Nonparametric inference of higher order interaction patterns in networks
<|reference_start|>Nonparametric inference of higher order interaction patterns in networks: 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.<|reference_end|>
@article{wegner2024nonparametric,
    title={Nonparametric inference of higher order interaction patterns in networks},
    author={Anatol E. Wegner and Sofia C. Olhede},
    journal={arXiv preprint arXiv:2403.15635},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.15635},
    primaryClass={cs.SI cond-mat.stat-mech cs.IT math.IT physics.soc-ph stat.ME}
}