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  Semi-supervised Regression using Hessian energy with an application to semi-supervised dimensionality reduction

Kim, K., Steinke, F., & Hein, M. (2010). Semi-supervised Regression using Hessian energy with an application to semi-supervised dimensionality reduction. In Y. Bengio, D. Schuurmans, J. Lafferty, C. Williams, & A. Culotta (Eds.), Advances in Neural Information Processing Systems 22 (pp. 979-987). Red Hook, NY, USA: Curran.

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 Creators:
Kim, KI, Author              
Steinke, F1, 2, Author              
Hein, M, Author              
Affiliations:
1Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497794              
2Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              

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 Abstract: Semi-supervised regression based on the graph Laplacian suffers from the fact that the solution is biased towards a constant and the lack of extrapolating power. Outgoing from these observations we propose to use the second-order Hessian energy for semi-supervised regression which overcomes both of these problems, in particular, if the data lies on or close to a low-dimensional submanifold in the feature space, the Hessian energy prefers functions which vary linearly with respect to the natural parameters in the data. This property makes it also particularly suited for the task of semi-supervised dimensionality reduction where the goal is to find the natural parameters in the data based on a few labeled points. The experimental result suggest that our method is superior to semi-supervised regression using Laplacian regularization and standard supervised methods and is particularly suited for semi-supervised dimensionality reduction.

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 Dates: 2010-04
 Publication Status: Published in print
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Title: 23rd Annual Conference on Neural Information Processing Systems (NIPS 2009)
Place of Event: Vancouver, BC, Canada
Start-/End Date: 2009-12-07 - 2009-12-10

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Title: Advances in Neural Information Processing Systems 22
Source Genre: Proceedings
 Creator(s):
Bengio, Y, Editor
Schuurmans, D, Editor
Lafferty, J, Editor
Williams, C, Editor
Culotta, A, Editor
Affiliations:
-
Publ. Info: Red Hook, NY, USA : Curran
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 979 - 987 Identifier: ISBN: 978-1-615-67911-9