On the maximal size of large-average and ANOVA-fit submatrices in a Gaussian random matrix

We investigate the maximal size of distinguished submatrices of a Gaussian random matrix. Of interest are submatrices whose entries have an average greater than or equal to a positive constant, and submatrices whose entries are well fit by a two-way ANOVA model. We identify size thresholds and assoc...

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Bibliographic Details
Published inBernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability Vol. 19; no. 1; p. 275
Main Authors Sun, Xing, Nobel, Andrew B
Format Journal Article
LanguageEnglish
Published England 01.02.2013
Subjects
random matrix theory
analysis of variance
second moment method
large average submatrix
data mining
Gaussian random matrix
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Summary:We investigate the maximal size of distinguished submatrices of a Gaussian random matrix. Of interest are submatrices whose entries have an average greater than or equal to a positive constant, and submatrices whose entries are well fit by a two-way ANOVA model. We identify size thresholds and associated (asymptotic) probability bounds for both large-average and ANOVA-fit submatrices. Probability bounds are obtained when the matrix and submatrices of interest are square and, in rectangular cases, when the matrix and submatrices of interest have fixed aspect ratios. Our principal result is an almost sure interval concentration result for the size of large average submatrices in the square case.
ISSN:1350-7265
DOI:10.3150/11-BEJ394