Probabilities of discrepancy between minima of cross-validation, Vapnik bounds and true risks
Two known approaches to complexity selection are taken under consideration: n-fold cross-validation and structural risk minimization. Obviously, in either approach, a discrepancy between the indicated optimal complexity (indicated as the minimum of a generalization error estimate or a bound) and the genuine minimum of unknown true risks is possible. In the paper, this problem is posed in a novel quantitative way. We state and prove theorems demonstrating how one can calculate pessimistic probabilities...