Unsupervised Domain Adaptation Regression (DAR) aims to bridge the domain gap between a labeled source dataset and an unlabelled target dataset for regression problems. Recent works mostly focus on learning a deep feature encoder by minimizing the discrepancy between source and target features. In this work, we present a different perspective for the DAR problem by analyzing the closed-form ordinary least square~(OLS) solution to the linear regressor in the deep domain adaptation context. Rather than aligning the original feature embedding space, we propose to align the inverse Gram matrix of the features, which is motivated by its presence in the OLS solution and the Gram matrix's ability to capture the feature correlations. Specifically, we propose a simple yet effective DAR method which leverages the pseudo-inverse low-rank property to align the scale and angle in a selected subspace generated by the pseudo-inverse Gram matrix of the two domains. We evaluate our method on three domain adaptation regression benchmarks. Experimental results demonstrate that our method achieves state-of-the-art performance. Our code is available at https://github.com/ismailnejjar/DARE-GRAM.

翻译：无监督领域自适应回归（DAR）旨在弥合有标注源数据集与无标注目标数据集在回归问题上的领域差异。现有研究多集中于通过最小化源域与目标域特征之间的差异来学习深度特征编码器。本文从深度领域自适应背景下线性回归器的闭式普通最小二乘（OLS）解出发，提出了一种针对DAR问题的新视角。不同于对齐原始特征嵌入空间，我们提出对齐特征的逆格拉姆矩阵——这一方法的动机源于逆格拉姆矩阵在OLS解中的存在性及其对特征相关性的捕获能力。具体而言，我们提出了一种简单而有效的DAR方法，利用伪逆低秩性质，在由两域伪逆格拉姆矩阵生成的选定子空间中对齐尺度与角度。在三个领域自适应回归基准上的实验结果表明，我们的方法达到了当前最优性能。代码已开源：https://github.com/ismailnejjar/DARE-GRAM。