Fast Gaussian Process Regression for Big Data

Abstract

Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also requires the storage of a large matrix in memory. These factors restrict the application of Gaussian Process regression to small and moderate size data sets. We present an algorithm based on empirically determined subset selection that works well on both real world and synthetic datasets. We also compare the performance of this algorithm with two other methods that are used to apply Gaussian Processes Regression on large datasets. On the synthetic and real world datasets used in this study, the algorithm demonstrated sub-linear time and space complexity. The accuracy obtained with this algorithm on the datasets used for this study is comparable to what is achieved with the two other methods commonly used to apply Gaussian Processes to large datasets.