542
Views
22
CrossRef citations to date
0
Altmetric
Original Articles

Approximate implementation of the logarithm of the matrix determinant in Gaussian process regression

&
Pages 329-348 | Received 06 Dec 2004, Published online: 16 Mar 2007

References

  • Martin , R. J. 1993 . Approximations to the determinant term in Gaussian maximum likelihood estimation of some spatial models . Communications in Statistics Part A: Theory and Methods , 22 : 189 – 205 .
  • Griffith , D. A. and Sone , A. 1995 . Trade-offs associated with normalizing constant computational simplifications for estimating spatial statistical models . Journal of Statistical Computation and Simulation , 51 : 165 – 183 .
  • Barry , R. P. and Pace , R. K. 1999 . Monte Carlo estimate of the log determinant of large sparse matrices . Linear Algebra and its Application , 289 : 41 – 54 .
  • Smirnov , O. and Anselin , L. 2001 . Fast maximum likelihood estimation of very large spatial autoregressive models: a characteristic polynomial approach . Computational Statistics and Data Analysis , 35 : 301 – 319 .
  • Pace , R. K. and LeSage , J. P. 2004 . Chebyshev approximation of log-determinant of spatial weight matrices . Computational Statistics and Data Analysis , 45 : 179 – 196 .
  • Griffith , D. A. 2004 . Extreme eigenfunctions of adjacency matrices for planar graphs employed in spatial analyses . Linear Algebra and its Applications , 388 : 201 – 219 .
  • Griffith , D. A. 2004 . Faster maximum likelihood estimation of very large spatial autoregressive models: an extension of the Smirnov–Anselin result . Journal of Statistical Computation and Simulation , 74 : 855 – 866 .
  • Skilling , J. 1993 . “ Bayesian numerical analysis ” . In Physics and Probability , Edited by: Grandy , W. T. and Milonni , P. 203 – 221 . Cambridge University Press .
  • Leithead , W. E. , Hardan , F. and Leith , D. J. Identification of aerodynamics and drive-train dynamics for a variable speed wind turbine . Proceedings of European Wind Energy Conference . Madrid.
  • Leithead , W. E. , Solak , E. and Leith , D. J. Direct identification of nonlinear structure using Gaussian process prior models . Proceedings of European Control Conference . Cambridge.
  • Rasmussen , C. E. 1996 . “ Evaluation of Gaussian processes and other methods for non-linear regression ” . University of Toronto . PhD thesis
  • Williams , C. K.I. and Barber , D. 1998 . Bayesian classification with Gaussian processes . IEEE Transactions on Pattern Analysis and Machine Intelligence , 20 : 1342 – 1351 .
  • Shi , J. Q. , Murray-Smith , R. and Titterington , D. M. 2003 . Bayesian regression and classification using mixtures of multiple Gaussian processes . International Journal of Adaptive Control and Signal Processing , 17 : 149 – 161 .
  • Gibbs , M. N. and MacKay , D. J.C. 1997 . “ Efficient implementation of Gaussian process ” . Cavendish Laboratory, Cambridge University . Technical Report
  • Seeger , M. 2000 . “ Skilling techniques for Bayesian analysis ” . Institute for Adaptive and Neural Computation, University of Edinburgh . Technical Report
  • Paciorek , C. J. 2003 . “ Nonstationary Gaussian processes for regression and spatial modelling ” . Department of Statistics, Carnegie Mellon University . PhD thesis
  • Yoshioka , T. and Ishii , S. Fast Gaussian process regression using representative data . Proceedings of International Joint Conference on Neural Networks . Vol. 1 , pp. 132 – 137 .
  • Leith , D. J. , Leithead , W. E. , Solak , E. and Murray-Smith , R. Divide and conquer identification using Gaussian process priors . Proceedings of the 41st IEEE Conference on Decision and Control . Vol. 1 , pp. 624 – 629 .
  • Solak , E. , Murray-Smith , R. , Leithead , W. E. , Leith , D. and Rasmussen , C. E. 2003 . “ Derivative observations in Gaussian process models of dynamic systems ” . In Advances in Neural Information Processing Systems , Vol. 15 , 1033 – 1040 . MIT Press .
  • Neal , R. M. 1997 . “ Monte Carlo implementation of Gaussian process models for Bayesian regression and classification ” . Department of Statistics, University of Toronto . Technical Report 9702
  • Nocedal , J. 1992 . “ Theory of algorithms for unconstrained optimisation ” . In Acta Numerica , 199 – 242 . Cambridge University Press .
  • Conn , A. R. , Gould , N. I.M. and Toint , Ph. L. 2000 . Trust Region Methods , Philadelphia : SIAM .
  • Wu , Z. , Phillips , G. N. Jr. , Tapia , R. and Zhang , Y. 2001 . A fast Newton method for entropy maximization in statistical phase estimation . Acta Crystallograhica , A57 : 681 – 685 .
  • Zhang , Y. and Wang , J. 2001 . Recurrent neural networks for nonlinear output regulation . Automatica , 37 : 1161 – 1173 .
  • Zhang , Y. , Jiang , D. and Wang , J. 2002 . A recurrent neural network for solving Sylvester equation with time-varying coefficients . IEEE Transactions on Neural Networks , 13 : 1053 – 1063 .
  • Golub , G. H. and Van Loan , C. F. 1996 . Matrix Computations , 566 Baltimore : Johns Hopkins University Press .
  • Hutchinson , M. F. 1990 . A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines . Communications in Statistics, Simulation, and Computation , 19 : 433 – 450 .
  • Press , W. H. , Flannery , B. P. , Teukolsky , S. A. and Vetterling , W. T. 1986 . Numerical Recipes: the Art of Scientific Computing , Vol. 2 , 64 – 66 . Cambridge : Cambridge University Press .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.