Likelihood-based model selection for stochastic block models
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In this paper, an approach based on the log likelihood ratio statistic and analysis of its asymptotic properties under model misspecification is presented. But the authors focus on estimating the latent node labels and the model parameters rather than the issue of choosing the number of blocks.Abstract:
The stochastic block model (SBM) provides a popular framework for modeling community structures in networks. However, more attention has been devoted to problems concerning estimating the latent node labels and the model parameters than the issue of choosing the number of blocks. We consider an approach based on the log likelihood ratio statistic and analyze its asymptotic properties under model misspecification. We show the limiting distribution of the statistic in the case of underfitting is normal and obtain its convergence rate in the case of overfitting. These conclusions remain valid when the average degree grows at a polylog rate. The results enable us to derive the correct order of the penalty term for model complexity and arrive at a likelihood-based model selection criterion that is asymptotically consistent. Our analysis can also be extended to a degree-corrected block model (DCSBM). In practice, the likelihood function can be estimated using more computationally efficient variational methods or consistent label estimation algorithms, allowing the criterion to be applied to large networks.read more
Citations
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References
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Brian Karrer,Mark Newman +1 more
TL;DR: This work demonstrates how the generalization of blockmodels to incorporate this missing element leads to an improved objective function for community detection in complex networks and proposes a heuristic algorithm forcommunity detection using this objective function or its non-degree-corrected counterpart.
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Mixed Membership Stochastic Blockmodels
TL;DR: In this article, the authors introduce a class of variance allocation models for pairwise measurements, called mixed membership stochastic blockmodels, which combine global parameters that instantiate dense patches of connectivity (blockmodel) with local parameters (mixed membership), and develop a general variational inference algorithm for fast approximate posterior inference.
Proceedings Article
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Jure Leskovec,Julian McAuley +1 more
TL;DR: A novel machine learning task of identifying users' social circles is defined as a node clustering problem on a user's ego-network, a network of connections between her friends, and a model for detecting circles is developed that combines network structure as well as user profile information.