Probabilistic Programs with Stochastic Conditioning

TL;DR

This paper introduces stochastic conditioning in probabilistic programming, enabling models to condition on distributions or summaries of data rather than just samples, broadening applicability in complex real-world scenarios.

Contribution

It formalizes stochastic conditioning, discusses its properties, and demonstrates inference methods and case studies, extending probabilistic programming capabilities.

Findings

Formal definition of stochastic conditioning

Inference methods for stochastic conditioning

Successful case studies demonstrating applicability

Abstract

We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic conditioning. However, in many real-life scenarios, the observations are given as marginal distributions, summary statistics, or samplers. Conventional probabilistic programming systems lack adequate means for modeling and inference in such scenarios. We propose a generalization of deterministic conditioning to stochastic conditioning, that is, conditioning on the marginal distribution of a variable taking a particular form. To this end, we first define the formal notion of stochastic conditioning and discuss its key properties. We then show how to perform inference in the presence of stochastic conditioning. We demonstrate potential usage of stochastic conditioning on several case studies which involve various kinds of stochastic conditioning and are difficult to solve otherwise. Although we present stochastic conditioning in the context of probabilistic programming, our formalization is general and applicable to other settings.