Fast Inference with Min-Sum Matrix Product

The MAP inference problem in many graphical models can be solved efficiently using a fast algorithm for computing min-sum products of n × n matrices. The class of models in question includes cyclic and skip-chain models that arise in many applications. Although the worst-case complexity of the min-s...

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Veröffentlicht in:IEEE transactions on pattern analysis and machine intelligence. - 1998. - 33(2011), 12 vom: 13. Dez., Seite 2549-54
1. Verfasser: Felzenszwalb, Pedro F (VerfasserIn)
Weitere Verfasser: McAuley, Julian J
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2011
Zugriff auf das übergeordnete Werk:IEEE transactions on pattern analysis and machine intelligence
Schlagworte:Journal Article
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520 |a The MAP inference problem in many graphical models can be solved efficiently using a fast algorithm for computing min-sum products of n × n matrices. The class of models in question includes cyclic and skip-chain models that arise in many applications. Although the worst-case complexity of the min-sum product operation is not known to be much better than O(n(3)), an O(n(2.5)) expected time algorithm was recently given, subject to some constraints on the input matrices. In this paper, we give an algorithm that runs in O(n(2) log n) expected time, assuming that the entries in the input matrices are independent samples from a uniform distribution. We also show that two variants of our algorithm are quite fast for inputs that arise in several applications. This leads to significant performance gains over previous methods in applications within computer vision and natural language processing 
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