A Tutorial on Dual Decomposition and Lagrangian Relaxation for Inference in Natural Language Processing
It offers a tutorial for researchers and practitioners in NLP and machine learning, presenting incremental insights by applying classical methods to modern inference problems.
This tutorial provides an overview of dual decomposition and Lagrangian relaxation, addressing inference problems in natural language processing by describing algorithms, formal guarantees, and practical implementation issues, with examples drawn from NLP but general relevance to machine learning.
Dual decomposition, and more generally Lagrangian relaxation, is a classical method for combinatorial optimization; it has recently been applied to several inference problems in natural language processing (NLP). This tutorial gives an overview of the technique. We describe example algorithms, describe formal guarantees for the method, and describe practical issues in implementing the algorithms. While our examples are predominantly drawn from the NLP literature, the material should be of general relevance to inference problems in machine learning. A central theme of this tutorial is that Lagrangian relaxation is naturally applied in conjunction with a broad class of combinatorial algorithms, allowing inference in models that go significantly beyond previous work on Lagrangian relaxation for inference in graphical models.