Bayesian inference on random simple graphs with power law degree distributions

Juho Lee, Creighton Heaukulani, Zoubin Ghahramani, Lancelot F. James, Seungjin Choi
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:2004-2013, 2017.

Abstract

We present a model for random simple graphs with power law (i.e., heavy-tailed) degree distributions. To attain this behavior, the edge probabilities in the graph are constructed from Bertoin–Fujita–Roynette–Yor (BFRY) random variables, which have been recently utilized in Bayesian statistics for the construction of power law models in several applications. Our construction readily extends to capture the structure of latent factors, similarly to stochastic block-models, while maintaining its power law degree distribution. The BFRY random variables are well approximated by gamma random variables in a variational Bayesian inference routine, which we apply to several network datasets for which power law degree distributions are a natural assumption. By learning the parameters of the BFRY distribution via probabilistic inference, we are able to automatically select the appropriate power law behavior from the data. In order to further scale our inference procedure, we adopt stochastic gradient ascent routines where the gradients are computed on minibatches (i.e., subsets) of the edges in the graph.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-lee17a, title = {{B}ayesian inference on random simple graphs with power law degree distributions}, author = {Juho Lee and Creighton Heaukulani and Zoubin Ghahramani and Lancelot F. James and Seungjin Choi}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {2004--2013}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/lee17a/lee17a.pdf}, url = {https://proceedings.mlr.press/v70/lee17a.html}, abstract = {We present a model for random simple graphs with power law (i.e., heavy-tailed) degree distributions. To attain this behavior, the edge probabilities in the graph are constructed from Bertoin–Fujita–Roynette–Yor (BFRY) random variables, which have been recently utilized in Bayesian statistics for the construction of power law models in several applications. Our construction readily extends to capture the structure of latent factors, similarly to stochastic block-models, while maintaining its power law degree distribution. The BFRY random variables are well approximated by gamma random variables in a variational Bayesian inference routine, which we apply to several network datasets for which power law degree distributions are a natural assumption. By learning the parameters of the BFRY distribution via probabilistic inference, we are able to automatically select the appropriate power law behavior from the data. In order to further scale our inference procedure, we adopt stochastic gradient ascent routines where the gradients are computed on minibatches (i.e., subsets) of the edges in the graph.} }
Endnote
%0 Conference Paper %T Bayesian inference on random simple graphs with power law degree distributions %A Juho Lee %A Creighton Heaukulani %A Zoubin Ghahramani %A Lancelot F. James %A Seungjin Choi %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-lee17a %I PMLR %P 2004--2013 %U https://proceedings.mlr.press/v70/lee17a.html %V 70 %X We present a model for random simple graphs with power law (i.e., heavy-tailed) degree distributions. To attain this behavior, the edge probabilities in the graph are constructed from Bertoin–Fujita–Roynette–Yor (BFRY) random variables, which have been recently utilized in Bayesian statistics for the construction of power law models in several applications. Our construction readily extends to capture the structure of latent factors, similarly to stochastic block-models, while maintaining its power law degree distribution. The BFRY random variables are well approximated by gamma random variables in a variational Bayesian inference routine, which we apply to several network datasets for which power law degree distributions are a natural assumption. By learning the parameters of the BFRY distribution via probabilistic inference, we are able to automatically select the appropriate power law behavior from the data. In order to further scale our inference procedure, we adopt stochastic gradient ascent routines where the gradients are computed on minibatches (i.e., subsets) of the edges in the graph.
APA
Lee, J., Heaukulani, C., Ghahramani, Z., James, L.F. & Choi, S.. (2017). Bayesian inference on random simple graphs with power law degree distributions. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:2004-2013 Available from https://proceedings.mlr.press/v70/lee17a.html.

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