A0280
Title: Robust cellwise regularized sparse regression
Authors: Samuel Muller - Macquarie University (Australia) [presenting]
Peng Su - School of Mathematics and Statistics, USYD (Australia)
Tarr Garth - The University of Sydney (Australia)
Suojin Wang - Texas A and M University (United States)
Abstract: The robust variable selection currently has some focus on dealing with cellwise contamination in the design matrix where only some but not all elements of an observation vector are contaminated. The problem is particularly challenging when the number of variables is large. Traditional robust methods can fail when the data is high-dimensional and too many observation rows experience some cellwise contamination. We explore how using initial robust empirical covariance matrix estimators, together with regularization approaches, helps in robustly selecting variables by simultaneously shrinking regression coefficients and identifying outlying cells in the data matrix. Specifically, we highlight the performance of CR-Lasso, a new approach which incorporates a constraint on the deviation of each cell in the loss function to detect outliers based on regression residuals and cell deviations by combining L1 and cellwise outlier regularization.
