1520-0450(1987)026-1589-cviscf-2.0.co;2.pdf

Set consists of predictions and targets

A set of prediction rule will be used to predict y₀ from

Let be the accuracy.
by least squares this will usually
in other words expected Err is

MSE

In cross validation

Cross-validation and bootstrapping are both methods for estimating generalization error based on “resampling”.

In k-fold cross-validation, you divide the data into k subsets of (approximately) equal size. You train the net k times, each time leaving out one of the subsets from training, but using only the omitted subset to compute whatever error criterion interests you. If k equals the sample size, this is called “leave-one-out” cross-validation.

This article presents an algorithm that constructs feedforward neural networks with a single hidden layer for pattern classification. The algorithm starts with a small number of hidden units in the network and adds more hidden units as needed to improve the network’s predictive accuracy. To determine when to stop adding new hidden units, the algorithm makes use of a subset of the available training samples for cross validation. New hidden units are added to the network only if they improve the classification accuracy of the network on the training samples and on the cross-validation samples.

Extensive experimental results show that the algorithm is effective in obtaining networks with predictive accuracy rates that are better than those obtained by state-of-the-art decision tree methods.

10.1.1.112.9536.pdf