Efficient Lagrangian relaxation algorithms for exact inference in natural language tasks

Abstract

For many tasks in natural language processing, finding the best solution requires a search over a large set of possible structures. Solving these combinatorial search problems exactly can be inefficient, and so researchers often use approximate techniques at the cost of model accuracy. In this thesis, we turn to Lagrangian relaxation as an alternative to approximate inference in natural language tasks. We demonstrate that Lagrangian relaxation algorithms provide efficient solutions while still maintaining formal guarantees. The approach leads to inference algorithms with the following properties: " The resulting algorithms are simple and efficient, building on standard combinatorial algorithms for relaxed problems. " The algorithms provably solve a linear programming (LP) relaxation of the original inference problem. " Empirically, the relaxation often leads to an exact solution to the original problem. We develop Lagrangian relaxation algorithms for several important tasks in natural language processing including higher-order non-projective dependency parsing, syntactic machine translation, integrated constituency and dependency parsing, and part-of-speech tagging with inter-sentence constraints. For each of these tasks, we show that the Lagrangian relaxation algorithms are often significantly faster than exact methods while finding the exact solution with a certificate of optimality in the vast majority of examples.