Solving submodular text processing problems using influence graphs

Submodular functions appear in a considerable number of important natural language processing problems such as text summarization and dataset selection. Current graph-based approaches to solving such problems do not pay special attention to the submodularity and simplistically do not learn the graph model. Instead, they roughly set the edge weights in the graph proportional to the similarity of their two endpoints. We argue that such a shallow modeling needs to be replaced by a deeper approach which learns the graph edge weights. As such, we propose a new method for learning the graph model corresponding the submodular function that is going to be maximized. In a number of real-world networks, our method leads to a 50% error reduction compared to the previously used baseline methods. Furthermore, we apply our proposed method followed by an influence maximization algorithm to two NLP tasks: text summarization and k-means initialization for topic selection. Using these case studies, we experimentally show the significance of our learning method over the previous shallow methods.