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 \url{https://github.com/DixianZhu/FAR}.

翻译：回归是机器学习中的一项基本任务，过去几十年来得到了广泛关注。传统回归方法主要采用聚焦于对齐每个数据样本的模型预测与真实值的损失函数，但我们证明，这种方法可能导致对样本间关系的预测欠优。近年来的研究通过引入标签相似性信息为回归提供了新视角，然而，这些方法在完全捕捉底层真实函数的复杂性方面仍存在显著不足。本文提出FAR（函数对齐回归），通过捕获函数导数，为拟合真实值的底层函数提供了一种更优且更高效的解决方案。我们在2个合成数据集和来自6个基准数据集的8项广泛真实世界任务上，与8个具有竞争力的基准方法对比，实证验证了所提方法的有效性。代码已开源在\url{https://github.com/DixianZhu/FAR}。