Causal Inference for Sequential Settings under Interference and Latent Confounding

We study causal inference under outcome interference for sequential, observational settings. 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 pairwise dependencies captured through an Ising model; and, each outcome is impacted through a latent external field capturing effects of 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 Pseudolikelihood Estimation (MPLE) for learning the model parameters. Under reasonable assumptions, we establish non-asymptotic consistency for parameter estimation. Therefore, sampling from the learnt model enables faithful estimation of causal quantities of interest. 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.