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

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 p...

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Bibliographic Details
Published in:SIAM journal on scientific computing Vol. 33; no. 4; pp. 1689 - 1706
Main Authors: Eriksson-Bique, Sylvester, Solbrig, Mary, Stefanelli, Michael, Warkentin, Sarah, Abbey, Ralph, Ipsen, Ilse C. F.
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2011
Subjects:
Accuracy
Algorithms
Approximation
Documents
Exact sciences and technology
Expected values
Experiments
Information retrieval
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Multiplication & division
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Numerical methods in probability and statistics
Probability
Random variables
Sciences and techniques of general use
68W20
Monte Carlo method
62P30
Multiplication
Numerical linear algebra
query
term-by-document matrix
Information retrieval
15B48
Probability distribution
randomized algorithm
Stochastic method
Algorithm
Variance
matching
Numerical analysis
Scientific computation
15A99
Distribution function
Matrix method
Sampling
expected value
68Q87
ISSN:1064-8275, 1095-7197
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:1064-8275
1095-7197
DOI:10.1137/10080659X