nips nips2003 nips2003-126 nips2003-126-reference knowledge-graph by maker-knowledge-mining

126 nips-2003-Measure Based Regularization


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Author: Olivier Bousquet, Olivier Chapelle, Matthias Hein

Abstract: We address in this paper the question of how the knowledge of the marginal distribution P (x) can be incorporated in a learning algorithm. We suggest three theoretical methods for taking into account this distribution for regularization and provide links to existing graph-based semi-supervised learning algorithms. We also propose practical implementations. 1


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[1] M. Belkin and P. Niyogi. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation, 15(6):1373–1396, 2003.

[2] M. Belkin and P. Niyogi. Semi-supervised learning on manifolds. Machine Learning journal, 2003. to appear.

[3] F. Girosi, M. Jones, and T. Poggio. Priors, stabilizers and basis functions: From regularization to radial, tensor and additive splines. Technical Report Artificial Intelligence Memo 1430, Massachusetts Institute of Technology, 1993.

[4] W. Hoeffding. Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association, 58:13–30, 1963.

[5] G. Kimeldorf and G. Wahba. Some results on tchebychean spline functions. Journal of Mathematics Analysis and Applications, 33:82–95, 1971.

[6] Doudou LaLoudouana and Mambobo Bonouliqui Tarare. Data set selection. In Advances in Neural Information Processing Systems, volume 15, 2002.

[7] A. Y. Ng, M. I. Jordan, and Y. Weiss. On spectral clustering: Analysis and an algorithm. In Advances in Neural Information Processing Systems, volume 14, 2001.

[8] B. Sch¨lkopf and A. Smola. Learning with kernels. MIT Press, Cambridge, MA, 2002. o

[9] A. Smola and B. Scholkopf. On a kernel-based method for pattern recognition, regression, approximation and operator inversion. Algorithmica, 22:211–231, 1998.

[10] M. Szummer and T. Jaakkola. Information regularization with partially labeled data. In Advances in Neural Information Processing Systems, volume 15. MIT Press, 2002.

[11] J. B. Tenenbaum, V. de Silva, and J. C. Langford. A global geometric framework for nonlinear dimensionality reduction. Science, 290(5500):2319–2323, 2000.

[12] P. Vincent and Y. Bengio. Density-sensitive metrics and kernels. Presented at the Snowbird Learning Workshop, 2003.

[13] U. von Luxburg and O. Bousquet. Distance-based classification with lipschitz functions. In Proceedings of the 16th Annual Conference on Computational Learning Theory, 2003.