31 citations · 103 across the 24 of their papers we have counts for
27 papers
The Catastrophic Failure of The k-Means Algorithm in High Dimensions, and How Hartigan's Algorithm Avoids It
Roy R. Lederman, David Silva-Sánchez, Ziling Chen +3
Lloyd's k-means algorithm is one of the most widely used clustering methods. We prove that in high-dimensional, high-noise settings, the algorithm exhibits catastrophic failure: wi…
An Observation on Lloyd's k-Means Algorithm in High Dimensions
David Silva-Sánchez, Roy R. Lederman
Clustering and estimating cluster means are core problems in statistics and machine learning, with k-means and Expectation Maximization (EM) being two widely used algorithms. In th…
Efficient high-resolution refinement in cryo-EM with stochastic gradient descent
Bogdan Toader, Marcus A. Brubaker, Roy R. Lederman
Electron cryomicroscopy (cryo-EM) is an imaging technique widely used in structural biology to determine the three-dimensional structure of biological molecules from noisy two-dime…
On Manifold Learning in Plato's Cave: Remarks on Manifold Learning and Physical Phenomena
Roy R. Lederman, Bogdan Toader
Many techniques in machine learning attempt explicitly or implicitly to infer a low-dimensional manifold structure of an underlying physical phenomenon from measurements without an…
Using VAEs to Learn Latent Variables: Observations on Applications in cryo-EM
Daniel G. Edelberg, Roy R. Lederman
Variational autoencoders (VAEs) are a popular generative model used to approximate distributions. The encoder part of the VAE is used in amortized learning of latent variables, pro…
Geometric Ergodicity in Modified Variations of Riemannian Manifold and Lagrangian Monte Carlo
James A. Brofos, Vivekananda Roy, Roy R. Lederman
Riemannian manifold Hamiltonian (RMHMC) and Lagrangian Monte Carlo (LMC) have emerged as powerful methods of Bayesian inference. Unlike Euclidean Hamiltonian Monte Carlo (EHMC) and…