seminar Nicolas Keriven / Inria F107 / November 14th, 2pm

[Julien Mairal]

Dear all,

tomorrow, we will have the visit of Nicolas Keriven from ENS Paris. He will give a seminar at Inria, room F107, Nov 14th. 2pm.

Best,

Julien

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Titre: Fisher metric, support stability and optimal number of 
measurements in compressive off-the-grid recovery

Abstract: Many problems in machine learning and imaging can be framed as 
an infinite dimensional Lasso problem to estimate a sparse measure. This 
includes for instance regression using a continuously parameterized
dictionary, mixture model estimation and super-resolution of images. To 
make the problem tractable, one typically sketches the observations
(often called compressive-sensing in imaging) using randomized 
projections. In this work, we provide a comprehensive treatment of the 
recovery performances of this class of approaches. We show that for a 
large class of operators, the Fisher-Rao distance induced by the 
measurement process is the natural way to enforce and generalize the 
classical minimal separation condition appearing in the literature. We 
then prove that (up to log factors) a number of sketches proportional to 
the sparsity is enough to identify the sought after measure with 
robustness to noise. Finally, we show that, under additional hypothesis, 
exact support stability holds (the number of recovered atoms matches 
that of the measure of interest) when the level of noise is smaller than 
a specified value. This is a joint work with Clarice Poon (Cambridge 
Uni.) and Gabriel Peyré (ENS).