Improved graph embedding through refined linear transformation and community recovery.
problem Identifying meaningful latent communities in graph data.
method Refined graph encoder embedding via linear transformation, self-training, and latent community recovery.
result Improved vertex embedding and better decision boundaries for vertex classification.
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 logn or higher. Starting from a roughly correct community partition …
Study on recovering hidden communities from data matrices.
problem Recovering a hidden community of cardinality K from a symmetric data matrix.
method Analyzes two types of asymptotic recovery guarantees for weak and exact recovery, deriving conditions for both sufficient and necessary recovery.
result Derives sufficient and necessary conditions for recovery under mild assumptions on probability distributions P and Q.
SDP helps recover hidden communities from symmetric data matrices.
problem Recovering hidden communities from symmetric data matrices.
method Semidefinite programming relaxation for maximum likelihood estimation.
result SDP achieves information-theoretic limits for large communities, but is suboptimal for smaller communities.
Paper finds exact recovery threshold in general hypergraph model.
problem Exact recovery of communities in general hypergraph model.
method Developed a two-stage polynomial-time algorithm for exact recovery.
result Sharp threshold for exact recovery in terms of generalized Chernoff-Hellinger divergence.
New system preserves message meaning in wireless networks, improving data rate.
problem Efficiently transmitting message meaning in wireless networks.
method Modeling semantics as hidden random variables, using Information Bottleneck for compression.
result 20 dB SNR improvement for semantic communication.
New algorithm recovers hidden community beyond Kesten-Stigum threshold.
problem Weak recovery of community in stochastic block model graphs.
method Belief propagation algorithm with O(∣E∣log∗n) complexity. result Achieves weak recovery if λ>1/e beyond Kesten-Stigum threshold. The study examines how side information quality and quantity affect community recovery in graphs.
problem Recovering a hidden community of size K=o(n) in a graph of size n. method Maximum likelihood detection and belief propagation are used to calculate necessary and sufficient conditions for exact and weak recovery. A local voting procedure is also designed and analyzed.
result Tight necessary and sufficient conditions for exact and weak recovery are derived, showing how side information needs to evolve with n to improve recovery thresholds. 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.
Semidefinite programming solves community detection in stochastic block models.
problem Identifying community-like structures in graphs with varying probabilities of connections.
method Semidefinite programming (SDP) algorithms for exact recovery in the Stochastic Block Model (SBM).
result SDP-based algorithms achieve exact recovery in the SBM with high probability under certain conditions.
New algorithm finds overlapping groups in network data.
problem Identifying overlapping communities in network data.
method Spectral algorithm with additive clustering based on SBMO model.
result Adaptive algorithm consistent under SBMO for logarithmic degrees.
New algorithm IAC recovers hidden communities in labeled SBM with optimal performance.
problem Recovering hidden communities in Labeled Stochastic Block Model with varying cluster sizes.
method IAC (Instance-Adaptive Clustering) algorithm, consisting of spectral clustering and iterative likelihood-based improvements.
result IAC achieves optimal performance matching instance-specific lower bounds in expectation and with high probability.
Paper explores exact recovery of communities in weighted graphs using Gaussian and exponential distributions.
problem Exact recovery of communities in weighted graphs with Gaussian and exponential distributions.
method Introduces a new semi-metric to describe conditions for exact recovery and analyzes conditions for both complete and incomplete graphs.
result Necessary and sufficient conditions for exact recovery are asymptotically tight and applicable to both complete and incomplete graphs.
Paper uses EXIT analysis for community detection with side information.
problem Community detection in the presence of side information.
method Imported EXIT method from iterative decoding of error control codes.
result Predicts asymptotic phase transition and residual errors for community detection.
New findings on community recovery in SBM with many communities.
problem Determining community recovery conditions in SBM with more than sqrt(n) communities.
method Constructing motifs and counting them to prove community recovery above the proposed threshold.
result Proving community recovery above the proposed threshold in SBM with K >= sqrt(n) communities.
Study recovers community structure from coarse graph measurements.
problem Community recovery from low-resolution graph measurements.
method Formalized coarsening process of graph measurements, developed conditions for perfect recovery.
result Simple and closed-form asymptotic conditions for perfect recovery of coarse graph communities.
