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We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem.
Adjustment of an inverse matrix corresponding to changes in the elements of a given column or a given row of the original matrix (abstract)
Jack Sherman and Winifred J. Morrison · 1949
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The stability of out-input matrices
Max A. Woodbury · 1949
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A stochastic approximation method
Hebert Robbins and Sutton Monro · 1951
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Linear recursive sequences
Jay P. Fillmore and Morris L. Marx · 1968
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Monotone operators and the proximal point algorithm
R. Tyrrell Rockafellar · 1976
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An algorithm for restricted least squares regression
R.L. Dykstra · 1983
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A method for finding projections onto the intersection of convex sets in Hilbert spaces
J.P. Boyle and R.L. Dykstra · 1986
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Randomized Algorithms
Rajeev Motwani and Prabhakar Raghavan · 1995
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On projection algorithms for solving convex feasibility problems
HH Bauschke and JM Borwein · 1996
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Randomized algorithms for probabilistic robustness with real and complex structured uncertainty
GC Calafiore, F Dabbene, and R Tempo · 2000
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Stochastic algorithms for exact and approximate feasibility of robust LMIs
GC Calafiore and BT Polyak · 2001
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Finding frequent items in data streams
Moses Charikar, Kevin Chen, and Martin Farach-Colton · 2002
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Iterative Methods for Sparse Linear Systems
Yousef Saad · 2003
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Introductory Lectures on Convex Optimization: A Basic Course (Applied Optimization)
Yurii Nesterov · 2004
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An improved data stream summary: the count-min sketch and its applications
Graham Cormode and S. Muthukrishnan · 2005
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An Introduction to Difference Equations
Saber Elaydi · 2005
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Fast monte carlo algorithms for matrices I: Approximating matrix multiplication
Petros Drineas, Ravi Kannan, and Michael W. Mahoney · 2006
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Fast monte carlo algorithms for matrices II: Computing a low-rank approximation to a matrix
Petros Drineas, Ravi Kannan, and Michael W. Mahoney · 2006
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A fast randomized algorithm for overdetermined linear least-squares regression
Vladimir Rokhlin and Mark Tygert · 2008
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Robust stochastic approximation approach to stochastic programming
Arkadi Nemirovski, Anatoli Juditsky, Guanghui Lan, and Alexander Shapiro · 2009
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A randomized Kaczmarz algorithm with exponential convergence
Thomas Strohmer and Roman Vershynin · 2009
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Blendenpik: Supercharging LAPACK’s least-squares solver
Haim Avron, Petar Maymounkov, and Sivan Toledo · 2010
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Randomized methods for linear constraints: Convergence rates and conditioning
Dennis Leventhal and Adrian S. Lewis · 2010
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Randomized Kaczmarz solver for noisy linear systems
Deana Needell · 2010
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Optimistic rates for learning with a smooth loss
Nathan Srebro, Karthik Sridharan, and Ambuj Tewari · 2010
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Random algorithms for convex minimization problems
Angelia Nedić · 2011
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Hogwild!: A lock-free approach to parallelizing stochastic gradient descent
Feng Niu, Benjamin Recht, Christopher Ré, and Stephen Wright · 2011
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Stochastic methods for ℓ 1 \ell_{1} -regularized loss minimization
Shai Shalev-Shwartz and Ambuj Tewari · 2011
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Paved with good intentions: analysis of a randomized block Kaczmarz method
Deanna Needell and Joel A. Tropp · 2012
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Efficiency of coordinate descent methods on huge-scale optimization problems
Yurii Nesterov · 2012
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Accelerating stochastic gradient descent using predictive variance reduction
Rie Johnson and Tong Zhang · 2013
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Stochastic dual coordinate ascent methods for regularized loss
Shai Shalev-Shwartz and Tong Zhang · 2013
Mini-batch semi-stochastic gradient descent in the proximal setting
Jakub Konečný, Jie Lu, Peter Richtárik, and Martin Takáč · 2016
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An accelerated randomized Kaczmarz algorithm
Ji Liu and Stephen J Wright · 2016
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A new perspective on randomized gossip algorithms
Nicolas Loizou and Peter Richtárik · 2016
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A new perspective on randomized gossip algorithms
Nicolas Loizou and Peter Richtárik · 2016
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Iterative Hessian sketch: Fast and accurate solution approximation for constrained least-squares
Mert Pilanci and Martin J. Wainwright · 2016
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Coordinate descent with arbitrary sampling I: algorithms and complexity
Zheng Qu and Richtárik · 2016
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Mini-batch primal and dual methods for SVMs
Martin Takáč, Avleen Bijral, Peter Richtárik, and Nathan Srebro · 2013
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Randomized Algorithms for Analysis and Control of Uncertain Systems
Roberto Tempo, Giuseppe Calafiore, and Fabrizio Dabbene · 2013
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Randomized extended Kaczmarz for solving least-squares
Anastasios Zouzias and Nikolaos M Freris · 2013
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SAGA: A fast incremental gradient method with support for non-strongly convex composite objectives
Aaron Defazio, Francis Bach, and Simon Lacoste-Julien · 2014
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LSRN: a parallel iterative solver for strongly over- and under-determined systems
X. Meng, Michael A. Saunders, and Michael W. Mahoney · 2014
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Rows vs columns for linear systems of equations - randomized Kaczmarz or coordinate descent ?
Aaditya Ramdas · 2014
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SDNA: stochastic dual Newton ascent for empirical risk minimization
Zheng Qu, Peter Richtárik, Martin Takáč, and Olivier Fercoq · 2016
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Distributed coordinate descent method for learning with big data
Peter Richtárik and Martin Takáč · 2016
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On optimal probabilities in stochastic coordinate descent methods
Peter Richtárik and Martin Takáč · 2016
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Parallel coordinate descent methods for big data optimization
Peter Richtárik and Martin Takáč · 2016
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Randomized quasi-Newton updates are linearly convergent matrix inversion algorithms
Robert Mansel Gower and Peter Richtárik · 2017
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Newton sketch: A linear-time optimization algorithm with linear-quadratic convergence
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Convergence analysis of inexact randomized iterative methods
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