Multiple Causal Inference with Latent Confounding
This work addresses causal inference for multiple treatments, which is incremental as it extends traditional single-treatment methods to more complex scenarios.
The paper tackles the problem of causal inference with multiple treatments in the presence of unobserved confounding by developing assumptions and a confounder estimator regularized by mutual information, validated on simulations and a clinical example.
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.