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arXiv · 2007.07494

Inference and mutual information on random factor graphs

Amin Coja-Oghlan·Max Hahn-Klimroth·Philipp Loick·Noela Müller·Konstantinos Panagiotou·Matija Pasch
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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 $k$-spin model from physics.

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Amin Coja-Oghlan, Max Hahn-Klimroth, Philipp Loick, Noela Müller, Konstantinos Panagiotou, Matija Pasch. 2020-07-15. Inference and mutual information on random factor graphs. https://doi.org/10.4230/lipics.stacs.2021.24

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