Projection Pursuit Regression for Multiple Responses

• Activity Number: 180
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Xin Lu Tan* and Andreas Buja and Zongming Ma
• Companies: The Wharton School and University of Pennsylvania and The Wharton School
• Keywords: additive model ; projection pursuit regression ; single index model ; reproducing kernel Hilbert space

Abstract

We study a regression problem in which a multivariate response depends on the set of predictors in a non-linear way. A method designed for such scenario is projection pursuit regression (PPR), where each response variable is modeled as a linear combination of ridge functions in the predictor variables, i.e. functions of linear combination of the predictors. Albeit a flexible regression tool, PPR can be hard to interpret in practice due to identifiability issues. In this paper, we provide mild sufficient conditions for the model to be identifiable. We then study the estimation of the model when the dimension of both predictors and responses are large relative to the sample size. We introduce a penalized least squares estimator, and provide a heuristic algorithm for efficient computation of the estimator. We demonstrate the merits of PPR on real data.