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Large-scale inference, random convex problems, and the risk of the LASSOMathematical Physics & Probability
|Speaker: ||Andrea Montanari, Stanford University|
|Location: ||3106 MSB|
|Start time: ||Wed, Nov 17 2010, 4:10PM|
The problem of estimating a high-dimensional vector from a set of
linear observations arises in many areas of science and engineering.
It becomes particularly challenging when the underlying signal has
some non-linear structure that needs to be exploited.
A reconstruction approach that ganed considerable popularity
over the last few years consists in solving a suitable
convex optimization problem, shose cost quantifies the quality
of the solution.
The analyisis of such procedures requires to characterize the optimum
of a high dimensional random convex function. I will survey
recent progress towards this goal, focusing on one specific such
function, known as the LASSO, which is often used within
compressed sensing applictons. Within a random measurements
model, we prove an asymptotcally exact result on the distribution
of the reconstruction vector.
The analysis is unveils connections with the theory
of graphical models, message passing algorithms and statistical
[Based on joint work with David L. Donoho and Arian Maleki,
and with Mohsen Bayati and Jose Bento.]