Given a classification problem and a family of classifiers, the Rashomon
ratio measures the proportion of classifiers that yield less than a given loss.
Previous work has explored the advantage of a large Rashomon ratio in the case
of a finite family of classifiers. Here we consider the more general case of an
infinite family. We show that a large Rashomon ratio guarantees that choosing
the classifier with the best empirical accuracy among a random subset of the
family, which is likely to improve generalizability, will not increase the
empirical loss too much. We quantify the Rashomon ratio in two examples
involving infinite classifier families in order to illustrate situations in
which it is large. In the first example, we estimate the Rashomon ratio of the
classification of normally distributed classes using an affine classifier. In
the second, we obtain a lower bound for the Rashomon ratio of a classification
problem with a modified Gram matrix when the classifier family consists of
two-layer ReLU neural networks. In general, we show that the Rashomon ratio can
be estimated using a training dataset along with random samples from the
classifier family and we provide guarantees that such an estimation is close to
the true value of the Rashomon ratio.

在给定分类问题和一系列分类器的情况下，Rashomon 比率度量了产生小于给定损失的分类器所占的比例。我们考虑了无限分类器组的更一般情况，证明了 Rashomon 比率的增加可以保证在从分类器组的随机子集中选择具有最佳经验准确性的分类器，从而提高泛化能力，不会增加太多经验损失。我们通过两个示例量化了无限分类器组中的 Rashomon 比率，以说明其中 Rashomon 比率较大的情况。一种示例是使用线性分类器对正态分布类别进行分类，我们估计了其 Rashomon 比率。另一种示例是当分类器组由双层 ReLU 神经网络组成时，根据修改的 Gram 矩阵，我们得到了 Rashomon 比率的下界。一般来说，我们证明可以使用训练数据集和分类器组的随机样本来估计 Rashomon 比率，并提供了这种估计接近真实 Rashomon 比率值的保证。