S-AMP for Non-linear Observation Models

Burak Çakmak; Ole Winther; Bernard H. Fleury

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arXiv · 1501.06216

S-AMP for Non-linear Observation Models

Burak Çakmak·Ole Winther·Bernard H. Fleury

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Abstract

Recently we extended Approximate message passing (AMP) algorithm to be able to handle general invariant matrix ensembles. In this contribution we extend our S-AMP approach to non-linear observation models. We obtain generalized AMP (GAMP) algorithm 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 algorithms 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.

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Burak Çakmak, Ole Winther, Bernard H. Fleury. 2015-01-25. S-AMP for Non-linear Observation Models. https://arxiv.org/abs/1501.06216

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