Search Results for author:
Found 26 papers, 3 papers with code
On latent position inference from doubly stochastic messaging activities
Each of the message-exchanging actors is modeled as a process in a latent space.
Statistical inference on errorfully observed graphs
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.
Universally consistent vertex classification for latent positions graphs
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.
Generalized Canonical Correlation Analysis for Classification
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.
Out-of-sample Extension for Latent Position Graphs
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.
A central limit theorem for scaled eigenvectors of random dot product graphs
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.
Perfect Clustering for Stochastic Blockmodel Graphs via Adjacency Spectral Embedding
Vertex clustering in a stochastic blockmodel graph has wide applicability and has been the subject of extensive research.
Empirical Bayes Estimation for the Stochastic Blockmodel
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.
Community Detection and Classification in Hierarchical Stochastic Blockmodels
We propose a robust, scalable, integrated methodology for community detection and community comparison in graphs.
Limit theorems for eigenvectors of the normalized Laplacian for random graphs
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.
Semiparametric spectral modeling of the Drosophila connectome
We present semiparametric spectral modeling of the complete larval Drosophila mushroom body connectome.
Supervised Dimensionality Reduction for Big Data
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.
Statistical inference on random dot product graphs: a survey
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.
A statistical interpretation of spectral embedding: the generalised random dot product graph
Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph.
The eigenvalues of stochastic blockmodel graphs
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.
On a 'Two Truths' Phenomenon in Spectral Graph Clustering
Clustering is concerned with coherently grouping observations without any explicit concept of true groupings.
Limit theorems for out-of-sample extensions of the adjacency and Laplacian spectral embeddings
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.
On Two Distinct Sources of Nonidentifiability in Latent Position Random Graph Models
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.
Learning 1-Dimensional Submanifolds for Subsequent Inference on Random Dot Product Graphs
We submit that techniques for manifold learning can be used to learn the unknown submanifold well enough to realize benefit from restricted inference.
Nonparametric Two-Sample Hypothesis Testing for Random Graphs with Negative and Repeated Eigenvalues
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
Exact Recovery of Community Structures Using DeepWalk and Node2vec
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.
Hypothesis Testing for Equality of Latent Positions in Random Graphs
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.
Popularity Adjusted Block Models are Generalized Random Dot Product Graphs
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.
Classification of high-dimensional data with spiked covariance matrix structure
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 $s$.
Perturbation Analysis of Randomized SVD and its Applications to High-dimensional Statistics
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 $\mathbf{M}$.
Adversarial contamination of networks in the setting of vertex nomination: a new trimming method
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.
