$\beta$-Intact-VAE: Identifying and Estimating Causal Effects under Limited Overlap

Pengzhou Abel Wu, Kenji Fukumizu

Keywords: VAE, variational autoencoder, balanced representation Learning, treatment effects, causal inference, identifiability, identification, CATE, ATE, weak overlap, limited overlap, Prognostic Model, Prognostic score

Abstract: As an important problem in causal inference, we discuss the identification and estimation of treatment effects (TEs) under limited overlap; that is, when subjects with certain features belong to a single treatment group. We use a latent variable to model a prognostic score 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 prognostic score, and the model identifies individualized treatment effects. The model is then learned as $\beta$-Intact-VAE––a new type of variational autoencoder (VAE). We derive the TE error bounds that enable representations balanced for treatment groups conditioned on individualized features. The proposed method is compared with recent methods using (semi-)synthetic datasets.

One-sentence Summary: See all these naturally in one: limited overlap, prognostic score, identifiable VAE, balanced representation Learning, CATE error bounds.