The Radial Basis Function (RBF) neural networks are nonparametric regression tools similar in formula to the Nadaraya-Watson kernel estimator. Starting from this resemblance, the relationships between the RBF neural nets and the kernel methods are discussed. Some results regarding the moment matrix of the radial basis functions are used to understand the linkage between these estimators and to show a different behaviour of their bandwidth. It is also recalled that the rate of convergence of RBF nets is not dependent on the dimension of the domain of the regression function unlike kernel methods. Afterwards the comparison moves on more applied aspects and a RBF net joint on an ARCH model is proposed to analyse financial time series.
Mancuso, D. A., Le reti neurali RBF: legami e differenze con i metodi kernel., in Atti del convegno MAF 2004 - Metodi matematici e statistici per l'analisi dei dati assicurativi e finanziari, (Università degli studi di Salerno, 15-16 April 2004), Cusl, Salerno 2004: 163-168 [http://hdl.handle.net/10807/21476]
Le reti neurali RBF: legami e differenze con i metodi kernel.
Mancuso, Diego Attilio
2004
Abstract
The Radial Basis Function (RBF) neural networks are nonparametric regression tools similar in formula to the Nadaraya-Watson kernel estimator. Starting from this resemblance, the relationships between the RBF neural nets and the kernel methods are discussed. Some results regarding the moment matrix of the radial basis functions are used to understand the linkage between these estimators and to show a different behaviour of their bandwidth. It is also recalled that the rate of convergence of RBF nets is not dependent on the dimension of the domain of the regression function unlike kernel methods. Afterwards the comparison moves on more applied aspects and a RBF net joint on an ARCH model is proposed to analyse financial time series.
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