Robust and Sparse Bridge Regression

• Activity Number: 80
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Bin Li*+ and Qingzhao Yu
• Companies: Louisiana State University and
• Keywords: bridge regression ; lasso ; robust ; huber loss ; non-convex optimization ; local linear approximation

Abstract

When there are heavy-tailed errors or outliers in the response, the least squares methods may fail to produce a reliable estimator. In this talk, we proposed a generalized Huber criterion which is highly flexible and robust for large errors. We applied the new criterion to the bridge regression family and called it: "Robust and Sparse Bridge Regression" (RSBR). Obtaining the RSBR estimator requires solving a non-convex minimization problem which is a computational challenge. We provide an efficient computational algorithm to solve this non-convex problem using recent developments in difference convex programming, coordinate descent algorithm, and local linear approximation. Some numerical examples show that the proposed RSBR algorithm performs well and is suitable for large-scale problems.