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Center for Nonlinear Studies |
The problem of estimating a high-dimensional vector from a set of linear observations arises in a number of engineering disciplines. It becomes particularly challenging when the underlying signal has some non-linear structure that needs to be exploited. I will present a new class of iterative algorithms inspired by probabilistic graphical models ideas, that appear to be asymptotically optimal in specific contexts.
The analysis of these algorithms allows to prove remarkably sharp results on the asymptotic behavior of some families of random convex problems. I will in particular discuss the mean square error for LASSO estimation in the context of compressed sensing problems.
[Based on joint work with David L. Donoho and Arian Maleki, and with Mohsen Bayati and Jose Bento.]
Host: Vadas Gintautas