Using probabilistic programs as proposals

TL;DR

This paper introduces a method for creating flexible, domain-informed proposal distributions in probabilistic inference by combining heuristic algorithms with neural networks within probabilistic programming, improving efficiency without losing theoretical guarantees.

Contribution

It proposes a framework for expressing proposal distributions as probabilistic programs, enabling offline optimization and integration of heuristics and neural models for faster inference.

Findings

Proposal programs can be used as proposals in importance sampling and MCMC.

Combining heuristics with neural networks improves inference speed.

The approach maintains asymptotic correctness while enhancing efficiency.

Abstract

Monte Carlo inference has asymptotic guarantees, but can be slow when using generic proposals. Handcrafted proposals that rely on user knowledge about the posterior distribution can be efficient, but are difficult to derive and implement. This paper proposes to let users express their posterior knowledge in the form of proposal programs, which are samplers written in probabilistic programming languages. One strategy for writing good proposal programs is to combine domain-specific heuristic algorithms with neural network models. The heuristics identify high probability regions, and the neural networks model the posterior uncertainty around the outputs of the algorithm. Proposal programs can be used as proposal distributions in importance sampling and Metropolis-Hastings samplers without sacrificing asymptotic consistency, and can be optimized offline using inference compilation. Support for optimizing and using proposal programs is easily implemented in a sampling-based probabilistic programming runtime. The paper illustrates the proposed technique with a proposal program that combines RANSAC and neural networks to accelerate inference in a Bayesian linear regression with outliers model.