Joshua Agterberg
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View article: A High-Dimensional Statistical Theory for Convex and Nonconvex Matrix Sensing
A High-Dimensional Statistical Theory for Convex and Nonconvex Matrix Sensing Open
The problem of matrix sensing, or trace regression, is a problem wherein one wishes to estimate a low-rank matrix from linear measurements perturbed with noise. A number of existing works have studied both convex and nonconvex approaches t…
View article: A Convex Relaxation Approach to Generalization Analysis for Parallel Positively Homogeneous Networks
A Convex Relaxation Approach to Generalization Analysis for Parallel Positively Homogeneous Networks Open
We propose a general framework for deriving generalization bounds for parallel positively homogeneous neural networks--a class of neural networks whose input-output map decomposes as the sum of positively homogeneous maps. Examples of such…
View article: Statistical Inference for Low-Rank Tensors: Heteroskedasticity, Subgaussianity, and Applications
Statistical Inference for Low-Rank Tensors: Heteroskedasticity, Subgaussianity, and Applications Open
In this paper, we consider inference and uncertainty quantification for low Tucker rank tensors with additive noise in the high-dimensional regime. Focusing on the output of the higher-order orthogonal iteration (HOOI) algorithm, a commonl…
View article: LoRanPAC: Low-rank Random Features and Pre-trained Models for Bridging Theory and Practice in Continual Learning
LoRanPAC: Low-rank Random Features and Pre-trained Models for Bridging Theory and Practice in Continual Learning Open
The goal of continual learning (CL) is to train a model that can solve multiple tasks presented sequentially. Recent CL approaches have achieved strong performance by leveraging large pre-trained models that generalize well to downstream t…
View article: Correcting a nonparametric two-sample graph hypothesis test for graphs with different numbers of vertices with applications to connectomics
Correcting a nonparametric two-sample graph hypothesis test for graphs with different numbers of vertices with applications to connectomics Open
Random graphs are statistical models that have many applications, ranging from neuroscience to social network analysis. Of particular interest in some applications is the problem of testing two random graphs for equality of generating dist…
View article: Semisupervised regression in latent structure networks on unknown manifolds
Semisupervised regression in latent structure networks on unknown manifolds Open
Random graphs are increasingly becoming objects of interest for modeling networks in a wide range of applications. Latent position random graph models posit that each node is associated with a latent position vector, and that these vectors…
View article: Distributional Theory and Statistical Inference for Linear Functions of Eigenvectors with Small Eigengaps
Distributional Theory and Statistical Inference for Linear Functions of Eigenvectors with Small Eigengaps Open
Spectral methods have myriad applications in high-dimensional statistics and data science, and while previous works have primarily focused on $\ell_2$ or $\ell_{2,\infty}$ eigenvector and singular vector perturbation theory, in many settin…
View article: An Overview of Asymptotic Normality in Stochastic Blockmodels: Cluster Analysis and Inference
An Overview of Asymptotic Normality in Stochastic Blockmodels: Cluster Analysis and Inference Open
This paper provides a selective review of the statistical network analysis literature focused on clustering and inference problems for stochastic blockmodels and their variants. We survey asymptotic normality results for stochastic blockmo…
View article: Semisupervised regression in latent structure networks on unknown manifolds
Semisupervised regression in latent structure networks on unknown manifolds Open
Random graphs are increasingly becoming objects of interest for modeling networks in a wide range of applications. Latent position random graph models posit that each node is associated with a latent position vector, and that these vectors…
View article: Estimating Higher-Order Mixed Memberships via the $\ell_{2,\infty}$ Tensor Perturbation Bound
Estimating Higher-Order Mixed Memberships via the $\ell_{2,\infty}$ Tensor Perturbation Bound Open
Higher-order multiway data is ubiquitous in machine learning and statistics and often exhibits community-like structures, where each component (node) along each different mode has a community membership associated with it. In this paper we…
View article: Joint Spectral Clustering in Multilayer Degree-Corrected Stochastic Blockmodels
