Causal Inference for Sequential Settings under Interference and Latent Confounding
Machine Learning
Summary
The authors study how to figure out cause-and-effect relationships when outcomes of multiple units influence each other over time. They model these outcomes as connected in a network (using an Ising model) and affected by treatments and hidden factors that can vary across units and time. Using just one set of observed data, they develop a method to estimate the model efficiently and prove it works well under certain conditions. They test their approach with simulations and real data, specifically looking at how vaccine rates impact COVID-19 death rates across US counties.
Authors
Phevos Paschalidis, Constantinos Daskalakis, Devavrat Shah
Abstract
We study causal inference under outcome interference for sequential, observational settings. Specifically, we consider settings where the binary outcomes over N units are Markovian across T time steps. At each time step, the outcomes of N units have dependencies captured through an Ising model; each outcome is also impacted through an external field capturing the effects of its treatment as well as latent confounders. Similar to panel data literature, these latent confounders are modeled to have a low-rank factor structure. Our data is a single sample from this high-dimensional distribution. To estimate causal quantities of interest, we provide a computationally efficient method based on Maximum Pseudo-Likelihood Estimation (MPLE) for learning the model parameters. Under mild assumptions, we establish non-asymptotic consistency for parameter estimation and show this translates to faithful estimation of causal quantities of interest after sampling from the learned model. We demonstrate the efficacy of the method through synthetic experiments as well as a real-world case-study investigating causal effects of vaccine rates on COVID-19 death rates within US counties nationwide.