251 citations · 1.4k across the 67 of their papers we have counts for
82 papers
Theoretical Foundations of Ordinal Spherical Multidimensional Scaling
Elizabeth Coda, Ery Arias-Castro
There has been general interest in spherically constrained embeddings as data with an inherently circular or spherical structure arise in a number of applications. While many metho…
Kernelized Stein Discrepancy for Goodness-of-Fit Tests and Stein Sampling in R
Junhao Gao, Ery Arias-Castro
Stein's method constructs computable discrepancies between a target distribution and a candidate distribution without requiring the target distribution's normalizing constant. Thes…
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…
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…
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…
Minimax Optimality of Classical Scaling Under General Noise Conditions
Siddharth Vishwanath, Ery Arias-Castro
We establish the consistency of classical scaling under a broad class of noise models, encompassing many commonly studied cases in literature. Our approach requires only finite fou…