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## Adaptive Damping and Mean Removal for the Generalized Approximate Message Passing Algorithm

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Jeremy Vila
• Function : Author
Philip Schniter
Sundeep Rangan
• Function : Author
Florent Krzakala
• Function : Author
Lenka Zdeborova
• Function : Author

#### Abstract

The generalized approximate message passing (GAMP) algorithm is an efficient method of MAP or approximate-MMSE estimation of $x$ observed from a noisy version of the transform coefficients $z = Ax$. In fact, for large zero-mean i.i.d sub-Gaussian $A$, GAMP is characterized by a state evolution whose fixed points, when unique, are optimal. For generic $A$, however, GAMP may diverge. In this paper, we propose adaptive damping and mean-removal strategies that aim to prevent divergence. Numerical results demonstrate significantly enhanced robustness to non-zero-mean, rank-deficient, column-correlated, and ill-conditioned $A$.

#### Domains

Physics [physics]

### Dates and versions

cea-01140721 , version 1 (09-04-2015)

### Identifiers

• HAL Id : cea-01140721 , version 1
• ARXIV :

### Cite

Jeremy Vila, Philip Schniter, Sundeep Rangan, Florent Krzakala, Lenka Zdeborova. Adaptive Damping and Mean Removal for the Generalized Approximate Message Passing Algorithm. 2015. ⟨cea-01140721⟩

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