Conditional Independence in Functional Probabilistic Programming

Abstract

Probabilistic programming languages are a relatively new field within computer science. As a result, not much research has been done on automatic improvements, such as static analyses and program transformations, that could increase the efficiency or usability of a probabilistic programming language. This is especially true for functional probabilistic programming languages, which are not widely used. We therefore set out to discover such improvements for probabilistic programming in a functional setting. Specifically, we look at methods to improve probabilistic programming that use information on the conditional dependencies between the variables of a probabilistic model.

In this thesis, we present a small but practical functional probabilistic programming language embedded in Haskell. We build a static analysis for this language that can automatically extract the conditional dependence information from a probabilistic model. Additionally, we implement a program transformation that uses the conditional dependence information that we have obtained to automatically perform complicated rewrites of probabilistic models, which previously had to be done by the user. Designing this language, the static analysis and the program transformation has given us many new insights on (functional) probabilistic programming language design, which will also be presented in the thesis.