EPFL
 Biomedical Imaging GroupSTI
EPFL
  Publications
English only   BIG > Publications > Message Passing


 CONTENTS
 Home Page
 News & Events
 People
 Publications
 Tutorials and Reviews
 Research
 Demos
 Download Algorithms

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

Approximate Message Passing with Consistent Parameter Estimation and Applications to Sparse Learning

U.S. Kamilov, S. Rangan, A.K. Fletcher, M. Unser

Proceedings of the Twenty-Sixth Annual Conference on Neural Information Processing Systems (NIPS'12), Lake Tahoe NV, USA, December 3-6, 2012, pp. 2447-2455.



We consider the estimation of an i.i.d. vector x ∈ ℝn from measurements y ∈ ℝm obtained by a general cascade model consisting of a known linear transform followed by a probabilistic componentwise (possibly nonlinear) measurement channel. We present a method, called adaptive generalized approximate message passing (Adaptive GAMP), that enables joint learning of the statistics of the prior and measurement channel along with estimation of the unknown vector x. Our method can be applied to a large class of learning problems including the learning of sparse priors in compressed sensing or identification of linear-nonlinear cascade models in dynamical systems and neural spiking processes. We prove that for large i.i.d. Gaussian transform matrices the asymptotic componentwise behavior of the adaptive GAMP algorithm is predicted by a simple set of scalar state evolution equations. This analysis shows that the adaptive GAMP method can yield asymptotically consistent parameter estimates, which implies that the algorithm achieves a reconstruction quality equivalent to the oracle algorithm that knows the correct parameter values. The adaptive GAMP methodology thus provides a systematic, general and computationally efficient method applicable to a large range of complex linear-nonlinear models with provable guarantees.


@INPROCEEDINGS(http://bigwww.epfl.ch/publications/kamilov1207.html,
AUTHOR="Kamilov, U.S. and Rangan, S. and Fletcher, A.K. and Unser, M.",
TITLE="Approximate Message Passing with Consistent Parameter Estimation
        and Applications to Sparse Learning",
BOOKTITLE="Proceedings of the Twenty-Sixth Annual Conference on Neural
        Information Processing Systems ({NIPS'12})",
YEAR="2012",
editor="",
volume="",
series="",
pages="2447--2455",
address="Lake Tahoe NV, USA",
month="December 3-6,",
organization="",
publisher="",
note="")

© 2012 NIPS. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from NIPS.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.