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Causal inference can be formalized as Bayesian inference that combines aprior distribution over causal models and likelihoods that account for bothobservations and interventions. We show that it is possible to implement thisapproach using a sufficiently expressive probabilistic programming language.Priors are represented using probabilistic programs that generate source codein a domain specific language. Interventions are represented usingprobabilistic programs that edit this source code to modify the originalgenerative process. This approach makes it straightforward to incorporate datafrom atomic interventions, as well as shift interventions, variance-scalinginterventions, and other interventions that modify causal structure. Thisapproach also enables the use of general-purpose inference machinery forprobabilistic programs to infer probable causal structures and parameters fromdata. This abstract describes a prototype of this approach in the Genprobabilistic programming language.

Bayesian causal inference via probabilistic program synthesis