S-AMP for non-linear observation models

Burak Cakmak, Ole Winther, Bernard H. Fleury

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


Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement matrix has zero-mean iid Gaussian entries. Our derivation is based upon 1) deriving expectation-propagation-(EP)-like equations from the stationary-points equations of the Gibbs free energy under first- and second-moment constraints and 2) applying additive free convolution in free probability theory to get low-complexity updates for the second moment quantities.
Original languageEnglish
Title of host publicationProceedings of the 2015 IEEE International Symposium on Information Theory (ISIT)
Publication date2015
ISBN (Print)978-1-4673-7704-1
Publication statusPublished - 2015
EventIEEE International Symposium on Information Theory (ISIT 2015) - Hong Kong, Hong Kong
Duration: 14 Jun 201519 Jun 2015


ConferenceIEEE International Symposium on Information Theory (ISIT 2015)
CountryHong Kong
CityHong Kong
Internet address


  • Approximate Message Passing
  • Expectation Propagation
  • Free Probability
  • Variational Inference


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