A comparison principle for functions of a uniformly random subspace

2011/02/28 by Joel A. Tropp · 1 citation
Mathematics · #math.PR #math.MG #math.ST #stat.TH #msc:60B20

paper · pdf · doi:10.1007/s00440-011-0360-9

published as Probab. Theory Related Fields, Vol. 153, num. 3-4, pp. 759-769, 2012 · 8 pages

arxiv created 2011/03/24 · arxiv updated 2014/04/29

Abstract

This note demonstrates that it is possible to bound the expectation of an arbitrary norm of a random matrix drawn from the Stiefel manifold in terms of the expected norm of a standard Gaussian matrix with the same dimensions. A related comparison holds for any convex function of a random matrix drawn from the Stiefel manifold. For certain norms, a reversed inequality is also valid.

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• Reduced-rank Generalized Bilinear Models

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