Approximate Message Passing with Restricted Boltzmann Machine Priors

The great convergence is upon us. From the following paper:

The present paper demonstrates the first steps in incorporating deep learned priors into generalized linear problems such as compressed sensing.

 

Approximate Message Passing with Restricted Boltzmann Machine Priors by Eric W. Tramel, Angélique Drémeau, Florent Krzakala

Approximate Message Passing (AMP) has been shown to be an excellent statistical approach to signal inference and compressed sensing problem. The AMP framework provides modularity in the choice of signal prior; here we propose a hierarchical form of the Gauss-Bernouilli prior which utilizes a Restricted Boltzmann Machine (RBM) trained on the signal support to push reconstruction performance beyond that of simple iid priors for signals whose support can be well represented by a trained binary RBM. We present and analyze two methods of RBM factorization and demonstrate how these affect signal reconstruction performance within our proposed algorithm. Finally, using the MNIST handwritten digit dataset, we show experimentally that using an RBM allows AMP to approach oracle-support performance.  

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