**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