Keith Levin
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View article: Testing for Repeated Motifs and Hierarchical Structure in Stochastic Blockmodels
Testing for Repeated Motifs and Hierarchical Structure in Stochastic Blockmodels Open
The rise in complexity of network data in neuroscience, social networks, and protein-protein interaction networks has been accompanied by several efforts to model and understand these data at different scales. A key multiscale network mode…
View article: Improved dependence on coherence in eigenvector and eigenvalue estimation error bounds
Improved dependence on coherence in eigenvector and eigenvalue estimation error bounds Open
Spectral estimators are fundamental in lowrank matrix models and arise throughout machine learning and statistics, with applications including network analysis, matrix completion and PCA. These estimators aim to recover the leading eigenva…
View article: Coherence-free Entrywise Estimation of Eigenvectors in Low-rank Signal-plus-noise Matrix Models
Coherence-free Entrywise Estimation of Eigenvectors in Low-rank Signal-plus-noise Matrix Models Open
Spectral methods are widely used to estimate eigenvectors of a low-rank signal matrix subject to noise. These methods use the leading eigenspace of an observed matrix to estimate this low-rank signal. Typically, the entrywise estimation er…
View article: Minimax rates for the linear-in-means model reveal an identifiability-estimability gap
Minimax rates for the linear-in-means model reveal an identifiability-estimability gap Open
The linear-in-means model is widely used to study peer influence in social networks. We consider estimation in the linear-in-means model when a randomized treatment is applied to nodes in a network. We show that even when peer effects are …
View article: Minimax rates for latent position estimation in the generalized random dot product graph
Minimax rates for latent position estimation in the generalized random dot product graph Open
Latent space models play an important role in the modeling and analysis of network data. Under these models, each node has an associated latent point in some (typically low-dimensional) geometric space, and network formation is driven by t…
View article: Estimating network-mediated causal effects via principal components network regression
Estimating network-mediated causal effects via principal components network regression Open
We develop a method to decompose causal effects on a social network into an indirect effect mediated by the network, and a direct effect independent of the social network. To handle the complexity of network structures, we assume that late…
View article: Predicting Responses from Weighted Networks with Node Covariates in an Application to Neuroimaging
Predicting Responses from Weighted Networks with Node Covariates in an Application to Neuroimaging Open
We consider the setting where many networks are observed on a common node set, and each observation comprises edge weights of a network, covariates observed at each node, and an overall response. The goal is to use the edge weights and nod…
View article: Fast Generation of Exchangeable Sequence of Clusters Data
Fast Generation of Exchangeable Sequence of Clusters Data Open
Recent advances in Bayesian models for random partitions have led to the formulation and exploration of Exchangeable Sequences of Clusters (ESC) models. Under ESC models, it is the cluster sizes that are exchangeable, rather than the obser…
View article: On the role of features in vertex nomination: Content and context together are better (sometimes).
On the role of features in vertex nomination: Content and context together are better (sometimes). Open
Vertex nomination is a lightly-supervised network information retrieval (IR) task in which vertices of interest in one graph are used to query a second graph to discover vertices of interest in the second graph. Similar to other IR tasks, …
View article: Vertex Nomination in Richly Attributed Networks
Vertex Nomination in Richly Attributed Networks Open
Vertex nomination is a lightly-supervised network information retrieval task in which vertices of interest in one graph are used to query a second graph to discover vertices of interest in the second graph. Similar to other information ret…
View article: Matrix Means and a Novel High-Dimensional Shrinkage Phenomenon
Matrix Means and a Novel High-Dimensional Shrinkage Phenomenon Open
Many statistical settings call for estimating a population parameter, most typically the population mean, based on a sample of matrices. The most natural estimate of the population mean is the arithmetic mean, but there are many other matr…
View article: Limit theorems for out-of-sample extensions of the adjacency and Laplacian spectral embeddings
Limit theorems for out-of-sample extensions of the adjacency and Laplacian spectral embeddings Open
Graph embeddings, a class of dimensionality reduction techniques designed for relational data, have proven useful in exploring and modeling network structure. Most dimensionality reduction methods allow out-of-sample extensions, by which a…
View article: Bootstrapping Networks with Latent Space Structure
Bootstrapping Networks with Latent Space Structure Open
A core problem in statistical network analysis is to develop network analogues of classical techniques. The problem of bootstrapping network data stands out as especially challenging, since typically one observes only a single network, rat…
View article: Recovering shared structure from multiple networks with unknown edge distributions
Recovering shared structure from multiple networks with unknown edge distributions Open
In increasingly many settings, data sets consist of multiple samples from a population of networks, with vertices aligned across these networks. For example, brain connectivity networks in neuroscience consist of measures of interaction be…
View article: Recovering low-rank structure from multiple networks with unknown edge distributions.
