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Francois Caron

 

Wednesday 6th April 2016

Time: 4.00pm

 

Ground Floor Seminar Room

25 Howland Street, London, W1T 4JG

 

Sparse and modular networks using exchangeable random measures

 

 

Statistical network modeling has focused on representing the graph as a
discrete structure, namely the adjacency matrix, and considering the
exchangeability of this array. In such cases, it is well known that the
graph is necessarily either dense (the number of edges scales
quadratically with the number of nodes) or trivially empty.
Here, we instead consider representing the graph as a measure on the
plane. For the associated definition of exchangeability, we rely on the
Kallenberg representation theorem (Kallenberg, 1990). For certain
choices of such exchangeable random measures underlying the graph
construction, the network process is sparse with power-law degree
distribution, and can accommodate an overlapping block-structure. I then
present a Markov chain Monte Carlo algorithm for efficient exploration
of the posterior distribution and demonstrate that we are able to
recover the structure of a range of networks graphs ranging from dense
to sparse based on our flexible formulation.

Joint work with Emily Fox and Adrien Todeschini
http://arxiv.org/abs/1401.1137
http://arxiv.org/abs/1602.02114