# Robust Synthetic Control

arXiv: https://arxiv.org/abs/1711.06940 · HTML: https://mlsanity.com/paper/1711.06940/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2017.

## Built on by (most cited first, 25 of 25)

- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [Causal Inference for Time series Analysis: Problems, Methods and Evaluation](https://mlsanity.com/paper/2102.05829/) (2021)
- [Explaining Latent Representations with a Corpus of Examples](https://mlsanity.com/paper/2110.15355/) (2021)
- [Policy Analysis using Synthetic Controls in Continuous-Time](https://mlsanity.com/paper/2102.01577/) (2021)
- [CausalSim: A Causal Framework for Unbiased Trace-Driven Simulation](https://mlsanity.com/paper/2201.01811/) (2022)
- [Doubly robust nearest neighbors in factor models](https://mlsanity.com/paper/2211.14297/) (2022)
- [Synthetically Controlled Bandits](https://mlsanity.com/paper/2202.07079/) (2022)
- [Learning Treatment Effects in Panels with General Intervention Patterns](https://mlsanity.com/paper/2106.02780/) (2021)
- [Adaptive Principal Component Regression with Applications to Panel Data](https://mlsanity.com/paper/2307.01357/) (2023)
- [Strategyproof Decision-Making in Panel Data Settings and Beyond](https://mlsanity.com/paper/2211.14236/) (2022)
- [Differentially Private Synthetic Control](https://mlsanity.com/paper/2303.14084/) (2023)
- [SCouT: Synthetic Counterfactuals via Spatiotemporal Transformers for Actionable Healthcare](https://mlsanity.com/paper/2207.04208/) (2022)
- [Synthetic Principal Component Design: Fast Covariate Balancing with Synthetic Controls](https://mlsanity.com/paper/2211.15241/) (2022)
- [Matrix Estimation for Individual Fairness](https://mlsanity.com/paper/2302.02096/) (2023)
- [ClusterSC: Advancing Synthetic Control with Donor Selection](https://mlsanity.com/paper/2503.21629/) (2025)
- [Time-Aware Synthetic Control](https://mlsanity.com/paper/2601.03099/) (2026)
- [Assessing the Impact: Does an Improvement to a Revenue Management System Lead to an Improved Revenue?](https://mlsanity.com/paper/2101.10249/) (2021)
- [Bounded (O(1)) Regret Recommendation Learning via Synthetic Controls Oracle](https://mlsanity.com/paper/2301.12571/) (2023)
- [SECRETS: Subject-Efficient Clinical Randomized Controlled Trials using Synthetic Intervention](https://mlsanity.com/paper/2305.05078/) (2023)
- [Incentive-Aware Synthetic Control: Accurate Counterfactual Estimation via Incentivized Exploration](https://mlsanity.com/paper/2312.16307/) (2023)
- [Latent Variable Modeling for Robust Causal Effect Estimation](https://mlsanity.com/paper/2508.20259/) (2025)
- [Fairness-Aware Insurance Pricing: A Multi-Objective Optimization Approach](https://mlsanity.com/paper/2512.24747/) (2025)
- [Causal Inference for Sequential Settings under Interference and Latent Confounding](https://mlsanity.com/paper/2607.14940/) (2026)
- [Spectral Truncation in Synthetic Control](https://mlsanity.com/paper/2607.25074/) (2026)
- [Synthetic Nearest Neighbors: Extending Synthetic Controls for Matrix Completion with Missing Not at Random Data](https://mlsanity.com/paper/2609.13586/) (2026)

## Abstract (arXiv)

We present a robust generalization of the synthetic control method for comparative case studies. Like the classical method, we present an algorithm to estimate the unobservable counterfactual of a treatment unit. A distinguishing feature of our algorithm is that of de-noising the data matrix via singular value thresholding, which renders our approach robust in multiple facets: it automatically identifies a good subset of donors, overcomes the challenges of missing data, and continues to work well in settings where covariate information may not be provided. To begin, we establish the condition under which the fundamental assumption in synthetic control-like approaches holds, i.e. when the linear relationship between the treatment unit and the donor pool prevails in both the pre- and post-intervention periods. We provide the first finite sample analysis for a broader class of models, the Latent Variable Model, in contrast to Factor Models previously considered in the literature. Further, we show that our de-noising procedure accurately imputes missing entries, producing a consistent estimator of the underlying signal matrix provided p = Omega( T-1 + zeta) for some zeta > 0; here, p is the fraction of observed data and T is the time interval of interest. Under the same setting, we prove that the mean-squared-error (MSE) in our prediction estimation scales as O(σ2/p + 1/√T), where σ2 is the noise variance. Using a data aggregation method, we show that the MSE can be made as small as O(T-1/2+γ) for any γ ∈ (0, 1/2), leading to a consistent estimator. We also introduce a Bayesian framework to quantify the model uncertainty through posterior probabilities. Our experiments, using both real-world and synthetic datasets, demonstrate that our robust generalization yields an improvement over the classical synthetic control method.