A fundamental notion of distance between train and test distributions from
the field of domain adaptation is discrepancy distance. While in general hard
to compute, here we provide the first set of provably efficient algorithms for
testing localized discrepancy distance, where discrepancy is computed with
respect to a fixed output classifier. These results imply a broad set of new,
efficient learning algorithms in the recently introduced model of Testable
Learning with Distribution Shift (TDS learning) due to Klivans et al. (2023).
Our approach generalizes and improves all prior work on TDS learning: (1) we
obtain universal learners that succeed simultaneously for large classes of test
distributions, (2) achieve near-optimal error rates, and (3) give exponential
improvements for constant depth circuits. Our methods further extend to
semi-parametric settings and imply the first positive results for
low-dimensional convex sets. Additionally, we separate learning and testing
phases and obtain algorithms that run in fully polynomial time at test time.

提供了可靠与高效的算法来测试本地化的差异距离，进一步扩展了 TDS 学习模型并改进了之前相关的工作，同时提供了针对常数深度电路的指数级改进，与低维凸集的首个正面结果。

学习中的分布偏移的高效差异性测试

Efficient Discrepancy Testing for Learning with Distribution Shift

The goal of the paper is to design active learning strategies which lead to
domain adaptation under an assumption of Lipschitz functions. Building on
previous work by Mansour et al. (2009) we adapt the concept of discrepancy
distance between source and target distributions to restrict the maximization
over the hypothesis class to a localized class of functions which are
performing accurate labeling on the source domain. We derive generalization
error bounds for such active learning strategies in terms of Rademacher average
and localized discrepancy for general loss functions which satisfy a regularity
condition. A practical K-medoids algorithm that can address the case of large
data set is inferred from the theoretical bounds. Our numerical experiments
show that the proposed algorithm is competitive against other state-of-the-art
active learning techniques in the context of domain adaptation, in particular
on large data sets of around one hundred thousand images.

论文旨在设计主动学习策略，实现基于 Lipschitz 函数假设的领域自适应。通过对 Mansour 等人（2009）的先前工作进行补充，我们将源和目标分布之间的差异距离概念适应于假设类的最大化，来局限于在源域上执行准确标记的函数类。我们针对满足正则条件的一般损失函数导出了这种主动学习策略的推广误差边界，用于兰德马赫平均值和局部差异度量。从理论边界中推导出实用的 K-medoids 算法，可以处理大数据集的情况。我们的数值实验表明，在领域自适应的情况下，特别是在约十万个图像的大数据集上，所提出的算法与其他最先进的主动学习技术具有竞争力。

基于差异性的域自适应主动学习

Discrepancy-Based Active Learning for Domain Adaptation

This paper addresses the general problem of domain adaptation which arises in
a variety of applications where the distribution of the labeled sample
available somewhat differs from that of the test data. Building on previous
work by Ben-David et al. (2007), we introduce a novel distance between
distributions, discrepancy distance, that is tailored to adaptation problems
with arbitrary loss functions. We give Rademacher complexity bounds for
estimating the discrepancy distance from finite samples for different loss
functions. Using this distance, we derive novel generalization bounds for
domain adaptation for a wide family of loss functions. We also present a series
of novel adaptation bounds for large classes of regularization-based
algorithms, including support vector machines and kernel ridge regression based
on the empirical discrepancy. This motivates our analysis of the problem of
minimizing the empirical discrepancy for various loss functions for which we
also give novel algorithms. We report the results of preliminary experiments
that demonstrate the benefits of our discrepancy minimization algorithms for
domain adaptation.

本文介绍了一种针对域自适应问题的新型分布距离度量 —— 偏差距离，并给出了不同损失函数的估计方法以及普遍推广界限。同时，本文也探讨了偏差距离减少和多种损失函数的最小化算法，并验证了其在不同应用场景的有效性。