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arXiv · 1405.2767

S-AMP: Approximate Message Passing for General Matrix Ensembles

Burak Çakmak·Ole Winther·Bernard H. Fleury
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Abstract

In this work we propose a novel iterative estimation algorithm for linear observation systems called S-AMP whose fixed points 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. 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.

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Burak Çakmak, Ole Winther, Bernard H. Fleury. 2014-05-12. S-AMP: Approximate Message Passing for General Matrix Ensembles. https://arxiv.org/abs/1405.2767

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