A Causal Inference Framework for Data Rich Environments

2025-04-02

AI Summary

This paper addresses counterfactual estimation under unobserved confounding in data-rich settings. Methodologically, it proposes a unified framework integrating structural causal models (SCMs) with latent factor models (LFMs), formally bridging graphical models and the potential outcomes paradigm. It establishes identifiability conditions for the average treatment effect (ATE), average treatment effect on the treated (ATT), and average treatment effect on the untreated (ATU), and derives general consistency conditions for estimation via principal component regression (PCR), latent factor modeling, and nonparametric smoothness analysis. The key contribution is a theoretical proof—under mild smoothness assumptions—that PCR consistently estimates all three average treatment effects, substantially relaxing conventional requirements of linearity, low dimensionality, and strong functional-form restrictions. This yields a robust, scalable solution for causal inference in high-dimensional observational data with large sample sizes.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

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.

Problem

• Estimating counterfactuals with unobserved confounding in data-rich environments
• Bridging structural causal models and latent factor models for causal inference
• Ensuring consistent estimation of average treatment effects using principal component regression

Innovation

• Causal inference with unobserved confounding
• Bridge between structural and latent models
• Principal component regression for consistency