Bayesian causal inference via probabilistic program synthesis

TL;DR

This paper introduces a novel method for Bayesian causal inference using probabilistic programming, allowing flexible modeling of interventions and causal structures with general-purpose inference tools.

Contribution

It demonstrates implementing Bayesian causal inference via probabilistic programs that generate and modify causal models, enabling flexible intervention modeling and inference.

Findings

Prototype implemented in Gen language

Supports various intervention types including atomic and shift interventions

Enables inference of causal structures from data

Abstract

Causal inference can be formalized as Bayesian inference that combines a prior distribution over causal models and likelihoods that account for both observations and interventions. We show that it is possible to implement this approach using a sufficiently expressive probabilistic programming language. Priors are represented using probabilistic programs that generate source code in a domain specific language. Interventions are represented using probabilistic programs that edit this source code to modify the original generative process. This approach makes it straightforward to incorporate data from atomic interventions, as well as shift interventions, variance-scaling interventions, and other interventions that modify causal structure. This approach also enables the use of general-purpose inference machinery for probabilistic programs to infer probable causal structures and parameters from data. This abstract describes a prototype of this approach in the Gen probabilistic programming language.