Response to the comments by J. Larsen and L.K. Hansen for Rivals, I., & Personnaz, L. (2000): construction of confidence intervals for neural networks based on least squares estimation

Authors:
I. Rivals;L. Personnaz
Affiliations:
Équipe de Statistique Appliquée, École Supérieure de Physique et de Chimie Industrielles, 10 rue Vauquelin, 75231 Paris Cedex 05, France;Équipe de Statistique Appliquée, École Supérieure de Physique et de Chimie Industrielles, 10 rue Vauquelin, 75231 Paris Cedex 05, France
Venue:
Neural Networks
Year:
2002

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Comments for: Rivals, I., & Personnaz, L. (2000).: construction of confidence intervals for neural networks based on least squares estimation

Neural Networks

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Abstract

We answer several comments made by Hansen and Larsen (2001) about our paper (Rivals & Personnaz, 2000). In this paper, we dealt with the construction of confidence intervals (CIs) for neural networks based on least squares (LS) estimation, using the linear Taylor expansion of the network output. We also suggested a method for the detection of the possible overfitting of a trained neural network, and an estimate of its leave-one-out (LOO) score that does not necessitate additional training. Finally, we showed that the frequentist approach we adopt compares favourably with other analytic approaches, such as the conceptually very different Bayesian approach.