Minimum entropy stochastic block models neglect edge distribution heterogeneity

Louis Duvivier (1) , Céline Robardet (1) , Rémy Cazabet (1, 2)

1 DM2L - Data Mining and Machine Learning
2 IXXI - Institut Rhône-Alpin des systèmes complexes

The statistical inference of stochastic block models as emerged as a mathematicaly principled method for identifying communities inside networks. Its objective is to find the node partition and the block-to-block adjacency matrix of maximum likelihood i.e. the one which has most probably generated the observed network. In practice, in the so-called microcanonical ensemble, it is frequently assumed that when comparing two models which have the same number and sizes of communities, the best one is the one of minimum entropy i.e. the one which can generate the less different networks. In this paper, we show that there are situations in which the minimum entropy model does not identify the most significant communities in terms of edge distribution, even though it generates the observed graph with a higher probability.

Mots clés: network; community detection; stochastic block model; statistical inference; entropy

Domaines: Réseaux et télécommunications [cs.NI]

Louis Duvivier, Céline Robardet, Rémy Cazabet. Minimum entropy stochastic block models neglect edge distribution heterogeneity. 8th International Conference on Complex Networks and Their Applications (COMPLEX NETWORKS 2019), Dec 2019, Lisbonne, Portugal. pp.545-555, ⟨10.1007/978-3-030-36687-2_45⟩. ⟨hal-03339803⟩