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SEMINARI DI PROBABILITA' E STATISTICA MATEMATICA
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DIPARTIMENTO DI MATEMATICA
UNIVERSITA' DI ROMA LA SAPIENZA
piazzale Aldo Moro 2, Roma
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Seminario Prof. Goldstein a Roma 1
Venerdi' 20 febbraio 2015, Ore 14:00, esatte, in Aula di Consiglio
Larry Goldstein (University of Southern California) terrà, presso il
Dipartimento di Matematica dell'Universita' La Sapienza, un seminario
dal titolo
Normal approximation for recovery of structured unknowns in high
dimension: Steining the Steiner formula
Abstract: Intrinsic volumes of convex sets are natural geometric
quantities that also play important roles in applications. In
particular, the discrete probability distribution L(VC) given by the
sequence v_{0},...,v_{d} of conic intrinsic volumes of a closed convex
cone C in Rd summarizes key information about the success of convex
programs used to solve for sparse vectors, and other structured
unknowns such as low rank matrices, in high dimensional regularized
inverse problems.
The concentration of VC implies the existence of phase transitions
for the probability of recovery of the unknown in the number of
observations. Additional information about the probability of recovery
success is provided by a normal approximation for VC. Such central
limit theorems can be shown by first considering the squared length GC
of the projection of a Gaussian vector on the cone C. Applying a
second order Poincaré inequality, proved using Stein’s method, then
produces a non-asymptotic total variation bound to the normal for
L(GC).
A conic version of the classical Steiner formula in convex geometry
translates finite sample bounds and a normal limit for GC to that for
VC.
Joint with Ivan Nourdin and
Giovanni Peccati.
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Tutti gli interessati sono invitati a partecipare
Giovanna Nappo