Before revision:  As a special case, this improves upon the 1/\sqrt{T_0 , we establish the parameter estimation and test error for Principal Component Regression (a key subroutine in SI and several SCvariants)under the setting of error-in-variable regression decays as 1/T_0, where T_0 is the number of samples observed; this improves the best prior test error bound of 1/\sqrt{T_0 .
After revision:  As a special case, this improves upon the 1/\sqrt{T_0 , we establish identification and inference results for SC as well. We further introduce a novel hypothesis test, with provable guarantees, to validate when to use SI (and thereby SC). Empirically, we showcase the efficacy of the SI framework on synthetic and real-world data. Finally, we discuss connections between the SI causal framework and tensor estimation .