A central problem in analyzing networks is partitioning them into modules or communities. One of the best tools for this is the stochastic block model, which clusters vertices into blocks with statistically homogeneous pattern of links. Despite its flexibility and popularity, there has been a lack of principled statist…
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48 results for “Stochastic Block Models”
We generalize the stochastic block model to the important case in which edges are annotated with weights drawn from an exponential family distribution. This generalization introduces several technical difficulties for model estimation, which we solve using a Bayesian approach. We introduce a variational algorithm that …
In the present paper we study a sparse stochastic network enabled with a block structure. The popular Stochastic Block Model (SBM) and the Degree Corrected Block Model (DCBM) address sparsity by placing an upper bound on the maximum probability of connections between any pair of nodes. As a result, sparsity describes o…
The tree reconstruction problem is to collect and analyze massive data at the th level of the tree, to identify whether there is non-vanishing information of the root, as goes to infinity. Its connection to the clustering problem in the setting of the stochastic block model, which has wide applications in machin…
Spectral clustering achieves strong consistency in the stochastic block model under certain conditions.
problem Achieving strong consistency in spectral clustering for the stochastic block model.
method Entrywise analysis of the Fielder eigenvector of graph Laplacians.
result Spectral clustering achieves exact recovery of hidden communities under matching information-theoretic limits.
Gradient descent and its many variants, including mini-batch stochastic gradient descent, form the algorithmic foundation of modern large-scale machine learning. Due to the size and scale of modern data, gradient computations are often distributed across multiple compute nodes. Unfortunately, such distributed implement…
Paper introduces a new edge exchangeable block model for complex networks.
problem Limitations of the stochastic block model in analyzing complex networks.
method Develops a Bayesian nonparametric edge exchangeable block model.
result The new model outperforms state-of-the-art SBMs for link prediction.
Tests if vertices in graphs have the same latent positions.
problem Testing equality of latent positions in random graphs.
method Empirical Mahalanobis distances from spectral embeddings.
result Test statistics follow chi-square distributions under null and local alternatives.
Efficient algorithm for robust recovery in stochastic block models.
problem Robust recovery in stochastic block models.
method Convex optimization framework, addressing optimization landscape challenges.
result Achieves robust recovery without a price of robustness.
The proliferation of models for networks raises challenging problems of model selection: the data are sparse and globally dependent, and models are typically high-dimensional and have large numbers of latent variables. Together, these issues mean that the usual model-selection criteria do not work properly for networks…
New method improves community detection for large networks.
problem Inefficient community detection for large sparse networks.
method Decouples row and column labels in likelihood function for fast alternating maximization.
result Strongly consistent estimates of communities with provable convergence guarantee.
We propose a semidefinite programming (SDP) algorithm for community detection in the stochastic block model, a popular model for networks with latent community structure. We prove that our algorithm achieves exact recovery of the latent communities, up to the information-theoretic limits determined by Abbe and Sandon (…
Novel model detects communities in noisy multilayer networks.
problem Understanding communities in noisy multilayer networks.
method Hierarchical variational inference for joint detection and typologizing.
result Discover communities of subjects with co-occurrent psychopathologies.
Spectral clustering for directed graphs using likelihood estimation.
problem Clustering directed graphs with edge directions.
method Maximum likelihood estimation on stochastic block models.
result Significant performance gains over existing methods.
Multi-block Min-max Bilevel Optimization with Applications in Multi-task Deep AUC Maximizationmath.OC
Paper tackles multi-block min-max optimization with applications in deep AUC maximization.
problem Multi-block min-max bilevel optimization with non-convex strongly-concave upper level and strongly convex lower level.
method Single-loop randomized stochastic algorithm for constant number of blocks per iteration.
result Sample complexity of O(1/ε^4) for finding ε-stationary point, matching optimal complexity.
We analyze the performance of spectral clustering for community extraction in stochastic block models. We show 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 $\l…
New algorithm optimally clusters networks with side information.
problem Improving network clustering with side information.
method Iterative clustering algorithm for Contextual Stochastic Block Model.
result Optimal performance under Contextual Symmetric Stochastic Block Model.
