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 (Neural Networks 13)

Isabelle Rivals (1) , Léon Personnaz (1)

1 ESA - Equipe de Statistique Appliquée (UMRS 1158)

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 and 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 trainings. Finally, we showed that the frequentist approach we adopt compares favourably with other analytic approaches such as the conceptually very different Bayesian approach.

Keywords: Taylor expansion; Approximate leave one out score; confidence intervals; cross validation; least squares estimation; Taylor expansion.

Domains: Computer Science [cs]; Neural and Evolutionary Computing [cs.NE]; Statistics [stat]; Machine Learning [stat.ML]

Isabelle Rivals, Léon Personnaz. 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 (Neural Networks 13). Neural Networks, 2002, 15 (1), pp.141-143. ⟨hal-00798661⟩