This paper investigates test-time adaptation (TTA) for regression, where a regression model pre-trained in a source domain is adapted to an unknown target distribution with unlabeled target data. Although regression is one of the fundamental tasks in machine learning, most of the existing TTA methods have classification-specific designs, which assume that models output class-categorical predictions, whereas regression models typically output only single scalar values. To enable TTA for regression, we adopt a feature alignment approach, which aligns the feature distributions between the source and target domains to mitigate the domain gap. However, we found that naive feature alignment employed in existing TTA methods for classification is ineffective or even worse for regression because the features are distributed in a small subspace and many of the raw feature dimensions have little significance to the output. For an effective feature alignment in TTA for regression, we propose Significant-subspace Alignment (SSA). SSA consists of two components: subspace detection and dimension weighting. Subspace detection finds the feature subspace that is representative and significant to the output. Then, the feature alignment is performed in the subspace during TTA. Meanwhile, dimension weighting raises the importance of the dimensions of the feature subspace that have greater significance to the output. We experimentally show that SSA outperforms various baselines on real-world datasets.

翻译：本文研究回归任务的测试时适应问题，即在源域预训练的回归模型通过未标注的目标域数据适应未知的目标分布。尽管回归是机器学习的基础任务之一，现有测试时适应方法大多针对分类任务设计，其假设模型输出类别预测，而回归模型通常仅输出单标量值。为实现回归任务的测试时适应，我们采用特征对齐方法，通过对齐源域与目标域的特征分布来缓解域间差异。然而，我们发现现有分类任务测试时适应方法中采用的朴素特征对齐对回归任务效果有限甚至有害，这是因为特征分布集中于低维子空间且原始特征维度中多数维度对输出贡献微弱。为实现回归任务测试时适应的有效特征对齐，我们提出显著子空间对齐方法。该方法包含两个核心组件：子空间检测与维度加权。子空间检测识别对输出具有代表性与显著性的特征子空间，随后在测试时适应过程中在该子空间内执行特征对齐。同时，维度加权机制提升对输出更具显著性的特征子空间维度的重要性权重。实验结果表明，该方法在真实数据集上优于多种基线模型。