{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T19:22:07Z","timestamp":1774034527236,"version":"3.50.1"},"reference-count":23,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2019,6,19]],"date-time":"2019-06-19T00:00:00Z","timestamp":1560902400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CMMI-1462158, CMMI-1634259, CNS-1523546"],"award-info":[{"award-number":["CMMI-1462158, CMMI-1634259, CNS-1523546"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006353","name":"Charles Stark Draper Laboratory","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006353","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["Proc. ACM Meas. Anal. Comput. Syst."],"published-print":{"date-parts":[[2019,6,19]]},"abstract":"<jats:p>When evaluating the impact of a policy (e.g., gun control) on a metric of interest (e.g., crime-rate), it may not be possible or feasible to conduct a randomized control trial. In such settings where only observational data is available, synthetic control (SC) methods [2-4] provide a popular data-driven approach to estimate a \"synthetic\" or \"virtual\" control by combining measurements of \"similar\" alternatives or units (called \"donors\"). Recently, robust synthetic control (RSC) [7] was proposed as a generalization of SC to overcome the challenges of missing data and high levels of noise, while removing the reliance on expert domain knowledge for selecting donors. However, both SC and RSC (and its variants) suffer from poor estimation when the pre-intervention period is too short. As the main contribution of this work, we propose a generalization of unidimensional RSC to multi-dimensional Robust Synthetic Control, mRSC. Our proposed mechanism, mRSC, incorporates multiple types of measurements (or metrics) in addition to the measurement of interest for estimating a synthetic control, thus overcoming the challenge of poor inference due to limited amounts of pre-intervention data. We show that the mRSC algorithm, when using K relevant metrics, leads to a consistent estimator of the synthetic control for the target unit of interest under any metric. Our finite-sample analysis suggests that the mean-squared error (MSE) of our predictions decays to zero at a rate faster than the RSC algorithm by a factor of K and \u221aK for the training (pre-intervention) and testing (post-intervention) periods, respectively. Additionally, we propose a principled scheme to combine multiple metrics of interest via a diagnostic test that evaluates if adding a metric can be expected to result in improved inference. Our mechanism for validating mRSC performance is also an important and related contribution of this work: time series prediction. We propose a method to predict the future evolution of a time series based on limited data when the notion of time is relative and not absolute, i.e., where we have access to a donor pool that has already undergone the desired future evolution. We conduct extensive experimentation to establish the efficacy of mRSC in three different scenarios: predicting the evolution of a metric of interest using synthetically generated data from a known factor model, and forecasting weekly sales and score trajectories of a Walmart store and Cricket game, respectively.<\/jats:p>","DOI":"10.1145\/3341617.3326152","type":"journal-article","created":{"date-parts":[[2019,6,20]],"date-time":"2019-06-20T12:18:56Z","timestamp":1561033136000},"page":"1-27","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["mRSC"],"prefix":"10.1145","volume":"3","author":[{"given":"Muhammad","family":"Amjad","sequence":"first","affiliation":[{"name":"Massachusetts Institute of Technology, Cambridge, MA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vishal","family":"Misra","sequence":"additional","affiliation":[{"name":"Columbia University, New York, NY, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Devavrat","family":"Shah","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology, Cambridge, MA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dennis","family":"Shen","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology, Cambridge, MA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2019,6,19]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"2014. Kaggle: Walmart Recruiting - Store Sales Forecasting. (2014). https:\/\/www.kaggle.com\/c\/ walmart- recruiting- store- sales- forecasting"},{"key":"e_1_2_1_2_1","doi-asserted-by":"crossref","unstructured":"A. Abadie A. Diamond and J. Hainmueller. 2010. Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California's Tobacco Control Program. J. Amer. Statist. Assoc. (2010).","DOI":"10.1198\/jasa.2009.ap08746"},{"key":"e_1_2_1_3_1","volume-title":"Synth: An R Package for Synthetic Control Methods in Comparative Case Studies. Journal of Statistical Software","author":"Abadie A.","year":"2011","unstructured":"A. Abadie, A. Diamond, and J. Hainmueller. 2011. Synth: An R Package for Synthetic Control Methods in Comparative Case Studies. Journal of Statistical Software (2011)."