Search Results for author: Minh Tang

Found 26 papers, 3 papers with code

Adversarial contamination of networks in the setting of vertex nomination: a new trimming method

no code implementations20 Aug 2022 Sheyda Peyman, Minh Tang, Vince Lyzinski

Here, a common suite of methods relies on spectral graph embeddings, which have been shown to provide both good algorithmic performance and flexible settings in which regularization techniques can be implemented to help mitigate the effect of an adversary.

Information Retrieval Retrieval

Perturbation Analysis of Randomized SVD and its Applications to High-dimensional Statistics

no code implementations19 Mar 2022 Yichi Zhang, Minh Tang

We first derive upper bounds for the $\ell_2$ (spectral norm) and $\ell_{2\to\infty}$ (maximum row-wise $\ell_2$ norm) distances between the approximate singular vectors of $\hat{\mathbf{M}}$ and the true singular vectors of the signal matrix $\mathbf{M}$.

Community Detection Matrix Completion

Classification of high-dimensional data with spiked covariance matrix structure

no code implementations5 Oct 2021 Yin-Jen Chen, Minh Tang

We study the classification problem for high-dimensional data with $n$ observations on $p$ features where the $p \times p$ covariance matrix $\Sigma$ exhibits a spiked eigenvalues structure and the vector $\zeta$, given by the difference between the whitened mean vectors, is sparse with sparsity at most $s$.

Classification Dimensionality Reduction

Popularity Adjusted Block Models are Generalized Random Dot Product Graphs

1 code implementation9 Sep 2021 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 case of the GRDPG in which communities correspond to mutually orthogonal subspaces of latent vectors.

Community Detection

Hypothesis Testing for Equality of Latent Positions in Random Graphs

no code implementations23 May 2021 Xinjie Du, Minh Tang

Special cases of this hypothesis test include testing whether two vertices in a stochastic block model or degree-corrected stochastic block model graph have the same block membership vectors, or testing whether two vertices in a popularity adjusted block model have the same community assignment.

Model Selection Stochastic Block Model

Exact Recovery of Community Structures Using DeepWalk and Node2vec

no code implementations18 Jan 2021 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 downstream inference tasks.

Community Detection Network Embedding

Nonparametric Two-Sample Hypothesis Testing for Random Graphs with Negative and Repeated Eigenvalues

no code implementations17 Dec 2020 Joshua Agterberg, Minh Tang, Carey Priebe

We propose a nonparametric two-sample test statistic for low-rank, conditionally independent edge random graphs whose edge probability matrices have negative eigenvalues and arbitrarily close eigenvalues.

Graph Embedding Statistics Theory Statistics Theory

Learning 1-Dimensional Submanifolds for Subsequent Inference on Random Dot Product Graphs

no code implementations15 Apr 2020 Michael W. Trosset, Mingyue Gao, Minh Tang, Carey E. Priebe

We submit that techniques for manifold learning can be used to learn the unknown submanifold well enough to realize benefit from restricted inference.

On Two Distinct Sources of Nonidentifiability in Latent Position Random Graph Models

no code implementations31 Mar 2020 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.

Limit theorems for out-of-sample extensions of the adjacency and Laplacian spectral embeddings

no code implementations29 Sep 2019 Keith Levin, Fred Roosta, Minh Tang, Michael W. Mahoney, Carey E. Priebe

In both cases, we prove that when the underlying graph is generated according to a latent space model called the random dot product graph, which includes the popular stochastic block model as a special case, an out-of-sample extension based on a least-squares objective obeys a central limit theorem about the true latent position of the out-of-sample vertex.

Dimensionality Reduction Graph Embedding +1

The eigenvalues of stochastic blockmodel graphs

no code implementations30 Mar 2018 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.

Statistical inference on random dot product graphs: a survey

no code implementations16 Sep 2017 Avanti Athreya, Donniell E. Fishkind, Keith Levin, Vince Lyzinski, Youngser Park, Yichen Qin, Daniel L. Sussman, Minh Tang, Joshua T. Vogelstein, Carey E. Priebe

In this survey paper, we describe a comprehensive paradigm for statistical inference on random dot product graphs, a paradigm centered on spectral embeddings of adjacency and Laplacian matrices.

Community Detection

Supervised Dimensionality Reduction for Big Data

1 code implementation5 Sep 2017 Joshua T. Vogelstein, Eric Bridgeford, Minh Tang, Da Zheng, Christopher Douville, Randal Burns, Mauro Maggioni

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 be able to build accurate data-driven inferences.

General Classification Supervised dimensionality reduction

Limit theorems for eigenvectors of the normalized Laplacian for random graphs

no code implementations28 Jul 2016 Minh Tang, Carey E. Priebe

As a corollary, we show that for stochastic blockmodel graphs, the rows of the spectral embedding of the normalized Laplacian converge to multivariate normals and furthermore the mean and the covariance matrix of each row are functions of the associated vertex's block membership.

Empirical Bayes Estimation for the Stochastic Blockmodel

no code implementations23 May 2014 Shakira Suwan, Dominic S. Lee, Runze Tang, Daniel L. Sussman, Minh Tang, Carey E. Priebe

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, citation networks, brain connectivity networks (connectomics), etc.

Perfect Clustering for Stochastic Blockmodel Graphs via Adjacency Spectral Embedding

no code implementations2 Oct 2013 Vince Lyzinski, Daniel Sussman, Minh Tang, Avanti Athreya, Carey Priebe

Vertex clustering in a stochastic blockmodel graph has wide applicability and has been the subject of extensive research.

A central limit theorem for scaled eigenvectors of random dot product graphs

no code implementations31 May 2013 Avanti Athreya, Vince Lyzinski, David J. Marchette, Carey E. Priebe, Daniel L. Sussman, Minh Tang

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 are unknown.

Out-of-sample Extension for Latent Position Graphs

no code implementations21 May 2013 Minh Tang, Youngser Park, Carey E. Priebe

We show that, under the latent position graph model and for sufficiently large $n$, the mapping of the out-of-sample vertices is close to its true latent position.

General Classification Graph Embedding

Generalized Canonical Correlation Analysis for Classification

no code implementations30 Apr 2013 Cencheng Shen, Ming Sun, Minh Tang, Carey E. Priebe

For multiple multivariate data sets, we derive conditions under which Generalized Canonical Correlation Analysis (GCCA) improves classification performance of the projected datasets, compared to standard Canonical Correlation Analysis (CCA) using only two data sets.

Classification General Classification

Universally consistent vertex classification for latent positions graphs

no code implementations5 Dec 2012 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 function $\kappa$, provided that the latent positions are i. i. d.

Classification General Classification

Statistical inference on errorfully observed graphs

no code implementations15 Nov 2012 Carey E. Priebe, Daniel L. Sussman, Minh Tang, Joshua T. Vogelstein

Thus we errorfully observe $G$ when we observe the graph $\widetilde{G} = (V,\widetilde{E})$ as the edges in $\widetilde{E}$ arise from the classifications of the "edge-features", and are expected to be errorful.

On latent position inference from doubly stochastic messaging activities

no code implementations26 May 2012 Nam H. Lee, Jordan Yoder, Minh Tang, Carey E. Priebe

Each of the message-exchanging actors is modeled as a process in a latent space.

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