Sharpness Estimation of Combinatorial Generalization Ability Bounds for Threshold Decision Rules

This article is devoted to the problem of calculating an exact upper bound for thefunctionals of the generalization ability of a family of one-dimensional threshold decision rules. Analgorithm is investigated that solves the stated problem and is polynomial in the total number ofsamples used for training and validation and in the number of training samples. A theorem isproved for calculating an estimate for the functional of expected overfitting and an estimate forthe error rate of the method for minimizing empirical risk on a validation set. The exact boundscalculated using the theorem are compared with the previously known quick-to-compute upperbounds so as to estimate the orders of overestimation of the bounds and to identify the boundsthat could be used in real problems.