Non-parametric methods for the dynamic stochastic block model and the time-dependent graphon
54 mins 15 secs,
788.45 MB,
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| Description: |
Pensky, M (University of Central Florida)
Wednesday 14th December 2016 - 14:45 to 15:30 |
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| Created: | 2016-12-20 15:01 |
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| Collection: | Theoretical Foundations for Statistical Network Analysis |
| Publisher: | Isaac Newton Institute |
| Copyright: | Pensky, M |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | 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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