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Local Overfitting Control via Leverages

Gaetan.Monari{at}sollac.usinor.com, Ecole Supérieure de Physique et de Chimie Industrielles de la Ville de Paris, Laboratoire d'Electronique, F 75005 Paris, France, and Usinor, DSI/DISA Sollac, F 13776 Fos-sur-Mer Cedex, France

Gérard Dreyfus

Gerard.Dreyfus{at}espci.fr, Ecole Supérieure de Physique et de Chimie Industrielles de la Ville de Paris, Laboratoire d'Electronique, F15005, Paris, France

We present a novel approach to dealing with overfitting in black box models. It is based on the leverages of the samples, that is, on the influence that each observation has on the parameters of the model. Since overfitting is the consequence of the model specializing on specific data points during training, we present a selection method for nonlinear models based on the estimation of leverages and confidence intervals. It allows both the selection among various models of equivalent complexities corresponding to different minima of the cost function (e.g., neural nets with the same number of hidden units) and the selection among models having different complexities (e.g., neural nets with different numbers of hidden units). A complete model selection methodology is derived.

This article has been cited by other articles:

				I. Rivals and L. Personnaz Jacobian Conditioning Analysis for Model Validation Neural Comput., February 1, 2004; 16(2): 401 - 418. [Abstract] [Full Text] [PDF]

				Y. Oussar, G. Monari, and G. Dreyfus Reply to the Comments on "Local Overfitting Control via Leverages" in "Jacobian Conditioning Analysis for Model Validation" by I. Rivals and L. Personnaz Neural Comput., February 1, 2004; 16(2): 419 - 443. [Abstract] [Full Text] [PDF]