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2008

High-dimensional support union recovery in multivariate regression

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High-dimensional support union recovery in multivariate regression
We study the behavior of block 1/ 2 regularization for multivariate regression, where a K-dimensional response vector is regressed upon a fixed set of p covariates. The problem of support union recovery is to recover the subset of covariates that are active in at least one of the regression problems. Studying this problem under high-dimensional scaling (where the problem parameters as well as sample size n tend to infinity simultaneously), our main result is to show that exact recovery is possible once the order parameter given by 1/ 2 (n, p, s) : = n/[2(B ) log(p - s)] exceeds a critical threshold. Here n is the sample size, p is the ambient dimension of the regression model, s is the size of the union of supports, and (B ) is a sparsity-overlap function that measures a combination of the sparsities and overlaps of the K-regression coefficient vectors that constitute the model. This sparsity-overlap function reveals that block 1/ 2 regularization for multivariate regression never har...
Guillaume Obozinski, Martin J. Wainwright, Michael
Added 29 Oct 2010
Updated 29 Oct 2010
Type Conference
Year 2008
Where NIPS
Authors Guillaume Obozinski, Martin J. Wainwright, Michael I. Jordan
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