Issue No. 12 - December (2011 vol. 33)

ISSN: 0162-8828

pp: 2549-2554

Julian J. McAuley , Australian National University/NICTA, Canberra

Pedro F. Felzenszwalb , University of Chicago, Chicago

ABSTRACT

The MAP inference problem in many graphical models can be solved efficiently using a fast algorithm for computing min-sum products of n \times 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.

INDEX TERMS

Graphical models, MAP inference, min-sum matrix product.

CITATION

Julian J. McAuley, Pedro F. Felzenszwalb, "Fast Inference with Min-Sum Matrix Product",

*IEEE Transactions on Pattern Analysis & Machine Intelligence*, vol. 33, no. , pp. 2549-2554, December 2011, doi:10.1109/TPAMI.2011.121