hal-00414774, version 1
Data-driven calibration of linear estimators with minimal penalties
Advances in Neural Information Processing Systems (NIPS 2009) 22 (2009) 46--54
Abstract: This paper tackles the problem of selecting among several linear estimators in non-parametric regression; this includes model selection for linear regression, the choice of a regularization parameter in kernel ridge regression or spline smoothing, and the choice of a kernel in multiple kernel learning. We propose a new algorithm which first estimates consistently the variance of the noise, based upon the concept of minimal penalty which was previously introduced in the context of model selection. Then, plugging our variance estimate in Mallows' $C_L$ penalty is proved to lead to an algorithm satisfying an oracle inequality. Simulation experiments with kernel ridge regression and multiple kernel learning show that the proposed algorithm often improves significantly existing calibration procedures such as 10-fold cross-validation or generalized cross-validation.
- 1:
- CNRS : UMR8548 – Ecole normale supérieure de Paris - ENS Paris
- 2:
- INRIA – Ecole normale supérieure de Paris - ENS Paris – Ecole des Ponts ParisTech – CNRS : UMR8548
- Domain : Mathematics/Statistics
Statistics/Statistics TheoryStatistics/Other StatisticsStatistics/Methodology - Keywords : Data-driven calibration – Non-parametric regression – Model selection by penalization – Minimal penalty – Kernel ridge regression – Multiple kernel learning
- Available versions : v1 (2009-09-10) v2 (2011-09-13)
- hal-00414774, version 1
- http://hal.archives-ouvertes.fr/hal-00414774
- oai:hal.archives-ouvertes.fr:hal-00414774
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- Submitted on: Wednesday, 9 September 2009 22:51:23
- Updated on: Wednesday, 26 January 2011 14:16:43
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