Train and Test Tightness of LP Relaxations in Structured Prediction


Structured prediction is used in areas including computer vision and natural language processing to predict structured outputs such as segmentations or parse trees. In these settings, prediction is performed by MAP inference or, equivalently, by solving an integer linear program. Because of the complex scoring functions required to obtain accurate predictions, both learning and inference typically require the use of approximate solvers. We propose a theoretical explanation for the striking observation that approximations based on linear programming (LP) relaxations are often tight (exact) on real-world instances. In particular, we show that learning with LP relaxed inference encourages integrality of training instances, and that this training tightness generalizes to test data.

Journal of Machine Learning Research
David Sontag
David Sontag
Professor of EECS

My research focuses on advancing machine learning and artificial intelligence, and using these to transform health care.