Gaussian Process Regression for Large Data Sets

Abstract

Gaussian Process Regression is a non parametric approach for estimating relationships in data sets. For large data sets least square estimates are not feasible because of the covariance matrix inversion which requires O(n^3) computation. In Gaussian Process Regression a matrix inversion is also needed, but approximation methods exists for large n. Some of those approaches are studied in this thesis, among them are the random projection of the covariance matrix, Nyström method and the Johnson-Lindenstrauß Theorem. Furthermore sampling methods for Hyperparameter estimation are explored.