},{"key":"e_1_2_1_4_1","doi-asserted-by":"crossref","unstructured":"A. Abadie and J. Gardeazabal. 2003. The Economic Costs of Conflict: A Case Study of the Basque Country. American Economic Review (2003).","DOI":"10.1257\/000282803321455188"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/3287319"},{"key":"e_1_2_1_6_1","volume-title":"Model Agnostic High-Dimensional Error-in-Variable Regression. arXiv preprint","author":"Agarwal Anish","year":"2019","unstructured":"Anish Agarwal, Devavrat Shah, Dennis Shen, and Dogyoon Song. 2019. Model Agnostic High-Dimensional Error-in-Variable Regression. arXiv preprint (2019)."},{"key":"e_1_2_1_7_1","first-page":"1","article-title":"Robust Synthetic Control","volume":"19","author":"Amjad Muhammad","year":"2018","unstructured":"Muhammad Amjad, Devavrat Shah, and Dennis Shen. 2018. Robust Synthetic Control. Journal of Machine Learning Research 19, 17 (2018), 1--50.","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_1_9_1","article-title":"Predicting the Match Outcome in One Day International Cricket Matches, while the Game is in Progress","volume":"5","author":"Bailey Michael","year":"2006","unstructured":"Michael Bailey and Stephen R Clarke. 2006. Predicting the Match Outcome in One Day International Cricket Matches, while the Game is in Progress. Journal of Sports Science & Medicine 5, 4 (12 2006), 480--487. http:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC3861745\/","journal-title":"Journal of Sports Science & Medicine"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1510507113"},{"key":"e_1_2_1_11_1","unstructured":"Christian Borgs Jennifer Chayes Christina E Lee and Devavrat Shah. 2017. Thy Friend is My Friend: Iterative Collaborative Filtering for Sparse Matrix Estimation. In Advances in Neural Information Processing Systems. 4718-- 4729."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1214\/14-AOS1272"},{"key":"e_1_2_1_14_1","volume-title":"Stein's Paradox in Statistics. 236 (05","author":"Efron Bradley","year":"1977","unstructured":"Bradley Efron and Carl Morris. 1977. Stein's Paradox in Statistics. 236 (05 1977), 119--127."},{"key":"e_1_2_1_15_1","volume-title":"Cricket and the Wasp: Shameless self promotion (Wonkish). (January","author":"Hogan Seamus","year":"2015","unstructured":"Seamus Hogan. 2015. Cricket and the Wasp: Shameless self promotion (Wonkish). (January 2015). http:\/\/offsettingbehaviour.blogspot.com\/2012\/11\/cricket- and- wasp- shameless- self.html"},{"key":"e_1_2_1_17_1","unstructured":"Phil Oliver Travis Basevi Will Luke and Freddie Wilde. 2018. CricViz. (2018). http:\/\/cricviz.com\/"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/70.1.41"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1214\/09-SS057"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/1859995.1860015"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.2307\/2529684"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1037\/h0037350"},{"key":"e_1_2_1_23_1","volume-title":"Cricket World Cup 2015: India and Pakistan fans usurp the limelight. (February","author":"Shemilt Stephan","year":"2015","unstructured":"Stephan Shemilt. 2015. Cricket World Cup 2015: India and Pakistan fans usurp the limelight. (February 2015). https:\/\/www.bbc.com\/sport\/cricket\/31479487"},{"key":"e_1_2_1_24_1","volume-title":"These global sporting events totally dwarf the SuperBowl. (February","author":"Tharoor Ishan","year":"2016","unstructured":"Ishan Tharoor. 2016. These global sporting events totally dwarf the SuperBowl. (February 2016). https:\/\/www.washingtonpost.com\/news\/worldviews\/wp\/2016\/02\/05\/these-global-sporting-events-totally-dwarf-the-super-bowl\/?noredirect=on&utm_term=.6f393cc4e52e"},{"key":"e_1_2_1_25_1","unstructured":"Christopher Xie Alex Talk and Emily Fox. 2016. A Unified Framework for Missing Data and Cold Start Prediction for Time Series Data. In Advances in neural information processing systems Time Series Workshop."},{"key":"e_1_2_1_26_1","volume-title":"Dhillon","author":"Yu Hsiang-Fu","year":"2015","unstructured":"Hsiang-Fu Yu, Nikhil Rao, and Inderjit S. Dhillon. 2015. Temporal Regularized Matrix Factorization. CoRR abs\/1509.08333 (2015)."}],"container-title":["Proceedings of the ACM on Measurement and Analysis of Computing Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3341617.3326152","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3341617.3326152","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3341617.3326152","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T22:41:29Z","timestamp":1750200089000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3341617.3326152"}},"subtitle":["Multi-dimensional Robust Synthetic Control"],"short-title":[],"issued":{"date-parts":[[2019,6,19]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,6,19]]}},"alternative-id":["10.1145\/3341617.3326152"],"URL":"https:\/\/doi.org\/10.1145\/3341617.3326152","relation":{},"ISSN":["2476-1249"],"issn-type":[{"value":"2476-1249","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,19]]},"assertion":[{"value":"2019-06-19","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}