We consider the community detection problem in sparse random hypergraphs. Angelini et al. (2015) conjectured the existence of a sharp threshold on model parameters for community detection in sparse hypergraphs generated by a hypergraph stochastic block model. We solve the positive part of the conjecture for the case of…
A main task in data analysis is to organize data points into coherent groups or clusters. The stochastic block model is a probabilistic model for the cluster structure. This model prescribes different probabilities for the presence of edges within a cluster and between different clusters. We assume that the cluster ass…
To capture the inherent geometric features of many community detection problems, we propose to use a new random graph model of communities that we call a Geometric Block Model. The geometric block model generalizes the random geometric graphs in the same way that the well-studied stochastic block model generalizes the …
The stochastic block model (SBM) is a probabilistic model for community structure in networks. Typically, only the adjacency matrix is used to perform SBM parameter inference. In this paper, we consider circumstances in which nodes have an associated vector of continuous attributes that are also used to learn the node-…
We analyze the information-theoretic limits for the recovery of node labels in several network models. This includes the Stochastic Block Model, the Exponential Random Graph Model, the Latent Space Model, the Directed Preferential Attachment Model, and the Directed Small-world Model. For the Stochastic Block Model, the…
Two spectral algorithms for community detection in graphs with covariates are compared.
problem Detecting community structure in graphs with covariates.
method Two model-based spectral algorithms are presented and compared.
result The second algorithm often better estimates block assignments by accounting for vertex covariates.
Signed graphs encode positive (attractive) and negative (repulsive) relations between nodes. We extend spectral clustering to signed graphs via the one-parameter family of Signed Power Mean Laplacians, defined as the matrix power mean of normalized standard and signless Laplacians of positive and negative edges. We pro…
We consider community detection in Degree-Corrected Stochastic Block Models (DC-SBM). 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 lowes…
Community detection is an important task in network analysis, in which we aim to learn a network partition that groups together vertices with similar community-level connectivity patterns. By finding such groups of vertices with similar structural roles, we extract a compact representation of the network's large-scale …
Network clustering reveals the organization of a network or corresponding complex system with elements represented as vertices and interactions as edges in a (directed, weighted) graph. Although the notion of clustering can be somewhat loose, network clusters or groups are generally considered as nodes with enriched in…
Paper uses SSC for identifying layers with identical community structures in DIMPLE networks.
problem Identifying layers with identical community structures in DIMPLE networks.
method Sparse Subspace Clustering (SSC) for identifying groups of layers with identical community structures.
result SSC leads to strongly consistent between-layer clustering under mild conditions.
Resolving a conjecture of Abbe, Bandeira and Hall, the authors have recently shown that the semidefinite programming (SDP) relaxation of the maximum likelihood estimator achieves the sharp threshold for exactly recovering the community structure under the binary stochastic block model of two equal-sized clusters. The s…
There exist various types of network block models such as the Stochastic Block Model (SBM), the Degree Corrected Block Model (DCBM), and the Popularity Adjusted Block Model (PABM). While this leads to a variety of choices, the block models do not have a nested structure. In addition, there is a substantial jump in the …
We present a method to estimate block membership of nodes in a random graph generated by a stochastic blockmodel. We use an embedding procedure motivated by the random dot product graph model, a particular example of the latent position model. The embedding associates each node with a vector; these vectors are clustere…
A new method speeds up community detection in graphs.
problem Efficiently detecting communities in large graphs.
method Subsampled semidefinite programming for faster clustering.
result Statistical limits of sketching for community detection established.
Information Theoretic Limits of Exact Recovery in Sub-hypergraph Models for Community Detectionstat.ML
Study information limits for community detection in sub-hypergraphs.
problem Identify limits for exact community detection in sub-hypergraphs.
method Use Fano's inequality to define model parameters and identify success and failure regions.
result Identify regions where algorithms succeed or fail in exact recovery.
