New method for mixed memberships using symmetrized Laplacian inverse matrix.
problem Mixed memberships in community detection.
method Spectral clustering on symmetrized Laplacian inverse matrix.
result Mixed-SLIM methods outperform state-of-the-art methods.
DiMMSB models directed mixed membership networks, identifying distinct community structures.
problem Modeling directed mixed membership networks with distinct community structures.
method Directed Mixed Membership Stochastic Blockmodel (DiMMSB) with DiSP algorithm.
result DiSP algorithm is asymptotically consistent and outperforms competitors.
Proposes a new model for mixed membership in Gaussian mixture.
problem Limited to single component membership in Gaussian mixture models.
method Mixed membership sub-Gaussian model, spectral algorithm.
result Estimation error can be made arbitrarily small with high probability.
In this article we discuss some of the consequences of the mixed membership perspective on time series analysis. In its most abstract form, a mixed membership model aims to associate an individual entity with some set of attributes based on a collection of observed data. Although much of the literature on mixed members…
New methods estimate mixed memberships in multi-layer networks.
problem Complex community structure in multi-layer networks.
method Spectral methods using eigen-decomposition of aggregate matrices.
result Theoretical guarantees and empirical validation for mixed membership estimation.
Global optimization algorithm finds sparse mixed membership matrix factorization's global optimum.
problem Sparse mixed membership matrix factorization problems with local optima.
method Derives a global optimization algorithm for sparse mixed membership matrix factorization.
result Guaranteed ε-global optimum across random initializations and multiple modes. Novel network model estimates mixed-membership structure with covariate information.
problem Estimating latent mixed-membership structure in networks with covariate information.
method Proposes a novel network model that incorporates both community information and node covariate similarities.
result Achieves optimal estimation accuracy for similarity matrix and mixed-membership.
New model for detecting communities in weighted bipartite networks.
problem No model for community detection in overlapping bipartite weighted networks.
method Introduces BiMMDF model allowing any distribution with block structure.
result Efficient algorithm with theoretical guarantee of consistent estimation.
Efficient algorithm for mixed membership models with large p.
problem Learning mixed membership models with high p and k.
method Efficient algorithm reducing tensor decomposition to sub-tensor factorization.
result Provable guarantees and competitive empirical results.
A new model for detecting overlapping communities in weighted networks.
problem Community detection in overlapping weighted networks with mixed membership and edge weights.
method Mixed membership distribution-free (MMDF) model with an efficient spectral algorithm and fuzzy weighted modularity.
result The MMDF model can estimate community memberships and evaluate community quality for weighted networks.
SS3M learns disease phenotypes from few labels.
problem Lack of supervised data for disease phenotyping.
method Semi-Supervised Mixed Membership Model (SS3M).
result SS3M learns interpretable disease phenotypes.
Paper addresses decontamination of mixed membership and partial label models.
problem Recovering base distributions from mutual contamination models.
method General setting with arbitrary probability spaces, algorithms for mixed membership and partial label models.
result Necessary and sufficient conditions for identifiability and algorithms for both models.
Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data with probabilisic models can be delicate because the simple exchangeability assu…
A new model estimates mixed memberships for categorical data with weighted responses.
problem Limited applicability of existing GoM model to weighted categorical data.
method Proposes Weighted Grade of Membership (WGoM) model, relaxing distribution constraints.
result WGoM can describe any response matrix with finite distinct elements.
Directional and pairwise measurements are often used to model inter-relationships in a social network setting. The Mixed-Membership Stochastic Blockmodel (MMSB) was a seminal work in this area, and many of its capabilities were extended since then. In this paper, we propose the \emph{Dynamic Infinite Mixed-Membership s…
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.
Modeling self-tracking data identifies subtypes of endometriosis.
problem No known biomarkers for endometriosis, highly enigmatic condition.
method Mixed-membership models on self-tracking data.
result Identifies potential subtypes robust to tracking variations.
New model integrates community and link clustering for network data.
problem Lack of embedded prior information and community evolution description in MMSB.
method Fragmentation coagulation process for community and link clustering, with Gibbs sampling for inference.
result Model infers community structure and evolution, improving MMSB.
Enhances MMSB for complex graph structures with HL-MRF priors.
problem Limited modeling of correlated graph structures in MMSB.
method HL-MRF as structured prior for mixed membership distributions.
result Improves log-likelihood by 15% on average across datasets.
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.
A new LDA model with covariates for mixed-membership clusters.
problem Modeling mixed-membership clusters in discrete data with covariates.
method Negative binomial regression embedded within LDA, slice sampling within Gibbs sampling.
result Model successfully retrieves true parameter values and predicts cluster abundances using covariates.
Proposes a new RNN model for grouped sequential data with varying time intervals.
problem Implicitly models fixed time intervals between observations and lacks group-level effects.
method Mixed membership framework for RNN, learning group-level base parameter.
result Demonstrates dynamic topic modeling with evolving topic distributions over time.
Transactional network data can be thought of as a list of one-to-many communications(e.g., email) between nodes in a social network. Most social network models convert this type of data into binary relations between pairs of nodes. We develop a latent mixed membership model capable of modeling richer forms of transacti…
New algorithm finds overlapping communities in networks.
problem Finding overlapping communities in networks.
method Linking NMF optimization to MMSB parameters, proposing GeoNMF.
result GeoNMF is provably optimal and consistent.
Community detection in graphs has been extensively studied both in theory and in applications. However, detecting communities in hypergraphs is more challenging. In this paper, we propose a tensor decomposition approach for guaranteed learning of communities in a special class of hypergraphs modeling social tagging sys…
New estimator for overlapping community detection in graphs.
problem Reconstructing community relations in graphs with overlapping memberships.
method Proposes a new estimator for Mixed-Membership Stochastic Block Model (MMSB) under diverging spiked eigenvalues condition.
result New estimator matches theoretical minimax lower bound on estimation error.
