Nonparametric inference of higher order interaction patterns in networks
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910394994393088 |
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| author | Wegner, Anatol E. Olhede, Sofia C. |
| author_facet | Wegner, Anatol E. Olhede, Sofia C. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15635 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonparametric inference of higher order interaction patterns in networks Wegner, Anatol E. Olhede, Sofia C. Social and Information Networks Statistical Mechanics Information Theory Physics and Society Methodology 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. |
| title | Nonparametric inference of higher order interaction patterns in networks |
| topic | Social and Information Networks Statistical Mechanics Information Theory Physics and Society Methodology |
| url | https://arxiv.org/abs/2403.15635 |