Systematic assessment of the quality of fit of the stochastic block model for empirical networksphysics.soc-ph
The stochastic block model accurately describes most empirical networks but struggles with large diameter and slow-mixing networks.
problem Assessing the quality of fit of the stochastic block model for empirical networks.
method Posterior predictive model checking using network descriptors.
result The stochastic block model can accurately describe most empirical networks but struggles with large diameter and slow-mixing networks.
Efficient private algorithms for estimating block models and mixture models.
problem Estimating block models and mixture models in high-dimensional settings.
method General tools for designing efficient private estimation algorithms.
result First efficient private algorithms for weak and exact recovery of stochastic block models.
A test for comparing networks using stochastic block models.
problem Determining if two network datasets come from the same model.
method Adopting stochastic block models, the study introduces an efficient algorithm to match estimated network parameters and develops a powerful test.
result The test is consistent and asymptotically follows a chi-squared distribution.
One of the most fundamental problems in network study is community detection. The stochastic block model (SBM) is a widely used model, for which various estimation methods have been developed with their community detection consistency results unveiled. However, the SBM is restricted by the strong assumption that all no…
We present a method based on the orthogonal symmetric non-negative matrix tri-factorization of the normalized Laplacian matrix for community detection in complex networks. While the exact factorization of a given order may not exist and is NP hard to compute, we obtain an approximate factorization by solving an optimiz…
ALMA improves clustering of multilayer networks.
problem Clustering multilayer networks with distinct layers and communities.
method Alternating minimization algorithm (ALMA) for simultaneous layer partition and community estimation.
result ALMA achieves higher accuracy than TWIST in clustering multilayer networks.
A Generic Sample Splitting Approach for Refined Community Recovery in Stochastic Block Modelsstat.ML
We propose and analyze a generic method for community recovery in stochastic block models and degree corrected block models. This approach can exactly recover the hidden communities with high probability when the expected node degrees are of order or higher. Starting from a roughly correct community partition …
We consider the problem of estimating the location of a single change point in a dynamic stochastic block model. We propose two methods of estimating the change point, together with the model parameters. The first employs a least squares criterion function and takes into consideration the full structure of the stochast…
New model for clustering graphs with multiple data sources.
problem Graph clustering with multiple data sources.
method Formalized multi-view stochastic block models and developed efficient algorithms.
result Provable improvement over previous approaches in multi-view graph clustering.
Sharp thresholds and contiguity for community detection in contextual SBM.
problem Community detection in graphs with high-dimensional node-covariates.
method Contextual Stochastic Block Model, non-rigorous cavity method, information theory.
result Established the sharp threshold for detection and weak recovery in the contextual SBM.
A new model detects complex network communities using node attributes.
problem Lack of methods integrating node attributes for community detection in attributed networks.
method BCSBM model that integrates betweenness centrality and clustering coefficient of nodes.
result BCSBM model outperforms other methods in detecting various network structures.
New model improves community detection in networks with strong assortativity.
problem Classic SBMs fail to recover assortative communities in networks with reduced information.
method Introduced a constrained SBM with strong assortativity constraints and efficient algorithms.
result Significant boost in community recovery capabilities, especially close to information-theoretic threshold.
Randomized spectral co-clustering speeds up large-scale directed networks.
problem Co-clustering directed networks efficiently for large-scale data.
method Randomized spectral co-clustering algorithms using random-projection and random-sampling techniques.
result Theoretical and numerical validation of approximation and misclustering error rates.
Method estimates number of clusters in Block Markov Chain trajectories.
problem Challenges in choosing number of clusters for sequential data.
method Spectral embedding and density-based clustering.
result Asymptotically consistent method for estimating clusters.
Estimates social network structure from random walk subgraphs.
problem Recovering population structure from random walk subgraphs in stochastic block models.
method Maximum likelihood estimation, SAEM algorithm, de-biasing techniques.
result New de-biased estimator provides more accurate recovery of network structure.