HICODE detects hidden communities in social networks.
problem Weak, natural communities hidden within strong, dominant communities.
method HICODE (HIdden COmmunity DEtection) that identifies both hidden and dominant communities.
result HICODE outperforms state-of-the-art methods in uncovering both hidden and dominant communities.
Community detection is the task of detecting hidden communities from observed interactions. Guaranteed community detection has so far been mostly limited to models with non-overlapping communities such as the stochastic block model. In this paper, we remove this restriction, and provide guaranteed community detection f…
New model for community detection with side information improves recovery accuracy.
problem Community detection in networks with additional node data.
method Data Block Model (DBM) with Chernoff--TV divergence for threshold characterization and efficient algorithm.
result Sharp exact recovery threshold and efficient algorithm for DBM.
The paper studies recovering hidden nearest neighbor graphs in large networks.
problem Discovering strong ties in social networks and assembling genome subsequences.
method Maximum likelihood estimator for recovering hidden 2k-nearest neighbor graphs. result The maximum likelihood estimator achieves asymptotic recovery guarantees under specific conditions.
The paper explores recovery thresholds in heterogeneous SBM with varying community sizes and densities.
problem Understanding the limits of community recovery in heterogeneous SBM.
method Generalized Stochastic Block Model with varying community sizes and densities.
result Exact recovery of very small communities is possible under certain conditions.
Bottom-up algorithms outperform top-down in hierarchical community detection at intermediate levels.
problem Finding the optimal hierarchical community structure in networks.
method A bottom-up algorithm for hierarchical clustering of networks.
result Bottom-up algorithms achieve the information-theoretic threshold for exact recovery at intermediate levels of the hierarchy.
Study exact community recovery in noisy SBM with limited queries.
problem Community recovery in noisy stochastic block models with limited queries.
method Balanced uniform querying, two-stage adaptive strategy, sublinear queries, subsampled graph.
result Adaptive querying can improve exact recovery limits in noisy SBM.
New findings support a new community recovery threshold for Stochastic Block Model with many communities.
problem Recovering communities in Stochastic Block Model with more than sqrt(n) communities.
method Counting specific motifs to achieve polynomial-time community recovery above a new threshold.
result LDP fails below the new threshold, but polynomial-time recovery is possible above it.
Study exact community detection in k-community Gaussian mixtures with different intensities.
problem Community detection in k-community Gaussian mixtures with varying intensities.
method Explicitly find the threshold for exact recovery of maximum likelihood estimation.
result Threshold for exact recovery of maximum likelihood estimation is identified.
This work tackles community recovery in hypergraphs with measurements of varying sizes.
problem Cluster data points into distinct communities based on measurements with varying sizes.
method Characterizes the fundamental limits on the number of measurements required for community reconstruction in hypergraphs with homogeneity and parity measurements, possibly corrupted by noise.
result Characterizes fundamental limits on the number of measurements required for community reconstruction in hypergraphs.
Paper tackles community recovery in binary symmetric SBM graphs.
problem Community detection in binary symmetric SBM graphs.
method Proposes a two-stage iterative method using projected power iterations and orthogonal iterations.
result Proposed method can exactly recover communities with high probability in logarithmic sparsity regime.
Exact recovery method for community detection in Gaussian mixtures with dependent noise.
problem Community detection in Gaussian mixtures with dependent and heterogeneous noise.
method Maximum likelihood estimator (MLE) for constrained quadratic optimization problem, using Σ-whitened separation and local inequalities. result Sharp exact-recovery threshold and no-gap mechanism in the unknown-size setting.
Paper models graph edge dependencies using latent variables for community detection.
problem Graphs' edge dependencies not fully explained by community membership.
method Introduces auxiliary latent variables to model edge dependencies and analyzes conditions for exact recovery.
result Exact recovery possible by semidefinite programming down to maximum likelihood threshold.
SDP approach recovers communities in multilayer hypergraphs from aggregated similarity matrices.
problem Community recovery in multilayer hypergraphs using aggregated similarity matrices.
method Semidefinite programming (SDP) approach.
result Information-theoretic conditions for exact recovery in both assortative and disassortative cases.
