p7math.NA

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math.NA

298 papers

Revisiting Natural Gradient for Deep Networks

Razvan Pascanu, Yoshua Bengio

1301.3584

Non-square matrix sensing without spurious local minima via the Burer-Monteiro approach

Dohyung Park, Anastasios Kyrillidis, Constantine Caramanis, Sujay Sanghavi

1609.03240

Pseudo Numerical Methods for Diffusion Models on Manifolds

Luping Liu, Yi Ren, Zhijie Lin, Zhou Zhao

2202.09778

On the Expressive Power of Deep Learning: A Tensor Analysis

Nadav Cohen, Or Sharir, Amnon Shashua

1509.05009

Tensor decompositions for learning latent variable models

Anima Anandkumar, Rong Ge, Daniel Hsu, Sham M. Kakade, Matus Telgarsky

1210.7559

Convex Optimization: Algorithms and Complexity

Sébastien Bubeck

1405.4980

Optimally Tuned Iterative Reconstruction Algorithms for Compressed Sensing

Arian Maleki, David L. Donoho

0909.0777

Global Optimality in Tensor Factorization, Deep Learning, and Beyond

Benjamin D. Haeffele, Rene Vidal

1506.07540

Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent

Zeyuan Allen-Zhu, Lorenzo Orecchia

1407.1537

Introduction to the non-asymptotic analysis of random matrices

Roman Vershynin

1011.3027

A geometric alternative to Nesterov's accelerated gradient descent

Sébastien Bubeck, Yin Tat Lee, Mohit Singh

1506.08187

Using Optimization to Obtain a Width-Independent, Parallel, Simpler, and Faster Positive SDP Solver

Zeyuan Allen-Zhu, Yin Tat Lee, Lorenzo Orecchia

1507.02259

Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black-Scholes Partial Differential Equations

Julius Berner, Philipp Grohs, Arnulf Jentzen

1809.03062

Randomized Iterative Methods for Linear Systems

Robert M. Gower, Peter Richtárik

1506.03296

A Linearly-Convergent Stochastic L-BFGS Algorithm

Philipp Moritz, Robert Nishihara, Michael I. Jordan

1508.02087

Even Faster Accelerated Coordinate Descent Using Non-Uniform Sampling

Zeyuan Allen-Zhu, Zheng Qu, Peter Richtárik, Yang Yuan

1512.09103

Accelerated Proximal Stochastic Dual Coordinate Ascent for Regularized Loss Minimization

Shai Shalev-Shwartz, Tong Zhang

1309.2375

Stochastic Dual Ascent for Solving Linear Systems

Robert Mansel Gower, Peter Richtarik

1512.06890

Phase transitions and sample complexity in Bayes-optimal matrix factorization

Yoshiyuki Kabashima, Florent Krzakala, Marc Mézard, Ayaka Sakata, Lenka Zdeborová

1402.1298

Semi-Stochastic Coordinate Descent

Jakub Konečný, Zheng Qu, Peter Richtárik

1412.6293

Stochastic Gradient Descent, Weighted Sampling, and the Randomized Kaczmarz algorithm

Deanna Needell, Nathan Srebro, Rachel Ward

1310.5715

ADMiRA: Atomic Decomposition for Minimum Rank Approximation

Kiryung Lee, Yoram Bresler

0905.0044

Efficient Accelerated Coordinate Descent Methods and Faster Algorithms for Solving Linear Systems

Yin Tat Lee, Aaron Sidford

1305.1922

A simple proof that random matrices are democratic

Mark A. Davenport, Jason N. Laska, Petros T. Boufounos, Richard G. Baraniuk

0911.0736

Randomized Distributed Mean Estimation: Accuracy vs Communication

Jakub Konečný, Peter Richtárik

1611.07555

Probabilistic Numerics and Uncertainty in Computations

Philipp Hennig, Michael A Osborne, Mark Girolami

1506.01326

An Efficient Parallel Solver for SDD Linear Systems

Richard Peng, Daniel A. Spielman

1311.3286

Computing in Operations Research using Julia

Miles Lubin, Iain Dunning

1312.1431

New error bounds for deep networks using sparse grids

Hadrien Montanelli, Qiang Du

1712.08688

ReLU Deep Neural Networks and Linear Finite Elements

Juncai He, Lin Li, Jinchao Xu, Chunyue Zheng

1807.03973

Eignets for function approximation on manifolds

H. N. Mhaskar

0909.5000

Using Optimization to Solve Positive LPs Faster in Parallel

Zeyuan Allen-Zhu, Lorenzo Orecchia

1407.1925

Implementing Randomized Matrix Algorithms in Parallel and Distributed Environments

Jiyan Yang, Xiangrui Meng, Michael W. Mahoney

1502.03032

Dimension-Free Iteration Complexity of Finite Sum Optimization Problems

Yossi Arjevani, Ohad Shamir

1606.09333

Incremental Gradient, Subgradient, and Proximal Methods for Convex Optimization: A Survey

Dimitri P. Bertsekas

1507.01030

Convergence properties of the randomized extended Gauss-Seidel and Kaczmarz methods

