Efficient Programmable Inference in Probabilistic Programs

2026-06-03

AI Summary

This work addresses the scalability challenges of probabilistic program inference on large-scale data, which often suffers from expensive recomputation of intermediate results. The authors propose a modular approach that compiles probabilistic programs into deterministic density-function programs and leverages compositional incremental optimization based on incremental λ-calculus, enabling Monte Carlo inference to efficiently reuse intermediate computations. By decoupling density evaluation from incremental optimization, the method supports nonparametric models and employs denotational logical relations to verify correctness in a stepwise manner. Experimental results demonstrate that the system achieves asymptotic speedups with respect to data size across a range of models and inference algorithms, with a Julia prototype confirming its practical efficacy.

Abstract

Inference in probabilistic programs generally requires evaluating many possible program executions to find those of high posterior density. To scale inference to large datasets, it is crucial that expensive intermediate results are shared across these many evaluations, rather than recomputed from scratch. This paper presents a new approach to realizing this sharing, based on \textit{incremental computation}, a technique for efficiently recomputing (deterministic) program outputs when program inputs change. First, we show how expressive probabilistic programs can be compiled to deterministic ones that compute their density functions. Then, building on the incremental $λ$-calculus, we develop a general technique for compositionally incrementalizing expressive functional programs, and apply it to these densities. The resulting incremental densities can be used to accelerate a broad range of Monte Carlo inference algorithms, including for nonparametric models not well supported by existing systems. Furthermore, our decomposition of incremental density computation into separate density and incrementalization steps allows for modular reasoning about correctness -- a key pain point in existing systems, where ad-hoc incrementalization features are a known source of soundness bugs. We develop denotational logical relations arguments for the correctness of each step independently, and implement the approach in a Julia prototype, finding that it leads to asymptotic runtime improvements in the size of the dataset on a range of models and inference algorithms.

Problem

• probabilistic programs
• inference
• incremental computation
• density functions
• Monte Carlo algorithms

Innovation

• incremental computation
• probabilistic programming
• density compilation
• compositional incrementalization
• Monte Carlo inference