Generalized Conditional Domain Adaptation: A Causal Perspective With Low-Rank Translators

Learning domain adaptive features aims to enhance the classification performance of the target domain by exploring the discriminant information from an auxiliary source set. Let X denote the feature and Y as the label. The most typical problem to be addressed is that P_XY has a so large variation between different domains that classification in the target domain is difficult. In this paper, we study the generalized conditional domain adaptation (DA) problem, in which both P_Y and P_X|Y change across domains, in a causal perspective. We propose transforming the class conditional probability matching to the marginal probability matching problem, under a proper assumption. We build an intermediate domain by employing a regression model. In order to enforce the most relevant data to reconstruct the intermediate representations, a low-rank constraint is placed on the regression model for regularization. The low-rank constraint underlines a global algebraic structure between different domains, and stresses the group compactness in representing the samples. The new model is considered under the discriminant subspace framework, which is favorable in simultaneously extracting the classification information from the source domain and adaptation information across domains. The model can be solved by an alternative optimization manner of quadratic programming and the alternative Lagrange multiplier method. To the best of our knowledge, this paper is the first to exploit low-rank representation, from the source domain to the intermediate domain, to learn the domain adaptive features. Comprehensive experimental results validate that the proposed method provides better classification accuracies with DA, compared with well-established baselines.