15 citations · 45 across the 5 of their papers we have counts for
7 papers
Perturbation Bounds for Procrustes, Classical Scaling, and Trilateration, with Applications to Manifold Learning
Ery Arias-Castro, Adel Javanmard, Bruno Pelletier
One of the common tasks in unsupervised learning is dimensionality reduction, where the goal is to find meaningful low-dimensional structures hidden in high-dimensional data. Somet…
On the Estimation of Latent Distances Using Graph Distances
Ery Arias-Castro, Antoine Channarond, Bruno Pelletier +1
We are given the adjacency matrix of a geometric graph and the task of recovering the latent positions. We study one of the most popular approaches which consists in using the grap…
Remember the Curse of Dimensionality: The Case of Goodness-of-Fit Testing in Arbitrary Dimension
Ery Arias-Castro, Bruno Pelletier, Venkatesh Saligrama
Despite a substantial literature on nonparametric two-sample goodness-of-fit testing in arbitrary dimensions spanning decades, there is no mention there of any curse of dimensional…
On the Consistency of the Crossmatch Test
Ery Arias-Castro, Bruno Pelletier
Rosenbaum (2005) proposed the crossmatch test for two-sample goodness-of-fit testing in arbitrary dimensions. We prove that the test is consistent against all fixed alternatives. I…
On the convergence of maximum variance unfolding
Ery Arias-Castro, Bruno Pelletier
Maximum Variance Unfolding is one of the main methods for (nonlinear) dimensionality reduction. We study its large sample limit, providing specific rates of convergence under stand…
The Normalized Graph Cut and Cheeger Constant: from Discrete to Continuous
Ery Arias-Castro, Bruno Pelletier, Pierre Pudlo
Let M be a bounded domain of a Euclidian space with smooth boundary. We relate the Cheeger constant of M and the conductance of a neighborhood graph defined on a random sample from…
Operator norm convergence of spectral clustering on level sets
Bruno Pelletier, Pierre Pudlo
Following Hartigan, a cluster is defined as a connected component of the t-level set of the underlying density, i.e., the set of points for which the density is greater than t. A c…