eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-03-10
24:1
24:15
10.4230/LIPIcs.STACS.2021.24
article
Inference and Mutual Information on Random Factor Graphs
Coja-Oghlan, Amin
1
Hahn-Klimroth, Max
1
Loick, Philipp
1
Müller, Noela
2
Panagiotou, Konstantinos
2
Pasch, Matija
2
Mathematics Institute, Goethe Universität Frankfurt am Main, Germany
Mathematics Institute, University of Munich, Germany
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 k-spin model from physics.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol187-stacs2021/LIPIcs.STACS.2021.24/LIPIcs.STACS.2021.24.pdf
Information theory
random factor graphs
inference problems
phase transitions