Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

Generalization and Overtraining

The problem with any modeling method which does not need any assumption about the type of model ("model-free methods") is that these models tend to adapt to any data - even noise - if they are used in the wrong way. In the specific case of neural networks, this effect is called overtraining or overfitting. Overtraining occurs if the neural network is too powerful for the current problem. It then does not "recognize" the underlying trend in the data, but learns the data by heart (including the noise in the data). This results in poor generalization and too good a fit to the training data. Click on this  interactive example  to get an impression of the adversive effects of overtraining.

As you can see from the interactive example above, good generalization is quite important for useful models. There are several methods available to check the degree of generalization and/or to detect overfitting:

  • cross-validation
  • noise addition
  • monitoring set: when monitoring the performance of the neural network on an independent data set while it is trained, the training process can be stopped when its performance on the independent data set is optimal. This monitoring set (also: validation set or inspection set) has to be an independent data set.