Causal programming: inference with structural causal models as finding instances of a relation

TL;DR

This paper introduces a unified framework called causal programming for causal inference using structural causal models, enabling formalization and solving of various causal problems including effect identification, discovery, and research design.

Contribution

It proposes a general relation and programming framework that unify multiple causal inference problems and facilitate formalization of new challenges.

Findings

Unifies causal effect identification, discovery, and bias recovery under a single relation.

Formalizes new causal inference problems like research design.

Introduces causal programming for optimizing causal inference tasks.

Abstract

This paper proposes a causal inference relation and causal programming as general frameworks for causal inference with structural causal models. A tuple, $\langle M, I, Q, F \rangle$, is an instance of the relation if a formula, $F$, computes a causal query, $Q$, as a function of known population probabilities, $I$, in every model entailed by a set of model assumptions, $M$. Many problems in causal inference can be viewed as the problem of enumerating instances of the relation that satisfy given criteria. This unifies a number of previously studied problems, including causal effect identification, causal discovery and recovery from selection bias. In addition, the relation supports formalizing new problems in causal inference with structural causal models, such as the problem of research design. Causal programming is proposed as a further generalization of causal inference as the problem of finding optimal instances of the relation, with respect to a cost function.