Belief propagation, robust reconstruction and optimal recovery of block models
Abstract
We consider the problem of reconstructing sparse symmetric block models with two blocks and connection probabilities $a/n$ and $b/n$ for inter and intrablock edge probabilities, respectively. It was recently shown that one can do better than a random guess if and only if $(ab)^2>2(a+b)$. Using a variant of belief propagation, we give a reconstruction algorithm that is optimal in the sense that if $(ab)^2>C(a+b)$ for some constant $C$ then our algorithm maximizes the fraction of the nodes labeled correctly. Ours is the only algorithm proven to achieve the optimal fraction of nodes labeled correctly. Along the way, we prove some results of independent interest regarding robust reconstruction for the Ising model on regular and Poisson trees.
 Publication:

arXiv eprints
 Pub Date:
 September 2013
 arXiv:
 arXiv:1309.1380
 Bibcode:
 2013arXiv1309.1380M
 Keywords:

 Mathematics  Probability;
 Computer Science  Social and Information Networks
 EPrint:
 Published at http://dx.doi.org/10.1214/15AAP1145 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)