High-Dimensional Multivariate Additive Regression

• Activity Number: 652
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Rodrigue Ngueyep Tzoumpe*+ and Nicoleta Serban
• Companies: Georgia Institute of Technology and Georgia Institute of Technology
• Keywords: Multivariate Regression ; Sparsity ; Additive Models ; Coordinate Descent

Abstract

In this paper, we propose a new methodology to tackle the problem of high- dimensional non-parametric learning in the multi-responses or multitask learning setting. We impose sparsity constraints that allow the recovery of the additive functions that are the most influential across tasks and responses. The methodology instead of applying l1\l_{\infty} as proposed by Liu et al. (2008), applies a functional l1\l2 norm to each group of additive functions. Each group contains all the additive functions associated with a specific predictor. We derive a novel thresholding condition for the union support recovery in the non-parametric setting. we propose a sparse backfitting based algorithm to solve for the additive functions. Through extensive simulations, we show the superior performance of the methodology. We also apply the methodology to a set of healthcare data.