Thursday, May 19, 2016

FISTA and "Maximal Sparsity with Deep Networks?", Learning MMSE Optimal Thresholds for FISTA

Ulugbek just sent me the following:  
Hi Igor,

I just saw your today’s post on Nuit Blanche on "Maximal Sparsity with Deep Networks?”.

You mentioned both FISTA and AMP, and the number of iterations required for convergence. I generally agree with your observations about studies on FISTA/AMP being hugely insightful. We have been investigating this from our side with Hassan, and I wanted to share a small update (see attached), which will be presented at iTWIST 2016 in Denmark this August. We haven’t uploaded the manuscript to arXiv as iTWIST anyways publishes its proceedings there.

Going from ISTA to FISTA is quite advantageous. We initialize the algorithm with 0 and also set the initial regularizer to 0, i.e. use identity operator instead of a shrinkage (which corresponds to having least-squares estimator) and converge much faster towards a regularizer that promotes sparsity.

Thank you having us all informed here,
Kind Regards,
- Ulugbek
Thanks Ulugbek and  Hassan ! Here is the paper:
Fast iterative shrinkage/thresholding algorithm (FISTA) is one of the most commonly used methods for solving linear inverse problems. In this work, we present a scheme that enables learning of optimal thresholding functions for FISTA from a set of training data. In particular, by relating iterations of FISTA to a deep neural network (DNN), we use the error backpropagation algorithm to find thresholding functions that minimize mean squared error (MSE) of the reconstruction for a given statistical distribution of data. Accordingly, the scheme can be used to computationally obtain MSE optimal variant of FISTA for performing statistical estimation.
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