Probabilistic Programs with Stochastic Conditioning
This addresses a limitation in probabilistic programming systems for real-life scenarios where observations are not deterministic, potentially benefiting fields like statistics and machine learning, though it appears incremental as an extension of existing conditioning methods.
The paper tackles the problem of conditioning probabilistic programs on distributions of observable variables, such as marginal distributions or summary statistics, rather than just samples, and proposes stochastic conditioning as a generalization to enable modeling and inference in such scenarios, demonstrating its utility on case studies that are difficult to solve otherwise.
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.