We propose a stochastic gradient Markov chain Monte Carlo (SG-MCMC) algorithm for scalable inference in mixed-membership stochastic blockmodels (MMSB). Our algorithm is based on the stochastic gradient Riemannian Langevin sampler and achieves both faster speed and higher accuracy at every iteration than the current sta…
Paper proposes a new tensor model for mixed memberships and provides error bounds.
problem Estimating mixed memberships in higher-order multiway data.
method Tensor mixed-membership blockmodel, higher-order orthogonal iteration algorithm (HOOI), simplex corner-finding algorithm.
result Consistency of estimation procedure with error bounds under specific conditions.
Mixed-SCORE+ improves community detection in weak signal networks.
problem Detecting communities in weak signal networks.
method Proposes Mixed-SCORE+ combining properties of Mixed-SCORE and SCORE+.
result Significantly improves detection error rates on Polblogs and weak signal networks.
The \emph{Mixed-Membership Stochastic Blockmodel (MMSB)} is a popular framework for modeling social network relationships. It can fully exploit each individual node's participation (or membership) in a social structure. Despite its powerful representations, this model makes an assumption that the distributions of relat…
The paper develops methods to infer membership probabilities and rank network nodes using the DCMM model.
problem Understanding the latent structure of network data, especially in mixed-membership models.
method Degree-Corrected Mixed Membership (DCMM) model, novel finite-sample expansion, asymptotic distributions, confidence intervals, multiplier bootstrap method.
result Valid inference on membership probabilities and node rankings, quantifying uncertainty.
Paper generalizes spectral embedding for better graph interpretation.
problem Modeling heterophilic connectivity and negative eigenvalues in graph data.
method Generalized latent position network model (Random Dot Product Graph).
result Consistent latent position estimates with asymptotically Gaussian error.
The majority of real-world networks are dynamic and extremely large (e.g., Internet Traffic, Twitter, Facebook, ...). To understand the structural behavior of nodes in these large dynamic networks, it may be necessary to model the dynamics of behavioral roles representing the main connectivity patterns over time. In th…
In a dynamic social or biological environment, the interactions between the actors can undergo large and systematic changes. In this paper we propose a model-based approach to analyze what we will refer to as the dynamic tomography of such time-evolving networks. Our approach offers an intuitive but powerful tool to in…
Many kinds of data can be represented as a network or graph. It is crucial to infer the latent structure underlying such a network and to predict unobserved links in the network. Mixed Membership Stochastic Blockmodel (MMSB) is a promising model for network data. Latent variables and unknown parameters in MMSB have bee…
A simple SVM model accurately infers overlapping clusters across various datasets.
problem Overlapping clusters in people, words, and books.
method A simple one-class SVM model that works for various overlapping clustering models.
result Simple SVM yields accurate and scalable inference for overlapping clusters.
Paper improves variational inference for complex models.
problem Improving statistical accuracy of variational inference in high-dimensional models.
method Developed a general framework for MFVI and proposed a partially grouped VI algorithm.
result Proposed algorithm works and outperforms vanilla MFVI in mixed membership stochastic blockmodel.
We propose a novel parameterized family of Mixed Membership Mallows Models (M4) to account for variability in pairwise comparisons generated by a heterogeneous population of noisy and inconsistent users. M4 models individual preferences as a user-specific probabilistic mixture of shared latent Mallows components. Our k…
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.
New method estimates node community memberships in networks.
problem Estimating community memberships of nodes in networks with overlapping communities.
method Sharp eigenvector deviation bounds for Mixed Membership Stochastic Blockmodel (MMSB).
result Uniform rates of convergence for node community membership vectors.
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…
Proposes a new algorithm to estimate invariant subspaces across multilayer networks.
problem Estimating invariant subspaces across heterogeneous multiple networks.
method Bias-corrected joint spectral embedding algorithm that recursively calibrates diagonal bias and iteratively updates the subspace estimator.
result Established entrywise subspace perturbation bound and entrywise eigenvector central limit theorem for the algorithm.
Unified model detects local and global changes in dynamic networks.
problem Detecting both local and global changes in complex dynamical networks.
method Proposes a unified generative model based on MMSB with SGLD sampler.
result Superior performance on synthetic and real-world data.
LDA-Link links sequences with sparse or no common events across data sets.
problem Linking sequences with no common events in different data sets.
method Formalizes sequence linkage problem, uses LDA-Link model based on Split-Document model.
result Robust sequence linkage even when sequences have sparse or no common events.
Model identifies key problems in HIV patients' records.
problem Complex and time-consuming task of identifying patient problems from electronic health records.
method Unsupervised phenotyping approach that jointly learns phenotypes from structured and unstructured data.
result Learned phenotypes and their relatedness are clinically valid and surpass existing methods.
A new model integrates covariates with grade of membership analysis for better latent structure recovery.
problem Improving latent structure recovery in multivariate categorical data analysis.
method Covariate-assisted grade of membership model exploiting shared low-rank simplex geometry.
result Auxiliary covariates can provably improve latent structure recovery, leading to faster convergence rates.
The paper introduces curvature-based clustering algorithms for graph analysis.
problem Identifying densely connected substructures in graphs for community detection.
method Discrete Ricci curvatures and geometric flows to reveal community structure.
result The curvature-based approach can identify overlapping communities in graphs.
We introduce the nonparametric metadata dependent relational (NMDR) model, a Bayesian nonparametric stochastic block model for network data. The NMDR allows the entities associated with each node to have mixed membership in an unbounded collection of latent communities. Learned regression models allow these memberships…