Consistency of maximum-likelihood and variational estimators in the stochastic block model
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TLDR
The identi ability of SBM is proved, while asymptotic properties of maximum-likelihood and variational esti- mators are provided, and the consistency of these estimators is settled, which is, to the best of the authors' knowledge, the rst result of this type for variational estimators with random graphs.Abstract:
The stochastic block model (SBM) is a probabilistic model de- signed to describe heterogeneous directed and undirected graphs. In this paper, we address the asymptotic inference on SBM by use of maximum- likelihood and variational approaches. The identi ability of SBM is proved, while asymptotic properties of maximum-likelihood and variational esti- mators are provided. In particular, the consistency of these estimators is settled, which is, to the best of our knowledge, the rst result of this type for variational estimators with random graphs.read more
Citations
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Variational Inference: A Review for Statisticians
TL;DR: For instance, mean-field variational inference as discussed by the authors approximates probability densities through optimization, which is used in many applications and tends to be faster than classical methods, such as Markov chain Monte Carlo sampling.
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Variational Inference: A Review for Statisticians
TL;DR: Variational inference (VI), a method from machine learning that approximates probability densities through optimization, is reviewed and a variant that uses stochastic optimization to scale up to massive data is derived.
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Consistency of spectral clustering in stochastic block models
Jing Lei,Alessandro Rinaldo +1 more
TL;DR: In this article, the performance of spectral clustering for community extraction in stochastic block models is analyzed and a combinatorial bound on the spectrum of binary random matrices, which is sharper than the conventional matrix Bernstein inequality, is established.
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Consistency of spectral clustering in stochastic block models
Jing Lei,Alessandro Rinaldo +1 more
TL;DR: It is shown that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden communities even when the order of the maximum expected degree is as small as $\log n$ with $n$ the number of nodes.
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Pseudo-likelihood methods for community detection in large sparse networks
TL;DR: In this paper, the authors proposed a fast pseudo-likelihood method for fitting the stochastic block model for networks, as well as a variant that allows for an arbitrary degree distribution by conditioning on degrees.
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