Estimation consistante de l'architecture des perceptrons multicouches

Joseph Rynkiewicz (1, 2)

1 CES - Centre d'économie de la Sorbonne
2 SAMOS - Statistique Appliquée et MOdélisation Stochastique

We consider regression models involving multilayer perceptrons (MLP) with one hidden layer and a Gaussian noise. The estimation of the parameters of the MLP can be done by maximizing the likelihood of the model. In this framework, it is difficult to determine the true number of hidden units because the information matrix of Fisher is not invertible if this number is overestimated. However, if the parameters of the MLP are in a compact set, we prove that the minimization of a suitable information criteria leads to consistent estimation of the true number of hidden units.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Joseph Rynkiewicz. Estimation consistante de l'architecture des perceptrons multicouches. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2006, 342 (9), pp.697-700. ⟨hal-00258098⟩