Fast Inference with Min-Sum Matrix Product

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 33; no. 12; pp. 2549 - 2554
• Main Authors: Felzenszwalb, Pedro F., McAuley, J. J.
• Format: Journal Article
• Language: English
• Published: Los Alamitos, CA IEEE 01.12.2011; IEEE Computer Society; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Applied sciences; Artificial intelligence; Belief propagation; Computational modeling; Computer science; control theory; systems; Exact sciences and technology; Gain; Graphical models; Heuristic algorithms; Independent sample; Inference; Inference algorithms; MAP inference; Mathematical analysis; Mathematical models; Matrices; Matrix methods; min-sum matrix product; Natural language (computers); Pattern recognition. Digital image processing. Computational geometry; Speech and sound recognition and synthesis. Linguistics; Studies; Computer vision; Computer language; Worst case method; Matrix product; Inference; Modeling; min-sum matrix product; Uniform distribution; Graphical models; MAP inference; Language processing; Natural language; Graphic method; Fast algorithm
• ISSN: 0162-8828; 1939-3539; 2160-9292; 1939-3539
• DOI: 10.1109/TPAMI.2011.121

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.