Anna Ma, Deanna Needell, Aaditya Ramdas

1503.08235

Coordinate Descent with Arbitrary Sampling I: Algorithms and Complexity

Zheng Qu, Peter Richtárik

1412.8060

Randomized Dual Coordinate Ascent with Arbitrary Sampling

Zheng Qu, Peter Richtárik, Tong Zhang

1411.5873

A Sufficient Condition for Convergences of Adam and RMSProp

Fangyu Zou, Li Shen, Zequn Jie, Weizhong Zhang, Wei Liu

1811.09358

Weak backward error analysis for Langevin process

Marie Kopec

1310.2599

Fast Multiple Splitting Algorithms for Convex Optimization

Donald Goldfarb, Shiqian Ma

0912.4570

Coordinate Descent with Arbitrary Sampling II: Expected Separable Overapproximation

Zheng Qu, Peter Richtárik

1412.8063

Relative Errors for Deterministic Low-Rank Matrix Approximations

Mina Ghashami, Jeff M. Phillips

1307.7454

WNGrad: Learn the Learning Rate in Gradient Descent

Xiaoxia Wu, Rachel Ward, Léon Bottou

1803.02865

Dropping Convexity for Faster Semi-definite Optimization

Srinadh Bhojanapalli, Anastasios Kyrillidis, Sujay Sanghavi

1509.03917

Error analysis of the transport properties of Metropolized schemes

Max Fathi, A. -A. Homman, G. Stoltz

1402.6537

Robust and efficient configurational molecular sampling via Langevin Dynamics

Benedict Leimkuhler, Charles Matthews

1304.3269

PyHessian: Neural Networks Through the Lens of the Hessian

Zhewei Yao, Amir Gholami, Kurt Keutzer, Michael Mahoney

1912.07145

Adaptive Proximal Gradient Method for Convex Optimization

Yura Malitsky, Konstantin Mishchenko

2308.02261

On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions

Francis Bach

1502.06800

Acceleration Methods

Alexandre d'Aspremont, Damien Scieur, Adrien Taylor

2101.09545

Probabilistic Interpretation of Linear Solvers

Philipp Hennig

1402.2058

Machine Learning of Linear Differential Equations using Gaussian Processes

Maziar Raissi, George Em. Karniadakis

1701.02440

Phase retrieval from noisy data based on sparse approximation of object phase and amplitude

Vladimir Katkovnik

1709.01071

Faster Subset Selection for Matrices and Applications

Haim Avron, Christos Boutsidis

1201.0127

Optimistic Dual Extrapolation for Coherent Non-monotone Variational Inequalities

Chaobing Song, Zhengyuan Zhou, Yichao Zhou, Yong Jiang, Yi Ma

2103.04410

Quasi-Monte Carlo Feature Maps for Shift-Invariant Kernels

Haim Avron, Vikas Sindhwani, Jiyan Yang, Michael Mahoney

1412.8293

Provably Faster Gradient Descent via Long Steps

Benjamin Grimmer

2307.06324

Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions

Nathan Halko, Per-Gunnar Martinsson, Joel A. Tropp

0909.4061

Accelerated, Parallel and Proximal Coordinate Descent

Olivier Fercoq, Peter Richtárik

1312.5799

Optimal Rates of Convergence for Noisy Sparse Phase Retrieval via Thresholded Wirtinger Flow

T. Tony Cai, Xiaodong Li, Zongming Ma

1506.03382

A decentralized proximal-gradient method with network independent step-sizes and separated convergence rates

Zhi Li, Wei Shi, Ming Yan

1704.07807

Phase Retrieval via Wirtinger Flow: Theory and Algorithms

Emmanuel Candes, Xiaodong Li, Mahdi Soltanolkotabi

1407.1065

Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems

Maziar Raissi, Paris Perdikaris, George Em Karniadakis

1801.01236

Proximal Quasi-Newton Methods for Regularized Convex Optimization with Linear and Accelerated Sublinear Convergence Rates

Hiva Ghanbari, Katya Scheinberg

1607.03081

Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints

Laurent Lessard, Benjamin Recht, Andrew Packard

1408.3595

Phase Retrieval via Matrix Completion

Emmanuel J. Candes, Yonina Eldar, Thomas Strohmer, Vlad Voroninski

1109.0573

Non-asymptotic mixing of the MALA algorithm

Nawaf Bou-Rabee, Martin Hairer, Eric Vanden-Eijnden

1008.3514

Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations

Maziar Raissi, Paris Perdikaris, George Em Karniadakis

1711.10566

Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations

Maziar Raissi

1801.06637

The local convexity of solving systems of quadratic equations

Chris D. White, Sujay Sanghavi, Rachel Ward

1506.07868

Adaptive Gradient Descent without Descent

Yura Malitsky, Konstantin Mishchenko

1910.09529

Pathwise Accuracy and Ergodicity of Metropolized Integrators for SDEs

Nawaf Bou-Rabee, Eric Vanden-Eijnden

0905.4218

DGM: A deep learning algorithm for solving partial differential equations

Justin Sirignano, Konstantinos Spiliopoulos

1708.07469

Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

Maziar Raissi, Paris Perdikaris, George Em Karniadakis

1711.10561

PDE-Net: Learning PDEs from Data

Zichao Long, Yiping Lu, Xianzhong Ma, Bin Dong

1710.09668

Weak backward error analysis for SDEs

Arnaud Debussche, Erwan Faou

1105.0489

Rational Construction of Stochastic Numerical Methods for Molecular Sampling

Benedict Leimkuhler, Charles Matthews

1203.5428

The non-convex Burer-Monteiro approach works on smooth semidefinite programs

Nicolas Boumal, Vladislav Voroninski, Afonso S. Bandeira

1606.04970

Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations

Maziar Raissi, Paris Perdikaris, George Em Karniadakis

1703.10230

Phase Retrieval from Coded Diffraction Patterns

Emmanuel Candes, Xiaodong Li, Mahdi Soltanolkotabi

1310.3240

Convergence of Numerical Time-Averaging and Stationary Measures via Poisson Equations

Jonathan C. Mattingly, Andrew M. Stuart, M. V. Tretyakov

0908.4450

Discretization errors in molecular dynamics simulations with deterministic and stochastic thermostats

Ruslan L. Davidchack

1412.7067

Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders

Kookjin Lee, Kevin Carlberg

1812.08373

Stable Architectures for Deep Neural Networks

Eldad Haber, Lars Ruthotto

1705.03341

PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming

Emmanuel J. Candes, Thomas Strohmer, Vladislav Voroninski

1109.4499

Revisiting the Nystrom Method for Improved Large-Scale Machine Learning

Alex Gittens, Michael W. Mahoney

1303.1849

An algorithm for the principal component analysis of large data sets

Nathan Halko, Per-Gunnar Martinsson, Yoel Shkolnisky, Mark Tygert

1007.5510

Improving CUR Matrix Decomposition and the Nyström Approximation via Adaptive Sampling

Shusen Wang, Zhihua Zhang

1303.4207

Improved matrix algorithms via the Subsampled Randomized Hadamard Transform

Christos Boutsidis, Alex Gittens

1204.0062

LSRN: A Parallel Iterative Solver for Strongly Over- or Under-Determined Systems

Xiangrui Meng, Michael A. Saunders, Michael W. Mahoney

1109.5981

The spectral norm error of the naive Nystrom extension

Alex Gittens

1110.5305

Improved analysis of the subsampled randomized Hadamard transform

Joel A. Tropp

1011.1595

Mori-Zwanzig reduced models for uncertainty quantification

Jing Li, Panos Stinis

1803.02826

An Explicit Sampling Dependent Spectral Error Bound for Column Subset Selection

Tianbao Yang, Lijun Zhang, Rong Jin, Shenghuo Zhu

1505.00526

Variable metric inexact line-search based methods for nonsmooth optimization

Silvia Bonettini, Ignace Loris, Federica Porta, Marco Prato

1506.00385

Fast Alternating Linearization Methods for Minimizing the Sum of Two Convex Functions

Donald Goldfarb, Shiqian Ma, Katya Scheinberg

0912.4571

Approximating the Exponential, the Lanczos Method and an \tilde{O}(m)-Time Spectral Algorithm for Balanced Separator

Lorenzo Orecchia, Sushant Sachdeva, Nisheeth K. Vishnoi

1111.1491

A Simple, Combinatorial Algorithm for Solving SDD Systems in Nearly-Linear Time

Jonathan A. Kelner, Lorenzo Orecchia, Aaron Sidford, Zeyuan Allen Zhu

1301.6628

Conservative model reduction for finite-volume models

Kevin Carlberg, Youngsoo Choi, Syuzanna Sargsyan

1711.11550

Guaranteed Non-Orthogonal Tensor Decomposition via Alternating Rank-$1$ Updates

Animashree Anandkumar, Rong Ge, Majid Janzamin

1402.5180

Templates for Convex Cone Problems with Applications to Sparse Signal Recovery

Stephen R. Becker, Emmanuel J. Candès, Michael Grant

1009.2065

Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems

Christoph Reisinger, Yufei Zhang

1903.06652

The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices

Zhouchen Lin, Minming Chen, Yi Ma

1009.5055

Conjugate gradient acceleration of iteratively re-weighted least squares methods

Massimo Fornasier, Steffen Peter, Holger Rauhut, Stephan Worm

1509.04063

LSMR: An iterative algorithm for sparse least-squares problems

David Fong, Michael Saunders

1006.0758

A General Analysis of the Convergence of ADMM

Robert Nishihara, Laurent Lessard, Benjamin Recht, Andrew Packard, Michael I. Jordan

1502.02009

Solving Multiple-Block Separable Convex Minimization Problems Using Two-Block Alternating Direction Method of Multipliers

Xiangfeng Wang, Mingyi Hong, Shiqian Ma, Zhi-Quan Luo

1308.5294

Effects of Depth, Width, and Initialization: A Convergence Analysis of Layer-wise Training for Deep Linear Neural Networks

Yeonjong Shin

1910.05874

Global Convergence of a Grassmannian Gradient Descent Algorithm for Subspace Estimation

Dejiao Zhang, Laura Balzano

1506.07405

Breaking Locality Accelerates Block Gauss-Seidel

Stephen Tu, Shivaram Venkataraman, Ashia C. Wilson, Alex Gittens, Michael I. Jordan, Benjamin Recht

1701.03863

Tight p-fusion frames

Christine Bachoc, Martin Ehler

1201.1798

Gradient Descent with Random Initialization: Fast Global Convergence for Nonconvex Phase Retrieval

Yuxin Chen, Yuejie Chi, Jianqing Fan, Cong Ma

1803.07726

A Theoretical Analysis of Deep Neural Networks and Parametric PDEs

Gitta Kutyniok, Philipp Petersen, Mones Raslan, Reinhold Schneider

1904.00377

Robust Spectral Compressed Sensing via Structured Matrix Completion

Yuxin Chen, Yuejie Chi

1304.8126

Efficient First-order Methods for Convex Minimization: a Constructive Approach

Yoel Drori, Adrien B. Taylor

1803.05676

Iterative Hard Thresholding for Compressed Sensing

Thomas Blumensath, Mike E. Davies

0805.0510

The Little Engine that Could: Regularization by Denoising (RED)

Yaniv Romano, Michael Elad, Peyman Milanfar

1611.02862

A path-dependent PDE solver based on signature kernels

Alexandre Pannier, Cristopher Salvi

2403.11738

Gradient Sparsification for Communication-Efficient Distributed Optimization

Jianqiao Wangni, Jialei Wang, Ji Liu, Tong Zhang

1710.09854

Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems

Yuxin Chen, Emmanuel J. Candes

1505.05114

Learning Neural PDE Solvers with Convergence Guarantees

Jun-Ting Hsieh, Shengjia Zhao, Stephan Eismann, Lucia Mirabella, Stefano Ermon

1906.01200

LazySVD: Even Faster SVD Decomposition Yet Without Agonizing Pain

Zeyuan Allen-Zhu, Yuanzhi Li

1607.03463

Asynchronous Parallel Stochastic Gradient for Nonconvex Optimization

Xiangru Lian, Yijun Huang, Yuncheng Li, Ji Liu

1506.08272

Stochastic Optimization for Large-scale Optimal Transport

Genevay Aude, Marco Cuturi, Gabriel Peyré, Francis Bach

1605.08527

Minimizing Communication in Linear Algebra

Grey Ballard, James Demmel, Olga Holtz, Oded Schwartz

0905.2485

On the Complexity Analysis of Randomized Block-Coordinate Descent Methods

Zhaosong Lu, Lin Xiao

1305.4723

A Simpler Approach to Matrix Completion

Benjamin Recht

0910.0651

Posterior Consistency for Gaussian Process Approximations of Bayesian Posterior Distributions

Andrew M. Stuart, Aretha L. Teckentrup

1603.02004

Faster Eigenvector Computation via Shift-and-Invert Preconditioning

Dan Garber, Elad Hazan, Chi Jin, Sham M. Kakade, Cameron Musco, Praneeth Netrapalli, Aaron Sidford

1605.08754

Distributed Matrix Completion and Robust Factorization

Lester Mackey, Ameet Talwalkar, Michael I. Jordan

1107.0789

Fast Exact Matrix Completion with Finite Samples

Prateek Jain, Praneeth Netrapalli

1411.1087

Stochastic Quasi-Newton Methods for Nonconvex Stochastic Optimization

Xiao Wang, Shiqian Ma, Donald Goldfarb, Wei Liu

1607.01231

Sparse Signal Recovery from Quadratic Measurements via Convex Programming

Xiaodong Li, Vladislav Voroninski

1209.4785

Automatic Gradient Descent: Deep Learning without Hyperparameters

Jeremy Bernstein, Chris Mingard, Kevin Huang, Navid Azizan, Yisong Yue

2304.05187

New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property

Felix Krahmer, Rachel Ward

1009.0744

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

Liu Yang, Dongkun Zhang, George Em Karniadakis

1811.02033

Optimally-Weighted Herding is Bayesian Quadrature

Ferenc Huszár, David Duvenaud

1204.1664

Recycling Randomness with Structure for Sublinear time Kernel Expansions

Krzysztof Choromanski, Vikas Sindhwani

1605.09049

Fast Stochastic Algorithms for SVD and PCA: Convergence Properties and Convexity

Ohad Shamir

1507.08788

Momentum and Stochastic Momentum for Stochastic Gradient, Newton, Proximal Point and Subspace Descent Methods

Nicolas Loizou, Peter Richtárik

1712.09677

Adaptive Thermostats for Noisy Gradient Systems

Benedict Leimkuhler, Xiaocheng Shang

1505.06889

A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations

Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse, Tuan Anh Nguyen

1901.10854

Unified Optimal Analysis of the (Stochastic) Gradient Method

Sebastian U. Stich

1907.04232

Graph Expansion and Communication Costs of Fast Matrix Multiplication

Grey Ballard, James Demmel, Olga Holtz, Oded Schwartz

1109.1693

Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier-Stokes equations

Giovanni Stabile, Gianluigi Rozza

1710.11580

MUSIC for Single-Snapshot Spectral Estimation: Stability and Super-resolution

Wenjing Liao, Albert Fannjiang

1404.1484

Renormalized reduced models for singular PDEs

Panagiotis Stinis

1106.1677

Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

Weinan E, Jiequn Han, Arnulf Jentzen

1706.04702

Randomized Block Kaczmarz Method with Projection for Solving Least Squares

Deanna Needell, Ran Zhao, Anastasios Zouzias

1403.4192

Finding Low-Rank Solutions via Non-Convex Matrix Factorization, Efficiently and Provably

Dohyung Park, Anastasios Kyrillidis, Constantine Caramanis, Sujay Sanghavi

1606.03168

Phase Retrieval for Sparse Signals

Yang Wang, Zhiqiang Xu

1310.0873

MINRES-QLP: a Krylov subspace method for indefinite or singular symmetric systems

Sou-Cheng T. Choi, Christopher C. Paige, Michael A. Saunders

1003.4042

Stochastic first-order methods: non-asymptotic and computer-aided analyses via potential functions

Adrien Taylor, Francis Bach

1902.00947

A Comparison of Automatic Differentiation and Continuous Sensitivity Analysis for Derivatives of Differential Equation Solutions

Yingbo Ma, Vaibhav Dixit, Mike Innes, Xingjian Guo, Christopher Rackauckas

1812.01892

A quasi-Newton proximal splitting method

Stephen Becker, M. Jalal Fadili

1206.1156

Scalable Gradients for Stochastic Differential Equations

Xuechen Li, Ting-Kam Leonard Wong, Ricky T. Q. Chen, David Duvenaud

2001.01328

A Unified Approach to Error Bounds for Structured Convex Optimization Problems

Zirui Zhou, Anthony Man-Cho So

1512.03518

Solving Quadratic Equations via PhaseLift when There Are About As Many Equations As Unknowns

Emmanuel J. Candes, Xiaodong Li

1208.6247

Deep backward schemes for high-dimensional nonlinear PDEs

Côme Huré, Huyên Pham, Xavier Warin

1902.01599

Golden Ratio Algorithms for Variational Inequalities

Yura Malitsky

1803.08832

Proximal Newton-type methods for minimizing composite functions

Jason D. Lee, Yuekai Sun, Michael A. Saunders

1206.1623

Machine Learning from a Continuous Viewpoint

Weinan E, Chao Ma, Lei Wu

1912.12777

Asymmetry Helps: Eigenvalue and Eigenvector Analyses of Asymmetrically Perturbed Low-Rank Matrices

Yuxin Chen, Chen Cheng, Jianqing Fan

1811.12804

Super-Resolution from Noisy Data

Emmanuel Candes, Carlos Fernandez-Granda

1211.0290

MADMM: a generic algorithm for non-smooth optimization on manifolds

Artiom Kovnatsky, Klaus Glashoff, Michael M. Bronstein

1505.07676

Efficient and Modular Implicit Differentiation

Mathieu Blondel, Quentin Berthet, Marco Cuturi, Roy Frostig, Stephan Hoyer, Felipe Llinares-López, Fabian Pedregosa, Jean-Philippe Vert

2105.15183

Understanding the Acceleration Phenomenon via High-Resolution Differential Equations

Bin Shi, Simon S. Du, Michael I. Jordan, Weijie J. Su

1810.08907

Faster Kernel Ridge Regression Using Sketching and Preconditioning

Haim Avron, Kenneth L. Clarkson, David P. Woodruff

1611.03220

An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems

Manya V. Afonso, José M. Bioucas-Dias, Mário A. T. Figueiredo

0912.3481

Solving high-dimensional partial differential equations using deep learning

Jiequn Han, Arnulf Jentzen, Weinan E

1707.02568

A non-adapted sparse approximation of PDEs with stochastic inputs

Alireza Doostan, Houman Owhadi

1006.2151

Equilibrated adaptive learning rates for non-convex optimization

Yann N. Dauphin, Harm de Vries, Yoshua Bengio

1502.04390

On Tensor Completion via Nuclear Norm Minimization

Ming Yuan, Cun-Hui Zhang

1405.1773

Space-time least-squares Petrov-Galerkin projection for nonlinear model reduction

Youngsoo Choi, Kevin Carlberg

1703.04560

SwitchNet: a neural network model for forward and inverse scattering problems

Yuehaw Khoo, Lexing Ying

1810.09675

Nearly-optimal Robust Matrix Completion

Yeshwanth Cherapanamjeri, Kartik Gupta, Prateek Jain

1606.07315

Phaseless Rcovery using Gauss-Newton Method

Bing Gao, Zhiqiang Xu

1606.08135

A Reduced Basis Technique for Long-Time Unsteady Turbulent Flows

Lambert Fick, Yvon Maday, Anthony T Patera, Tommaso Taddei

1710.03569

Coordinate Friendly Structures, Algorithms and Applications

Zhimin Peng, Tianyu Wu, Yangyang Xu, Ming Yan, Wotao Yin

1601.00863

A convergent blind deconvolution method for post-adaptive-optics astronomical imaging

M. Prato, A. La Camera, S. Bonettini, M. Bertero

1305.0421

Parallel Tensor Compression for Large-Scale Scientific Data

Woody Austin, Grey Ballard, Tamara G. Kolda

1510.06689

Phase Retrieval: Stability and Recovery Guarantees

Yonina C. Eldar, Shahar Mendelson

1211.0872

PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network

Zichao Long, Yiping Lu, Bin Dong

1812.04426

Convergence Analysis of Inexact Randomized Iterative Methods

Nicolas Loizou, Peter Richtárik

1903.07971

On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations

Weinan E, Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse

1708.03223

Graph Expansion Analysis for Communication Costs of Fast Rectangular Matrix Multiplication

Grey Ballard, James Demmel, Olga Holtz, Benjamin Lipshitz, Oded Schwartz

1209.2184

Pod-Galerkin Reduced Order Methods for CFD Using Finite Volume Discretisation: Vortex Shedding Around a Circular Cylinder

Giovanni Stabile, Saddam Hijazi, Andrea Mola, Stefano Lorenzi, Gianluigi Rozza

1701.03424

Online Stochastic Gradient Descent with Arbitrary Initialization Solves Non-smooth, Non-convex Phase Retrieval

Yan Shuo Tan, Roman Vershynin

1910.12837

Galerkin v. least-squares Petrov--Galerkin projection in nonlinear model reduction

Kevin Carlberg, Matthew Barone, Harbir Antil

1504.03749

Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems

Nikos Komodakis, Jean-Christophe Pesquet

1406.5429

Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decomposition

Cameron Musco, Christopher Musco

1504.05477

Super-resolution via superset selection and pruning

Laurent Demanet, Deanna Needell, Nam Nguyen

1302.6288

Strong Scaling of Matrix Multiplication Algorithms and Memory-Independent Communication Lower Bounds

Grey Ballard, James Demmel, Olga Holtz, Benjamin Lipshitz, Oded Schwartz

1202.3177

Stabilization of (G)EIM in presence of measurement noise: application to nuclear reactor physics

J. P. Argaud, B. Bouriquet, H. Gong, Y. Maday, O. Mula

1611.02219

Towards a Mathematical Understanding of Neural Network-Based Machine Learning: what we know and what we don't

Weinan E, Chao Ma, Stephan Wojtowytsch, Lei Wu

2009.10713

Breaking Reversibility Accelerates Langevin Dynamics for Global Non-Convex Optimization

Xuefeng Gao, Mert Gurbuzbalaban, Lingjiong Zhu

1812.07725

Active subspace methods in theory and practice: applications to kriging surfaces

Paul G. Constantine, Eric Dow, Qiqi Wang

1304.2070

Accelerated Spectral Clustering Using Graph Filtering Of Random Signals

Nicolas Tremblay, Gilles Puy, Pierre Borgnat, Remi Gribonval, Pierre Vandergheynst

1509.08863

Convergence of the Deep BSDE Method for Coupled FBSDEs

Jiequn Han, Jihao Long

1811.01165

Numerical computation of solutions of the critical nonlinear Schrodinger equation after the singularity

Panagiotis Stinis

1010.2246

Parallel Algorithms for Constrained Tensor Factorization via the Alternating Direction Method of Multipliers

Athanasios P. Liavas, Nicholas D. Sidiropoulos

1409.2383

Adaptive ADMM with Spectral Penalty Parameter Selection

Zheng Xu, Mario A. T. Figueiredo, Tom Goldstein

1605.07246

Linear Convergence of the Douglas-Rachford Method for Two Closed Sets

Hung M. Phan

1401.6509

Efficient deconvolution methods for astronomical imaging: algorithms and IDL-GPU codes

M. Prato, R. Cavicchioli, L. Zanni, P. Boccacci, M. Bertero

1210.2258

Paved with Good Intentions: Analysis of a Randomized Block Kaczmarz Method

Deanna Needell, Joel A. Tropp

1208.3805

Hypersolvers: Toward Fast Continuous-Depth Models

Michael Poli, Stefano Massaroli, Atsushi Yamashita, Hajime Asama, Jinkyoo Park

2007.09601

Complexity Guarantees for Polyak Steps with Momentum

Mathieu Barré, Adrien Taylor, Alexandre d'Aspremont

2002.00915

On the complexity of nonnegative matrix factorization

Stephen A. Vavasis

0708.4149

Subspace Pursuit for Compressive Sensing Signal Reconstruction

Wei Dai, Olgica Milenkovic

0803.0811

On the Nuclear Norm and the Singular Value Decomposition of Tensors

Harm Derksen

1308.3860

Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities

Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse

1912.02571

PETSc/TS: A Modern Scalable ODE/DAE Solver Library

Shrirang Abhyankar, Jed Brown, Emil M. Constantinescu, Debojyoti Ghosh, Barry F. Smith, Hong Zhang

1806.01437

Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints

I. Daubechies, M. Fornasier, I. Loris

0706.4297

Signal Recovery from Incomplete and Inaccurate Measurements via Regularized Orthogonal Matching Pursuit

Deanna Needell, Roman Vershynin

0712.1360

Optimization Techniques on Riemannian Manifolds

Steven Thomas Smith

1407.5965

Stable optimizationless recovery from phaseless linear measurements

Laurent Demanet, Paul Hand

1208.1803

Spectra of general hypergraphs

Anirban Banerjee, Arnab Char, Bibhash Mondal

1601.02136

FMMformer: Efficient and Flexible Transformer via Decomposed Near-field and Far-field Attention

Tan M. Nguyen, Vai Suliafu, Stanley J. Osher, Long Chen, Bao Wang

2108.02347

A strong restricted isometry property, with an application to phaseless compressed sensing

Vladislav Voroninski, Zhiqiang Xu

1404.3811

A machine learning framework for data driven acceleration of computations of differential equations

Siddhartha Mishra

1807.09519

Quantitative convergence analysis of iterated expansive, set-valued mappings

D. Russell Luke, Nguyen H. Thao, Matthew K. Tam

1605.05725

A systematic approach to Lyapunov analyses of continuous-time models in convex optimization

Céline Moucer, Adrien Taylor, Francis Bach

2205.12772

Recovering missing CFD data for high-order discretizations using deep neural networks and dynamics learning

Kevin T. Carlberg, Antony Jameson, Mykel J. Kochenderfer, Jeremy Morton, Liqian Peng, Freddie D. Witherden

1812.01177

Solving for high dimensional committor functions using artificial neural networks

Yuehaw Khoo, Jianfeng Lu, Lexing Ying

1802.10275

Faster gradient descent and the efficient recovery of images

Hui Huang, Uri Ascher

1308.2464

Randomized Kaczmarz solver for noisy linear systems

Deanna Needell

0902.0958

Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems

Bernhard Schmitzer

1610.06519

Exact Support Recovery for Sparse Spikes Deconvolution

Vincent Duval, Gabriel Peyré

1306.6909

Communication-Optimal Parallel Algorithm for Strassen's Matrix Multiplication

Grey Ballard, James Demmel, Olga Holtz, Benjamin Lipshitz, Oded Schwartz

1202.3173

Convex Tensor Decomposition via Structured Schatten Norm Regularization

Ryota Tomioka, Taiji Suzuki

1303.6370

Bayesian Numerical Homogenization

Houman Owhadi

1406.6668

A literature survey of low-rank tensor approximation techniques

Lars Grasedyck, Daniel Kressner, Christine Tobler

1302.7121

New convergence results for the scaled gradient projection method

Silvia Bonettini, Marco Prato

1406.6601

A generalized model for optimal transport of images including dissipation and density modulation

Jan Maas, Martin Rumpf, Carola Schönlieb, Stefan Simon

1504.01988

Separation of Variables and the Computation of Fourier Transforms on Finite Groups, II

David Maslen, Daniel N. Rockmore, Sarah Wolff

1512.02445

A Rank-Corrected Procedure for Matrix Completion with Fixed Basis Coefficients

Weimin Miao, Shaohua Pan, Defeng Sun

1210.3709

ResNets Ensemble via the Feynman-Kac Formalism to Improve Natural and Robust Accuracies

Bao Wang, Binjie Yuan, Zuoqiang Shi, Stanley J. Osher

1811.10745

Subspace Iteration Randomization and Singular Value Problems

Ming Gu

1408.2208

A Field Guide to Forward-Backward Splitting with a FASTA Implementation

Tom Goldstein, Christoph Studer, Richard Baraniuk

1411.3406

Data-Driven Model Reduction for the Bayesian Solution of Inverse Problems

Tiangang Cui, Youssef M. Marzouk, Karen E. Willcox

1403.4290

Towards a Mathematical Theory of Super-Resolution

Emmanuel Candes, Carlos Fernandez-Granda

1203.5871

An exact tree projection algorithm for wavelets

Coralia Cartis, Andrew Thompson

1304.4570

Mixed Precision Training of Convolutional Neural Networks using Integer Operations

Dipankar Das, Naveen Mellempudi, Dheevatsa Mudigere, Dhiraj Kalamkar, Sasikanth Avancha, Kunal Banerjee, Srinivas Sridharan, Karthik Vaidyanathan, Bharat Kaul, Evangelos Georganas, Alexander Heinecke, Pradeep Dubey, Jesus Corbal, Nikita Shustrov, Roma Dubtsov, Evarist Fomenko, Vadim Pirogov

1802.00930

Neural Network Approximation

Ronald DeVore, Boris Hanin, Guergana Petrova

2012.14501

Global registration of multiple point clouds using semidefinite programming

Kunal N. Chaudhury, Yuehaw Khoo, Amit Singer

1306.5226

Data-based stochastic model reduction for the Kuramoto--Sivashinsky equation

Fei Lu, Kevin Lin, Alexandre J. Chorin

1509.09279

Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions

Philipp Grohs, Lukas Herrmann

2007.05384

A blob method for diffusion

José Antonio Carrillo, Katy Craig, Francesco S. Patacchini

1709.09195

PEPit: computer-assisted worst-case analyses of first-order optimization methods in Python

Baptiste Goujaud, Céline Moucer, François Glineur, Julien Hendrickx, Adrien Taylor, Aymeric Dieuleveut

2201.04040

Randomized algorithms for low-rank matrix factorizations: sharp performance bounds

Rafi Witten, Emmanuel Candes

1308.5697

Projecting onto the intersection of a cone and a sphere

Heinz H. Bauschke, Minh N. Bui, Xianfu Wang

1708.00585

Tradeoffs between Convergence Speed and Reconstruction Accuracy in Inverse Problems

Raja Giryes, Yonina C. Eldar, Alex M. Bronstein, Guillermo Sapiro

1605.09232

Symmetric tensors and symmetric tensor rank

Pierre Comon, Gene Golub, Lek-Heng Lim, Bernard Mourrain

0802.1681

Is There an Analog of Nesterov Acceleration for MCMC?

Yi-An Ma, Niladri Chatterji, Xiang Cheng, Nicolas Flammarion, Peter Bartlett, Michael I. Jordan

1902.00996

Flexpoint: An Adaptive Numerical Format for Efficient Training of Deep Neural Networks

Urs Köster, Tristan J. Webb, Xin Wang, Marcel Nassar, Arjun K. Bansal, William H. Constable, Oğuz H. Elibol, Scott Gray, Stewart Hall, Luke Hornof, Amir Khosrowshahi, Carey Kloss, Ruby J. Pai, Naveen Rao

1711.02213

Linear and strong convergence of algorithms involving averaged nonexpansive operators

Heinz H. Bauschke, Dominikus Noll, Hung M. Phan

1402.5460

Adaptive Smolyak Pseudospectral Approximations

Patrick R. Conrad, Youssef M. Marzouk

1209.1406

Quadratically-Regularized Optimal Transport on Graphs

Montacer Essid, Justin Solomon

1704.08200

Generalization error of minimum weighted norm and kernel interpolation

Weilin Li

2008.03365

Fourier Neural Operator for Parametric Partial Differential Equations

Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar

2010.08895

Multilevel Picard iterations for solving smooth semilinear parabolic heat equations

Weinan E, Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse

1607.03295

The connections between Lyapunov functions for some optimization algorithms and differential equations

J. M. Sanz-Serna, Konstantinos C. Zygalakis

2009.00673

Accelerated Gossip via Stochastic Heavy Ball Method

Nicolas Loizou, Peter Richtárik

1809.08657

Iterative Bregman Projections for Regularized Transportation Problems

Jean-David Benamou, Guillaume Carlier, Marco Cuturi, Luca Nenna, Gabriel Peyré

1412.5154

An efficient, partitioned ensemble algorithm for simulating ensembles of evolutionary MHD flows at low magnetic Reynolds number

Nan Jiang, Michael Schneier

1709.05447

An $\ell_{\infty}$ Eigenvector Perturbation Bound and Its Application to Robust Covariance Estimation

Jianqing Fan, Weichen Wang, Yiqiao Zhong

1603.03516

Variance components and generalized Sobol' indices

Art B. Owen

1205.1774

Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis

A. Cichocki, D. Mandic, A-H. Phan, C. Caiafa, G. Zhou, Q. Zhao, L. De Lathauwer

1403.4462

Linearly convergent stochastic heavy ball method for minimizing generalization error

Nicolas Loizou, Peter Richtárik

1710.10737

Coherence-Pattern Guided Compressive Sensing with Unresolved Grids

A. Fannjiang, W. Liao

1106.5177

Alternating Projections and Douglas-Rachford for Sparse Affine Feasibility

Robert Hesse, D. Russell Luke, Patrick Neumann

1307.2009

Multipole Graph Neural Operator for Parametric Partial Differential Equations

Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar

2006.09535

Model Reduction and Neural Networks for Parametric PDEs

Kaushik Bhattacharya, Bamdad Hosseini, Nikola B. Kovachki, Andrew M. Stuart

2005.03180

Neural Operator: Graph Kernel Network for Partial Differential Equations

Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, Anima Anandkumar

2003.03485

A Gradient Descent Algorithm on the Grassman Manifold for Matrix Completion

Raghunandan H. Keshavan, Sewoong Oh

0910.5260

Combining geometry and combinatorics: A unified approach to sparse signal recovery

R. Berinde, A. C. Gilbert, P. Indyk, H. Karloff, M. J. Strauss

0804.4666

Stable and robust sampling strategies for compressive imaging

Felix Krahmer, Rachel Ward

1210.2380

Geometric Optimization Methods for Adaptive Filtering

Steven Thomas Smith

1305.1886

Recovering low-rank matrices from few coefficients in any basis

David Gross

0910.1879

Microlocal Analysis of the Geometric Separation Problem

David L. Donoho, Gitta Kutyniok

1004.3006

Compressed Sensing with Coherent and Redundant Dictionaries

Emmanuel J. Candes, Yonina C. Eldar, Deanna Needell, Paige Randall

1005.2613

ShearLab: A Rational Design of a Digital Parabolic Scaling Algorithm

Gitta Kutyniok, Morteza Shahram, Xiaosheng Zhuang

1106.1319

Convex optimization

Evgeniya Vorontsova, Roland Hildebrand, Alexander Gasnikov, Fedor Stonyakin

2106.01946

Two-subspace Projection Method for Coherent Overdetermined Systems (Technical Report)

Deanna Needell, Rachel Ward

1204.0279

Randomized Extended Kaczmarz for Solving Least-Squares

Anastasios Zouzias, Nikolaos Freris

1205.5770

Acceleration of Randomized Kaczmarz Method via the Johnson-Lindenstrauss Lemma

Yonina C. Eldar, Deanna Needell

1008.4397

The rate of convergence in the method of alternating projections

Catalin Badea, Sophie Grivaux, Vladimir Muller

1006.2047

Block Kaczmarz Method with Inequalities

Jonathan Briskman, Deanna Needell

1406.7339

Randomized Methods for Linear Constraints: Convergence Rates and Conditioning

D. Leventhal, A. S. Lewis

0806.3015

Metric Subregularity and the Proximal Point Method

D. Leventhal

0902.4200

Riemannian Manifold Hamiltonian Monte Carlo

Mark Girolami, Ben Calderhead, Siu A. Chin

0907.1100

Uniform Uncertainty Principle and signal recovery via Regularized Orthogonal Matching Pursuit

Deanna Needell, Roman Vershynin

0707.4203

Second-Order Optimization for Non-Convex Machine Learning: An Empirical Study

Peng Xu, Farbod Roosta-Khorasani, Michael W. Mahoney

1708.07827

Semi-Stochastic Gradient Descent Methods

Jakub Konečný, Peter Richtárik

1312.1666

Reflection methods for user-friendly submodular optimization

Stefanie Jegelka, Francis Bach, Suvrit Sra

1311.4296

An Introduction to Matrix Concentration Inequalities

Joel A. Tropp

1501.01571

An Asynchronous Parallel Randomized Kaczmarz Algorithm

Ji Liu, Stephen J. Wright, Srikrishna Sridhar

1401.4780