Functional Gaussian Process Model for Bayesian Nonparametric Analysis

• Activity Number: 305
• Type: Topic Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Leo Duan* and Xia Wang and Rhonda Szczesniak
• Companies: and University of Cincinnati and Cincinnati Children's Hospital Medical Center
• Keywords: Scalable Gaussian Process ; Spectral Density ; Non-Stationarity ; Spatial-Temporal Model ; Mixture Model

Abstract

Gaussian process regression provides a functional description about how correlation decays over space/time distance. However, due to the expensive computation, this nicely interpretable form becomes unsuitable for handling extremely large data or incorporating more sophisticated structure. To solve this problem, we propose a new Bayesian approach called the Functional Gaussian Process, which not only significantly reduces the computational cost to O(n log_2 n), but also retains the model accuracy and simplicity. In our model, the data are assumed to be partial and noisy realization from a latent lattice process, which can be rapidly sampled with its spectral properties. This process enables rapid updates of the missing values, controls the numerical errors and can be easily extended to model non-stationary data. For the data application, we demonstrate the prediction with a large and correlated dataset consisting of 30-year annual surface air temperature in North America. We use the Functional Gaussian Process to facilitate the estimation of 3 non-stationary models, including one with non-separable space-time interactions. Our approach shows great performance and interpretability.