Causal Effect Identification in a Sub-Population with Latent Variables

TL;DR

This paper extends causal effect identification methods to sub-populations with latent variables, introducing new graphical tools and a sound algorithm to address the complexities introduced by unobserved variables.

Contribution

It develops an extension of the s-ID problem to include latent variables, along with new graphical definitions and a sound algorithm for this setting.

Findings

Extended graphical definitions for latent variables

Proposed a sound algorithm for s-ID with latent variables

Addresses challenges of unobserved variables in causal effect identification

Abstract

The s-ID problem seeks to compute a causal effect in a specific sub-population from the observational data pertaining to the same sub population (Abouei et al., 2023). This problem has been addressed when all the variables in the system are observable. In this paper, we consider an extension of the s-ID problem that allows for the presence of latent variables. To tackle the challenges induced by the presence of latent variables in a sub-population, we first extend the classical relevant graphical definitions, such as c-components and Hedges, initially defined for the so-called ID problem (Pearl, 1995; Tian & Pearl, 2002), to their new counterparts. Subsequently, we propose a sound algorithm for the s-ID problem with latent variables.