Causal programming: inference with structural causal models as finding instances of a relation
It provides a theoretical framework for causal inference, potentially benefiting researchers in statistics and machine learning, but appears incremental as it builds on existing concepts.
The paper introduces a causal inference relation and causal programming as general frameworks for unifying problems like causal effect identification and discovery, and formalizing new issues such as research design in structural causal models.
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.