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

TL;DR

This paper introduces $eta$-Intact-VAE, a novel variational autoencoder model that identifies and estimates causal treatment effects under limited overlap by modeling a prognostic score with theoretical guarantees.

Contribution

It proposes a new VAE-based approach that recovers prognostic scores and estimates individualized treatment effects with proven error bounds.

Findings

The model accurately recovers prognostic scores.

It provides balanced representations conditioned on individual features.

Outperforms recent methods on synthetic datasets.

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.