Inference by replication in densely connected systems


An efficient Bayesian inference method for problems that can be mapped onto dense graphs is presented. The approach is based on message passing where messages are averaged over a large number of replicated variable systems exposed to the same evidential nodes. An assumption about the symmetry of the solutions is required for carrying out the averages; here we extend the previous derivation based on a replica-symmetric- (RS)-like structure to include a more complex one-step replica-symmetry-breaking-like (1RSB-like) ansatz. To demonstrate the potential of the approach it is employed for studying critical properties of the Ising linear perceptron and for multiuser detection in code division multiple access (CDMA) under different noise models. Results obtained under the RS assumption in the noncritical regime give rise to a highly efficient signal detection algorithm in the context of CDMA; while in the critical regime one observes a first-order transition line that ends in a continuous phase transition point. Finite size effects are also observed. While the 1RSB ansatz is not required for the original problems, it was applied to the CDMA signal detection problem with a more complex noise model that exhibits RSB behavior, resulting in an improvement in performance. © 2007 The American Physical Society.

Publication DOI:
Divisions: College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
Uncontrolled Keywords: efficient Bayesian inference method,dense graphs,Physics and Astronomy(all),Condensed Matter Physics,Statistical and Nonlinear Physics,Mathematical Physics
Publication ISSN: 1550-2376
Last Modified: 07 Jun 2024 07:07
Date Deposited: 19 Jul 2010 14:44
Full Text Link:
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
http://link.aps ... sRevE.76.046121 (Publisher URL)
PURE Output Type: Article
Published Date: 2007-10-30
Authors: Neirotti, Juan P. (ORCID Profile 0000-0002-2409-8917)
Saad, David (ORCID Profile 0000-0001-9821-2623)



Version: Accepted Version

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