• Corpus ID: 2017776

Information-theoretic bounds for exact recovery in weighted stochastic block models using the Renyi divergence

@article{Jog2015InformationtheoreticBF,
  title={Information-theoretic bounds for exact recovery in weighted stochastic block models using the Renyi divergence},
  author={Varun Jog and Po-Ling Loh},
  journal={ArXiv},
  year={2015},
  volume={abs/1509.06418}
}
We derive sharp thresholds for exact recovery of communities in a weighted stochastic block model, where observations are collected in the form of a weighted adjacency matrix, and the weight of each edge is generated independently from a distribution determined by the community membership of its endpoints. Our main result, characterizing the precise boundary between success and failure of maximum likelihood estimation when edge weights are drawn from discrete distributions, involves the Renyi… 
Recovering communities in weighted stochastic block models
  • Varun Jog, Po-Ling Loh
  • Computer Science
    2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)
  • 2015
We derive sharp thresholds for exact recovery of communities in a weighted stochastic block model, where observations are collected in the form of a weighted adjacency matrix, and the weight of each
Exact Recovery in the General Hypergraph Stochastic Block Model
TLDR
This paper develops a polynomial-time two-stage algorithm that meets the threshold of exact recovery in the general d-uniform hypergraph stochastic block model and recovers prior results for the standard SBM and d-HSBM with two symmetric communities as special cases.
Optimal hypothesis testing for stochastic block models with growing degrees
TLDR
A class of adaptive tests that are computationally tractable and completely data-driven that achieve nontrivial powers in the contiguous regime and consistency in the singular regime whenever $n p_{n,av} \to\infty$ is the average connection probability.
Exact Recovery for a Family of Community-Detection Generative Models
TLDR
A new toy model for planted generative models called planted Random Energy Model (REM), inspired by Derrida’s REM is proposed, which provides the asymptotic behaviour of the probability of error for the maximum likelihood estimator and hence the exact recovery threshold.
Optimal rates for community estimation in the weighted stochastic block model
TLDR
A weighted generalization of the stochastic block models, in which observations are collected in the form of a weighted adjacency matrix and the weight of each edge is generated independently from an unknown probability density determined by the community membership of its endpoints, is studied.
Community detection and stochastic block models: recent developments
  • E. Abbe
  • Computer Science
    J. Mach. Learn. Res.
  • 2017
TLDR
The recent developments that establish the fundamental limits for community detection in the stochastic block model are surveyed, both with respect to information-theoretic and computational thresholds, and for various recovery requirements such as exact, partial and weak recovery.
Community Detection and Stochastic Block Models
  • E. Abbe
  • Computer Science
    Found. Trends Commun. Inf. Theory
  • 2018
TLDR
The recent developments that establish the fundamental limits for community detection in the stochastic block model are surveyed, both with respect to information-theoretic and computational thresholds, and for various recovery requirements such as exact, partial and weak recovery.
Community detection and the stochastic block model : recent developments
TLDR
The recent developments that establish the fundamental limits for community detection in the stochastic block model are surveyed, both with respect to statistical and computational tradeoffs, and for various recovery requirements such as exact, partial and weak recovery.
Detection in the stochastic block model with multiple clusters: proof of the achievability conjectures, acyclic BP, and the information-computation gap
TLDR
The paper proves the efficient detection to non-symmetrical SBMs with a generalized notion of detection and KS threshold, and connects ABP to a power iteration method with a nonbacktracking operator of generalized order, formalizing the interplay between message passing and spectral methods.
On the Fundamental Limits of Matrix Completion: Leveraging Hierarchical Similarity Graphs
TLDR
The optimal sample complexity is analyzed and different regimes whose characteristics rely on quality metrics of side information of the hierarchical similarity graph are identified and it is shown that the characterized information-theoretic limit can be asymptotically achieved.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 48 REFERENCES
Asymptotic Mutual Information for the Two-Groups Stochastic Block Model
TLDR
An information-theoretic view of the stochastic block model, a popular statistical model for the large-scale structure of complex networks, is developed and an explicit `single-letter' characterization of the per-vertex mutual information between the vertex labels and the graph is established.
Reconstruction in the labeled stochastic block model
TLDR
It is shown that when above the threshold by a specific constant, reconstruction is achieved by (1) minimum bisection, and (2) a spectral method combined with removal of nodes of high degree.
Decoding Binary Node Labels from Censored Edge Measurements: Phase Transition and Efficient Recovery
TLDR
The first goal of this paper is to determine how the edge probabilityp needs to scale to allow exact recovery in the presence of noise and an efficient recovery algorithm based on semidefinite programming is proposed and shown to succeed in the threshold regime up to twice the optimal rate.
Exact Recovery in the Stochastic Block Model
TLDR
An efficient algorithm based on a semidefinite programming relaxation of ML is proposed, which is proved to succeed in recovering the communities close to the threshold, while numerical experiments suggest that it may achieve the threshold.
Consistency Thresholds for Binary Symmetric Block Models
TLDR
This work considers the problem of reconstructing symmetric block models with two blocks of n vertices each and connection probabilities pn and qn for interand intra-block edge probabilities respectively and gives efficient algorithms for consistent estimators whenever one exists.
Consistency thresholds for the planted bisection model
TLDR
It is shown that the planted bisection is recoverable asymptotically if and only if with high probability every node belongs to the same community as the majority of its neighbors.
Minimax Rates of Community Detection in Stochastic Block Models
TLDR
A general minimax theory for community detection is provided, which gives minimax rates of the mis-match ratio for a wide rage of settings including homogeneous and inhomogeneous SBMs, dense and sparse networks, finite and growing number of communities.
Information recovery from pairwise measurements: A shannon-theoretic approach
TLDR
A unified framework is developed to characterize a sufficient and a necessary condition for exact information recovery, which accommodates general graph structures, alphabet sizes, and channel transition measures and plays a central role in determining the recovery limits.
Community detection in general stochastic block models: fundamental limits and efficient recovery algorithms
TLDR
This paper investigates the partial and exact recovery of communities in the general SBM (in the constant and logarithmic degree regimes), and uses the generality of the results to tackle overlapping communities.
Conditional Random Fields, Planted Satisfaction, and Entropy Concentration
TLDR
It is shown that under mild assumptions on the kernel, the conditional entropy of the node variables given the edge variables concentrates around a deterministic threshold, which implies in particular the concentration of the number of solutions in a broad class of planted CSPs.
...
1
2
3
4
5
...