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Found 12 papers, 9 papers with code
Communication-efficient distributed eigenspace estimation with arbitrary node failures
We develop an eigenspace estimation algorithm for distributed environments with arbitrary node failures, where a subset of computing nodes can return structurally valid but otherwise arbitrarily chosen responses.
Linear Time Kernel Matrix Approximation via Hyperspherical Harmonics
We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning.
Model Preserving Compression for Neural Networks
After training complex deep learning models, a common task is to compress the model to reduce compute and storage demands.
The Fast Kernel Transform
Kernel methods are a highly effective and widely used collection of modern machine learning algorithms.
Over-parametrized neural networks as under-determined linear systems
We draw connections between simple neural networks and under-determined linear systems to comprehensively explore several interesting theoretical questions in the study of neural networks.
Communication-efficient distributed eigenspace estimation
Spectral methods are a collection of such problems, where solutions are orthonormal bases of the leading invariant subspace of an associated data matrix, which are only unique up to rotation and reflections.
Fast Matrix Square Roots with Applications to Gaussian Processes and Bayesian Optimization
Matrix square roots and their inverses arise frequently in machine learning, e. g., when sampling from high-dimensional Gaussians $\mathcal{N}(\mathbf 0, \mathbf K)$ or whitening a vector $\mathbf b$ against covariance matrix $\mathbf K$.
Entrywise convergence of iterative methods for eigenproblems
Several problems in machine learning, statistics, and other fields rely on computing eigenvectors.
Variational formulation for Wannier functions with entangled band structure
When paired with an initial guess based on the selected columns of the density matrix (SCDM) method, our method can robustly find Wannier functions for systems with entangled band structure.
Computational Physics Numerical Analysis Chemical Physics 65Z05, 82D25, 65F30, 65K10
Disentanglement via entanglement: A unified method for Wannier localization
Currently, the most widely used method for treating systems with entangled eigenvalues is to first obtain a reduced subspace (often referred to as disentanglement) and then to solve the Wannier localization problem by treating the reduced subspace as an isolated system.
Computational Physics Chemical Physics 65Z05
Robust and efficient multi-way spectral clustering
We present a new algorithm for spectral clustering based on a column-pivoted QR factorization that may be directly used for cluster assignment or to provide an initial guess for k-means.
Numerical Analysis Numerical Analysis Social and Information Networks Physics and Society 68W01, 65F99
A recursive skeletonization factorization based on strong admissibility
We introduce the strong recursive skeletonization factorization (RS-S), a new approximate matrix factorization based on recursive skeletonization for solving discretizations of linear integral equations associated with elliptic partial differential equations in two and three dimensions (and other matrices with similar hierarchical rank structure).
Numerical Analysis 65R20 (primary), 65F08, 65F05 (secondary)
