Local rules for global MAP: When do they work?
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3810-local-rules-for-global-map-when-do-they-work.pdf
Description
Published version
Size
182.84 KB
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Unknown
Checksum (MD5)
37564e7b9098ebd522521f6f33c6821f
Author(s)
Jung, Kyomin
Kohli, Pushmeet
Shah, Devavrat
Date Issued
2009
Journal
NIPS '09 - Proceedings of the 22nd International Conference on Neural Information Proceeding Systems
Publisher
MIT Press
Citation
Shah, Devavrat. 2009. "Local rules for global MAP: When do they work?."
Version
Final published version
Abstract
We consider the question of computing Maximum A Posteriori (MAP) assignment in an arbitrary pair-wise Markov Random Field (MRF). We present a randomized iterative algorithm based on simple local updates. The algorithm, starting with an arbitrary initial assignment, updates it in each iteration by first, picking a random node, then selecting an (appropriately chosen) random local neighborhood and optimizing over this local neighborhood. Somewhat surprisingly, we show that this algorithm finds a near optimal assignment within n log 2 n iterations with high probability for any n node pair-wise MRF with geometry (i.e. MRF graph with polynomial growth) with the approximation error depending on (in a reasonable manner) the geometric growth rate of the graph and the average radius of the local neighborhood - this allows for a graceful tradeoff between the complexity of the algorithm and the approximation error. Through extensive simulations, we show that our algorithm finds extremely good approximate solutions for various kinds of MRFs with geometry.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://papers.nips.cc/paper/3810-local-rules-for-global-map-when-do-they-work