Recovering low-rank structure from multiple networks with unknown edge distributions. Open
In increasingly many settings, data sets consist of multiple samples from a population of networks, with vertices aligned across these networks. For example, brain connectivity networks in neuroscience consist of measures of interaction be…
View article: Connectal Coding: Discovering the Structures Linking Cognitive Phenotypes to Individual Histories
Connectal Coding: Discovering the Structures Linking Cognitive Phenotypes to Individual Histories Open
Cognitive phenotypes characterize our memories, beliefs, skills, and preferences, and arise from our ancestral, developmental, and experiential histories. These histories are written into our brain structure through the building and modifi…
View article: Out-of-sample extension of graph adjacency spectral embedding
Out-of-sample extension of graph adjacency spectral embedding Open
Many popular dimensionality reduction procedures have out-of-sample extensions, which allow a practitioner to apply a learned embedding to observations not seen in the initial training sample. In this work, we consider the problem of obtai…
View article: Vertex nomination: The canonical sampling and the extended spectral\n nomination schemes
Vertex nomination: The canonical sampling and the extended spectral\n nomination schemes Open
Suppose that one particular block in a stochastic block model is of interest,\nbut block labels are only observed for a few of the vertices in the network.\nUtilizing a graph realized from the model and the observed block labels, the\nvert…
View article: Estimating a network from multiple noisy realizations
Estimating a network from multiple noisy realizations Open
Complex interactions between entities are often represented as edges in a network. In practice, the network is often constructed from noisy measurements and inevitably contains some errors. In this paper we consider the problem of estimati…
View article: On consistent vertex nomination schemes
On consistent vertex nomination schemes Open
Given a vertex of interest in a network $G_1$, the vertex nomination problem seeks to find the corresponding vertex of interest (if it exists) in a second network $G_2$. A vertex nomination scheme produces a list of the vertices in $G_2$, …
View article: Statistical inference on random dot product graphs: a survey
Statistical inference on random dot product graphs: a survey Open
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 wide range of random graphs, from relatively simple stochastic…
View article: Query-by-Example Search with Discriminative Neural Acoustic Word Embeddings
Query-by-Example Search with Discriminative Neural Acoustic Word Embeddings Open
Query-by-example search often uses dynamic time warping (DTW) for comparing queries and proposed matching segments. Recent work has shown that comparing speech segments by representing them as fixed-dimensional vectors --- acoustic word em…
View article: A central limit theorem for an omnibus embedding of multiple random graphs and implications for multiscale network inference
A central limit theorem for an omnibus embedding of multiple random graphs and implications for multiscale network inference Open
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 describe an "omnibus" embedding in which multiple graphs on the s…
View article: A central limit theorem for an omnibus embedding of random dot product graphs
A central limit theorem for an omnibus embedding of random dot product graphs Open
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 describe an embedding in which multiple graphs on the same verte…
View article: Laplacian Eigenmaps From Sparse, Noisy Similarity Measurements
Laplacian Eigenmaps From Sparse, Noisy Similarity Measurements Open
Manifold learning and dimensionality reduction techniques are ubiquitous in science and engineering, but can be computationally expensive procedures when applied to large data sets or when similarities are expensive to compute. To date, li…
View article: On the Consistency of the Likelihood Maximization Vertex Nomination Scheme: Bridging the Gap Between Maximum Likelihood Estimation and Graph Matching
On the Consistency of the Likelihood Maximization Vertex Nomination Scheme: Bridging the Gap Between Maximum Likelihood Estimation and Graph Matching Open
Given a graph in which a few vertices are deemed interesting a priori, the vertex nomination task is to order the remaining vertices into a nomination list such that there is a concentration of interesting vertices at the top of the list. …