Causal Inference with Categorical Unobserved Confounder via Mixture Learning

TL;DR

This paper introduces a novel method for causal inference with categorical unobserved confounders, leveraging mixture learning and tensor decomposition to achieve consistent estimation under certain conditions.

Contribution

It establishes the identifiability of causal effects in settings with categorical unobserved confounders and proposes a tensor decomposition-based estimation method with theoretical guarantees.

Findings

Method performs well with limited data in simulations.

Achieves consistent recovery of latent confounders.

Applicable to both proxy variable and multiple treatment settings.

Abstract

Unobserved confounding is a fundamental challenge for estimating causal effects. To address unobserved confounding, recent literature has turned to two different approaches -- proxy variables and the use of multiple treatments. The first approach, commonly referred to as proximal causal inference, requires proxies to be assigned to specific asymmetric roles: treatment-inducing proxies (negative control exposures), variables that act as common causes of the treatment and outcome, and outcome-inducing proxies (negative control outcomes). In practice, however, identifying variables that satisfy these asymmetric roles can be difficult depending on the application domain. The second approach, commonly referred to as the ``Deconfounder," deals with multiple conditionally independent treatments. There has been limited progress towards developing a consistent estimation method for this setting. As the primary contribution of this work, we establish that causal effects are identifiable in both settings when the unobserved confounder is categorical under suitable conditions. Our approach builds on a mixture learning perspective: we show that the underlying confounding structure can be recovered by identifying the corresponding mixture distribution. We propose an estimation procedure based on tensor decomposition, which allows consistent recovery of the latent structure and comes with non-asymptotic guarantees. Simulation studies and real data experiments demonstrate that the proposed method performs well even with limited data.