Conference paper
S-AMP: Approximate Message Passing for General Matrix Ensembles
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.
| Language: | English |
|---|---|
| Publisher: | IEEE |
| Year: | 2014 |
| Pages: | 192-196 |
| Proceedings: | 2014 IEEE Information Theory Workshop |
| ISBN: | 1479959995 , 1479960004 , 9781479959990 and 9781479960002 |
| ISSN: | 16629019 |
| Types: | Conference paper |
| DOI: | 10.1109/ITW.2014.6970819 |
| ORCIDs: | Winther, Ole |
Approximate message passing Free energy optimization S-transform in free probability Variational inference
Approximation methods Compressed sensing Equations Information theory Mathematical model Message passing S-AMP S-transform Vectors approximate message passing approximate message-passing algorithm exact Gibbs free energy first-moment consistency constraints free energy free energy optimization free probability iterative estimation algorithm iterative methods large system size limit linear observation models matrix algebra matrix ensembles measurement matrix message passing probability second-moment consistency constraints stationary points variational techniques
