Axiomatic effect propagation in structural causal models

Raghav Singal; George Michailidis

We study effect propagation in a causal directed acyclic graph (DAG), with the goal of providing a flow-based decomposition of the effect (i.e., change in the outcome variable) as a result of changes in the source variables. We first compare various ideas on causality to quantify effect propagation, such as direct and indirect effects, path-specific effects, and degree of responsibility. We discuss the shortcomings of such approaches and propose a flow-based methodology, which we call recursive Shapley value (RSV). By considering a broader set of counterfactuals than existing methods, RSV obeys a unique adherence to four desirable flow-based axioms. Further, we provide a general path-based characterization of RSV for an arbitrary non-parametric structural equations model (SEM) defined on the underlying DAG. Interestingly, for the special class of linear SEMs, RSV exhibits a simple and tractable characterization (and hence, computation), which recovers the classical method of path coefficients and is equivalent to path-specific effects. For non-parametric SEMs, we use our general characterization to develop an unbiased Monte-Carlo estimation procedure with an exponentially decaying sample complexity. We showcase the application of RSV on two challenging problems on causality (causal overdetermination and causal unfairness).

Axiomatic effect propagation in structural causal models

Abstract