Bayesian Gaussian Process Regression for High-Dimensional Data

• Activity Number: 40
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Qing He*+ and Jian Kang and Qi Long
• Companies: Emory University and Emory University and Emory University
• Keywords: Bayesian Learning ; High Dimensional Data ; Gaussian Process ; Brain Imagining Data

Abstract

There has been a growing interest in fitting non-parametric regression models via Gaussian processes (GPs) from a Bayesian perspective.~ Although the posterior inference for the GP regression model is mathematically tractable, the computational costs can be very huge for high-dimensional data analyses.~ Recently, some statistical methods have been proposed to mitigate this problem,~ e.g. a Gaussian predictive process model for large spatial data (Baynerjee et. al. 2008) and a method projecting data onto a lower dimensional subspace (Banerjee et. al. 2011). Alternatively, in this paper, we investigate an efficient posterior computation method that is developed from a fast GP simulation procedure (Wood & Chan 1994). This method is particularly useful for the analysis of imaging data where the observed intensities are equally spaced. We apply the Metropolis adjusted Langevin algorithm (Roberts & Stramer, 2003) and Riemann manifold Langevin/Hamiltonian Monte Carlo algorithm (Girolami & Calderhead 2011) to this method. We conduct numerical studies to compare the performance of these different methods.