Model-Robust Counterfactual Prediction Method

In many casual inference problems, the subject or unit of analysis belongs to a group, indexed by z, and is associated with a continuous outcome (or response) y. For instance, groups z {0,1} may correspond to'not receiving' or'receiving' medication. The inferential question is then typically posed in counterfactual terms: "What would the outcome have been, had the unit belonged to a different group z z?" The ability to address this question using observational data is relevant in a wide variety of fields, including clinical trials, epidemiology, econometrics, policy evaluation, etc. [1] Each unit is typically associated with a range of covariates (or features), collected in a vector x, which may affect its outcome and/or group selection. When x contains all variables that simultaneously affect both y and z, it is possible to provide causal interpretations from observed data. The onus is on the researcher to include such potentially confounding variables [2]. Under this standard condition, the dependencies between group, outcome and covariates can be encoded by a graph as in Figure 1 along with an associated joint distribution p(x, y, z).