Algorithms & Randomness Center (ARC)
Monday, October 26, 2015
Klaus 1116 West – 1:00 pm
(Refreshments will be served in Klaus 2222 at 2 pm)
Title:
The Stochastic Block Model and Communities in Sparse Random Graphs: Detection at Optimal Rate
Abstract:
We consider the problem of communities detection in sparse random graphs. Our model is the so-called Stochastic Block Model, which has been immensely popular in the recent statistics literature. Let X1,...Xk be vertex sets of size n each (where k is fixed and n is large). One draws random edges inside each Xi with probability a/n, and between Xi and Xj with probability b/n, for some constants a and b. Given one instance of this sparse random graph, our goal is to recover the sets Xi as correctly as possible. We are going to present a fast spectral algorithm which does this job at the optimal rate (namely the relation between a,b and the number of mistakes in the recovery is optimal). Our algorithm is based on spectral properties of random sparse matrices and is easy to implement. We will also discuss some related works with spectral algorithms and an open question concerning random matrices.