In Stochastic blockmodels, which are among the most prominent statistical models for cluster analysis of complex networks, clusters are defined as groups of nodes with statistically similar link probabilities within and between groups. A recent extension by Karrer and Newman incorporates a node degree correction to mod…
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48 results for “degree correction”
The paper corrects for node degree in spectral clustering using random walk Laplacian.
problem Node degree heterogeneity in spectral clustering.
method Graph spectral embedding using the random walk Laplacian.
result The embedding provides uniformly consistent estimates of degree-corrected latent positions.
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…
Develops a new tensor model for clustering with degree correction.
problem Clustering with unknown degree heterogeneity in multiway data.
method Degree-corrected tensor block model with estimation guarantees.
result Demonstrates an intrinsic statistical-to-computational gap for tensors of order three or greater.
New algorithm clusters networks with outliers, achieving exact recovery.
problem Clustering networks with outliers and degree corrections.
method Convex optimization with a penalization term for positive deviations.
result Achieves exact recovery of clusters under mild conditions.
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 a central problem of network data analysis. Given a network, the goal of community detection is to partition the network nodes into a small number of clusters, which could often help reveal interesting structures. The present paper studies community detection in Degree-Corrected Block Models (DCB…
Spectral clustering on spherical coordinates under the degree-corrected stochastic blockmodelstat.ML
New spectral clustering method for graphs with uneven node degrees.
problem Challenges in community detection for graphs with heterogeneous degree distributions.
method Spectral clustering on spherical coordinates with degree correction.
result Improved performance in representing computer networks.
The stochastic block model is a powerful tool for inferring community structure from network topology. However, it predicts a Poisson degree distribution within each community, while most real-world networks have a heavy-tailed degree distribution. The degree-corrected block model can accommodate arbitrary degree distr…
Motivated by community detection, we characterise the spectrum of the non-backtracking matrix in the Degree-Corrected Stochastic Block Model. Specifically, we consider a random graph on vertices partitioned into two equal-sized clusters. The vertices have i.i.d. weights with second moment $Φ…
A new model corrects SBM's bias for power-law degree networks.
problem SBM's incapability to handle power-law degree distributions.
method Introducing degree decay variables to encode varying degree distributions.
result PLD-SBM approximately preserves the scale-free feature in real networks and corrects SBM's bias.
Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for improved statistical performance. The current paper extends the previous statistical…
Improved model for grouping nodes in bipartite networks.
problem Challenges in grouping nodes in bipartite graphs.
method Introduced DC-LBM and developed variational EM algorithm.
result Significantly enhanced performance on real-world data.
Derives log-corrections in AdS4/CFT3 using supergravity localization.
problem Factorizing log-corrections in AdS4/CFT3.
method Supergravity localization, Atiyah-Singer index theorem, fixed points (NUTs), fixed two-manifolds (Bolts).
result General fixed-point formula for log-corrections in large N expansion.
Improved spectral clustering for community detection in networks.
problem Community detection in networks.
method Improved spectral clustering (ISC) based on k-means clustering on weighted eigenvectors of a regularized Laplacian matrix.
result ISC yields stable consistent community detection under mild conditions and outperforms classical methods.
Paper characterizes optimal graph clustering limits under a new model.
problem Graph clustering under varying edge density signals.
method Introduced Popularity-Adjusted Block Model (PABM) to address SBM and DCBM limitations.
result Cluster recovery possible even when edge density signals vanish, highlighting local connectivity differences.
The stochastic block model (SBM) is a popular framework for studying community detection in networks. This model is limited by the assumption that all nodes in the same community are statistically equivalent and have equal expected degrees. The degree-corrected stochastic block model (DCSBM) is a natural extension of S…
Community detection or clustering is a fundamental task in the analysis of network data. Many real networks have a bipartite structure which makes community detection challenging. In this paper, we consider a model which allows for matched communities in the bipartite setting, in addition to node covariates with inform…
The purpose of this erratum is to correct a mistake in the proof of Theorem 4.1 of our paper \cite{CF}.
