An alternating direction method for dual MAP LP relaxation

Ofer Meshi; Amir Globerson

doi:10.1007/978-3-642-23783-6_30

An alternating direction method for dual MAP LP relaxation

Ofer Meshi
, Amir Globerson

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Maximum a-posteriori (MAP) estimation is an important task in many applications of probabilistic graphical models. Although finding an exact solution is generally intractable, approximations based on linear programming (LP) relaxation often provide good approximate solutions. In this paper we present an algorithm for solving the LP relaxation optimization problem. In order to overcome the lack of strict convexity, we apply an augmented Lagrangian method to the dual LP. The algorithm, based on the alternating direction method of multipliers (ADMM), is guaranteed to converge to the global optimum of the LP relaxation objective. Our experimental results show that this algorithm is competitive with other state-of-the-art algorithms for approximate MAP estimation.

Original language	English GB
Title of host publication	Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2011, Proceedings
Publisher	Springer Verlag
Pages	470-483
Number of pages	14
Edition	PART 2
ISBN (Print)	9783642237829
DOIs	https://doi.org/10.1007/978-3-642-23783-6_30
State	Published - 2011
Externally published	Yes

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Number	PART 2
Volume	6912 LNAI

Keywords

Approximate Inference
Augmented Lagrangian Methods
Graphical Models
LP Relaxation
Maximum a-posteriori

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-23783-6_30

Cite this

Meshi, O., & Globerson, A. (2011). An alternating direction method for dual MAP LP relaxation. In Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2011, Proceedings (PART 2 ed., pp. 470-483). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6912 LNAI, No. PART 2). Springer Verlag. https://doi.org/10.1007/978-3-642-23783-6_30

Meshi, Ofer ; Globerson, Amir. / An alternating direction method for dual MAP LP relaxation. Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2011, Proceedings. PART 2. ed. Springer Verlag, 2011. pp. 470-483 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 2).

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Meshi, O & Globerson, A 2011, An alternating direction method for dual MAP LP relaxation. in Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2011, Proceedings. PART 2 edn, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 2, vol. 6912 LNAI, Springer Verlag, pp. 470-483. https://doi.org/10.1007/978-3-642-23783-6_30

An alternating direction method for dual MAP LP relaxation. / Meshi, Ofer; Globerson, Amir.
Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2011, Proceedings. PART 2. ed. Springer Verlag, 2011. p. 470-483 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6912 LNAI, No. PART 2).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - Maximum a-posteriori (MAP) estimation is an important task in many applications of probabilistic graphical models. Although finding an exact solution is generally intractable, approximations based on linear programming (LP) relaxation often provide good approximate solutions. In this paper we present an algorithm for solving the LP relaxation optimization problem. In order to overcome the lack of strict convexity, we apply an augmented Lagrangian method to the dual LP. The algorithm, based on the alternating direction method of multipliers (ADMM), is guaranteed to converge to the global optimum of the LP relaxation objective. Our experimental results show that this algorithm is competitive with other state-of-the-art algorithms for approximate MAP estimation.

AB - Maximum a-posteriori (MAP) estimation is an important task in many applications of probabilistic graphical models. Although finding an exact solution is generally intractable, approximations based on linear programming (LP) relaxation often provide good approximate solutions. In this paper we present an algorithm for solving the LP relaxation optimization problem. In order to overcome the lack of strict convexity, we apply an augmented Lagrangian method to the dual LP. The algorithm, based on the alternating direction method of multipliers (ADMM), is guaranteed to converge to the global optimum of the LP relaxation objective. Our experimental results show that this algorithm is competitive with other state-of-the-art algorithms for approximate MAP estimation.

KW - Approximate Inference

KW - Augmented Lagrangian Methods

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KW - LP Relaxation

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BT - Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2011, Proceedings

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Meshi O, Globerson A. An alternating direction method for dual MAP LP relaxation. In Machine Learning and Knowledge Discovery in Databases - European Conference, ECML PKDD 2011, Proceedings. PART 2 ed. Springer Verlag. 2011. p. 470-483. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 2). doi: 10.1007/978-3-642-23783-6_30

An alternating direction method for dual MAP LP relaxation

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