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LCN2 Seminar: Network model selection via the Minimum Description Length principle: the effects of ensemble non-equivalence

Friday 26 May 2023


Non-equivalence between canonical (soft constraints) and microcanonical (hard constraints) ensembles has been shown to arise in network models that have an extensive number of local constraints, such as Configuration Models [1]. This presentation explores the implications of ensemble non-equivalence on network model selection within the framework defined by the Minimum Description Length (MDL) principle [2]. MDL methods aim to identify the model that provides the shortest description of the data. We will first introduce the MDL framework and its key concepts. Specifically, we will employ the Normalized Maximum Likelihood approach to define model description lengths, which encompass a likelihood and a complexity term. We will finally illustrate how this technique is applied to microcanonical and canonical Maximum Entropy Models for networks, highlighting the effects of (non-)equivalence on both the likelihood and complexity terms of the description lengths.

1. T. Squartini, J. de Mol, F. den Hollander, D. Garlaschelli, Phys. Rev. Lett. 115, 268701 (2015).
2. P. Gr├╝nwald, The Minimum Description Length Principle, The MIT Press (2007).

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