[Ml-stat-talks] Simon Foucart (Drexel) in Wilks Statistics Seminar, TODAY december 7, 12:30

Philippe Rigollet rigollet at Princeton.EDU
Fri Dec 7 09:01:37 EST 2012

Just a friendly reminder: Simon Foucart is talking today in the Wilks statistics seminar. See below.

DATE:   Friday, December 7, 2012

TIME:   12:30pm

LOCATION:   Room 101, Sherrerd Hall

SPEAKER:   Simon Foucart. Department of Mathematics, Drexel Univeristy.

TITLE:   L-1 minimizations with Weibull matrices

ABSTRACT: We investigate the recovery of almost sparse vectors from undersampled and inaccurate random measurements using L-1 minimizations subject to inequality constraints and subject to equality constraints. We are especially interested in measurement matrices with subexponential entries, for which the classical restricted isometry property does not hold in the optimal regime. Nonetheless, we prove that in this regime the L-1 minimizations remain stable and robust if Weibull random matrices are used. The arguments are based on two key ingredients, namely the robust null space property and the quotient property. The robust null space property relies on a variant of the restricted isometry property where the inner norm is replaced by the L-1 norm and the outer norm is replaced by a norm comparable to the L-2 norm. This yields stability and robustness results that are also valid when considering sparsity relative to a redundant dictionary. As for the quotient property, it relies on lower estimates for the tail probability of sums of independent Weibull random variables.

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