AbstractDomain divergence plays a significant role in estimating the performance of a model in new domains. While there is a significant literature on divergence measures, researchers find it hard to choose an appropriate divergence for a given NLP application. We address this shortcoming by both surveying the literature and through an empirical study. We develop a taxonomy of divergence measures consisting of three classes — Information-theoretic, Geometric, and Higher-order measures and identify the relationships between them. Further, to understand the common use-cases of these measures, we recognise three novel applications – 1) Data Selection, 2) Learning Representation, and 3) Decisions in the Wild – and use it to organise our literature. From this, we identify that Information-theoretic measures are prevalent for 1) and 3), and Higher-order measures are more common for 2). To further help researchers choose appropriate measures to predict drop in performance – an important aspect of Decisions in the Wild, we perform correlation analysis spanning 130 domain adaptation scenarios, 3 varied NLP tasks and 12 divergence measures identified from our survey. To calculate these divergences, we consider the current contextual word representations (CWR) and contrast with the older distributed representations. We find that traditional measures over word distributions still serve as strong baselines, while higher-order measures with CWR are effective.