Approximate Message Passing with Restricted Boltzmann Machine Priors

Eric W. Tramel (1) , Angélique Dremeau (2) , Florent Krzakala (1)

1 LPS - Laboratoire de Physique Statistique de l'ENS
2 Lab-STICC_ENSTAB_CID_TOMS

Approximate message passing (AMP) has been shown to be an excellent statistical approach to signal inference and compressed sensing problems. The AMP framework provides modularity in the choice of signal prior; here we propose a hierarchical form of the Gauss Bernoulli prior which utilizes a restricted Boltzmann machine (RBM) trained on the signal support to push reconstruction performance beyond that of simple i.i.d. 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.

Mots clés: networks; random graphs; message-passing algorithms; statistical inference

Domaines: Traitement du signal et de l'image [eess.SP]; Physique [physics]

Eric W. Tramel, Angélique Dremeau, Florent Krzakala. Approximate Message Passing with Restricted Boltzmann Machine Priors. Journal of Statistical Mechanics: Theory and Experiment, 2016, 2016, ⟨10.1088/1742-5468/2016/07/073401⟩. ⟨hal-01374620⟩