Causal Inference with Conditional Front-Door Adjustment and Identifiable Variational Autoencoder

TL;DR

This paper introduces a novel causal inference method that relaxes traditional assumptions using conditional front-door adjustment and employs an identifiable variational autoencoder to learn representations from data, validated through synthetic and real-world experiments.

Contribution

It proposes the concept of conditional front-door adjustment, develops a theorem for its identifiability, and introduces CFDiVAE, a deep generative model for learning the adjustment variable from data.

Findings

CFDiVAE outperforms existing methods in synthetic data experiments.

Performance of CFDiVAE is less sensitive to unobserved confounding strength.

Successful application to real-world data demonstrates practical utility.

Abstract

An essential and challenging problem in causal inference is causal effect estimation from observational data. The problem becomes more difficult with the presence of unobserved confounding variables. The front-door adjustment is a practical approach for dealing with unobserved confounding variables. However, the restriction for the standard front-door adjustment is difficult to satisfy in practice. In this paper, we relax some of the restrictions by proposing the concept of conditional front-door (CFD) adjustment and develop the theorem that guarantees the causal effect identifiability of CFD adjustment. Furthermore, as it is often impossible for a CFD variable to be given in practice, it is desirable to learn it from data. By leveraging the ability of deep generative models, we propose CFDiVAE to learn the representation of the CFD adjustment variable directly from data with the identifiable Variational AutoEncoder and formally prove the model identifiability. Extensive experiments on synthetic datasets validate the effectiveness of CFDiVAE and its superiority over existing methods. The experiments also show that the performance of CFDiVAE is less sensitive to the causal strength of unobserved confounding variables. We further apply CFDiVAE to a real-world dataset to demonstrate its potential application.