Referred to as the third rung of the causal inference ladder, counterfactual queries typically ask the What if?

Referred to as the third rung of the causal inference ladder, counterfactual queries typically ask the "What if?" question retrospectively. The standard approach to estimate counterfactuals resides in using a structural equation model that accurately reflects the underlying data generating process. However, such models are seldom available in practice and one usually wishes to infer them from observational data alone. Unfortunately, the correct structural equation model is in general not identifiable from the observed factual distribution. Nevertheless, in this work, we show that under the assumption that the main latent contributors to the treatment responses are categorical, the counterfactuals can be still reliably predicted.