# Efficiently Learning Synthetic Control Models for High-dimensional Disaggregated Data

arXiv: https://arxiv.org/abs/2510.22828 · HTML: https://mlsanity.com/paper/2510.22828/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 40 references that are in the map.
- First posted on arXiv 26 Oct 2025.

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

- [An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls](https://mlsanity.com/paper/1712.09089/) (2017)
- [Synthetic Interventions](https://mlsanity.com/paper/2006.07691/) (2020)
- [The Augmented Synthetic Control Method](https://mlsanity.com/paper/1811.04170/) (2018)
- [A Design-Based Perspective on Synthetic Control Methods](https://mlsanity.com/paper/2101.09398/) (2021)
- [Synthetic Controls for Experimental Design](https://mlsanity.com/paper/2108.02196/) (2021)
- [New insights for the multivariate square-root lasso](https://mlsanity.com/paper/1909.05041/) (2019)
- [Synthetic Control, Synthetic Interventions, and COVID-19 spread: Exploring the impact of lockdown measures and herd immunity](https://mlsanity.com/paper/2009.09987/) (2020)
- [Heterogeneous Synthetic Learner for Panel Data](https://mlsanity.com/paper/2212.14580/) (2022)
- [An explicit mean-covariance parameterization for multivariate response linear regression](https://mlsanity.com/paper/1808.10558/) (2018)

## Abstract (arXiv)

The Synthetic Control method (SC) has become a valuable tool for estimating causal effects. Originally designed for single-treated unit scenarios, it has recently found applications in high-dimensional disaggregated settings with multiple treated units. However, challenges in practical implementation and computational efficiency arise in such scenarios. To tackle these challenges, we propose a novel approach that integrates the Multivariate Square-root Lasso method into the synthetic control framework. We rigorously establish the estimation error bounds for fitting the Synthetic Control weights using Multivariate Square-root Lasso, accommodating high-dimensionality and time series dependencies. Additionally, we quantify the estimation error for the Average Treatment Effect on the Treated (ATT). Through simulation studies, we demonstrate that our method offers superior computational efficiency without compromising estimation accuracy. We apply our method to assess the causal impact of COVID-19 Stay-at-Home Orders on the monthly unemployment rate in the United States at the county level.