Inference and mutual information on random factor graphs
Abstract
Random factor graphs provide a powerful framework for the study of inference problems such as decoding problems or the stochastic block model. Information-theoretically the key quantity of interest is the mutual information between the observed factor graph and the underlying ground truth around which the factor graph was created; in the stochastic block model, this would be the planted partition. The mutual information gauges whether and how well the ground truth can be inferred from the observable data. For a very general model of random factor graphs we verify a formula for the mutual information predicted by physics techniques. As an application we prove a conjecture about low-density generator matrix codes from [Montanari: IEEE Transactions on Information Theory 2005]. Further applications include phase transitions of the stochastic block model and the mixed -spin model from physics.
Cite
@article{arxiv.2007.07494,
title = {Inference and mutual information on random factor graphs},
author = {Amin Coja-Oghlan and Max Hahn-Klimroth and Philipp Loick and Noela Müller and Konstantinos Panagiotou and Matija Pasch},
journal= {arXiv preprint arXiv:2007.07494},
year = {2021}
}