# Global and Local Information in Clustering Labeled Block Models

@article{Kanade2016GlobalAL, title={Global and Local Information in Clustering Labeled Block Models}, author={Varun Kanade and Elchanan Mossel and Tselil Schramm}, journal={IEEE Transactions on Information Theory}, year={2016}, volume={62}, pages={5906-5917} }

The stochastic block model is a classical cluster exhibiting random graph model that has been widely studied in statistics, physics, and computer science. In its simplest form, the model is a random graph with two equal-sized clusters, with intracluster edge probability p, and intercluster edge probability q. We focus on the sparse case, i.e., p, q = O(1/n), which is practically more relevant and also mathematically more challenging. A conjecture of Decelle, Krzakala, Moore, and Zdeborova…

## 38 Citations

### Active learning for community detection in stochastic block models

- Computer Science2016 IEEE International Symposium on Information Theory (ISIT)
- 2016

This work shows that sampling the labels of a vanishingly small fraction of nodes is sufficient for exact community detection even when D(a; b) <; 1, and provides an efficient learning algorithm which recovers the community memberships of all nodes w.p. as long as the number of sampled points meets the sufficient condition.

### Find Your Place: Simple Distributed Algorithms for Community Detection

- Computer Science, MathematicsSODA
- 2017

It is proved that the process resulting from this dynamics produces a clustering that exactly or approximately reflects the underlying cut in logarithmic time, under various graph models that exhibit a sparse balanced cut, including the stochastic block model.

### Recovering asymmetric communities in the stochastic block model

- Computer Science2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- 2016

This work considers the sparse stochastic block model in the case where the degrees are uninformative and shows that if the community of a vanishing fraction of the vertices is revealed, then a local algorithm is optimal down to Kesten Stigum threshold and quantifies explicitly its performance.

### The Computer Science and Physics of Community Detection: Landscapes, Phase Transitions, and Hardness

- Computer ScienceBull. EATCS
- 2017

Community detection in graphs is the problem of finding groups of vertices which are more densely connected than they are to the rest of the graph, which provides a window into the cultures of statistical physics and statistical inference, and how those cultures think about distributions of instances, landscapes of solutions, and hardness.

### Contextual Stochastic Block Model: Sharp Thresholds and Contiguity

- MathematicsArXiv
- 2020

It is expected that the conjecture holds as soon as the average degree exceeds one, so that the graph has a giant component, and the sharp threshold for detection and weak recovery is characterized.

### Streaming Belief Propagation for Community Detection

- Computer ScienceNeurIPS
- 2021

This work introduces a simple model for networks growing over time which it is referred to as streaming stochastic block model (StSBM) and proves that voting algorithms have fundamental limitations, and develops a streaming belief-propagation approach which proves optimality in certain regimes.

### Mutual information for the sparse stochastic block model

- Computer Science, Mathematics
- 2022

A conjecture for the limit of this quantity is expressed in terms of a Hamilton-Jacobi equation posed over a space of probability measures, and a proof that this conjectured limit provides a lower bound for the asymptotic mutual information is shown.

### Ising Model on Locally Tree-like Graphs: Uniqueness of Solutions to Cavity Equations

- Mathematics, Computer Science
- 2022

This work proves there is at most at most one non-trivial fixed point for Ising models with zero or random (but “unbised”) external fields.

### Information Limits for Community Detection in Hypergraph with Label Information

- Computer ScienceSymmetry
- 2021

This work investigating the effect of label information on the exact recovery of communities in an m-uniform Hypergraph Stochastic Block Model (HSBM) derives sharp boundaries for exact recovery under both scenarios from an information-theoretical point of view.

### Density Evolution in the Degree-correlated Stochastic Block Model

- Computer Science, MathematicsCOLT
- 2016

This paper addresses the more refined question of how many vertices that will be misclassified on average under the stochastic block model, and shows that the minimum misclassified fraction on average is attained by a local algorithm, namely belief propagation, in time linear in the number of edges.

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