Abstract

Recent advances in probabilistic generative modeling have motivated learning Structural Causal Models (SCM) from observational datasets using deep conditional generative models, also known as Deep Structural Causal Model (DSCM). If successful, DSCM s can be utilized for causal estimation tasks, e.g., for answering counterfactual queries ([Pawlowski et al.(2020)Pawlowski, Coelho de Castro, and Glocker]). In this work, we warn practitioners about non-identifiability of counterfactual inference from observational data, even in the absence of unobserved confounding and assuming known causal structure. We prove counterfactual identifiability of monotonic generation mechanisms with single dimensional exogenous variables. For general generation mechanisms with multi-dimensional exogenous variables, we provide an impossibility result for counterfactual identifiability, motivating the need for parametric assumptions. As a practical approach, we propose a method for estimating worst-case errors of learned DSCM s’ counterfactual predictions. The size of this error can be an essential metric for deciding whether or not DSCM s are a viable approach for counterfactual inference in a specific pro