### Abstract

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 language | English |
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Title of host publication | Proceedings of 2014 IEEE Information Theory Workshop (ITW) |

Publisher | IEEE |

Publication date | 2014 |

Pages | 192-196 |

ISBN (Print) | 978-1-4799-5999-0 |

DOIs | |

Publication status | Published - 2014 |

Event | IEEE Information Theory Workshop 2014 - Hobart, Tasmania, Australia Duration: 2 Nov 2014 → 5 Nov 2014 |

### Workshop

Workshop | IEEE Information Theory Workshop 2014 |
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Country | Australia |

City | Hobart, Tasmania |

Period | 02/11/2014 → 05/11/2014 |

### Keywords

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

## Cite this

Cakmak, B., Winther, O., & Fleury, B. H. (2014). S-AMP: Approximate Message Passing for General Matrix Ensembles. In

*Proceedings of 2014 IEEE Information Theory Workshop (ITW)*(pp. 192-196). IEEE. https://doi.org/10.1109/ITW.2014.6970819