Nonparametric inference of higher order interaction patterns in networks

Anatol E. Wegner; Sofia C. Olhede

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arXiv · 2403.15635

Nonparametric inference of higher order interaction patterns in networks

Anatol E. Wegner·Sofia C. Olhede

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Abstract

We propose a method for obtaining parsimonious decompositions of networks into higher order interactions which can take the form of arbitrary motifs.The method is based on a class of analytically solvable generative models, where vertices are connected via explicit copies of motifs, which in combination with non-parametric priors allow us to infer higher order interactions from dyadic graph data without any prior knowledge on the types or frequencies of such interactions. Crucially, we also consider 'degree--corrected' models that correctly reflect the degree distribution of the network and consequently prove to be a better fit for many real world--networks compared to non-degree corrected models. We test the presented approach on simulated data for which we recover the set of underlying higher order interactions to a high degree of accuracy. For empirical networks the method identifies concise sets of atomic subgraphs from within thousands of candidates that cover a large fraction of edges and include higher order interactions of known structural and functional significance. The method not only produces an explicit higher order representation of the network but also a fit of the network to analytically tractable models opening new avenues for the systematic study of higher order network structures.

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cs.SI cond-mat.stat-mech cs.IT math.IT physics.soc-ph stat.ME

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Anatol E. Wegner, Sofia C. Olhede. 2024-03-22. Nonparametric inference of higher order interaction patterns in networks. https://arxiv.org/abs/2403.15635

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