Multi-Dimensional Robust Synthetic Control: Exploring Counterfactuals and Predicting Cricket Scores
The “what ifs?” or ability to explore counterfactuals is central to the study of causal inference. Randomized control and A/B testing provides an approach to address this when counterfactuals can be experimented simultaneously. However, in a large number of scenarios such as policy evaluation, this is not feasible: we can’t have two Massachusetts, one having Gun Control and the other not at the same time, so that we can evaluate the impact of Gun Control on crime rate!
To address this challenge in a data-driven manner, the method of synthetic control was proposed by Abadie et al (2003) where synthetic or virtual counterfactuals are formed using historical data: impose Gun Control in Massachusetts to observe the crime rate under Gun Control and estimate the crime rate of Massachusetts without Gun Control as a combination of the crime rate of other states (without Gun Control). Despite tremendous success of this method, it suffers from two limitations: it is not robust to noisy, missing observations and it is not able to incorporate auxiliary information such as High School Dropout rate for estimating counterfactuals with respect to Crime Rate. In this talk, we will describe a method to address these limitations building on recent advances in Matrix and Tensor estimation, and present a novel application as a forecasting method for time series trajectories exemplified through the game of Cricket.
This is based on a collection of works in collaboration with Anish Agarwal, Muhammad J Amjad, Dennis Shen, Dogyoon Song (all at MIT) and Vishal Misra (Columbia).
Devavrat Shah is a Professor with the department of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology. His current research interests are at the interface of Statistical Inference and Social Data Processing. His work has been recognized through prize paper awards in Machine Learning, Operations Research and Computer Science, as well as career prizes including 2010 Erlang prize from the INFORMS Applied Probability Society and 2008 ACM Sigmetrics Rising Star Award. He is a distinguished young alumni of his alma mater IIT Bombay.