An Adversarially Robust Formulation of Linear Regression with Missing Data

51 Pages Posted: 19 Oct 2023

See all articles by Alireza Aghasi

Alireza Aghasi

Oregon State University

Saeed Ghadimi

University of Waterloo

Yue Xing

Michigan State University

Mohammed Javad Feizollahi

Georgia State University - J. Mack Robinson College of Business

Date Written: September 22, 2023

Abstract

We 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. We show that the proposed formulation, which naturally takes into account the dependency between different variables, ultimately reduces to a convex program, for which we develop a customized and scalable solver. We analyze the consistency and structural behavior of the proposed framework in asymptotic regimes, and present technical discussions to estimate the required input parameters. We complement our analysis with experiments performed on synthetic, semi-synthetic, and real data, and show how the proposed formulation improves the prediction accuracy and robustness, and outperforms the competing techniques.

Keywords: Robustness, Missing data

JEL Classification: C13

Suggested Citation

Aghasi, Alireza and Ghadimi, Saeed and Xing, Yue and Feizollahi, Mohammed Javad, An Adversarially Robust Formulation of Linear Regression with Missing Data (September 22, 2023). Available at SSRN: https://ssrn.com/abstract=4580532 or http://dx.doi.org/10.2139/ssrn.4580532

Alireza Aghasi (Contact Author)

Oregon State University ( email )

Bexell Hall 200
Corvallis, OR 97331
United States

Saeed Ghadimi

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

Yue Xing

Michigan State University ( email )

619 Red Cedar Road
C413 Wells Hall
East Lansing, MI 48824-1027
United States

Mohammed Javad Feizollahi

Georgia State University - J. Mack Robinson College of Business ( email )

P.O. Box 4050
Atlanta, GA 30303-3083
United States

HOME PAGE: http://https://robinson.gsu.edu/profile/m-javad-feizollahi/

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