Causal Inference for Sequential Settings under Interference and Latent Confounding

2026-07-16

AI Summary

Estimating causal effects from high-dimensional binary time series is highly challenging in the presence of temporal dependencies, interference across units, and latent confounders. This work proposes the first causal inference framework that integrates a dynamic Ising model with a low-rank latent factor structure to jointly capture complex interference patterns and unobserved confounding. The model parameters are efficiently learned via maximum pseudolikelihood estimation, and non-asymptotic statistical theory is established to guarantee estimation consistency—even from a single observed trajectory. By unifying the modeling of interference and latent confounding within one sample, the method substantially improves estimation accuracy. Empirical evaluations on both synthetic data and a real-world application—assessing the effect of county-level vaccination rates on COVID-19 mortality in the United States—demonstrate the effectiveness of the proposed approach.

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.

Problem

• causal inference
• interference
• latent confounding
• sequential settings
• Ising model

Innovation

• Causal Inference
• Outcome Interference
• Latent Confounding
• Ising Model
• Maximum Pseudo-Likelihood Estimation