Multiple Causal Inference with Latent Confounding

TL;DR

This paper introduces new methods for causal inference involving multiple treatments with unobserved confounding, leveraging shared confounding assumptions and mutual information regularization to estimate effects accurately.

Contribution

It proposes a novel framework for estimating causal effects with multiple treatments under unobserved confounding using shared confounding assumptions and mutual information regularization.

Findings

Validated on simulations showing accurate effect estimation.

Applied to clinical medicine example demonstrating practical utility.

Developed a tractable lower bound for mutual information regularization.

Abstract

Causal inference from observational data requires assumptions. These assumptions range from measuring confounders to identifying instruments. Traditionally, causal inference assumptions have focused on estimation of effects for a single treatment. In this work, we construct techniques for estimation with multiple treatments in the presence of unobserved confounding. We develop two assumptions based on shared confounding between treatments and independence of treatments given the confounder. Together, these assumptions lead to a confounder estimator regularized by mutual information. For this estimator, we develop a tractable lower bound. To recover treatment effects, we use the residual information in the treatments independent of the confounder. We validate on simulations and an example from clinical medicine.