7 papers
A Geometric View of Adaptive Cross Approximation via Exterior Algebra
Trevor Loe, Longxiu Huang, Deanna Needell
Adaptive cross approximation (ACA) constructs low-rank CUR approximations from selected rows and columns of a matrix, making it attractive when individual entries are inexpensive t…
Numerical Instabilities in the Kaczmarz Method and Stabilization by Iterative Refinement
Michał Dereziński, Ethan N. Epperly, Deanna Needell +1
The randomized Kaczmarz method and its accelerated variants are a powerful class of iterative methods for solving large-scale linear systems, offering guaranteed convergence with l…
Stable Phase Retrieval: Optimal Rates in Poisson and Heavy-tailed Models
Gao Huang, Song Li, Deanna Needell
We investigate stable recovery guarantees for phase retrieval under two realistic and challenging noise models: the Poisson model and the heavy-tailed model. Our analysis covers bo…
Convergence of the alternating least squares algorithm for CP tensor decompositions
Nicholas Hu, Mark A. Iwen, Deanna Needell +1
The alternating least squares (ALS/AltLS) method is a widely used algorithm for computing the CP decomposition of a tensor. However, its convergence theory is still incompletely un…
Manifold Learning with Normalizing Flows: Towards Regularity, Expressivity and Iso-Riemannian Geometry
Willem Diepeveen, Deanna Needell
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis…
Curvature Corrected Nonnegative Manifold Data Factorization
Joyce Chew, Willem Diepeveen, Deanna Needell
Data with underlying nonlinear structure are collected across numerous application domains, necessitating new data processing and analysis methods adapted to nonlinear domain struc…
Lower Memory Oblivious (Tensor) Subspace Embeddings with Fewer Random Bits: Modewise Methods for Least Squares
M. A. Iwen, D. Needell, E. Rebrova +1
In this paper new general modewise Johnson-Lindenstrauss (JL) subspace embeddings are proposed that are both considerably faster to generate and easier to store than traditional JL…