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Exploiting Hessian matrix and trust-region algorithm in hyperparameters estimation of Gaussian process

Zhang, Y. and Leithead, W.E. (2005) Exploiting Hessian matrix and trust-region algorithm in hyperparameters estimation of Gaussian process. Applied Mathematics and Computation, 171 (2). pp. 1264-1281. ISSN 0096-3003

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Abstract

Gaussian process (GP) regression is a Bayesian non-parametric regression model, showing good performance in various applications. However, it is quite rare to see research results on log-likelihood maximization algorithms. Instead of the commonly used conjugate gradient method, the Hessian matrix is first derived/simplified in this paper and the trust-region optimization method is then presented to estimate GP hyperparameters. Numerical experiments verify the theoretical analysis, showing the advantages of using Hessian matrix and trust-region algorithms. In the GP context, the trust-region optimization method is a robust alternative to conjugate gradient method, also in view of future researches on approximate and/or parallel GP-implementation.

Item type: Article
ID code: 4701
Keywords: Gaussian process, log likelihood maximization, conjugate gradient, trust region, Hessian matrix, Electrical engineering. Electronics Nuclear engineering, Computational Mathematics, Applied Mathematics
Subjects: Technology > Electrical engineering. Electronics Nuclear engineering
Department: Faculty of Engineering > Electronic and Electrical Engineering
Related URLs:
    Depositing user: Strathprints Administrator
    Date Deposited: 10 Nov 2007
    Last modified: 04 Sep 2014 16:53
    URI: http://strathprints.strath.ac.uk/id/eprint/4701

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