Causal Identification with Relaxed Positivity

Inwoo Hwang, Yesong Choe, Yeahoon Kwon, Sanghack Lee

Keywords: causality, causal inference, causal effect identification, causal graph, positivity condition

TL;DR: We provide a formal treatment to the positivity condition underlying in causal identification formulas.

Abstract: Identifying and estimating a causal effect is a fundamental task when researchers want to infer a causal effect using an observational study without experiments. A conventional assumption is the strict positivity of the given distribution, or so called positivity (or overlap) under the unconfounded assumption that the probabilities of treatments are positive. However, there exist many environments where neither observational data exhibits strict positivity nor unconfounded assumption holds. In this work, we examine the graphical counterpart of the conventional positivity condition so as to license the use of an identification formula without strict positivity. In particular, we explore various approaches, including analysis in a post-hoc manner, do-calculus, $Q$-decomposition, and algorithmic, to yielding a positivity condition for an identification formula. We relate these approaches, providing a comprehensive view.

Submission Number: 14