Probability seminar series
Saeed Ghadimi
University of À¶Ý®ÊÓƵ
Room: M3 3127
An Adversarially Robust Formulation of Linear Regression with Missing Data
In this talk, I'll present a robust framework to perform linear regression with missing entries in the features. By considering an elliptical data distribution, and specifically a multivariate normal model, we are able to conditionally formulate a distribution for the missing entries and present a robust framework, which minimizes the worst-case error caused by the uncertainty in the missing data. The proposed formulation ultimately reduces to a convex program, for which we develop a customized and scalable solver. I'll also discuss the consistency and structural behavior of the proposed framework in asymptotic regimes. Finally, I'll present some numerical experiments performed on synthetic, semi-synthetic, and real data, and show how the proposed formulation improves the prediction accuracy and robustness.