BrAINs seminar: Edge-Copying Random Hypergraphs скачать в хорошем качестве

BrAINs seminar: Edge-Copying Random Hypergraphs

Seminar by Phil Grochow (online) https://www.philchodrow.prof Title: Edge-Copying Random Hypergraphs Abstract:We propose a generative model of growing hypergraphs in which hyperedges form via noisy copying of previous hyperedges. This model is motivated by the observation that empirical hypergraphs tend to have much higher rates of large intersections between hyperedges than would be expected by random chance. Although edge-copying is a known mechanism, our proposed model offers a distinctive combination of attractive features: it is easily interpretable; it reproduces several stylized facts from many empirical hypergraphs; and it is efficiently learnable from data. Analyzing our model, we derive a power-law for the asymptotic degree distribution as well as large fluctuations in the sizes of edges. We also make a detailed study of the intersections of edges. We offer a mathematical formalization of the idea that some generative models have asymptotically large intersections, and prove that our model is in this class. This contrasts to many extant generative hypergraph models which have asymptotically small intersections. We provide a scalable stochastic expectation maximization algorithm for estimation from hypergraphs with millions of nodes and edges. We then assess our model on a link prediction task, finding favorable predictive performance despite our model’s simplicity. Joint work with Xie He and Peter Mucha