Abstract
The Relevance Vector Machine (RVM) is a generalized linear model that can use kernel functions as basis functions. Experiments with the Matérn kernel indicate that the kernel choice has a significant impact on the sparsity of the solution. Furthermore, not every kernel is suitable for the RVM. Our experiments indicate that the Matérn kernel of order 3 is a good initial choice for many types of data.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Juditsky, H. Hjalmarsson, A. Beneviste, B. Delyon, L. Ljung, J. Sjoberg, Q. Zhang (1995), Nonlinear Black-box Models in System Identification: Mathematical Foundations, Automatica, 31(12), pp. 1725–1750.
M.G. Genton (2001). Classes of Kernels for Machine Learning: A Statistics Perspective. Journal of Machine Learning Research 2, pages 299–312.
B. Matérn (1960). Spatial Variation. New York, Springer.
M.E. Tipping (2001). Sparse Bayesian Learning and the Relevance Vector Machine. Journal of Machine Learning Research 1, 211–244.
A. Shmilovici (2005). Support Vector Machines. In O. Maimon and L. Rokach (editors), Data Mining and Knowledge Discovery Handbook: A Complete Guide for Practitioners and Researchers, Springer.
C.E. Rasmussen, J. Quinonero-Candela, (2005). Healing the Relevance Vector Machine through Augmentation. Proceedings of the 22nd International Conference on Machine Learning, August 7–11, Bonn, Germany.
D. Wipf, J. Palmer, B. Rao (2004). Perspectives on Sparse Bayesian Learning. Advances in Neural Information Processing systems, 16. Cambridge, Massachussettes, MIT Press.
D. Ben-Shimon, A. Shmilovici (2006). Accelerating the Relevance Vector Machine via Data Partitioning, Journal of Computing and Decision Sciences, forthcoming.
J.R. Gilbert, C. Moler, R. Schreiber (1992). Sparse matrices in MATLAB design and implementation. SIAM Journal on Matrix Analysis, 13(1), pages 333–356.
N. Cristianini, J. Shawe-Taylor (2003). An Introduction to Support Vector Machines and other kernel-based learning methods. Cambridge University Press.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Ben-Shimon, D., Shmilovici, A. (2006). Kernels for the Relevance Vector Machine - An Empirical Study. In: Last, M., Szczepaniak, P.S., Volkovich, Z., Kandel, A. (eds) Advances in Web Intelligence and Data Mining. Studies in Computational Intelligence, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33880-2_26
Download citation
DOI: https://doi.org/10.1007/3-540-33880-2_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33879-6
Online ISBN: 978-3-540-33880-2
eBook Packages: EngineeringEngineering (R0)