Abstract
Regularisation is a well-known technique for working with ill-posed and ill-conditioned problems that have been explored in a variety of different areas, including Bayesian inference, functional analysis, optimisation, numerical analysis and connectionist systems. In this paper we present the equivalence between the Bayesian approach to the regularisation theory and the Tikhonov regularisation into the function approximation theory framework, when radial basis functions networks are employed. This equivalence can be used to avoid expensive calculations when regularisation techniques are employed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Find the latest articles, discoveries, and news in related topics.References
Bertero, M., Poggio, T. and Torre, V.: Ill-posed problems in early vision. In: Proc. of the IEEE, Vol. 76, pp. 869–889, 1988.
Bossley, K. M.: Regularisation theory applied to neurofuzzy modelling, Southampton University Tech. Report ISIS-TR3, 1993.
Broomhead, D. S. and Lowe, D.: Multivariable functional interpolation and adaptive networks, Complex Systems 2 (1988), 321–355.
Girosi, F.: An equivalence between sparse approximation and support vector machines, MIT CBCL Lab., Massachusetts Inst. Technol., Cambridge, MA, A.I. Memo 1606, 1997.
Poggio, T. and Girosi, F.: A theory of networks for approximation and learning, Massachusetts Inst. Technol., Cambridge, MA, A.I. Memo 1140, 1994.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Català, A., Angulo, C. A Comparison between the Tikhonov and the Bayesian Approaches to Calculate Regularisation Matrices. Neural Processing Letters 11, 185–195 (2000). https://doi.org/10.1023/A:1009607425536
Issue Date:
DOI: https://doi.org/10.1023/A:1009607425536