Confounding is a central concept in causal inference, but it is notoriously difficult to give it a positive definition. In this talk, I will break down this concept in two steps. In the first step, I will use the linear equation model and linear algebra to understand the semantics of an acyclic directed mixed graphs (ADMGs) and introduce a notational system for “words” (special types of walks/paths) in ADGMs. In the second step, I will break down Pearl’s celebrated back-door criterion and introduce an alternative approach to confounder selection by iterative graph expansion.
This talk is based on several working papers: https://arxiv.org/abs/2407.15744, https://arxiv.org/abs/2309.06053 (with F Richard Guo), and to a less degree, https://www.statslab.cam.ac.uk/~qz280/publication/admg-model/paper.pdf.