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Non-parametric methods for the dynamic stochastic block model and the time-dependent graphon

Presented by: 
Marianna Pensky
Wednesday 14th December 2016 - 14:45 to 15:30
INI Seminar Room 1
 The Dynamic Stochastic Block Model (DSBM) and the dynamic graphon are natural extensions of the, respectively, Stochastic Block Model and the graphon, from the time-independent to the time-dependent setting. The objective of the present talk is estimation of the tensor of the connection probabilities  when it is generated by the  DSBM  and the dynamic graphon. In particular, in the context of the DSBM, under very few simple non-parametric assumptions,  we derive a penalized least squares  estimator  and show that it satisfies an oracle inequality and also attains the minimax lower bounds for the risk.  We extend  those results to estimation in the context of the dynamic graphon. The estimators   are adaptive to the unknown number of blocks in the context of DSBM or of the smoothness of the graphon function.  The technique relies on the vectorization of the model and leads to to much simpler mathematical arguments  than the ones used previously in the stationary set up. In addition, all our results are non-asymptotic and allow a variety of  extensions.  

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