{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/robust-synthetic-control","title":"Robust Synthetic Control","arxiv_id":"1711.06940","date":"2017-11-18","proceeding":null,"authors":["Muhammad Jehangir Amjad","Devavrat Shah","Dennis Shen"],"abstract":"We present a robust generalization of the synthetic control method for\ncomparative case studies. Like the classical method, we present an algorithm to\nestimate the unobservable counterfactual of a treatment unit. A distinguishing\nfeature of our algorithm is that of de-noising the data matrix via singular\nvalue thresholding, which renders our approach robust in multiple facets: it\nautomatically identifies a good subset of donors, overcomes the challenges of\nmissing data, and continues to work well in settings where covariate\ninformation may not be provided. To begin, we establish the condition under\nwhich the fundamental assumption in synthetic control-like approaches holds,\ni.e. when the linear relationship between the treatment unit and the donor pool\nprevails in both the pre- and post-intervention periods. We provide the first\nfinite sample analysis for a broader class of models, the Latent Variable\nModel, in contrast to Factor Models previously considered in the literature.\nFurther, we show that our de-noising procedure accurately imputes missing\nentries, producing a consistent estimator of the underlying signal matrix\nprovided $p = \\Omega( T^{-1 + \\zeta})$ for some $\\zeta > 0$; here, $p$ is the\nfraction of observed data and $T$ is the time interval of interest. Under the\nsame setting, we prove that the mean-squared-error (MSE) in our prediction\nestimation scales as $O(\\sigma^2/p + 1/\\sqrt{T})$, where $\\sigma^2$ is the\nnoise variance. Using a data aggregation method, we show that the MSE can be\nmade as small as $O(T^{-1/2+\\gamma})$ for any $\\gamma \\in (0, 1/2)$, leading to\na consistent estimator. We also introduce a Bayesian framework to quantify the\nmodel uncertainty through posterior probabilities. Our experiments, using both\nreal-world and synthetic datasets, demonstrate that our robust generalization\nyields an improvement over the classical synthetic control method.","url_abs":"http://arxiv.org/abs/1711.06940v1","url_pdf":"http://arxiv.org/pdf/1711.06940v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"robust-synthetic-control","repo_url":"https://github.com/jehangiramjad/tslib","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":null,"task_name":"counterfactual"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1711.06940","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}