Joint Spectral Clustering in Multilayer Degree-Corrected Stochastic Blockmodels Open
Modern network datasets are often composed of multiple layers, either as different views, time-varying observations, or independent sample units, resulting in collections of networks over the same set of vertices but with potentially diffe…
View article: Entrywise Estimation of Singular Vectors of Low-Rank Matrices With Heteroskedasticity and Dependence
Entrywise Estimation of Singular Vectors of Low-Rank Matrices With Heteroskedasticity and Dependence Open
We propose an estimator for the singular vectors of high-dimensional low-rank\nmatrices corrupted by additive subgaussian noise, where the noise matrix is\nallowed to have dependence within rows and heteroskedasticity between them. We\npro…
View article: Entrywise Recovery Guarantees for Sparse PCA via Sparsistent Algorithms
Entrywise Recovery Guarantees for Sparse PCA via Sparsistent Algorithms Open
Sparse Principal Component Analysis (PCA) is a prevalent tool across a plethora of subfields of applied statistics. While several results have characterized the recovery error of the principal eigenvectors, these are typically in spectral …
View article: Spectral graph clustering via the expectation-solution algorithm
Spectral graph clustering via the expectation-solution algorithm Open
The stochastic blockmodel (SBM) models the connectivity within and between disjoint subsets of nodes in networks. Prior work demonstrated that the rows of an SBM’s adjacency spectral embedding (ASE) and Laplacian spectral embedding (LSE) b…
View article: Valid two‐sample graph testing via optimal transport Procrustes and multiscale graph correlation with applications in connectomics
Valid two‐sample graph testing via optimal transport Procrustes and multiscale graph correlation with applications in connectomics Open
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, the nonparametric hypothesis testing framework consists of …
View article: Entrywise Estimation of Singular Vectors of Low-Rank Matrices with Heteroskedasticity and Dependence
Entrywise Estimation of Singular Vectors of Low-Rank Matrices with Heteroskedasticity and Dependence Open
We propose an estimator for the singular vectors of high-dimensional low-rank matrices corrupted by additive subgaussian noise, where the noise matrix is allowed to have dependence within rows and heteroskedasticity between them. We prove …
View article: Nonparametric Two-Sample Hypothesis Testing for Random Graphs with Negative and Repeated Eigenvalues
Nonparametric Two-Sample Hypothesis Testing for Random Graphs with Negative and Repeated Eigenvalues Open
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. Our proposed test statistic involv…
View article: Correcting a Nonparametric Two-sample Graph Hypothesis Test for Graphs with Different Numbers of Vertices with Applications to Connectomics
Correcting a Nonparametric Two-sample Graph Hypothesis Test for Graphs with Different Numbers of Vertices with Applications to Connectomics Open
Random graphs are statistical models that have many applications, ranging from neuroscience to social network analysis. Of particular interest in some applications is the problem of testing two random graphs for equality of generating dist…
View article: On Two Distinct Sources of Nonidentifiability in Latent Position Random Graph Models
On Two Distinct Sources of Nonidentifiability in Latent Position Random Graph Models Open
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 paper we define and examine these two nonidentifiabilities, d…
View article: Spectral graph clustering via the Expectation-Solution algorithm
Spectral graph clustering via the Expectation-Solution algorithm Open
The stochastic blockmodel (SBM) models the connectivity within and between disjoint subsets of nodes in networks. Prior work demonstrated that the rows of an SBM's adjacency spectral embedding (ASE) and Laplacian spectral embedding (LSE) b…
View article: Vertex nomination, consistent estimation, and adversarial modification
Vertex nomination, consistent estimation, and adversarial modification Open
Given a pair of graphs $G_1$ and $G_2$ and a vertex set of interest in $G_1$, the vertex nomination (VN) problem seeks to find the corresponding vertices of interest in $G_2$ (if they exist) and produce a rank list of the vertices in $G_2$…
View article: Valid Two-Sample Graph Testing via Optimal Transport Procrustes and Multiscale Graph Correlation with Applications in Connectomics
Valid Two-Sample Graph Testing via Optimal Transport Procrustes and Multiscale Graph Correlation with Applications in Connectomics Open
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, the nonparametric hypothesis testing frame-work consists of…