Intact-VAE: Estimating Treatment Effects under Unobserved Confounding

Abstract

NOTE: This preprint has a flawed theoretical formulation. Please avoid it and refer to the ICLR22 publication https://openreview.net/forum?id=q7n2RngwOM. Also, arXiv:2109.15062 contains some new ideas on unobserved Confounding. As an important problem of causal inference, we discuss the identification and estimation of treatment effects under unobserved confounding. Representing the confounder as a latent variable, we propose Intact-VAE, a new variant of variational autoencoder (VAE), motivated by the prognostic score that is sufficient for identifying treatment effects. We theoretically show that, under certain settings, treatment effects are identified by our model, and further, based on the identifiability of our model (i.e., determinacy of representation), our VAE is a consistent estimator with representation balanced for treatment groups. Experiments on (semi-)synthetic datasets show state-of-the-art performance under diverse settings.

This preprint has a flawed theoretical formulation. It was intended as a theoretical update of https://openreview.net/forum?id=D3TNqCspFpM

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• Semi-Supervised Learning with Deep Generative Models
• The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables
• Identifiability of parameters in latent structure models with many observed variables
• CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training
• Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)
• CausalVAE: Structured Causal Disentanglement in Variational Autoencoder
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Cited by in corpus (3)

• Desiderata for Representation Learning: A Causal Perspective
• Assisting Clinical Decisions for Scarcely Available Treatment via Disentangled Latent Representation
• $\beta$-Intact-VAE: Identifying and Estimating Causal Effects under Limited Overlap