Publications (55)
Central Limit Theorems for Classical Multidimensional Scaling
Gongkai Li, Minh Tang, Nichlas Charon +1
Classical multidimensional scaling is a widely used method in dimensionality reduction and manifold learning. The method takes in a dissimilarity matrix and outputs a low-dimension…
Valid Two-Sample Graph Testing via Optimal Transport Procrustes and Multiscale Graph Correlation with Applications in Connectomics
Jaewon Chung, Bijan Varjavand, Jesus Arroyo +5
Testing whether two graphs come from the same distribution is of interest in many real world scenarios, including brain network analysis. Under the random dot product graph model,…
On spectral embedding performance and elucidating network structure in stochastic block model graphs
Joshua Cape, Minh Tang, Carey E. Priebe
Statistical inference on graphs often proceeds via spectral methods involving low-dimensional embeddings of matrix-valued graph representations, such as the graph Laplacian or adja…
The two-to-infinity norm and singular subspace geometry with applications to high-dimensional statistics
Joshua Cape, Minh Tang, Carey E. Priebe
The singular value matrix decomposition plays a ubiquitous role throughout statistics and related fields. Myriad applications including clustering, classification, and dimensionali…
On latent position inference from doubly stochastic messaging activities
Nam H. Lee, Jordan Yoder, Minh Tang +1
We model messaging activities as a hierarchical doubly stochastic point process with three main levels, and develop an iterative algorithm for inferring actors' relative latent pos…
A statistical interpretation of spectral embedding: the generalised random dot product graph
Patrick Rubin-Delanchy, Joshua Cape, Minh Tang +1
Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network mo…
Generalized Canonical Correlation Analysis for Disparate Data Fusion
Ming Sun, Carey E. Priebe, Minh Tang
Manifold matching works to identify embeddings of multiple disparate data spaces into the same low-dimensional space, where joint inference can be pursued. It is an enabling method…
Two-sample Testing on Latent Distance Graphs With Unknown Link Functions
Yiran Wang, Minh Tang, Soumendra Nath Lahiri
We propose a valid and consistent test for the hypothesis that two latent distance random graphs on the same vertex set have the same generating latent positions, up to some uniden…
Consistent adjacency-spectral partitioning for the stochastic block model when the model parameters are unknown
Donniell E. Fishkind, Daniel L. Sussman, Minh Tang +2
For random graphs distributed according to a stochastic block model, we consider the inferential task of partioning vertices into blocks using spectral techniques. Spectral partion…
Exact Recovery of Community Structures Using DeepWalk and Node2vec
Yichi Zhang, Minh Tang
Random-walk based network embedding algorithms like DeepWalk and node2vec are widely used to obtain Euclidean representation of the nodes in a network prior to performing downstrea…
Semiparametric spectral modeling of the Drosophila connectome
Carey E. Priebe, Youngser Park, Minh Tang +8
We present semiparametric spectral modeling of the complete larval Drosophila mushroom body connectome. Motivated by a thorough exploratory data analysis of the network via Gaussia…
A consistent adjacency spectral embedding for stochastic blockmodel graphs
Daniel L. Sussman, Minh Tang, Donniell E. Fishkind +1
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…
Asymptotically efficient estimators for stochastic blockmodels: the naive MLE, the rank-constrained MLE, and the spectral
Minh Tang, Joshua Cape, Carey E. Priebe
We establish asymptotic normality results for estimation of the block probability matrix in stochastic blockmodel graphs using spectral embedding when the average degr…
Regression for matrix-valued data via Kronecker products factorization
Yin-Jen Chen, Minh Tang
We study the matrix-variate regression problem $Y_i = \sum_{k} β_{1k} X_i β_{2k}^{\top} + E_i$ for in the high dimensional regime wherein the response are ma…
Community Detection and Classification in Hierarchical Stochastic Blockmodels
Vince Lyzinski, Minh Tang, Avanti Athreya +2
We propose a robust, scalable, integrated methodology for community detection and community comparison in graphs. In our procedure, we first embed a graph into an appropriate Eucli…
On a 'Two Truths' Phenomenon in Spectral Graph Clustering
Carey E. Priebe, Youngser Park, Joshua T. Vogelstein +6
Clustering is concerned with coherently grouping observations without any explicit concept of true groupings. Spectral graph clustering - clustering the vertices of a graph based o…
On estimation and inference in latent structure random graphs
Avanti Athreya, Minh Tang, Youngser Park +1
We define a latent structure model (LSM) random graph as a random dot product graph (RDPG) in which the latent position distribution incorporates both probabilistic and geometric c…
Chain-linked multiple matrix integration via embedding alignment
Runbing Zheng, Minh Tang
Motivated by the increasing demand for multi-source data integration in various scientific fields, in this paper we study matrix completion in scenarios where the data exhibits cer…
On Two Distinct Sources of Nonidentifiability in Latent Position Random Graph Models
Joshua Agterberg, Minh Tang, Carey E. Priebe
