A1402
Title: Scalable variational inference for hypergraph stochastic blockmodels via sample-to-population approximation
Authors: Luca Brusa - University of Milano-Bicocca (Italy) [presenting]
Catherine Matias - CNRS - Universite Pierre et Marie Curie (France)
Abstract: Hypergraphs provide a natural framework for representing higher-order interactions, where relationships may involve more than two nodes. Stochastic blockmodels extend model-based clustering to these structures by grouping nodes according to latent interaction patterns, but their practical use is limited by the combinatorial cost of accounting for all possible hyperedges, especially in sparse and large-scale settings. A scalable inference procedure for hypergraph stochastic blockmodels is proposed based on a sample-to-population approximation of the complete likelihood. The method includes all observed hyperedges and a controlled sample of non-occurring hyperedges, whose contribution is reweighted to recover population-level information. This criterion is embedded in a variational expectation-maximization algorithm, yielding fast updates for latent node memberships and connectivity parameters while preserving the interpretation of the original model. The approach applies to non-uniform simple hypergraphs and allows the sampling rate of non-occurring hyperedges to vary with hyperedge size. The resulting algorithm enables likelihood-based clustering and parameter estimation for substantially larger hypergraphs than those accessible to exhaustive likelihood computations. The method is implemented in fully parallelized C++ code and made available through an R interface. Experiments on synthetic and real data assess its accuracy and computational gains.