Improved community detection in sparse graphs using Bethe-Hessian matrix.
problem Community detection in sparse heterogeneous graphs.
method Spectral clustering based on the Bethe-Hessian matrix for degree-corrected stochastic block models.
result Clustering is insensitive to degree heterogeneity for .
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 …
Corrects GCV for inconsistent risk estimation in finite ensembles of penalized estimators.
problem Inconsistent risk estimation of GCV for finite ensembles of penalized estimators.
method Identifies a correction involving an additional scalar correction based on degrees of freedom adjusted training errors from each ensemble component.
result CGCV maintains computational advantages of GCV and is model-free uniformly consistent for ridge regression.
Bayesian method corrects for model selection multiplicity in regression.
problem Model selection multiplicity in regression analysis.
method Developed a Bayesian prior distribution based on Holm procedure analogy.
result Adequate multiplicity correction requires sparsity not provided by recommended priors.
A goodness-of-fit test for DCSBM improves scalability and power for large sparse networks.
problem Testing goodness-of-fit for degree-corrected stochastic block models (DCSBM) in large sparse networks.
method Proposes an adjusted chi-square test statistic for multinomial distributions, adjusted for degree-corrected networks, and applies it to compressed adjacency matrices.
result The test statistic converges in distribution under null, and is consistent in recovering the number of communities.
The paper proposes a new model to analyze directed networks and accurately estimate community memberships.
problem Modeling and estimating community memberships in directed networks with heterogeneous degrees.
method Directed Degree Corrected Mixed Membership (DiDCMM) model and DiMSC algorithm.
result The proposed DiMSC algorithm is asymptotically consistent and provides error bounds for community membership vectors.
New method for community detection in graphs faster than DCBM inference.
problem Efficiently detecting communities in graphs with heterogeneous node degrees.
method Reformulated constrained nonnegative matrix factorization for DCBM inference.
result Faster community detection (4 minutes for 100k nodes vs. DCBM's 10+ minutes).
We compute the sets of degrees of maps between principal -bundles over , i.e. between any of the manifolds and . We show that the Steenrod squares provide the only obstruction to the existence of a mapping degree between these manifolds, and construct explicit maps realizing each in…
We provide local expressions for Chern-Weil type forms built from superconnections associated with families of Dirac operators previously investigated in work by S. Scott and later work by S. Scott and the second author. When the underlying fibration of manifolds is trivial, the even degree forms can be interpreted as …
We present a method to desingularize a compact G_2 manifold with isolated conical singularities by cutting out a neighbourhood of each singular point and glueing in an asymptotically conical G_2 manifold. Controlling the error on the overlap glueing region enables us to use a result of Joyce to conclude that the result…
A fast spectral algorithm detects community structure in evolving graphs.
problem Detecting community structure in time-evolving sparse graphs.
method Extension of the Bethe-Hessian matrix for spectral community detection.
result The algorithm reaches the optimal detectability threshold and outperforms other methods.
The paper studies a method to sample nodes from a massive graph using personalized PageRank.
problem Sampling from a massive network is expensive and impractical; the paper provides an alternative.
method The paper introduces a crawling method to approximate the personalized PageRank vector without querying the entire graph.
result The adjusted personalized PageRank vector can effectively select nodes within the same block as the seed node.
Study improves understanding of network degree distributions using non-linear ERGs.
problem Lack of models capable of accounting for the variance of empirical degree distributions.
method Defined a fitness-induced variant of the two-star model to reproduce sample variance.
result Non-linear ERGs can reproduce the sample variance of empirical degree distributions.
Deep Autotuner corrects singing pitch without scores, using vocal and accompaniment spectral data.
problem Automatic pitch correction without musical scores for singing performances.
method Convolutional Gated Recurrent Unit (CGRU) model trained on karaoke data.
result The model predicts pitch correction from vocal and accompaniment spectral contents, making the voice sound in tune with the accompaniment.
