#  Probabilitas Series: Allan Sly 

 



####  calendar\_today Date and Time 

 **October 25, 2024** 

 10:30AM - 11:30PM EDT 

####  pin\_drop Location 

 **Science Center 316**  



 

 



 

 The Probabilitas Seminar series focuses on high-dimensional problems that combine statistics, probability, information theory, computer science, and other related fields. The upcoming seminar takes place on Friday, March 8, from 10:30-11:30am EST. The talk will be hybrid, both in-person in Science Center 316 and on Zoom (please contact the department for Zoom information). This week's guest will be Allan Sly of the Princeton University Mathematics Department.

 **Stochastic Blocks Models: Detection and Recovery**

 The stochastic block model is a canonical model of communities in random graphs. Given a sparse stochastic block model, the two standard inference tasks are: (i) Weak recovery: can we estimate the communities with non-trivial overlap with the true communities? (ii) Detection/Hypothesis testing: can we distinguish if the sample was drawn from the block model or from a random graph with no community structure with probability tending to 1 as the graph size tends to infinity? We show that the thresholds for these two phenomena coincide and that the two inference tasks are equivalent except possibly at a critical point. In the case of the symmetric models with up to 4 communities and large average degree, we show that this threshold coincides with the Kesten-Stigum bound.

 Joint work with Elchanan Mossel and Youngtak Sohn



 

 



 

 

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