On the Analysis of Adaptability in Multi-Source Domain Adaptation

Abstract

In many real-world applications, it may be desirable to benefit from a classifier trained on a given source task from some largely annotated dataset in order to address a different but related target task for which only weakly labeled data are available. Domain adaptation (DA) is the framework which aims at leveraging the statistical similarities between the source and target distributions to learn well. Current theoretical results show that the efficiency of DA algorithms depends on (i) their capacity of minimizing the divergence between the source and target domains and (ii) the existence of a good hypothesis that commits few errors in both domains. While most of the work in DA has focused on new divergence measures, the second aspect, often modeled as the capability term , remains surprisingly under-investigated. In this paper, we show that the problem of the best joint hypothesis estimation can be reformulated using a Wasserstein distance-based error function in the context of multi-source DA. Based on this idea, we provide a theoretical analysis of the capability term and derive inequalities allowing us to estimate it from finite samples. We empirically illustrate the proposed idea on different data sets.