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A Bayesian approach to network modularity: inferring the structure and scale of modular networks

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If you have a question about this talk, please contact Zoubin Ghahramani .

We present an efficient, principled, and interpretable technique for inferring module assignments and identifying the optimal number of modules in relational data. Our approach is based on a generative model equivalent to an infinite-range spin-glass Potts model on the irregular lattice defined by a given network; the problem of identifying modules is then tantamount to inferring posterior distributions over both the latent module assignments (i.e. spin states) and the model parameters (i.e. coupling constants) while also identifying the number of modules (i.e. number of occupied spin states) in the network. Using the variational Bayes framework we derive a mean-field free energy, the minimization of which provides controlled approximations to the distributions of interest. We show how several existing methods for finding modules can be described as variant, special, or limiting cases of our work, and how related methods for complexity control—identification of the true number of modules—are outperformed. We apply the technique to synthetic and real networks and outline how the method naturally allows for model selection among competing network models.

This talk is part of the Machine Learning @ CUED series.

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