Multiscale Gaussian graphical models and algorithms for large-scale inference
Name
191870466-MIT.pdf
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Full printable version
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7.8 MB
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Checksum (MD5)
1570dc2edea508b4c19a68d16d259396
Author(s)
Choi, Myung Jin, S.M. Massachusetts Institute of Technology
Advisor(s)
Alan S. Willsky.
Date Issued
2007
Publisher
Massachusetts Institute of Technology
Abstract
Graphical models provide a powerful framework for stochastic processes by representing dependencies among random variables compactly with graphs. In particular, multiscale tree-structured graphs have attracted much attention for their computational efficiency as well as their ability to capture long-range correlations. However, tree models have limited modeling power that may lead to blocky artifacts. Previous works on extending trees to pyramidal structures resorted to computationally expensive methods to get solutions due to the resulting model complexity. In this thesis, we propose a pyramidal graphical model with rich modeling power for Gaussian processes, and develop efficient inference algorithms to solve large-scale estimation problems. The pyramidal graph has statistical links between pairs of neighboring nodes within each scale as well as between adjacent scales. Although the graph has many cycles, its hierarchical structure enables us to develop a class of fast algorithms in the spirit of multipole methods. The algorithms operate by guiding far-apart nodes to communicate through coarser scales and considering only local interactions at finer scales. The consistent stochastic structure of the pyramidal graph provides great flexibilities in designing and analyzing inference algorithms. Based on emerging techniques for inference on Gaussian graphical models, we propose several different inference algorithms to compute not only the optimal estimates but also approximate error variances as well. In addition, we consider the problem of rapidly updating the estimates based on some new local information, and develop a re-estimation algorithm on the pyramidal graph. Simulation results show that this algorithm can be applied to reconstruct discontinuities blurred during the estimation process or to update the estimates to incorporate a new set of measurements introduced in a local region.
Description
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.
Includes bibliographical references (p. 119-123).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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