Estimating Shape Constrained Functions Using Gaussian Processes

• Activity Number: 649
• Type: Topic Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Xiaojing Wang*+ and James Berger
• Companies: Duke University and Duke University
• Keywords: Gaussian processes ; shape constraints ; Gibbs sampling ; derivatives ; monotone function ; nonparametric function

Abstract

Gaussian processes are a popular tool for nonparametric function estimation because of their flexibility and the fact that much of the ensuing computation is parametric Gaussian computation. However, their flexibility can be detrimental sometimes, when the function is known to be in a shape-constrained class, such as the class of monotonic functions, convex functions and so on. In solution to this, this paper will propose a generic method to introduce such a kind of shape constraints by using the interesting property of derivatives of Gaussian processes with the squared exponential correlation function. When it maintains computationally handleable, such constraints cannot be globally imposed upon infinite derivative points of the Gaussian process, but a Gibbs sampling scheme is feasible at a finite set of derivative points. The behavior of the proposed procedure will be demonstrated on several simulation examples.