B1441
Title: Iterative methods for full-scale Gaussian process approximations for large spatial data
Authors: Tim Gyger - Lucerne University of Applied Sciences (Switzerland) [presenting]
Fabio Sigrist - ETH Zurich (Switzerland)
Reinhard Furrer - University of Zurich (Switzerland)
Abstract: Gaussian processes are flexible probabilistic regression models widely used in statistics and machine learning. However, a drawback is their limited scalability to large data sets. To alleviate this, full-scale approximations (FSAs) are considered that combine inducing points, or predictive process, methods and covariance tapering, thus approximating both global and local correlations. It is shown how iterative methods can reduce the computational costs for calculating likelihoods, gradients, and predictive means and variances with FSAs. Specifically, computational costs are reduced to growing linearly instead of quadratic in the average number of non-zero entries per row in the tapered covariance matrix compared to using the Cholesky decomposition. Further, a novel, accurate and fast way is presented to approximate predictive variances relying on a stochastic diagonal estimation technique and iterative methods. Runtimes are analyzed and compared, and the accuracy of the novel iterative methods in simulated and real-world experiments. In addition, different approaches for determining inducing points are compared (random selection, kMeans++, CoverTree algorithm) in the predictive process and FSA models.
