8 papers
Cluster and then Embed: A Modular Approach for Visualization
Elizabeth Coda, Ery Arias-Castro, Gal Mishne
Dimensionality reduction methods such as t-SNE and UMAP are popular methods for visualizing data with a potential (latent) clustered structure. They are known to group data points…
Confidence Bands for the Gradient Lines of a Density Function
Ery Arias-Castro, Wanli Qiao
We consider the problem of estimating the gradient ascent line of a density originating at a given point. Going beyond mere consistency, we establish a weak convergence result for…
Graph Max Shift: A Hill-Climbing Method for Graph Clustering
Ery Arias-Castro, Elizabeth Coda, Wanli Qiao
We present a method for graph clustering that is analogous to gradient ascent methods previously proposed for clustering points in space. The algorithm, which can be viewed as a ma…
Sparse Anomaly Detection Across Referentials: A Rank-Based Higher Criticism Approach
Ivo V. Stoepker, Rui M. Castro, Ery Arias-Castro
Detecting anomalies in large sets of observations is crucial in various applications, such as epidemiological studies, gene expression studies, and systems monitoring. We consider…
Confidence Sets for Multidimensional Scaling
Siddharth Vishwanath, Ery Arias-Castro
We develop a formal statistical framework for classical multidimensional scaling (CMDS) applied to noisy dissimilarity data. We establish distributional convergence results for the…
Theoretical Foundations of Ordinal Multidimensional Scaling, Including Internal and External Unfolding
Ery Arias-Castro, Clément Berenfeld, Daniel Kane
We provide a comprehensive theory of multiple variants of ordinal multidimensional scaling,including internal unfolding and external unfolding. We first follow Shepard (1966) and w…