4 papers · 1 filter
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…
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…
Repelling-Attracting Hamiltonian Monte Carlo
Siddharth Vishwanath, Hyungsuk Tak
We propose a variant of Hamiltonian Monte Carlo (HMC), called the Repelling-Attracting Hamiltonian Monte Carlo (RAHMC), for sampling from multimodal distributions. The key idea tha…
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…