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Reduced rank stochastic regression with a sparse singular value decomposition
Author(s) -
Chen Kun,
Chan KungSik,
Stenseth Nils Chr.
Publication year - 2012
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2011.01002.x
Subject(s) - singular value decomposition , mathematics , regularization (linguistics) , rank (graph theory) , singular value , qr decomposition , smoothness , regression , mathematical optimization , algorithm , computer science , statistics , combinatorics , artificial intelligence , mathematical analysis , eigenvalues and eigenvectors , physics , quantum mechanics
Summary. For a reduced rank multivariate stochastic regression model of rank r * , the regression coefficient matrix can be expressed as a sum of r * unit rank matrices each of which is proportional to the outer product of the left and right singular vectors. For improving predictive accuracy and facilitating interpretation, it is often desirable that these left and right singular vectors be sparse or enjoy some smoothness property. We propose a regularized reduced rank regression approach for solving this problem. Computation algorithms and regularization parameter selection methods are developed, and the properties of the new method are explored both theoretically and by simulation. In particular, the regularization method proposed is shown to be selection consistent and asymptotically normal and to enjoy the oracle property. We apply the proposed model to perform biclustering analysis with microarray gene expression data.