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SUMMARY: Risk Hull Methods for Inverse Problems - Laurent Cavalier (Marsei
 lle)
DTSTART:20091030T160000Z
DTEND:20091030T170000Z
UID:TALK20071@talks.cam.ac.uk
CONTACT:Richard Nickl
DESCRIPTION:We study a standard method of regularization by projections of
  the\nlinear inverse problem $Y=Af+\\epsilon$\, where $\\epsilon$ is a\nwh
 ite Gaussian noise\, and $A$ is a known compact operator with singular\nva
 lues  converging to zero with polynomial decay. The unknown\nfunction $f$ 
 is recovered by a projection method using the SVD of\n$A$.  The bandwidth 
 choice of this projection regularization is\ngoverned by a data-driven pro
 cedure which is based on the\nprinciple of the risk hull minimization. We 
 provide\nnon--asymptotic upper bounds for the mean square risk of this\nme
 thod and we show\, in particular\, that in numerical simulations\,\nthis a
 pproach may substantially improve the classical method of\nunbiased risk e
 stimation.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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