This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.
Abstract Details
Activity Number:
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48
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Type:
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Invited
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Date/Time:
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Sunday, August 1, 2010 : 4:00 PM to 5:50 PM
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Sponsor:
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JCGS-Journal of Computational and Graphical Statistics
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Abstract - #306045 |
Title:
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Discovering Sparse Covariance Structures with the Isomap
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Author(s):
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Amy Wagaman*+ and Elizaveta Levina
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Companies:
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Amherst College and University of Michigan
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Address:
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Amherst College, Campus Box 2239, Amherst, MA, 01002,
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Keywords:
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covariance estimation ;
sparsity ;
regularization ;
manifold projections ;
large p small n
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Abstract:
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Regularization of covariance matrices in high dimensions usually either is based on a known ordering of variables or ignores the ordering entirely. We propose a method for discovering meaningful orderings of variables based on their correlations using the Isomap, a nonlinear dimension reduction technique. These orderings are used to construct a sparse covariance estimator, which is possibly block-diagonal and/or banded. We show that in situations where the variables do have such a structure, the Isomap does very well at discovering it, and the resulting regularized estimator performs better for covariance estimation than other regularization methods that ignore variable order. We also propose a bootstrap approach to constructing the neighborhood graph used by the Isomap, and show it leads to better estimation with an illustration on a gene expression dataset.
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Authors who are presenting talks have a * after their name.
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