### Abstract

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 language | English |
---|---|

Title of host publication | Proceedings of the 2015 IEEE International Symposium on Information Theory (ISIT) |

Publisher | IEEE |

Publication date | 2015 |

Pages | 2807-2811 |

ISBN (Print) | 978-1-4673-7704-1 |

DOIs | |

Publication status | Published - 2015 |

Event | IEEE International Symposium on Information Theory (ISIT 2015) - Hong Kong, Hong Kong Duration: 14 Jun 2015 → 19 Jun 2015 http://www.isit2015.org/ |

### Conference

Conference | IEEE International Symposium on Information Theory (ISIT 2015) |
---|---|

Country | Hong Kong |

City | Hong Kong |

Period | 14/06/2015 → 19/06/2015 |

Internet address |

### Keywords

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

## Cite this

Cakmak, B., Winther, O., & Fleury, B. H. (2015). S-AMP for non-linear observation models. In

*Proceedings of the 2015 IEEE International Symposium on Information Theory (ISIT)*(pp. 2807-2811). IEEE. https://doi.org/10.1109/ISIT.2015.7282968