NDLI: Importance Sampling for a Monte Carlo Matrix Multiplication Algorithm, with Application to Information Retrieval

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Solbrig, Mary Ipsen, Ilse C. F. Stefanelli, Michael Warkentin, Sarah Eriksson-Bique, Sylvester Abbey, Ralph
Copyright Year	2011
Abstract	We perform importance sampling for a randomized matrix multiplication algorithm by Drineas, Kannan, and Mahoney and derive probabilities that minimize the expected value (with regard to the distributions of the matrix elements) of the variance. We compare these optimized probabilities with uniform probabilities and derive conditions under which the actual variance of the optimized probabilities is lower. Numerical experiments with query matching in information retrieval applications illustrate that the optimized probabilities produce more accurate matchings than the uniform probabilities and that they can also be computed efficiently.
Starting Page	1689
Ending Page	1706
Page Count	18
File Format	PDF
ISSN	10648275
DOI	10.1137/10080659X
e-ISSN	10957197
Issue Number	4
Volume Number	33
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2011-07-26
Access Restriction	Subscribed
Subject Keyword	Probability in computer science variance term-by-document matrix Applications in engineering and industry query matching Randomized algorithms Miscellaneous topics Positive matrices and their generalizations; cones of matrices randomized algorithm expected value
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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