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Weighted low rank approximation is a fundamental problem in numerical linear algebra, and it has many applications in machine learning.
Maximum likelihood estimation and factor analysis
Gale Young · 1941
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A weighted-least-squares matrix decomposition method with application to the design of two-dimensional digital filters
Dale J Shpak · 1990
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Weighted low-rank approximation of general complex matrices and its application in the design of 2-d digital filters
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Random vectors in the isotropic position
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New method for weighted low-rank approximation of complex-valued matrices and its application for the design of 2-d digital filters
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Weighted low-rank approximations
Nathan Srebro and Tommi Jaakkola · 2003
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The element-wise weighted total least-squares problem
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Yehuda Koren, Robert Bell, and Chris Volinsky · 2009
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The power of convex relaxation: Near-optimal matrix completion
Emmanuel J. Candès and Terence Tao · 2010
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Low-rank matrix approximation with weights or missing data is np-hard
Nicolas Gillis and François Glineur · 2011
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Can matrix coherence be efficiently and accurately estimated?
Mehryar Mohri and Ameet Talwalkar · 2011
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Exact matrix completion via convex optimization
Emmanuel Candès and Benjamin Recht · 2012
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Low-rank approximation and regression in input sparsity time
Kenneth L Clarkson and David P Woodruff · 2013
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Low-rank matrix completion using alternating minimization
Prateek Jain, Praneeth Netrapalli, and Sujay Sanghavi · 2013
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Faster ridge regression via the subsampled randomized hadamard transform
Yichao Lu, Paramveer Dhillon, Dean P Foster, and Lyle Ungar · 2013
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Local low-rank matrix approximation
Joonseok Lee, Seungyeon Kim, Guy Lebanon, and Yoram Singer · 2013
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Osnap: Faster numerical linear algebra algorithms via sparser subspace embeddings
Jelani Nelson and Huy L Nguyên · 2013
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Universal matrix completion
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Optimal cur matrix decompositions
Christos Boutsidis and David P Woodruff · 2014
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Understanding alternating minimization for matrix completion
Moritz Hardt · 2014
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Glove: Global vectors for word representation
Jeffrey Pennington, Richard Socher, and Christopher D Manning · 2014
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Wemarec: Accurate and scalable recommendation through weighted and ensemble matrix approximation
Chao Chen, Dongsheng Li, Yingying Zhao, Qin Lv, and Li Shang · 2015
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A latent variable model approach to pmi-based word embeddings
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Optimal principal component analysis in distributed and streaming models
Christos Boutsidis, David P. Woodruff, and Peilin Zhong · 2016
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Nearly tight oblivious subspace embeddings by trace inequalities
Michael B Cohen · 2016
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Recovery guarantee of weighted low-rank approximation via alternating minimization
Yuanzhi Li, Yingyu Liang, and Andrej Risteski · 2016
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Weighted low rank approximations with provable guarantees
Ilya Razenshteyn, Zhao Song, and David P Woodruff · 2016
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Fast regression with an ℓ ∞ \ell_{\infty} guarantee
Eric Price, Zhao Song, and David P Woodruff · 2017
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Low rank approximation with entrywise l1-norm error
Zhao Song, David P Woodruff, and Peilin Zhong · 2017
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Sketching for kronecker product regression and p-splines
Huaian Diao, Zhao Song, Wen Sun, and David Woodruff · 2018
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Regularized weighted low rank approximation
Frank Ban, David Woodruff, and Richard Zhang · 2019
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Optimal sketching for kronecker product regression and low rank approximation
Huaian Diao, Rajesh Jayaram, Zhao Song, Wen Sun, and David Woodruff · 2019
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Solving empirical risk minimization in the current matrix multiplication time
Yin Tat Lee, Zhao Song, and Qiuyi Zhang · 2019
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Fast attention requires bounded entries
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On algorithms for weighted low rank approximation
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Average case column subset selection for entrywise ℓ 1 \ell_{1} -norm loss
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Towards a zero-one law for column subset selection
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Relative error tensor low rank approximation
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Additive error guarantees for weighted low rank approximation
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Solving linear programs in the current matrix multiplication time
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Local convergence of approximate newton method for two layer nonlinear regression
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A nearly-optimal bound for fast regression with ℓ ∞ \ell_{\infty} guarantee
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Streaming semidefinite programs: o ( n ) o(\sqrt{n}) passes, small space and fast runtime
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The fine-grained complexity of gradient computation for training large language models
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Fast gradient computation for rope attention in almost linear time
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Log-concave sampling from a convex body with a barrier: a robust and unified dikin walk
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Low rank matrix completion via robust alternating minimization in nearly linear time
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On differentially private string distances
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Inverting the leverage score gradient: An efficient approximate newton method
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Solving attention kernel regression problem via pre-conditioner
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A new complexity metric for nonconvex rank-one generalized matrix completion
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An iterative algorithm for rescaled hyperbolic functions regression
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Faster algorithms for structured linear and kernel support vector machines
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Fast and efficient matching algorithm with deadline instances
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