Train and Test Tightness of LP Relaxations in Structured Prediction
This provides a theoretical explanation for a practical observation in structured prediction, which is incremental but addresses a known bottleneck in approximate inference.
The paper tackles the problem of why linear programming relaxations are often tight in structured prediction tasks, showing that learning with LP relaxed inference encourages integrality on training instances and that this tightness generalizes to test data.
Structured prediction is used in areas such as 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 to the striking observation that approximations based on linear programming (LP) relaxations are often tight on real-world instances. In particular, we show that learning with LP relaxed inference encourages integrality of training instances, and that tightness generalizes from train to test data.