S-AMP: Approximate Message Passing for General Matrix Ensembles

Burak Cakmak, Ole Winther, Bernard H. Fleury

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review


We propose a novel iterative estimation algorithm for linear observation models called S-AMP. The fixed points of S-AMP are the stationary points of the exact Gibbs free energy under a set of (first- and second-) moment consistency constraints in the large system limit. S-AMP extends the approximate message-passing (AMP) algorithm to general matrix ensembles with a well-defined large system size limit. The generalization is based on the S-transform (in free probability) of the spectrum of the measurement matrix. Furthermore, we show that the optimality of S-AMP follows directly from its design rather than from solving a separate optimization problem as done for AMP.
Original languageEnglish
Title of host publicationProceedings of 2014 IEEE Information Theory Workshop (ITW)
Publication date2014
ISBN (Print)978-1-4799-5999-0
Publication statusPublished - 2014
Event2014 IEEE Information Theory Workshop - Hobart, Australia
Duration: 2 Nov 20145 Nov 2014


Workshop2014 IEEE Information Theory Workshop


  • Variational inference
  • Free energy optimization
  • Approximate message passing
  • S-transform in free probability


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