Domain Adaptation with Optimal Transport for Extended Variable Space

Abstract

Domain adaptation aims to transfer knowledge of labeled instances obtained from a source domain to a target domain to fill the gap between the domains. Most domain adaptation methods assume that the source and target domains have the same dimensionality. Methods that are applicable when the number of variables is different in each domain have rarely been studied, especially when no label information is given for the test data obtained from the target domain. In this paper, it is assumed that common variables exist in both domains and that extra (new additional) variables are observed in the target domain; hence, the dimensionality of the target domain is higher than that of the source domain. To leverage the homogeneity of the common variables, the adaptation between these source and target domains is formulated as an optimal transport (OT) problem. In addition, a learning bound in the target domain for the proposed OT-based method is derived. The proposed algorithm is validated using both simulated and real-world data.