Estimating Heterogeneous Treatment Effects: Mutual Information Bounds and Learning Algorithms

Estimating heterogeneous treatment effects (HTE) from observational studies is rising in importance due to the widespread accumulation of data in many fields. Due to the selection bias behind the inaccessibility of counterfactual data, the problem differs fundamentally from supervised learning in a challenging way. However, existing works on modeling selection bias and corresponding algorithms do not naturally generalize to non-binary treatment spaces. To address this limitation, we propose to use mutual information to describe selection bias in estimating HTE and derive a novel error bound using the mutual information between the covariates and the treatments, which is the first error bound to cover general treatment schemes including multinoulli or continuous spaces. We then bring forth theoretically justified algorithms, the Mutual Information Treatment Network (MitNet), using adversarial optimization to reduce selection bias and obtain more accurate HTE estimations. Our algorithm reaches remarkable performance in both simulation study and empirical evaluation.