On Multi-Cause Approaches to Causal Inference with Unobserved Counfounding: Two Cautionary Failure Cases and A Promising Alternative

Unobserved confounding is a central barrier to drawing causal inferences from observational data. Several authors have recently proposed that this barrier can be overcome in the case where one attempts to infer the effects of several variables simultaneously. In this paper, we present two simple, analytical counterexamples that challenge the general claims that are central to these approaches. We discuss some reasons for these failures and suggest directions for obtaining sufficient conditions for causal identifiaciton. Despite these negative results, we show that a simple modification to the multi-cause setting, incorporating a proxy or negative control variable, solves many of the problems highlighted by the examples, and suggest a way forward for causal inference with high-dimensional action spaces.