Two separate and distinct sources of nonidentifiability arise naturally in the context of latent position random graph models, though neither are unique to this setting. In this pa…
Independence testing for inhomogeneous random graphs
Yukun Song, Carey E. Priebe, Minh Tang
Testing for independence between graphs is a problem that arises naturally in social network analysis and neuroscience. In this paper, we address independence testing for inhomogen…
Predictive Subsampling for Scalable Inference in Networks
Arpan Kumar, Minh Tang, Srijan Sengupta
Current methods for statistical inference in networks often encounter substantial computational bottlenecks when applied to the massive network datasets that are increasingly commo…
Empirical Bayes Estimation for the Stochastic Blockmodel
Shakira Suwan, Dominic S. Lee, Runze Tang +3
Inference for the stochastic blockmodel is currently of burgeoning interest in the statistical community, as well as in various application domains as diverse as social networks, c…
Universally consistent vertex classification for latent positions graphs
Minh Tang, Daniel L. Sussman, Carey E. Priebe
In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate feature maps for latent position graphs with positive definite link f…
Learning 1-Dimensional Submanifolds for Subsequent Inference on Random Dot Product Graphs
Michael W. Trosset, Mingyue Gao, Minh Tang +1
A random dot product graph (RDPG) is a generative model for networks in which vertices correspond to positions in a latent Euclidean space and edge probabilities are determined by…
Limit results for distributed estimation of invariant subspaces in multiple networks inference and PCA
Runbing Zheng, Minh Tang
Several statistical problems, such as multiple heterogeneous graph analysis, distributed PCA, integrative data analysis, and simultaneous dimension reduction of images, can involve…
Statistical inference on errorfully observed graphs
Carey E. Priebe, Daniel L. Sussman, Minh Tang +1
Statistical inference on graphs is a burgeoning field in the applied and theoretical statistics communities, as well as throughout the wider world of science, engineering, business…
Universally Consistent Latent Position Estimation and Vertex Classification for Random Dot Product Graphs
Daniel L. Sussman, Minh Tang, Carey E. Priebe
In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate latent positions for random dot product graphs provided the latent po…
Generalized Canonical Correlation Analysis for Classification
Cencheng Shen, Ming Sun, Minh Tang +1
For multiple multivariate data sets, we derive conditions under which Generalized Canonical Correlation Analysis (GCCA) improves classification performance of the projected dataset…
A Unified Framework for Community Detection and Model Selection in Blockmodels
Subhankar Bhadra, Minh Tang, Srijan Sengupta
Blockmodels are a foundational tool for modeling community structure in networks, with the stochastic blockmodel (SBM), degree-corrected blockmodel (DCBM), and popularity-adjusted…
A nonparametric two-sample hypothesis testing problem for random dot product graphs
Minh Tang, Avanti Athreya, Daniel L. Sussman +2
We consider the problem of testing whether two finite-dimensional random dot product graphs have generating latent positions that are independently drawn from the same distribution…
Nonparametric two-sample hypothesis testing for low-rank random graphs of differing sizes
Joshua Agterberg, Minh Tang, Carey Priebe
Given two networks of differing sizes, it is of interest to test whether the two networks belong to the same distribution. We formalize the notion of "equality of distribution" und…
Supervised Dimensionality Reduction for Big Data
Joshua T. Vogelstein, Eric Bridgeford, Minh Tang +4
To solve key biomedical problems, experimentalists now routinely measure millions or billions of features (dimensions) per sample, with the hope that data science techniques will b…
Perturbation Analysis of Randomized SVD and its Applications to Statistics
Yichi Zhang, Minh Tang
Randomized singular value decomposition (RSVD) is a class of computationally efficient algorithms for computing the truncated SVD of large data matrices. Given an matr…
Perfect Clustering for Stochastic Blockmodel Graphs via Adjacency Spectral Embedding
Vince Lyzinski, Daniel Sussman, Minh Tang +2
Vertex clustering in a stochastic blockmodel graph has wide applicability and has been the subject of extensive research. In thispaper, we provide a short proof that the adjacency…
A central limit theorem for scaled eigenvectors of random dot product graphs
Avanti Athreya, Vince Lyzinski, David J. Marchette +3
We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions…
Statistical inference on random dot product graphs: a survey
Avanti Athreya, Donniell E. Fishkind, Keith Levin +7
The random dot product graph (RDPG) is an independent-edge random graph that is analytically tractable and, simultaneously, either encompasses or can successfully approximate a wid…
Numerical tolerance for spectral decompositions of random matrices
Avanti Athreya, Michael Kane, Bryan Lewis +5
We precisely quantify the impact of statistical error in the quality of a numerical approximation to a random matrix eigendecomposition, and under mild conditions, we use this to i…
