Yanlin Zhang, Sungyong Chung, Alireza Talebpour
arXiv 16 Oct 2026 · Machine Learning
arXiv:2610.24113 · PDF · Extracted main text
Synthetic control methods estimate counterfactual outcomes by weighting untreated donor units to match a treated unit before treatment. In recent applications, however, the donor pool can be large, highly correlated, and short in pre-treatment history, yielding many near-equivalent solutions with unstable and difficult-to-interpret donor weights. We propose Graph-Regularized Synthetic Control (Graph-SC), a convex estimator that augments the classical pre-treatment matching objective with a graph Laplacian penalty. The graph encodes similarity among donor trajectories, encouraging coherent weights over structurally related donors while preserving the transparency of synthetic controls. We provide theoretical results characterizing the bias-variance tradeoff induced by graph regularization and establish efficient convergence guarantees with an accelerated proximal gradient method. Across a controlled simulation under donor redundancy, the California Proposition 99 benchmark, and observational counterfactual analyses on the Waymo Open Motion Dataset, Graph-SC improves weight stability, reduces sensitivity to redundant donor pools, and maintains competitive pre- and post-treatment accuracy relative to classical and regularized synthetic control baselines. Our results suggest that graph regularization is most valuable not as a universal accuracy booster, but as a principled mechanism for selecting stable and interpretable counterfactuals from near-equivalent synthetic controls with comparable pre-treatment fit.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Abadie, Alberto and Gardeazabal, Javier (2003) The economic costs of conflict: A case study of the Basque Country | 1.000 | 7 | 3 | 100% |
| 2 | Abadie, Alberto and Diamond, Alexis and Hainmueller, Jens (2010) Synthetic control methods for comparative case studies: Estimating the effect of California’s tobacco control program | 0.928 | 5 | 4 | 80% |
| 3 | Abadie, Alberto and L’hour, Jérémy (2021) A penalized synthetic control estimator for disaggregated data | 0.874 | 5 | 2 | 100% |
| 4 | Amjad, Muhammad and Shah, Devavrat and Shen, Dennis (2018) Robust synthetic control | 0.874 | 5 | 2 | 100% |
| 5 | Arkhangelsky, Dmitry and Athey, Susan and Hirshberg, David A and Imb… (2021) Synthetic difference-in-differences | 0.874 | 5 | 2 | 100% |
| 6 | Ben-Michael, Eli and Feller, Avi and Rothstein, Jesse (2021) The augmented synthetic control method | 0.874 | 5 | 2 | 100% |
| 7 | Xu, Yiqing (2017) Generalized synthetic control method: Causal inference with interactive fixed effects models | 0.874 | 5 | 2 | 100% |
| 8 | Beck, Amir and Teboulle, Marc (2009) A fast iterative shrinkage-thresholding algorithm for linear inverse problems | 0.737 | 4 | 3 | 50% |
| 9 | Kellogg, Maxwell and Mogstad, Magne and Pouliot, Guillaume A and Tor… (2021) Combining matching and synthetic control to tradeoff biases from extrapolation and interpolation | 0.644 | 4 | 1 | 100% |
| Chung2025 | unmatched citation key Chung2025 | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 16 scored citations. 1 of these could not be matched to a bibliography entry, so only the citation key is shown.