In fair machine learning, one source of performance disparities between
groups is over-fitting to groups with relatively few training samples. We
derive group-specific bounds on the generalization error of welfare-centric
fair machine learning that benefit from the larger sample size of the majority
group. We do this by considering group-specific Rademacher averages over a
restricted hypothesis class, which contains the family of models likely to
perform well with respect to a fair learning objective (e.g., a power-mean).
Our simulations demonstrate these bounds improve over a naive method, as
expected by theory, with particularly significant improvement for smaller group
sizes.

公平机器学习中，性能差异的一个原因是对训练样本较少的群体过拟合。本文推导了福利为中心的公平机器学习的群体特定的泛化误差界，从而得益于多数群体较大的样本量。通过考虑一个受限假设类中的群体特定的 Rademacher 平均，该假设类包含了在公平学习目标（如 power-mean）方面表现良好的模型族。我们的模拟实验证明，这些界限相对于朴素方法有所改进，并且对于较小的群体大小改进尤为显著。

是否合并：对共享模型中群体公平训练的正则化效果分析

To Pool or Not To Pool: Analyzing the Regularizing Effects of Group-Fair  Training on Shared Models

The contraction inequality for Rademacher averages is extended to Lipschitz
functions with vector-valued domains, and it is also shown that in the bounding
expression the Rademacher variables can be replaced by arbitrary iid symmetric
and sub-gaussian variables. Example applications are given for multi-category
learning, K-means clustering and learning-to-learn.

本文将 Rademacher 平均值不等式扩展到向量值域的 Lipschitz 函数，并且也表明在边界表达式中 Rademacher 变量可以被任意 iid 对称和次高斯变量替代，给出了多类别学习、K 均值聚类和学习到学习的示例应用。

Rademacher 复杂度的向量收缩不等式

A vector-contraction inequality for Rademacher complexities

We propose new bounds on the error of learning algorithms in terms of a
data-dependent notion of complexity. The estimates we establish give optimal
rates and are based on a local and empirical version of Rademacher averages, in
the sense that the Rademacher averages are computed from the data, on a subset
of functions with small empirical error. We present some applications to
classification and prediction with convex function classes, and with kernel
classes in particular.

本文提出了基于数据依赖性复杂度概念的学习算法误差的新界限，利用局部和经验版本的 Rademacher 平均值对估计进行优化，适用于具有小样本误差函数子集的情况，并应用于凸函数类和核函数类的分类和预测问题。