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Home Multivariate Data Modeling Neural Networks Extrapolation  
See also: Generalization and Overtraining, Extrapolation  
Neural Networks  ExtrapolationNeural networks exhibit a major drawback when compared to linear methods
of function approximation: they cannot extrapolate. This is due to the
fact that a neural network can map virtually any function by adjusting
its parameters according to the presented training data. For regions of
the variable space where no training data is available, the output of a
neural network is not reliable.
Basically, the data space which can be processed by a trained neural network is split into two regions:
In order to overcome this problem, one should in some form record the range of the variable space where training data is available. In principle, this could be done by calculating the convex hull of the training data set. If unknown data presented to the net are within this hull, the output of the net can be considered as reliable. However, the concept of the convex hull is not satisfactory since this hull is complicated to calculate and provides no solution for problems where the input data space is concave. A better method, proposed by Leonard et al. , is to estimate the local density of training data by using Parzen windows . This would be suitable for all types of networks. Radial basis function networks provide another elegant yet simple method of detecting extrapolation regions.


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