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Referred to as the third rung of the causal inference ladder, counterfactualqueries typically ask the "What if ?" question retrospectively. The standardapproach to estimate counterfactuals resides in using a structural equationmodel that accurately reflects the underlying data generating process. However,such models are seldom available in practice and one usually wishes to inferthem from observational data alone. Unfortunately, the correct structuralequation model is in general not identifiable from the observed factualdistribution. Nevertheless, in this work, we show that under the assumptionthat the main latent contributors to the treatment responses are categorical,the counterfactuals can be still reliably predicted. Building upon thisassumption, we introduce CounterFactual Query Prediction (CFQP), a novel methodto infer counterfactuals from continuous observations when the backgroundvariables are categorical. We show that our method significantly outperformspreviously available deep-learning-based counterfactual methods, boththeoretically and empirically on time series and image data. Our code isavailable at https://github.com/edebrouwer/cfqp.

Deep Counterfactual Estimation with Categorical Background Variables