Abstract Details
Activity Number:
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106
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Type:
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Invited
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Date/Time:
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Monday, August 5, 2013 : 8:30 AM to 10:20 AM
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Sponsor:
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IMS
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Abstract - #307098 |
Title:
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Binary Matrix Completion
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Author(s):
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Yaniv Plan*+ and Mark Davenport and Mary Wootters and Ewout van den Berg
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Companies:
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University of Michigan and Georgia Institute of Technology and University of Michigan and Stanford
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Keywords:
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matrix completion ;
logistic regression ;
maximum likelihood ;
convex optimization
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Abstract:
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The problem of recovering a matrix from an incomplete sampling of its entries-also known as matrix completion-arises in a wide variety of practical situations. In many of these settings, however, the observations are not only incomplete, but also highly quantized, often even to a single bit. Thus we ask, "Given just the signs of a subset of noisy entries of an unknown matrix, can the unknown matrix be reconstructed?" We show that under an approximate low-rank assumption, nuclear-norm constrained maximum-likelihood estimation gives a nearly minimax solution, and that in some regimes almost no information is lost by quantizing to a single bit.
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Authors who are presenting talks have a * after their name.
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