Estimating Exact Form of Generalisation Errors

Abs t r ac t . A novel approach to estimate generalisation errors of the simple perceptron of the worst case is introduced. It is well known that the generaiisation error of the simple perceptron is of the form d# with an unknown constant d which depends only on the dimension of inputs, where t is the number of learned examples. Based upon extreme value theory in statistics we obtain an exact form of the generalisation error of the simple perceptron. The method introduced in this paper opens up new possibilities to consider generalisation errors of a class of neural networks.