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).