Deep Autotuner corrects singing pitch using neural networks.
problem Automatic pitch correction for singing performances.
method Neural network model trained on spectrograms of singing and accompaniment.
result Neural network predicts continuous pitch shifts, allowing for improvisation and harmonization.
Anytime-valid confirmation of label-shift corrections
problem Small-batch scientific deployments with scarce labeled outcomes
method Conditional e-value and martingale-based rule
result Nonnegative martingale and anytime-valid confirmation rule
Paper addresses hypothesis space misspecification in learning from human demonstrations and corrections.
problem Hypothesis space misspecification in learning from human demonstrations and corrections.
method Reason explicitly about how well the robot can explain human inputs given its hypothesis space.
result Demonstrates method on a 7 DOF robot manipulator.
Develops a theory for equivariant networks with partial domain symmetry.
problem Limited analysis of equivariant networks with partial domain symmetry.
method Proposes pointwise definitions of correct, incorrect, and extrinsic equivariance.
result Establishes error lower bounds for networks with partial symmetry.
Closed formulas for η-corrections in the once-punctured torus identified.
problem Identifying η-corrections in the Kauffman bracket skein algebra of the once-punctured torus.
method Explicit closed formulas for Chebyshev-threaded families and η-corrections.
result Explicit Chebyshev expansions and coefficients for η-corrections.
Improves community detection in directed networks with theoretical guarantees.
problem Degree heterogeneity affects community detection in directed networks.
method Introduced D-SCORE algorithm and established theoretical guarantees for Directed-DCBM.
result Established theoretical guarantees and provided improvements for D-SCORE.
Measures neural network complexity via effective degrees of freedom.
problem Challenges in quantifying neural network complexity.
method Adapts generalized degrees of freedom (GDF) for binary outcomes and compares with cross-validation and null degrees of freedom.
result GDF provides a robust measure of model complexity for neural networks.
Deep neural networks correct Mie scattering in FTIR spectra of biological samples.
problem Mie scattering obscures biochemically relevant spectral information in FTIR spectra of biological samples.
method Deep neural networks to approximate the preprocessing function that removes Mie scattering.
result The model is faster and more generalizable across different tissue types.
We study recursive-cube-of-rings (RCR), a class of scalable graphs that can potentially provide rich inter-connection network topology for the emerging distributed and parallel computing infrastructure. Through rigorous proof and validating examples, we have corrected previous misunderstandings on the topological prope…
A new method for community detection in networks is presented.
problem Community detection in network analysis.
method Mixed regularized spectral clustering (Mixed-RSC) based on the regularized Laplacian matrix.
result The method is asymptotically consistent under mild conditions.
New algorithm recovers communities in broader network models.
problem Finding communities in complex networks is challenging.
method Spectral clustering on Preference Frame Models with Normalized Laplacian.
result Spectral clustering works on broader network models with similar guarantees.
We consider the Degree-Corrected Stochastic Block Model (DC-SBM): a random graph on nodes, having i.i.d. weights (possibly heavy-tailed), partitioned into asymptotically equal-sized clusters. The model parameters are two constants and the finite second moment of the weights $Φ^{…
Tree-Transformer improves grammar correction in code and natural language.
problem Grammar correction in tree-structured data.
method Tree-Transformer neural network architecture for tree-structured data.
result Significant improvement in grammar correction accuracy.
The paper explores how different network architectures learn logical functions under GOTU, finding that a min-degree-interpolator is learned.
problem Learning logical functions with a focus on generalization on the unseen.
method Study of different network architectures trained by SGD under GOTU.
result For sparse functions and certain network models, a min-degree-interpolator is learned on the unseen.
SIMPLE method quantifies uncertainty in network membership profiles.
problem Quantifying statistical uncertainty in network membership profiles.
method Degree-corrected mixed membership model, Hotelling-type statistics.
result Established exact limiting distributions of test statistics.