Exploiting Tradeoffs for Exact Recovery in Heterogeneous Stochastic Block Models
نویسندگان
چکیده
The Stochastic Block Model (SBM) is a widely used random graph model for networks with communities. Despite the recent burst of interest in community detection under the SBM from statistical and computational points of view, there are still gaps in understanding the fundamental limits of recovery. In this paper, we consider the SBM in its full generality, where there is no restriction on the number and sizes of communities or how they grow with the number of nodes, as well as on the connectivity probabilities inside or across communities. For such stochastic block models, we provide guarantees for exact recovery via a semidefinite program as well as upper and lower bounds on SBM parameters for exact recoverability. Our results exploit the tradeoffs among the various parameters of heterogenous SBM and provide recovery guarantees for many new interesting SBM configurations.
منابع مشابه
Community detection and stochastic block models: recent developments
The stochastic block model (SBM) is a random graph model with planted clusters. It is widely employed as a canonical model to study clustering and community detection, and provides generally a fertile ground to study the statistical and computational tradeoffs that arise in network and data sciences. This note surveys the recent developments that establish the fundamental limits for community d...
متن کاملExponential error rates of SDP for block models: Beyond Grothendieck's inequality
In this paper we consider the cluster estimation problem under the Stochastic Block Model. We show that the semidefinite programming (SDP) formulation for this problem achieves an error rate that decays exponentially in the signal-to-noise ratio. The error bound implies weak recovery in the sparse graph regime with bounded expected degrees, as well as exact recovery in the dense regime. An imme...
متن کاملMAT 585: Exact Recovery of the Semidefinite Relaxation for Stochastic Block Model
Today we consider a semidefinite programming relaxation algorithm for SBM and derive conditions for exact recovery. The main ingredient for the proof will be duality theory.
متن کاملRecovering Communities in the General Stochastic Block Model Without Knowing the Parameters
The stochastic block model (SBM) has recently gathered significant attention due to new threshold phenomena. However, most developments rely on the knowledge of the model parameters, or at least on the number of communities. This paper introduces efficient algorithms that do not require such knowledge and yet achieve the optimal information-theoretic tradeoffs identified in Abbe-Sandon FOCS15. ...
متن کاملA spectral method for community detection in moderately-sparse degree-corrected stochastic block models
We consider community detection in Degree-Corrected Stochastic Block Models (DCSBM). We propose a spectral clustering algorithm based on a suitably normalized adjacency matrix. We show that this algorithm consistently recovers the block-membership of all but a vanishing fraction of nodes, in the regime where the lowest degree is of order log(n) or higher. Recovery succeeds even for very heterog...
متن کامل