31 citations · 103 across the 24 of their papers we have counts for
8 papers · 1 filter
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…
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…
Manifold Density Estimation via Generalized Dequantization
James A. Brofos, Marcus A. Brubaker, Roy R. Lederman
Density estimation is an important technique for characterizing distributions given observations. Much existing research on density estimation has focused on cases wherein the data…
Magnetic Manifold Hamiltonian Monte Carlo
James A. Brofos, Roy R. Lederman
Markov chain Monte Carlo (MCMC) algorithms offer various strategies for sampling; the Hamiltonian Monte Carlo (HMC) family of samplers are MCMC algorithms which often exhibit impro…
Non-Canonical Hamiltonian Monte Carlo
James A. Brofos, Roy R. Lederman
Hamiltonian Monte Carlo is typically based on the assumption of an underlying canonical symplectic structure. Numerical integrators designed for the canonical structure are incompa…
Common Variable Learning and Invariant Representation Learning using Siamese Neural Networks
Uri Shaham, Roy Lederman
We consider the statistical problem of learning common source of variability in data which are synchronously captured by multiple sensors, and demonstrate that Siamese neural netwo…