Regularized Additive Principal Components

• Activity Number: 178
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Xin Lu Tan*+ and Andreas Buja and Zongming Ma
• Companies: Wharton School and Wharton School and Wharton School
• Keywords: additive models ; nonlinear multivariate analysis ; kernel methods ; reproducing kernel Hilbert space

Abstract

Additive principal components (APCs) are a nonlinear generalization of linear principle components. The smallest APCs describe the nonlinear additive constraints that the data nearly satisfies. In multivariate analysis, estimation of such approximate implicit equations is more natural than the conventional regression approaches since variables are treated in a symmetric fashion. In this paper, we propose a regularized data-analytic procedure for APC estimation using kernel methods. In contrast to subspace regularization used in existing transformational multivariate analysis literature, shrinkage regularization in the proposed method grants distinctive flexibility in APC estimation by allowing the use of infinite-dimensional functions spaces for searching APC transformation, while retaining computational feasibility. To connect population APCs and regularized finite-sample APCs, we study regularized population APCs and their associated eigenproblems. Time permitting, we will discuss theoretical aspects of the problem.