Abstract
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 this https URL.
Abstract (translated)
Unsupervisedsupervised domain adaptation regression(DAR)的目标是在分类问题中，将标记源数据集和未标记目标数据集之间的域差桥接起来。最近的研究大多关注通过学习深度特征编码器来最小化源和目标特征之间的差异。在这项工作中，我们对DAR问题提出了不同的视角，通过分析深度域适配上下文中线性回归器的开括形式最小二乘法解决方案。我们不建议对齐原始特征嵌入空间，而是建议对齐特征的逆 Gram 矩阵，这受到OLS解决方案中存在的特征逆Gram矩阵和Gram矩阵捕捉特征相关性的启发。具体而言，我们提出了一种简单但有效的DAR方法，该方法利用伪逆低秩性质，在两个域的伪逆Gram矩阵生成的选定子空间中对齐大小和角度。我们评估了我们的方法和三个域适配回归基准数据集。实验结果显示，我们的方法和最先进的性能达到了水平。我们的代码可在该httpsURL上获取。
URL
https://arxiv.org/abs/2303.13325
