Bayesian inference on random simple graphs with power law degree distributions
This work addresses the need for scalable Bayesian inference methods for network datasets with heavy-tailed degree distributions, such as social or biological networks, but it is incremental as it builds on existing BFRY-based models.
The authors tackled the problem of modeling random simple graphs with power law degree distributions by constructing edge probabilities from BFRY random variables, enabling automatic selection of power law behavior from data and scaling inference with stochastic gradient ascent on minibatches.
We present a model for random simple graphs with a degree distribution that obeys a power law (i.e., is heavy-tailed). 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 blockmodels, 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.