Identifying and Estimating Causal Effects under Weak Overlap by Generative Prognostic Model

As an important problem of causal inference, we discuss the identification and estimation of treatment effects (TEs) under weak overlap, i.e., subjects with certain features all belong to a single treatment group. We use a latent variable to model a prognostic score (PGS), which is widely used in biostatistics and sufficient for TEs, i.e., we build a generative prognostic model. We prove that the latent variable recovers a PGS, and the model identifies individualized treatment effects. The model is then learned as the Intact-VAE, a new type of variational autoencoder (VAE). We derive counterfactual generalization bounds which motivate representation balanced for treatment groups conditioned on individualized features. The proposed method is compared with recent methods using (semi-)synthetic datasets.