# A Causal Inference Framework for Data Rich Environments

arXiv: https://arxiv.org/abs/2504.01702 · HTML: https://mlsanity.com/paper/2504.01702/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 19 references that are in the map.
- First posted on arXiv 2 Apr 2025.

## Builds on (most cited first, 9 of 9)

- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [Synthetic Difference in Differences](https://mlsanity.com/paper/1812.09970/) (2018)
- [Rates of Convergence of Spectral Methods for Graphon Estimation](https://mlsanity.com/paper/1709.03183/) (2017)
- [On Robustness of Principal Component Regression](https://mlsanity.com/paper/1902.10920/) (2019)
- [Causal Inference with Corrupted Data: Measurement Error, Missing Values, Discretization, and Differential Privacy](https://mlsanity.com/paper/2107.02780/) (2021)
- [Synthetic Combinations: A Causal Inference Framework for Combinatorial Interventions](https://mlsanity.com/paper/2303.14226/) (2023)
- [Doubly robust nearest neighbors in factor models](https://mlsanity.com/paper/2211.14297/) (2022)
- [Adaptive Principal Component Regression with Applications to Panel Data](https://mlsanity.com/paper/2307.01357/) (2023)
- [On Model Identification and Out-of-Sample Prediction of Principal Component Regression: Applications to Synthetic Controls](https://mlsanity.com/paper/2010.14449/) (2020)

## Built on by (most cited first, 2 of 2)

- [On Evolution-Based Models for Experimentation Under Interference](https://mlsanity.com/paper/2511.21675/) (2025)
- [Synthetic Survival Control: Extending Synthetic Controls for "When-If" Decision](https://mlsanity.com/paper/2511.14133/) (2025)

## Abstract (arXiv)

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.