Bossley, K.M., Brown, M. and Harris, C.J.
Neurofuzzy Model Weight Identification With Multiple Priors
IEEE Trans Neural Networks
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The structure of neurofuzzy systems is restricted by the need for a fuzzy rule interpretation. This often results in some redundant structure, which is hard to identify using conventional ML estimation i.e. conventional supervised learning. This paper investigates the application of regularisation techniques to these neurofuzzy models to help improve their generalisation capabilities. In particular, this theory is applied to the additive neurofuzzy structure identified by B-spline neurofuzzy construction algorithms. Bayesian inferencing techniques in the form of MAP estimation are applied to these models resulting regularisation and an effective method for identifying the regularisation coefficient (or hyperparameters) i.e. evidence maximisation is derived. These techniques are extended to local regularisation, where a weight prior is defined for each submodel. The construction of these priors in both global and local regularisation is described. Two methods are proposed for the identification of the multiple hyperparameters: evidence maximisation and a method combining backfitting and conventional evidence maximisation techniques. These are both shown to work well on a numerical example, but due to seemly correlated inputs backfitting takes significantly longer to converge.
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