Doubly Robust Inference in Causal Latent Factor Models

This article presents a novel framework for the estimation of average treatment effects in modern data-rich environments in the presence of unobserved confounding. Modern data-rich environments are characterized by repeated measurements of outcomes, such as clinical metrics or purchase history, across a substantial number of units--be it patients in medical contexts or customers in online retail. As an example, consider an internet-retail platform where customers interact with various product categories. For each consumer-category pair, the platform makes decisions to either offer a discount or not, and records whether the consumer purchased a product in the category. Given an observational dataset capturing such interactions, our objective is to infer the causal effect of offering the discount on consumer purchase behavior. More specifically, we aim to infer two kinds of treatment effects: (a) tailored to product categories, the average impact of the discount on a product across consumers, and (b) tailored to consumers, the average impact of the discount on a consumer across product categories. This task is challenging due to unobserved confounding that may cause spurious associations between discount allocation and product purchase.