Neural networks have been successfully applied to solve a variety of application problems including classification and function approximation. They are especially useful as function approximators because they do not require prior knowledge of the input data distribution and they have been shown to be universal approximators. In many applications, it is desirable to extract knowledge that can explain how the problems are solved by the networks. Most existing approaches have focused on extracting symbolic rules for classification. Few methods have been devised to extract rules from trained neural networks for regression. This article presents an approach for extracting rules from trained neural networks for regression. Each rule in the extracted rule set corresponds to a subregion of the input space and a linear function involving the relevant input attributes of the data approximates the network output for all data samples in this subregion. Extensive experimental results on 32 benchmark data sets demonstrate the effectiveness of the proposed approach in generating accurate regression rules.

Abstract Neural networks have been successfully applied to solve a variety of application problems including classification and function approximation. They are especially useful as function approximators because they do not require prior knowledge of the input data distribution and they have been shown to be universal approximators. In many applications, it is desirable to extract knowledge that can explain how the problems are solved by the networks. Most existing approaches have focused on extracting symbolic rules for classification. Few methods have been devised to extract rules from trained neural networks for regression. This article presents an approach for extracting rules from trained neural networks for regression. Each rule in the extracted rule set corresponds to a subregion of the input space and a linear function involving the relevant input attributes of the data approximates the network output for all data samples in this subregion. Extensive experimental results on 32 benchmark data sets demonstrate the effectiveness of the proposed approach in generating accurate regression rules. Index terms: Regression, network pruning, rule extraction. \Lambda This author's work was sponsored in part by the Department of the Navy, Office of Naval Research, Grant N00014-98-1-0568. The content of this information does not necessarily reflect the position of the Government.

As we have seen in the preceding chapters, interpretability plays an important role in the QAR modeling process. The statistical and machine learning literature pro-vide a wide variety of modeling methods to choose from, ranging from linear regression

Abstract. In this paper we propose a new algorithm for rule extraction from a trained Multilayer Feedforward network. The algorithm is based on an interval arithmetic network inversion for particular target outputs. The types of rules extracted are N-dimensional intervals in the input space. We have performed experiments with four database and the results are very interesting. One rule extracted by the algorithm can cover 86 % of the neural network output and in other cases 64 rules cover 100 % of the neural network output. 1.