A Novel Coordinate-Descent Algorithm for Median Regression

• Activity Number: 294
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Wenjiang Fu and Martina Fu*+
• Companies: Michigan State University and Michigan State University
• Keywords: Coordinate-Descent ; Lasso penalty ; Median regression ; Oracle properties ; Robust

Abstract

Compared to the least-squares regression, median regression is more robust to extreme data values. The development of computer technology facilitates the algorithms for median regression and makes it promising to fit complex data. Yet, fast and efficient algorithms are desirable for both least-squares regression and median regression, in particular, when the study data are sparse in high dimensional space. In this talk, we will present a novel coordinate-descent algorithm for median regression and will further extend it to the penalized median regression with the Lasso (L1) penalty. The new algorithms follow the same spirit of the Shooting algorithm for the least-squares regression with the Lasso penalty, and enjoy the fashion of simple coordinate-descent iteration similar to the Shooting algorithm. We demonstrate with simulations and real data that the new algorithms make the once complex algorithms simpler and easy for programming, and efficient to implement. We also demonstrate that the Lasso penalty median regression enjoys the oracle properties as studied in Xu and Ying (2008).