Title :
Uniformly Distributed Seeds for Randomized Trace Estimator on O(N2)-operation log-det Approximation in Gaussian Process Regression
Author_Institution :
Inst. of Hamilton, Nat. Univ. of Ireland, Maynooth
Abstract :
Maximum likelihood estimation (MLE) of hyper-parameters in Gaussian process regression as well as other computational models usually and frequently requires the evaluation of the logarithm of the determinant of a positive-definite matrix (denoted by C hereafter). In general, the exact computation of log det C is of O(N3) operations where N is the matrix dimension. The approximation of log det C could be developed with O(N2) operations based on power-series expansion and randomized trace estimator. In this paper, the accuracy and effectiveness of using uniformly distributed seeds for log det C approximation is investigated. The presented approximation scheme requires 50N2 operations, generating an average computational error of 9% as shown by a large number of numerical experiments
Keywords :
Gaussian processes; computational complexity; matrix algebra; maximum likelihood estimation; randomised algorithms; regression analysis; Gaussian process regression; O(N2)-operation log-det approximation; maximum likelihood estimation; positive-definite matrix; power-series expansion; randomized trace estimator; uniformly distributed seeds; Bayesian methods; Computational modeling; Gaussian noise; Gaussian processes; Machine learning; Matrix decomposition; Maximum likelihood estimation; Robots; Sparse matrices; Statistics;
Conference_Titel :
Networking, Sensing and Control, 2006. ICNSC '06. Proceedings of the 2006 IEEE International Conference on
Conference_Location :
Ft. Lauderdale, FL
Print_ISBN :
1-4244-0065-1
DOI :
10.1109/ICNSC.2006.1673196