The stochastic block model guides community detection limits and algorithms.
problem Understanding community detection limits in stochastic block models.
method Information-theoretic and computational tradeoffs, algorithms derivation.
result Phase transitions and mutual information tradeoffs for community detection.
New method uses word embedding techniques for better graph community discovery.
problem Discovering communities in graphs without labeled data.
method Developed a novel algorithm using neural node embeddings for unsupervised community discovery.
result Empirically attains information-theoretic limits for community recovery and outperforms existing methods.
Develops a semidefinite program for various blockmodel instances.
problem Community detection and blockmodel instances.
method Semidefinite programming tailored to different blockmodel types.
result Establishes label recovery conditions and excess risk bounds.
New method for community detection in sparse directed SBMs with exact recovery guarantees.
problem Exact recovery in sparse directed SBMs, especially with growing communities.
method Two-stage procedure: neighborhood-smoothing followed by K-means clustering. result Exact recovery of all community labels with probability tending to one under mild sparsity and separation conditions.
New findings on computational limits for estimating hidden structures.
problem Estimating hidden structures in noisy data.
method Use of low-degree polynomials as a restricted model of computation.
result Established low-degree hardness of recovery problems for easy detection problems.
Auto-encoders can recover true signals under certain conditions.
problem Signal recovery from auto-encoders.
method Highly incoherent weight matrices and unit ℓ2 row length, negative bias vectors equal to data mean. result True hidden representation can be approximately recovered with increasing sparsity.
Spectral clustering for geometric graphs achieves strong consistency in community recovery.
problem Community recovery in dense geometric graphs.
method Spectral clustering algorithm using eigenvectors of adjacency matrix.
result Strong consistency in community recovery proved.
These notes review six lectures given by Prof. Andrea Montanari on the topic of statistical estimation for linear models. The first two lectures cover the principles of signal recovery from linear measurements in terms of minimax risk. Subsequent lectures demonstrate the application of these principles to several pract…
Paper uses SDP for community detection with side information.
problem Community detection in graphs with additional non-graph data.
method Formulates SDP relaxation for maximum likelihood node labeling with side information.
result SDP achieves same exact recovery threshold as maximum likelihood with side information.
Sharp threshold for exact recovery in non-uniform hypergraph stochastic block model.
problem Community detection in random hypergraphs with non-uniform hyperedge probabilities.
method Sharp threshold established; two efficient algorithms for exact recovery.
result Sharp threshold for exact recovery; information-theoretic lower bound on misclassification.
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.
New method amplifies hidden structure in complex networks.
problem Difficulty in uncovering hidden structure in complex networks.
method Iterative weakening of dominant structure through randomization.
result Theoretical support for the effectiveness of structure amplification.
Gradient descent recovers neural networks with cross entropy.
problem Recovering weights of one-hidden-layer neural networks from labeled data.
method Empirical risk minimization using cross entropy with gradient descent.
result Gradient descent converges linearly to a close approximation of the ground truth weights.
Federated learning supports exact support recovery with minimal communication.
problem Learning the exact support of sparse linear regression in federated learning.
method One-shot communication algorithm for exact support recovery without optimization.
result Polynomial sample complexity and logarithmic number of clients required.
Distributed-OMP recovers sparse vectors with low communication costs.
problem High-dimensional sparse linear regression with limited computation and communication.
method Distributed orthogonal matching pursuit (OMP) scheme.
result Support of the regression vector can be recovered with linear communication per machine and logarithmic in dimension.
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a certain "contrast function" over the unit sphere. These algorithms, partly inspired by…
Spectral method for joint community detection and group synchronization.
problem Jointly detecting communities and synchronizing orthogonal groups in graphs.
method Spectral decomposition followed by CPQR factorization.
result Near-optimal guarantees for exact and stable recovery of cluster memberships and orthogonal transforms.
This paper advances FL algorithms for composite optimization and statistical recovery.
problem Federated learning optimization and statistical recovery in composite settings.
method Proposes Fast Federated Dual Averaging for strongly convex and smooth loss, and Multi-stage Federated Dual Averaging for restricted strongly convex and smooth loss.
result Establishes state-of-the-art iteration and communication complexity, and high probability complexity bound with linear speedup.