# Asymptotic law of likelihood ratio for multilayer perceptron models.

Abstract : We consider regression models involving multilayer perceptrons (MLP) with one hidden layer and a Gaussian noise. The data are assumed to be generated by a true MLP model and the estimation of the parameters of the MLP is done by maximizing the likelihood of the model. When the number of hidden units of the true model is known, the asymptotic distribution of the maximum likelihood estimator (MLE) and the likelihood ratio (LR) statistic is easy to compute and converge to a $\chi^2$ law. However, if the number of hidden unit is over-estimated the Fischer information matrix of the model is singular and the asymptotic behavior of the MLE is unknown. This paper deals with this case, and gives the exact asymptotic law of the LR statistics. Namely, if the parameters of the MLP lie in a suitable compact set, we show that the LR statistics is the supremum of the square of a Gaussian process indexed by a class of limit score functions.
Keywords :
Type de document :
Pré-publication, Document de travail
19 pages. 2010
Domaine :

Littérature citée [9 références]

https://hal.archives-ouvertes.fr/hal-00540383
Contributeur : Joseph Rynkiewicz <>
Soumis le : vendredi 26 novembre 2010 - 15:47:31
Dernière modification le : mardi 28 novembre 2017 - 01:18:21
Document(s) archivé(s) le : dimanche 27 février 2011 - 02:57:49

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• HAL Id : hal-00540383, version 1
• ARXIV : 1011.6039

### Citation

Joseph Rynkiewicz. Asymptotic law of likelihood ratio for multilayer perceptron models.. 19 pages. 2010. 〈hal-00540383〉

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