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Unsupervised Domain Adaptation Regression (DAR) aims to bridge the domain gapbetween a labeled source dataset and an unlabelled target dataset forregression problems. Recent works mostly focus on learning a deep featureencoder by minimizing the discrepancy between source and target features. Inthis work, we present a different perspective for the DAR problem by analyzingthe closed-form ordinary least square~(OLS) solution to the linear regressor inthe deep domain adaptation context. Rather than aligning the original featureembedding 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'sability to capture the feature correlations. Specifically, we propose a simpleyet effective DAR method which leverages the pseudo-inverse low-rank propertyto align the scale and angle in a selected subspace generated by thepseudo-inverse Gram matrix of the two domains. We evaluate our method on threedomain adaptation regression benchmarks. Experimental results demonstrate thatour method achieves state-of-the-art performance. Our code is available athttps://github.com/ismailnejjar/DARE-GRAM.

DARE-GRAM : Unsupervised Domain Adaptation Regression by Aligning Inverse Gram Matrices