Recently, transductive learning methods, which leverage holdout sets during
training, have gained popularity for their potential to improve speed,
accuracy, and fairness in machine learning models. Despite this, the
composition of the holdout set itself, particularly the balance of sensitive
sub-groups, has been largely overlooked. Our experiments on CIFAR and CelebA
datasets show that compositional changes in the holdout set can substantially
influence fairness metrics. Imbalanced holdout sets exacerbate existing
disparities, while balanced holdouts can mitigate issues introduced by
imbalanced training data. These findings underline the necessity of
constructing holdout sets that are both diverse and representative.

最近，在机器学习模型的速度、准确性和公平性方面改进的潜力上，利用留置集在训练过程中的转导学习方法已经越来越受欢迎。然而，留置集本身的构成，特别是敏感子群的平衡，却一直被忽视。我们在 CIFAR 和 CelebA 数据集上的实验表明，留置集中的构成变化可以大大影响公平度量。失衡的留置集加剧了现有的不平等问题，而平衡的留置集可以缓解由于不平衡训练数据引入的问题。这些发现强调了构建既多样又具有代表性的留置集的必要性。

AI 公平性的感知 - 思维模型的效益与风险

The Benefits and Risks of Transductive Approaches for AI Fairness

We introduce a new tool, Transductive Local Rademacher Complexity (TLRC), to
analyze the generalization performance of transductive learning methods and
motivate new transductive learning algorithms. Our work extends the idea of the
popular Local Rademacher Complexity (LRC) to the transductive setting with
considerable changes compared to the analysis of typical LRC methods in the
inductive setting. We present a localized version of Rademacher complexity
based tool wihch can be applied to various transductive learning problems and
gain sharp bounds under proper conditions. Similar to the development of LRC,
we build TLRC by starting from a sharp concentration inequality for independent
variables with variance information. The prediction function class of a
transductive learning model is then divided into pieces with a sub-root
function being the upper bound for the Rademacher complexity of each piece, and
the variance of all the functions in each piece is limited. A carefully
designed variance operator is used to ensure that the bound for the test loss
on unlabeled test data in the transductive setting enjoys a remarkable
similarity to that of the classical LRC bound in the inductive setting. We use
the new TLRC tool to analyze the Transductive Kernel Learning (TKL) model,
where the labels of test data are generated by a kernel function. The result of
TKL lays the foundation for generalization bounds for two types of transductive
learning tasks, Graph Transductive Learning (GTL) and Transductive
Nonparametric Kernel Regression (TNKR). When the target function is
low-dimensional or approximately low-dimensional, we design low rank methods
for both GTL and TNKR, which enjoy particularly sharper generalization bounds
by TLRC which cannot be achieved by existing learning theory methods, to the
best of our knowledge.

我们介绍了一种新工具，Transductive Local Rademacher Complexity (TLRC)，用于分析转导学习方法的泛化性能，并激发新的转导学习算法。我们的工作将热门的 Local Rademacher Complexity (LRC) 的概念扩展到转导设置，并与归纳设置中典型的 LRC 方法的分析相比，进行了相当大的改变。我们提出了一种基于局部化的 Rademacher 复杂度的工具，可以应用于各种转导学习问题，并在适当条件下获得尖锐的界限。类似于 LRC 的发展，我们通过从具有方差信息的独立变量的尖锐集中不等式开始，构建了 TLRC，然后将转导学习模型的预测函数类划分为多个片段，其中每个片段的 Rademacher 复杂度上界由一个子根函数表示，并且每个片段中所有函数的方差都受到限制。我们使用精心设计的方差运算符，确保在转导设置中未标记的测试数据的测试损失的界限与归纳设置中经典 LRC 界限具有显著的相似性。我们使用新的 TLRC 工具分析了转导核学习 (TKL) 模型，其中测试数据的标签由一个核函数生成。TKL 的结果为两类转导学习任务，即图转导学习 (GTL) 和转导非参数核回归 (TNKR)，奠定了泛化界限的基础。当目标函数是低维度或近似低维度时，我们为 GTL 和 TNKR 设计了低秩方法，通过 TLRC，这些方法可以获得特别尖锐的泛化界限，据我们所知，这是现有的学习理论方法无法实现的。