Neural Networks: An Overview - Neural Networks: Methodology and Applications - page 19

Fig. 1.11. A real-life situation: a finite number of measurements are available. Note
that the measurements are equally spaced in the present example, but that is by no
means necessary
differences between the values predicted by the network and the measured
values is minimum, as shown on Fig. 1.12.
A neural network can thus predict, from examples, the values of a quantity
that depends on several variables, for values of the variables that are not
present in the database used for estimating the parameters of the model. In
the case shown on Fig. 1.12, the neural network can predict values of the quan-
tity of interest for points that lie between the measured points. That ability is
termed “statistical inference” in the statistics literature, and is called “gener-
alization” in the neural network literature. It should be absolutely clear that
the generalization ability is necessarily limited: it cannot extend beyond the
boundaries of the region of input space where training examples are present, as
shown on Fig. 1.9. The estimation of the generalization ability is an important
question that will be examined in detail in the present topic.
Fig. 1.12. An approximation of the regression function, performed by a neural
network, from the experimental points of Fig. 1.11