Signal-plus-noise matrix models: eigenvector deviations and fluctuations
Joshua Cape, Minh Tang, Carey E. Priebe
Estimating eigenvectors and low-dimensional subspaces is of central importance for numerous problems in statistics, computer science, and applied mathematics. This paper characteri…
Robust Estimation from Multiple Graphs under Gross Error Contamination
Runze Tang, Minh Tang, Joshua T. Vogelstein +1
Estimation of graph parameters based on a collection of graphs is essential for a wide range of graph inference tasks. In practice, weighted graphs are generally observed with edge…
Consistency of adjacency spectral embedding for the mixed membership stochastic blockmodel
Patrick Rubin-Delanchy, Carey E. Priebe, Minh Tang
The mixed membership stochastic blockmodel is a statistical model for a graph, which extends the stochastic blockmodel by allowing every node to randomly choose a different communi…
Classification of high-dimensional data with spiked covariance matrix structure
Yin-Jen Chen, Minh Tang
We study the classification problem for high-dimensional data with observations on features where the covariance matrix exhibits a spiked eigenvalue struc…
The eigenvalues of stochastic blockmodel graphs
Minh Tang
We derive the limiting distribution for the largest eigenvalues of the adjacency matrix for a stochastic blockmodel graph when the number of vertices tends to infinity. We show tha…
Locality statistics for anomaly detection in time series of graphs
Heng Wang, Minh Tang, Youngser Park +1
The ability to detect change-points in a dynamic network or a time series of graphs is an increasingly important task in many applications of the emerging discipline of graph signa…
Hypothesis Testing for Equality of Latent Positions in Random Graphs
Xinjie Du, Minh Tang
We consider the hypothesis testing problem that two vertices and of a generalized random dot product graph have the same latent positions, possibly up to scaling. Special c…
Limit theorems for out-of-sample extensions of the adjacency and Laplacian spectral embeddings
Keith Levin, Fred Roosta, Minh Tang +2
Graph embeddings, a class of dimensionality reduction techniques designed for relational data, have proven useful in exploring and modeling network structure. Most dimensionality r…
Adversarial contamination of networks in the setting of vertex nomination: a new trimming method
Sheyda Peyman, Minh Tang, Vince Lyzinski
As graph data becomes more ubiquitous, the need for robust inferential graph algorithms to operate in these complex data domains is crucial. In many cases of interest, inference is…
Out-of-sample Extension for Latent Position Graphs
Minh Tang, Youngser Park, Carey E. Priebe
We consider the problem of vertex classification for graphs constructed from the latent position model. It was shown previously that the approach of embedding the graphs into some…
A semiparametric two-sample hypothesis testing problem for random dot product graphs
Minh Tang, Avanti Athreya, Daniel L. Sussman +2
Two-sample hypothesis testing for random graphs arises naturally in neuroscience, social networks, and machine learning. In this paper, we consider a semiparametric problem of two-…
Out-of-Sample Embedding with Proximity Data: Projection versus Restricted Reconstruction
Michael W. Trosset, Kaiyi Tan, Minh Tang +1
The problem of using proximity (similarity or dissimilarity) data for the purpose of "adding a point to a vector diagram" was first studied by J.C. Gower in 1968. Since then, a num…
Popularity Adjusted Block Models are Generalized Random Dot Product Graphs
John Koo, Minh Tang, Michael W. Trosset
We connect two random graph models, the Popularity Adjusted Block Model (PABM) and the Generalized Random Dot Product Graph (GRDPG), by demonstrating that the PABM is a special cas…
Vertex nomination between graphs via spectral embedding and quadratic programming
Runbing Zheng, Vince Lyzinski, Carey E. Priebe +1
Given a network and a subset of interesting vertices whose identities are only partially known, the vertex nomination problem seeks to rank the remaining vertices in such a way tha…
Limit theorems for eigenvectors of the normalized Laplacian for random graphs
Minh Tang, Carey E. Priebe
We prove a central limit theorem for the components of the eigenvectors corresponding to the largest eigenvalues of the normalized Laplacian matrix of a finite dimensional rand…
A central limit theorem for an omnibus embedding of multiple random graphs and implications for multiscale network inference
Keith Levin, Avanti Athreya, Minh Tang +3
Performing statistical analyses on collections of graphs is of import to many disciplines, but principled, scalable methods for multi-sample graph inference are few. Here we descri…
The Kato--Temple inequality and eigenvalue concentration with applications to graph inference
Joshua Cape, Minh Tang, Carey E. Priebe
We present an adaptation of the Kato--Temple inequality for bounding perturbations of eigenvalues with applications to statistical inference for random graphs, specifically hypothe…
Eigenvector fluctuations and limit results for random graphs with infinite rank kernels
Minh Tang, Joshua R. Cape
This paper systematically studies the behavior of the leading eigenvectors for independent edge undirected random graphs generated from a general latent position model whose link f…