s-ID: Causal Effect Identification in a Sub-Population
This addresses a gap in causal inference for specific subgroups affected by sampling biases, though it appears incremental as it builds on existing identification frameworks.
The paper tackles the problem of identifying causal effects in a sub-population using only observational data from that sub-group, introducing the s-ID problem and providing necessary and sufficient conditions for identifiability, along with a sound and complete algorithm.
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.