A Causal Inference Framework for Data Rich Environments
This work addresses causal inference challenges for researchers in statistics and machine learning dealing with high-dimensional data, though it appears incremental by integrating existing frameworks.
The paper tackles the problem of counterfactual estimation with unobserved confounding in data-rich environments by proposing a formal model that bridges structural causal models and latent factor models, showing that principal component regression can achieve consistent estimation for causal parameters like the average treatment effect.
We propose a formal model for counterfactual estimation with unobserved confounding in "data-rich" settings, i.e., where there are a large number of units and a large number of measurements per unit. Our model provides a bridge between the structural causal model view of causal inference common in the graphical models literature with that of the latent factor model view common in the potential outcomes literature. We show how classic models for potential outcomes and treatment assignments fit within our framework. We provide an identification argument for the average treatment effect, the average treatment effect on the treated, and the average treatment effect on the untreated. For any estimator that has a fast enough estimation error rate for a certain nuisance parameter, we establish it is consistent for these various causal parameters. We then show principal component regression is one such estimator that leads to consistent estimation, and we analyze the minimal smoothness required of the potential outcomes function for consistency.