High-arity Interactions, Polyhedral Relaxations, and Cutting Plane Algorithm for Soft Constraint Optimisation (MAP-MRF)

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F08%3A03150804" target="_blank" >RIV/68407700:21230/08:03150804 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

High-arity Interactions, Polyhedral Relaxations, and Cutting Plane Algorithm for Soft Constraint Optimisation (MAP-MRF)

Original language description

LP relaxation approach to soft constraint optimisation (i.e. MAP-MRF) has been mostly considered only for binary problems. We present its generalisation to n-ary problems, including a simple algorithm to optimise the LP bound, n-ary max-sum diffusion. Asapplications, we show that a hierarchy of gradually tighter polyhedral relaxations of MAP-MRF is obtained by adding zero interactions. We propose a cutting plane algorithm, where cuts correspond to adding zero interactions and the separation problem tofinding an unsatisfiable constraint satisfaction subproblem. Next, we show that certain high-arity interactions, e.g. certain global constraints, can be included into the framework in a principled way. Finally, we prove that n-ary max-sum diffusion findsglobal optimum for n-ary supermodular problems.

Czech name

High-arity Interactions, Polyhedral Relaxations, and Cutting Plane Algorithm for Soft Constraint Optimisation (MAP-MRF)

Czech description

LP relaxation approach to soft constraint optimisation (i.e. MAP-MRF) has been mostly considered only for binary problems. We present its generalisation to n-ary problems, including a simple algorithm to optimise the LP bound, n-ary max-sum diffusion. Asapplications, we show that a hierarchy of gradually tighter polyhedral relaxations of MAP-MRF is obtained by adding zero interactions. We propose a cutting plane algorithm, where cuts correspond to adding zero interactions and the separation problem tofinding an unsatisfiable constraint satisfaction subproblem. Next, we show that certain high-arity interactions, e.g. certain global constraints, can be included into the framework in a principled way. Finally, we prove that n-ary max-sum diffusion findsglobal optimum for n-ary supermodular problems.

Type

D - Article in proceedings

CEP classification

JD - Use of computers, robotics and its application

OECD FORD branch

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Project

<a href="/en/project/7E08031" target="_blank" >7E08031: Dynamic Interactive Perception-action Learning in Cognitive Systems</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2008

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

CVPR 2008: Proceedings of the 2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition

ISBN

978-1-4244-2242-5

ISSN

1063-6919

e-ISSN

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Number of pages

8

Pages from-to

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Publisher name

Omnipress

Place of publication

Medison

Event location

Anchorage, Alaska

Event date

Jun 24, 2008

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

000259736800015