Scalable Maximum Likelihood Calculations for Gaussian Processes

• Activity Number: 666
• Type: Invited
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Mihai Anitescu*+ and Michael L Stein and Jie Chen
• Companies: Argonne National Laboratory and The University of Chicago and Argonne National Laboratory
• Keywords: Gaussian Processes ; Maximum Likelihood ; Scalable Computations ; Stochastic Optimization ; Fast Multipole Methods

Abstract

We discuss the computational and statistical properties of a recently introduced unbiased stochastic approximation to the score equations for maximum likelihood calculation for Gaussian processes. Under certain conditions, including bounded condition number of the covariance matrix, the approach achieves O(n) storage and nearly O(n) computational effort per optimization step, where n is the number of data sites. Moreover, we prove that if the condition number of the covariance matrix is bounded, then the approximate score equations are nearly optimal in a well-defined sense. Our findings are validated by numerical experiments on simulated datasets of up to 1 million observations. We also report the performance and outcome of the approach to fit a space-time model to over 80,000 observations of total column ozone contained in the latitude band 40-50 degrees N during April 2012.