s-ID: Causal Effect Identification in a Sub-Population

TL;DR

This paper addresses the challenge of identifying causal effects within a specific sub-population using only observational data from that subgroup, providing necessary conditions and a complete algorithm for this task.

Contribution

It introduces the s-ID problem, establishes necessary and sufficient conditions for causal effect identifiability in sub-populations, and offers a sound, complete algorithm for solving it.

Findings

Derived necessary and sufficient conditions for s-ID.

Developed a sound and complete algorithm for causal inference in sub-populations.

Clarified the limitations of existing methods when applied to sub-population data.

Abstract

Causal inference in a sub-population involves identifying the causal effect of an intervention on a specific subgroup, which is distinguished from the whole population through the influence of systematic biases in the sampling process. However, ignoring the subtleties introduced by sub-populations can either lead to erroneous inference or limit the applicability of existing methods. We introduce and advocate for a causal inference problem in sub-populations (henceforth called s-ID), in which we merely have access to observational data of the targeted sub-population (as opposed to the entire population). Existing inference problems in sub-populations operate on the premise that the given data distributions originate from the entire population, thus, cannot tackle the s-ID problem. To address this gap, we provide necessary and sufficient conditions that must hold in the causal graph for a causal effect in a sub-population to be identifiable from the observational distribution of that sub-population. Given these conditions, we present a sound and complete algorithm for the s-ID problem.