Inference by replication in densely connected systems
Abstract
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 replicasymmetric (RS)like structure to include a more complex onestep replicasymmetrybreakinglike (1RSBlike) 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 firstorder 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.
 Publication:

Physical Review E
 Pub Date:
 October 2007
 DOI:
 10.1103/PhysRevE.76.046121
 arXiv:
 arXiv:0707.1217
 Bibcode:
 2007PhRvE..76d6121N
 Keywords:

 84.35.+i;
 89.70.+c;
 75.10.Nr;
 64.60.Cn;
 Neural networks;
 Information theory and communication theory;
 Spinglass and other random models;
 Orderdisorder transformations;
 statistical mechanics of model systems;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 47 pages, 7 figures