Completely random measures for modelling block-structured sparse networks

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Many statistical methods for network data parameterize the edge-probability by attributing latent traits to the vertices such as block structure and assume exchangeability in the sense of the Aldous-Hoover representation theorem. Empirical studies of networks indicate that many real-world networks have a power-law distribution of the vertices which in turn implies the number of edges scale slower than quadratically in the number of vertices. These assumptions are fundamentally irreconcilable as the Aldous-Hoover theorem implies quadratic scaling of the number of edges. Recently Caron and Fox [2014] proposed the use of a different notion of exchangeability due to Kallenberg [2006] and obtained a network model which admits power-law behaviour while retaining desirable statistical properties, however this model does not capture latent vertex traits such as block-structure. In this work we re-introduce the use of block-structure for network models obeying allenberg’s notion of exchangeability and thereby obtain a model which admits the inference of block-structure and edge inhomogeneity. We derive a simple expression for the likelihood and an efficient sampling method. The obtained model is not significantly more difficult to implement than existing approaches to block-modelling and performs well on real network datasets.
Original languageEnglish
Title of host publicationAdvances in Neural Information Processing (NIPS 2016)
Number of pages12
PublisherNeural Information Processing Systems Foundation
Publication date2016
Publication statusPublished - 2016
Event29th Annual Conference on Neural Information Processing Systems (NIPS 2016) - Barcelona, Spain
Duration: 5 Dec 201610 Dec 2016
Conference number: 29


Conference29th Annual Conference on Neural Information Processing Systems (NIPS 2016)
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