Fractal Gaussian Networks: A sparse random graph model based on Gaussian Multiplicative Chaos

Subhroshekhar Ghosh, Krishna Balasubramanian, Xiaochuan Yang
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:3545-3555, 2020.

Abstract

We propose a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. Such fractal structures have been empirically observed in diverse applications. FGNs interpolate continuously between the popular purely random geometric graphs (a.k.a. the Poisson Boolean network), and random graphs with increasingly fractal behavior. In fact, they form a parametric family of sparse random geometric graphs that are parametrised by a fractality parameter $\nu$ which governs the strength of the fractal structure. FGNs are driven by the latent spatial geometry of Gaussian Multiplicative Chaos (GMC), a canonical model of fractality in its own right. We explore the natural question of detecting the presence of fractality and the problem of parameter estimation based on observed network data. Finally, we explore fractality in community structures by unveiling a natural stochastic block model in the setting of FGNs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-ghosh20a, title = {Fractal {G}aussian Networks: A sparse random graph model based on {G}aussian Multiplicative Chaos}, author = {Ghosh, Subhroshekhar and Balasubramanian, Krishna and Yang, Xiaochuan}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {3545--3555}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/ghosh20a/ghosh20a.pdf}, url = {https://proceedings.mlr.press/v119/ghosh20a.html}, abstract = {We propose a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. Such fractal structures have been empirically observed in diverse applications. FGNs interpolate continuously between the popular purely random geometric graphs (a.k.a. the Poisson Boolean network), and random graphs with increasingly fractal behavior. In fact, they form a parametric family of sparse random geometric graphs that are parametrised by a fractality parameter $\nu$ which governs the strength of the fractal structure. FGNs are driven by the latent spatial geometry of Gaussian Multiplicative Chaos (GMC), a canonical model of fractality in its own right. We explore the natural question of detecting the presence of fractality and the problem of parameter estimation based on observed network data. Finally, we explore fractality in community structures by unveiling a natural stochastic block model in the setting of FGNs.} }
Endnote
%0 Conference Paper %T Fractal Gaussian Networks: A sparse random graph model based on Gaussian Multiplicative Chaos %A Subhroshekhar Ghosh %A Krishna Balasubramanian %A Xiaochuan Yang %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-ghosh20a %I PMLR %P 3545--3555 %U https://proceedings.mlr.press/v119/ghosh20a.html %V 119 %X We propose a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. Such fractal structures have been empirically observed in diverse applications. FGNs interpolate continuously between the popular purely random geometric graphs (a.k.a. the Poisson Boolean network), and random graphs with increasingly fractal behavior. In fact, they form a parametric family of sparse random geometric graphs that are parametrised by a fractality parameter $\nu$ which governs the strength of the fractal structure. FGNs are driven by the latent spatial geometry of Gaussian Multiplicative Chaos (GMC), a canonical model of fractality in its own right. We explore the natural question of detecting the presence of fractality and the problem of parameter estimation based on observed network data. Finally, we explore fractality in community structures by unveiling a natural stochastic block model in the setting of FGNs.
APA
Ghosh, S., Balasubramanian, K. & Yang, X.. (2020). Fractal Gaussian Networks: A sparse random graph model based on Gaussian Multiplicative Chaos. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:3545-3555 Available from https://proceedings.mlr.press/v119/ghosh20a.html.

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