Constructing Bayesian formulations of sparse kernel learning methods

Cawley, Gavin C. ORCID: and Talbot, Nicola L. C. (2005) Constructing Bayesian formulations of sparse kernel learning methods. Neural Networks, 18 (5-6). pp. 674-683. ISSN 0893-6080

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We present here a simple technique that simplifies the construction of Bayesian treatments of a variety of sparse kernel learning algorithms. An incomplete Cholesky factorisation is employed to modify the dual parameter space, such that the Gaussian prior over the dual model parameters is whitened. The regularisation term then corresponds to the usual weight-decay regulariser, allowing the Bayesian analysis to proceed via the evidence framework of MacKay. There is in addition a useful by-product associated with the incomplete Cholesky factorisation algorithm, it also identifies a subset of the training data forming an approximate basis for the entire dataset in the kernel-induced feature space, resulting in a sparse model. Bayesian treatments of the kernel ridge regression (KRR) algorithm, with both constant and heteroscedastic (input dependent) variance structures, and kernel logistic regression (KLR) are provided as illustrative examples of the proposed method, which we hope will be more widely applicable.

Item Type: Article
Faculty \ School: Faculty of Science > School of Computing Sciences

UEA Research Groups: Faculty of Science > Research Groups > Computational Biology
Faculty of Science > Research Groups > Data Science and Statistics
Faculty of Science > Research Groups > Centre for Ocean and Atmospheric Sciences
Depositing User: Vishal Gautam
Date Deposited: 08 May 2011 13:24
Last Modified: 21 Apr 2023 22:31
DOI: 10.1016/j.neunet.2005.06.002

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