Abstract
The problems of variable selection and inference of statistical dependence have been addressed by modeling in the gradients learning framework based on the representer theorem. In this paper, we propose a new gradients learning algorithm in the Bayesian framework, called Gaussian Processes Gradient Learning (GPGL) model, which can achieve higher accuracy while returning the credible intervals of the estimated gradients that existing methods cannot provide. The simulation examples are used to verify the proposed algorithm, and its advantages can be seen from the experimental results.
This research was supported by the National High Technology Research and Development (863) Program of China (2007AA01Z161).
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
Wu, Q., Guinney, J., Maggioni, M., Mukherjee, S.: Learning gradients: predictive models that infer geometry and dependence. Technical report, Duke University (2007)
Vapnik, V.: Statistical Learning Theory. Wiley, Chichester (1998)
Xia, Y., Tong, H., Li, W.K., Zhu, L.X.: An adaptive estimation of dimension reduction space. Journal of Royal Statistical Society 64(3), 363–410 (2002)
Mukherjee, S., Zhou, D.X.: Learning coordinate covariances via gradients. Journal of Machine Learning Research 7, 519–549 (2006)
Mukherjee, S., Wu, Q.: Estimation of gradients and coordinate covariation in classification. Journal of Machine Learning Research 7, 2481–2514 (2006)
West, M.: Bayesian factor regression models in the ”large p, small n” paradigm. In: Bayesian Statistics, vol. 7, pp. 723–732. Oxford University Press, Oxford (2003)
Mukherjee, S., Wu, Q., Zhou, D.X.: Learning gradients and feature selection on manifolds. Technical report, Duke University (2007)
Dollar, P., Rabaud, V., Belongie, S.: Non-isometric manifold learning: Analysis and an algorithm. In: International Conference on Machine Learning, pp. 241–248 (2007)
Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. The MIT Press, Cambridge (2006)
Schoelkopf, B., Smola, A.: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. The MIT Press, Cambridge (2001)
Bonilla, E.V., Chai, K.M.A., Williams, C.K.I.: Multi-task gaussian process prediction. In: Advances in Neural Information Processing Systems, vol. 20, pp. 153–160 (2008)
Brookes, M.: The Matrix Reference Manual (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jiang, X., Gao, J., Wang, T., Kwan, P.W. (2010). Learning Gradients with Gaussian Processes. In: Zaki, M.J., Yu, J.X., Ravindran, B., Pudi, V. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2010. Lecture Notes in Computer Science(), vol 6119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13672-6_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-13672-6_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13671-9
Online ISBN: 978-3-642-13672-6
eBook Packages: Computer ScienceComputer Science (R0)