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Subsampling, symmetry and averaging in networks

Presented by: 
Peter Orbanz Columbia University
Monday 11th July 2016 - 14:30 to 15:00
INI Seminar Room 1
Consider a very large graph---say, the link graph of a large social network. Now invent a randomized algorithm that extracts a smaller subgraph. If we use the subgraph as sample data and perform statistical analysis on this sample, what can we learn about the underlying network? Clearly, that should depend on the subsampling algorithm. I show how the choice of algorithm defines a notion of (1) distributional invariance and (2) of averaging within a single large graph. Under suitable conditions, the resulting averages satisfy a law of large numbers, such that statistical inference from a single sample graph is indeed possible. From this algorithmic point of view, graphon models arise from a specific choice of sampling algorithm, various known pathologies of these models are explained as a selection bias.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons