# Learning Treatment Effects in Panels with General Intervention Patterns

arXiv: https://arxiv.org/abs/2106.02780 · HTML: https://mlsanity.com/paper/2106.02780/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 46 references that are in the map.
- First posted on arXiv 5 Jun 2021.

## Builds on (most cited first, 15 of 15)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolution](https://mlsanity.com/paper/1711.10467/) (2017)
- [Noisy Matrix Completion: Understanding Statistical Guarantees for Convex Relaxation via Nonconvex Optimization](https://mlsanity.com/paper/1902.07698/) (2019)
- [Synthetic Difference in Differences](https://mlsanity.com/paper/1812.09970/) (2018)
- [Inference and Uncertainty Quantification for Noisy Matrix Completion](https://mlsanity.com/paper/1906.04159/) (2019)
- [An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls](https://mlsanity.com/paper/1712.09089/) (2017)
- [On Robustness of Principal Component Regression](https://mlsanity.com/paper/1902.10920/) (2019)
- [Robust Synthetic Control](https://mlsanity.com/paper/1711.06940/) (2017)
- [The Augmented Synthetic Control Method](https://mlsanity.com/paper/1811.04170/) (2018)
- [Bridging Convex and Nonconvex Optimization in Robust PCA: Noise, Outliers, and Missing Data](https://mlsanity.com/paper/2001.05484/) (2020)
- [Optimal Experimental Design for Staggered Rollouts](https://mlsanity.com/paper/1911.03764/) (2019)
- [mRSC: Multi-dimensional Robust Synthetic Control](https://mlsanity.com/paper/1905.06400/) (2019)
- [Nuclear Norm Regularized Estimation of Panel Regression Models](https://mlsanity.com/paper/1810.10987/) (2018)

## Built on by (most cited first, 5 of 5)

- [Markovian Interference in Experiments](https://mlsanity.com/paper/2206.02371/) (2022)
- [Synthetically Controlled Bandits](https://mlsanity.com/paper/2202.07079/) (2022)
- [Uncertainty Quantification For Low-Rank Matrix Completion With Heterogeneous and Sub-Exponential Noise](https://mlsanity.com/paper/2110.12046/) (2021)
- [Heterogeneous Treatment Effects in Panel Data](https://mlsanity.com/paper/2406.05633/) (2024)
- [Synthetic Nearest Neighbors: Extending Synthetic Controls for Matrix Completion with Missing Not at Random Data](https://mlsanity.com/paper/2609.13586/) (2026)

## Abstract (arXiv)

The problem of causal inference with panel data is a central econometric question. The following is a fundamental version of this problem: Let M^* be a low rank matrix and E be a zero-mean noise matrix. For a `treatment' matrix Z with entries in 0,1 we observe the matrix O with entries Oij := M^*ij + Eij + Tij Zij where Tij  are unknown, heterogenous treatment effects. The problem requires we estimate the average treatment effect τ^* := sumij Tij Zij / sumij Zij. The synthetic control paradigm provides an approach to estimating τ^* when Z places support on a single row. This paper extends that framework to allow rate-optimal recovery of τ^* for general Z, thus broadly expanding its applicability. Our guarantees are the first of their type in this general setting. Computational experiments on synthetic and real-world data show a substantial advantage over competing estimators.