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We study low rank approximation of tensors, focusing on the tensor train and Tucker decompositions, as well as approximations with tree tensor networks and more general tensor networks.
Tensor rank is np-complete
Johan Håstad · 1990
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Hierarchical singular value decomposition of tensors
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Tensor-train decomposition
Ivan V Oseledets · 2011
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Boaz Barak, Fernando GSL Brandao, Aram W Harrow, Jonathan Kelner, David Steurer, and Yuan Zhou · 2012
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Fast solution of parabolic problems in the tensor train/quantized tensor train format with initial application to the fokker–planck equation
S. V. Dolgov, B. N. Khoromskij, and I. V. Oseledets · 2012
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Changing the topology of tensor networks
Stefan Handschuh · 2012
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Tensors-structured numerical methods in scientific computing: Survey on recent advances
Boris N. Khoromskij · 2012
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Low-rank explicit qtt representation of the laplace operator and its inverse
Vladimir A. Kazeev and Boris N. Khoromskij · 2012
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Sketching structured matrices for faster nonlinear regression
Haim Avron, Vikas Sindhwani, and David P. Woodruff · 2013
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Most tensor problems are np-hard
C. J. Hillar and L.-H. Lim · 2013
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Low-distortion subspace embeddings in input-sparsity time and applications to robust linear regression
Xiangrui Meng and Michael W. Mahoney · 2013
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OSNAP: faster numerical linear algebra algorithms via sparser subspace embeddings
Jelani Nelson and Huy L. Nguyen · 2013
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Fast and scalable polynomial kernels via explicit feature maps
Ninh Pham and Rasmus Pagh · 2013
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Linear Hamilton Jacobi Bellman equations in high dimensions
M K Horowitz, A Damle, and J W Burdick · 2014
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Sparser johnson-lindenstrauss transforms
Daniel M. Kane and Jelani Nelson · 2014
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A practical introduction to tensor networks: Matrix product states and projected entangled pair states
Román Orús · 2014
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Sketching as a tool for numerical linear algebra
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Dimensionality reduction for k-means clustering and low rank approximation
Michael B. Cohen, Sam Elder, Cameron Musco, Christopher Musco, and Madalina Persu · 2015
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Input sparsity and hardness for robust subspace approximation
Kenneth L. Clarkson and David P. Woodruff · 2015
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Polynomial chaos expansion of random coefficients and the solution of stochastic partial differential equations in the tensor train format
Sergey Dolgov, Boris N. Khoromskij, Alexander Litvinenko, and Hermann G. Matthies · 2015
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Efficient high-dimensional stochastic optimal motion control using tensor-train decomposition
Alex Gorodetsky, Sertac Karaman, and Youssef Marzouk · 2015
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Sublinear time numerical linear algebra for structured matrices
Xiaofei Shi and David P. Woodruff · 2019
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Relative error tensor low rank approximation
Zhao Song, David P. Woodruff, and Peilin Zhong · 2019
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Oblivious sketching of high-degree polynomial kernels
Thomas D. Ahle, Michael Kapralov, Jakob Bæk Tejs Knudsen, Rasmus Pagh, Ameya Velingker, David P. Woodruff, and Amir Zandieh · 2020
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Contracting projected entangled pair states is average-case hard
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Projection-cost-preserving sketches: Proof strategies and constructions
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Randomized algorithms for low-rank tensor decompositions in the tucker format
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Streaming and distributed algorithms for robust column subset selection
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In-database regression in input sparsity time
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A sampling-based method for tensor ring decomposition
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