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SUMMARY:Greedy-LASSO\, Greedy-Net: Generalization and unrolling of greedy 
 sparse recovery algorithms - Sina Mohammadtaheri
DTSTART:20240502T140000Z
DTEND:20240502T150000Z
UID:TALK215536@talks.cam.ac.uk
CONTACT:Matthew Colbrook
DESCRIPTION:Sparse recovery generally aims at reconstructing a sparse vect
 or\, given linear measurements performed via a mixture (or sensing) matrix
 \, typically underdetermined. Greedy (and thresholding) sparse recovery al
 gorithms have known to serve well as a suitable alternative for convex opt
 imization techniques\, in particular in low sparsity regimes. In this talk
 \, I take orthogonal matching pursuit (OMP) as an example\, and establish 
 a connection between OMP and convex optimization decoders in one side and 
 neural networks on the other side. To achieve the former\, we adopt a loss
  function-based perspective and propose a framework based on OMP that lead
 s to greedy algorithms for a large class of loss functions including the w
 ell-known (weighted-)LASSO family\, with explicit formulas for the choice 
 of the ``greedy selection criterion". We show numerically that these greed
 y algorithms inherit properties of their ancestor convex decoder. In the s
 econd part of the talk\, we leverage ``softsoring"\, to resolve the non-di
 fferentiability issue of OMP due to (arg)sorting\, in order to derive a di
 fferentiable version of OMP that we call ``Soft-OMP"\, which we demonstrat
 e numerically and theoretically that is a good approximation for OMP. We t
 hen unroll iterations of OMP onto layers of a neural network with weights 
 as semantic trainable parameters that capture the structure within the dat
 a. Doing so\, we also connect our approach to learning weights in weighted
  sparse recovery. I will conclude the talk by presenting implications of o
 ur framework for other greedy algorithms such as CoSaMP and IHT\, and high
 light some open problems. This is joint work with Simone Brugiapaglia (Con
 cordia University) and Matthew Colbrook (University of Cambridge).
LOCATION:Centre for Mathematical Sciences\, MR12
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