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Goodness of fit of logistic models for random graphs

Presented by: 
Pierre Latouche Université Paris 1
Tuesday 26th July 2016 - 09:30 to 10:00
INI Seminar Room 1
We consider  binary networks along with covariate information on the edges. In order to take these covariates into account, logistic-type models for random graphs are often considered. One of the main questions which arises in practice is to assess the goodness of fit of a  model. To address this problem, we add a general term, related to the graphon function of W-graph models, to the logistic models. Such an extra term can be approximated from a blockwise constant function obtained using  stochastic block models with increasing number of clusters. If the given network is fully explained by the covariates, then a sole block should be estimated from data. This framework allows to derive a testing procedure from a model based selection context. Bayes factors or posterior odds can then be used for decision making. Overall, the logistic model considered necessitates two types of variational approximations to derive the model selection approach. 
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons