no code implementations • 31 May 2022 • Vasileios Charisopoulos, Anil Damle

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.

no code implementations • 8 Feb 2022 • John Paul Ryan, Anil Damle

We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning.

1 code implementation • 30 Jul 2021 • Jerry Chee, Megan Renz, Anil Damle, Christopher De Sa

After training complex deep learning models, a common task is to compress the model to reduce compute and storage demands.

1 code implementation • 8 Jun 2021 • John Paul Ryan, Sebastian Ament, Carla P. Gomes, Anil Damle

Kernel methods are a highly effective and widely used collection of modern machine learning algorithms.

no code implementations • 29 Oct 2020 • Austin R. Benson, Anil Damle, Alex Townsend

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.

1 code implementation • 5 Sep 2020 • Vasileios Charisopoulos, Austin R. Benson, Anil Damle

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.

1 code implementation • NeurIPS 2020 • Geoff Pleiss, Martin Jankowiak, David Eriksson, Anil Damle, Jacob R. Gardner

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 $\mathbf K$.

1 code implementation • NeurIPS 2020 • Vasileios Charisopoulos, Austin R. Benson, Anil Damle

Several problems in machine learning, statistics, and other fields rely on computing eigenvectors.

1 code implementation • 25 Jan 2018 • Anil Damle, Antoine Levitt, Lin Lin

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

1 code implementation • 20 Mar 2017 • Anil Damle, Lin Lin

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

1 code implementation • 27 Sep 2016 • Anil Damle, Victor Minden, Lexing Ying

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

3 code implementations • 26 Sep 2016 • Victor Minden, Kenneth L. Ho, Anil Damle, Lexing Ying

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)

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