Global Inference Using Integer Linear Programming

This report is a supplemental document of some of our papers [5, 3, 4]. It gives a simple but complete step-by-step case study, which demonstrates how we apply integer linear programming to solve a global inference problem in natural language processing. This framework first transforms an optimization problem into an integer linear program. The program can then be solved using existing numerical packages. The goal here is to provide readers an easy-to-follow example to model their own problems in this framework. There are two main parts in this report. Sec. 2 describe a problem of labeling entities and relations simultaneously as our inference task. It then discusses the constraints among the labels and shows how the objective function and constraints are transformed to an integer linear program. Although transforming the constraints to their linear forms is not di cult in this entity and relation example, sometimes it can be tricky, especially when more variables are involved. Therefore, we discuss how to handle di erent types of constraints in Sec. 3.