### Abstract

Markov random fields (MRFs) are a powerful tool for modelling statistical dependencies for a set of random variables using a graphical representation. An important computational problem related to MRFs, called maximum a posteriori (MAP) inference, is finding a joint variable assignment with the maximal probability. It is well known that the two popular optimisation techniques for this task, linear programming (LP) relaxation and dual decomposition (DD), have a strong connection both providing an optimal solution to the MAP problem when a corresponding LP relaxation is tight. However, less is known about their relationship in the opposite and more realistic case. In this paper, we explain how the fully integral assignments obtained via DD partially agree with the optimal fractional assignments via LP relaxation when the latter is not tight. In particular, for binary pairwise MRFs the corresponding result suggests that both methods share the partial optimality property of their solutions.

Original language | English |
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Publication status | Published - 2020 Jan 1 |

Event | 22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019 - Naha, Japan Duration: 2019 Apr 16 → 2019 Apr 18 |

### Conference

Conference | 22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019 |
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Country | Japan |

City | Naha |

Period | 19/4/16 → 19/4/18 |

### ASJC Scopus subject areas

- Artificial Intelligence
- Statistics and Probability

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## Cite this

*Partial optimality of dual decomposition for map inference in pairwise MrFs*. Paper presented at 22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019, Naha, Japan.