Do-Calculus When the True Graph Is Unknown

Abstract

The basic task of causal discovery is to estimate the causal effect of some set of variables on another given a set of data. In this work, we bridge the gap between causal structure discovery and the do-calculus by proposing a method for the identification of causal effects on the basis of arbitrary (equivalence) classes of semi-Markovian causal models. The approach uses a general logical representation of the d-separation constraints obtained from a causal structure discovery algorithm, which can then be queried by procedures implementing the do-calculus inference for causal effects. We show that the method is more efficient than a determination of causal effects using a naive enumeration of graphs in the equivalence class. Moreover, the method is complete with regard to the identifiability of causal effects for settings, in which extant methods not assuming the true graph to be known, only offer incomplete results. The method is entirely modular and easily adapted for different background settings.