  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.
