A Formal Definition of Importance for Summarization.

Research on summarization has mainly been driven by empirical approaches, crafting systems to perform well on standard datasets with the notion of information Importance remaining latent. We argue that establishing formal theories of Importance will advance our understanding of the task and further improve summarization systems. Therefore, we attempt a definition of several concepts: Redundancy, Relevance, and Informativeness within an abstract theoretical framework. Importance arises as a single quantity naturally unifying these concepts. Finally, we provide intuitions to interpret the proposed quantities especially Importance.