Regression is a fundamental task in machine learning that has garnered
extensive attention over the past decades. The conventional approach for
regression involves employing loss functions that primarily concentrate on
aligning model prediction with the ground truth for each individual data
sample, which, as we show, can result in sub-optimal prediction of the
relationships between the different samples. Recent research endeavors have
introduced novel perspectives by incorporating label similarity information to
regression. However, a notable gap persists in these approaches when it comes
to fully capturing the intricacies of the underlying ground truth function. In
this work, we propose FAR (Function Aligned Regression) as a arguably better
and more efficient solution to fit the underlying function of ground truth by
capturing functional derivatives. We demonstrate the effectiveness of the
proposed method practically on 2 synthetic datasets and on 8 extensive
real-world tasks from 6 benchmark datasets with other 8 competitive baselines.
The code is open-sourced at https://github.com/DixianZhu/FAR.

通过函数导数的方法，我们提出了 FAR（函数对齐回归）作为一种更好更高效的解决方案，以适应底层真实函数，并在 2 个合成数据集和 6 个基准数据集的 8 个广泛真实世界任务中，与其他 8 个竞争基线进行实证展示。

函数对齐回归：一种从数据中显式学习函数导数的方法

Function Aligned Regression: A Method Explicitly Learns Functional  Derivatives from Data

Generalizing knowledge to unseen domains, where data and labels are
unavailable, is crucial for machine learning models. We tackle the domain
generalization problem to learn from multiple source domains and generalize to
a target domain with unknown statistics. The crucial idea is to extract the
underlying invariant features across all the domains. Previous domain
generalization approaches mainly focused on learning invariant features and
stacking the learned features from each source domain to generalize to a new
target domain while ignoring the label information, which will lead to
indistinguishable features with an ambiguous classification boundary. For this,
one possible solution is to constrain the label-similarity when extracting the
invariant features and to take advantage of the label similarities for
class-specific cohesion and separation of features across domains. Therefore we
adopt optimal transport with Wasserstein distance, which could constrain the
class label similarity, for adversarial training and also further deploy a
metric learning objective to leverage the label information for achieving
distinguishable classification boundary. Empirical results show that our
proposed method could outperform most of the baselines. Furthermore, ablation
studies also demonstrate the effectiveness of each component of our method.

我们提出了一种基于优化输运的机器学习方法，该方法不仅提取不变特征，而且在提取特征时还限制了标签相似性，以实现跨多个领域的分类。实验结果表明，该方法优于大部分基线方法，各组件的消融研究也证明了方法的有效性。