Evaluating Misclassification Probability Using Empirical Risk

* The work is supported by RFBR, grant 04-01-00858-a

The goal of the paper is to estimate misclassification probability for decision function by training sample. Here are presented results of investigation an empirical risk bias for nearest neighbours, linear and decision tree classifier in comparison with exact bias estimations for a discrete (multinomial) case. This allows to find out how far Vapnik–Chervonenkis risk estimations are off for considered decision function classes and to choose optimal complexity parameters for constructed decision functions. Comparison of linear classifier and decision trees capacities is also performed.