Abstract

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

中文翻译：

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阈值决策规则组合泛化能力边界的锐度估计

摘要

本文致力于计算一维阈值决策规则族泛化能力泛函的精确上限问题。研究了一种算法，该算法解决了所述问题，并且在用于训练和验证的样本总数以及训练样本数方面是多项式的。证明了一个定理，用于计算预期过度拟合的函数估计和最小化验证集经验风险的方法的错误率估计。将使用该定理计算出的确切界限与先前已知的快速计算上限进行比较，以估计高估界限的阶数，并确定可以在实际问题中使用的界限。