Abstract: Unsupervised Domain Adaptation aims to learn a model for an unlabelled target domain, given access to a single labelled but differently distributed source domain. However, often multiple labelled sources which share complementary information are present, resulting in the more practical problem of multi-source domain adaptation (MSDA). Recent works in MSDA learn a domain-invariant space from the sources and target. However, they treat each source to be equally relevant to the target and are not sensitive towards the intrinsic statistical similarities amongst domains. In this work, we propose a novel method for MSDA, termed WAMDA, which utilizes the multiple sources based on their relative importance to the target. Our aim is to explore the relevance of each source-target alignment and source-source alignment, and then perform weighted alignment of domains by using the relevance scores. We experimentally validate the performance of our proposed method on multiple datasets, and achieve either state-of-the-art results or competitive performances across all these datasets.