Multiple Causal Inference with Latent Confounding

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.

References in corpus (7)

• Auto-Encoding Variational Bayes
• Markov Chain Monte Carlo and Variational Inference: Bridging the Gap
• Causal Effect Inference with Deep Latent-Variable Models
• Auxiliary Deep Generative Models
• CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training
• Implicit Causal Models for Genome-wide Association Studies
• The Blessings of Multiple Causes

Cited by in corpus (11)

• On Multi-Cause Causal Inference with Unobserved Confounding: Counterexamples, Impossibility, and Alternatives
• Using Embeddings to Correct for Unobserved Confounding in Networks
• Desiderata for Representation Learning: A Causal Perspective
• Time Series Deconfounder: Estimating Treatment Effects over Time in the Presence of Hidden Confounders
• The Medical Deconfounder: Assessing Treatment Effects with Electronic Health Records
• Identifiability of causal effects with multiple causes and a binary outcome
• General Control Functions for Causal Effect Estimation from Instrumental Variables
• Automated Meta-Analysis: A Causal Learning Perspective
• DoGR: Disaggregated Gaussian Regression for Reproducible Analysis of Heterogeneous Data
• Causal Estimation with Functional Confounders
• Causal Discovery from Conditionally Stationary Time Series