CUED Publications database

Bayesian inference on random simple graphs with power law degree distributions

Lee, J and Heaukulani, C and Ghahramani, Z and James, LF and Choi, S (2017) Bayesian inference on random simple graphs with power law degree distributions. 34th International Conference on Machine Learning, ICML 2017, 4. pp. 3153-3168.

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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.

Item Type: Article
Uncontrolled Keywords: stat.ML stat.ML
Divisions: Div F > Computational and Biological Learning
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:32
Last Modified: 10 Apr 2021 22:24