作者：Ismail Nejjar Qin Wang Olga Fink
无监督领域自适应回归（DAR）旨在弥合回归问题的标记源数据集和未标记目标数据集之间的领域差距。最近的工作主要集中在通过最小化源特征和目标特征之间的差异来学习深度特征编码器。在这项工作中，我们通过分析深域自适应背景下线性回归器的闭式普通最小二乘解，为DAR问题提供了一个不同的视角。我们建议对齐特征的逆Gram矩阵，而不是对齐原始特征嵌入空间，这是由其在OLS解决方案中的存在和Gram矩阵捕获特征相关性的能力所驱动的。具体而言，我们提出了一种简单而有效的DAR方法，该方法利用伪逆低秩特性来对齐由两个域的伪逆Gram矩阵生成的选定子空间中的尺度和角度。我们在三个doma上评估我们的方法
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.
论文链接：http://arxiv.org/pdf/2303.13325v1
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