6 papers · 1 filter
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…
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…
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…
Stability of Sequential Lateration and of Stress Minimization in the Presence of Noise
Ery Arias-Castro, Siddharth Vishwanath
Sequential lateration is a class of methods for multidimensional scaling where a suitable subset of nodes is first embedded by some method, e.g., a clique embedded by classical sca…
The Coreness and H-Index of Random Geometric Graphs
Eddie Aamari, Ery Arias-Castro, Clément Berenfeld
In network analysis, a measure of node centrality provides a scale indicating how central a node is within a network. The coreness is a popular notion of centrality that accounts f…