Minimization methods for non-differentiable functions
Minimization methods for non-differentiable functions
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Polyhedral characterization of discrete dynamic programming
Operations Research
Conditional Random Fields: Probabilistic Models for Segmenting and Labeling Sequence Data
ICML '01 Proceedings of the Eighteenth International Conference on Machine Learning
Computational Combinatorial Optimization, Optimal or Provably Near-Optimal Solutions [based on a Spring School]
Three generative, lexicalised models for statistical parsing
ACL '98 Proceedings of the 35th Annual Meeting of the Association for Computational Linguistics and Eighth Conference of the European Chapter of the Association for Computational Linguistics
Convex Optimization
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Fast decoding and optimal decoding for machine translation
ACL '01 Proceedings of the 39th Annual Meeting on Association for Computational Linguistics
Statistical phrase-based translation
NAACL '03 Proceedings of the 2003 Conference of the North American Chapter of the Association for Computational Linguistics on Human Language Technology - Volume 1
Feature-rich part-of-speech tagging with a cyclic dependency network
NAACL '03 Proceedings of the 2003 Conference of the North American Chapter of the Association for Computational Linguistics on Human Language Technology - Volume 1
Integer linear programming inference for conditional random fields
ICML '05 Proceedings of the 22nd international conference on Machine learning
Efficient Belief Propagation for Early Vision
International Journal of Computer Vision
Convergent Tree-Reweighted Message Passing for Energy Minimization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Word alignment via quadratic assignment
HLT-NAACL '06 Proceedings of the main conference on Human Language Technology Conference of the North American Chapter of the Association of Computational Linguistics
Discriminative learning and spanning tree algorithms for dependency parsing
Discriminative learning and spanning tree algorithms for dependency parsing
Linear Programming Relaxations and Belief Propagation -- An Empirical Study
The Journal of Machine Learning Research
Combinatorial Optimization: Theory and Algorithms
Combinatorial Optimization: Theory and Algorithms
Incremental integer linear programming for non-projective dependency parsing
EMNLP '06 Proceedings of the 2006 Conference on Empirical Methods in Natural Language Processing
Dependency parsing by belief propagation
EMNLP '08 Proceedings of the Conference on Empirical Methods in Natural Language Processing
Approximate Primal Solutions and Rate Analysis for Dual Subgradient Methods
SIAM Journal on Optimization
Concise integer linear programming formulations for dependency parsing
ACL '09 Proceedings of the Joint Conference of the 47th Annual Meeting of the ACL and the 4th International Joint Conference on Natural Language Processing of the AFNLP: Volume 1 - Volume 1
On dual decomposition and linear programming relaxations for natural language processing
EMNLP '10 Proceedings of the 2010 Conference on Empirical Methods in Natural Language Processing
Dual decomposition for parsing with non-projective head automata
EMNLP '10 Proceedings of the 2010 Conference on Empirical Methods in Natural Language Processing
MRF Energy Minimization and Beyond via Dual Decomposition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Exact decoding of syntactic translation models through Lagrangian relaxation
HLT '11 Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies - Volume 1
Model-based aligner combination using dual decomposition
HLT '11 Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies - Volume 1
HLT '11 Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies - Volume 1
An alternating direction method for dual MAP LP relaxation
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part II
Fast and robust joint models for biomedical event extraction
EMNLP '11 Proceedings of the Conference on Empirical Methods in Natural Language Processing
Exact decoding of phrase-based translation models through Lagrangian relaxation
EMNLP '11 Proceedings of the Conference on Empirical Methods in Natural Language Processing
Dual decomposition with many overlapping components
EMNLP '11 Proceedings of the Conference on Empirical Methods in Natural Language Processing
MAP estimation via agreement on trees: message-passing and linear programming
IEEE Transactions on Information Theory
Coordination structure analysis using dual decomposition
EACL '12 Proceedings of the 13th Conference of the European Chapter of the Association for Computational Linguistics
Implicitly intersecting weighted automata using dual decomposition
NAACL HLT '12 Proceedings of the 2012 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies
An exact dual decomposition algorithm for shallow semantic parsing with constraints
SemEval '12 Proceedings of the First Joint Conference on Lexical and Computational Semantics - Volume 1: Proceedings of the main conference and the shared task, and Volume 2: Proceedings of the Sixth International Workshop on Semantic Evaluation
Improved parsing and POS tagging using inter-sentence consistency constraints
EMNLP-CoNLL '12 Proceedings of the 2012 Joint Conference on Empirical Methods in Natural Language Processing and Computational Natural Language Learning
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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.