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Almost Optimal Tensor Sketch [article]

Thomas D. Ahle, Jakob B. T. Knudsen
2019 arXiv   pre-print
The factors of λ, ε^-2 and log1/δ can all be shown to be necessary making our sketch optimal up to log factors.  ...  Combining these two results give an efficient sketch for tensors of any size.  ...  However the direct applications of the theorem doesn't use that we know how to efficiently sketch order 2 tensors. While the number of rows are near optimal, the application time suffers.  ... 
arXiv:1909.01821v1 fatcat:xkv54j6wbzb6nipamsf557wkqm

Online sketching for big data subspace learning

Morteza Mardani, Georgios B. Giannakis
2015 2015 23rd European Signal Processing Conference (EUSIPCO)  
To cope with these challenges, the present paper brings forth a novel real-time sketching scheme that exploits the correlations across data stream to learn a latent subspace based upon tensor PARAFAC decomposition  ...  Sketching (a.k.a. subsampling) high-dimensional data is a crucial task to facilitate data acquisition process e.g., in magnetic resonance imaging, and to render affordable 'Big Data' analytics.  ...  {A[ − 1], B[ −1]} to solve the inner optimization which yieldsˆ= arg min (A[ −1], B[ −1]; ).  ... 
doi:10.1109/eusipco.2015.7362837 dblp:conf/eusipco/MardaniG15 fatcat:mt2plztsvfebrajmtaornol2ou

Tight Dimensionality Reduction for Sketching Low Degree Polynomial Kernels

Michela Meister, Tamás Sarlós, David P. Woodruff
2019 Neural Information Processing Systems  
This is the first high probability sketch for tensor products that has optimal sketch size and can be implemented in m • q i=1 nnz(x i ) time, where nnz(x i ) is the number of non-zero entries of x i .  ...  We give a new analysis of this sketch, providing nearly optimal bounds.  ...  Tensorized Random Projection's max error is almost an order of magnitude smaller at the same sketch size.  ... 
dblp:conf/nips/MeisterSW19 fatcat:36pxkzd57rhvpmdgayypicdbzi

Fast Alignment-Free Similarity Estimation By Tensor Sketching [article]

Amir Joudaki, Andre Kahles, Gunnar Ratsch
2020 bioRxiv   pre-print
In our experiments, Tensor Sketch had 0.88 Spearman's rank correlation with the exact edit distance, almost doubling the 0.466 correlation of the closest competitor while running 8.8 times faster.  ...  Our tensor-sketching technique's main advantages are three-fold: 1) Tensor Sketch has higher accuracy than any of the other assessed sketching methods used in practice. 2) All sketches can be computed  ...  For integer D, tensor sketch Φ : R m t → R D sketches an m t -dimensional tensor into R D .  ... 
doi:10.1101/2020.11.13.381814 fatcat:fypyvor7rza3xjmncej5kpjr4u

Tensor-structured sketching for constrained least squares [article]

Ke Chen, Ruhui Jin
2021 arXiv   pre-print
In this work, we utilize a general class of row-wise tensorized sub-Gaussian matrices as sketching matrices in constrained optimizations for the sketching design's compatibility with tensor structures.  ...  In the context of unconstrained linear regressions, we obtain an optimal estimate for the sketching dimension.  ...  Our guarantee for the row-wise tensor sub-Gaussian sketch (12) almost matches the optimal result for unstructured sub-Gaussian developed in [37] .  ... 
arXiv:2010.09791v3 fatcat:57uiq2qu75hxfjgewnk3avl7pe

Higher-order Count Sketch: Dimensionality Reduction That Retains Efficient Tensor Operations [article]

Yang Shi, Animashree Anandkumar
2019 arXiv   pre-print
We apply HCS to tensorized neural networks where we replace fully connected layers with sketched tensor operations.  ...  We derive efficient (approximate) computation of various tensor operations such as tensor products and tensor contractions directly on the sketched data.  ...  Figure 2 : 2 Fibers and slices of a third-order tensor. Ma et al. (2019); Shi et al. (2016) optimize tensor matrix contraction on GPUs by avoiding data transformation.  ... 
arXiv:1901.11261v5 fatcat:75kha2ajufg3tjchuny7hzad7q

Streaming Tensor Train Approximation [article]

Daniel Kressner, Bart Vandereycken, Rik Voorhaar
2022 arXiv   pre-print
Our results show that STTA can be expected to attain a nearly optimal approximation error if the sizes of the sketches are suitably chosen.  ...  STTA accesses 𝒯 exclusively via two-sided random sketches of the original data, making it streamable and easy to implement in parallel – unlike existing deterministic and randomized tensor train approximations  ...  By the assumptions, both T ≤µ X µ and Y µ T ≤µ X µ have full column rank almost surely.  ... 
arXiv:2208.02600v1 fatcat:o6o5ar7mhzh77dbe2cbc3tstmm

A descriptor for large scale image retrieval based on sketched feature lines [article]

Mathias Eitz, Kristian Hildebrand, Tamy Boubekeur, Marc Alexa
2009 Sketch-Based Interfaces and Modeling  
We address the problem of large scale sketch based image retrieval, searching in a database of over a million images.  ...  The proposed descriptor is constructed such that both the full color image and the sketch undergo exactly the same preprocessing steps.  ...  As x T guv attains a maximum if x guv we pose the definition of x as the following optimization x = arg max x =1 ∑ (u,v)∈Ci j x T guv 2 . ( 6 ) Figure 2 : The tensor descriptor subdivides the image into  ... 
doi:10.2312/sbm/sbm09/029-036 fatcat:5t63veksyzam5mtjvy3h5ltjty

A descriptor for large scale image retrieval based on sketched feature lines

Mathias Eitz, Kristian Hildebrand, Tamy Boubekeur, Marc Alexa
2009 Proceedings of the 6th Eurographics Symposium on Sketch-Based Interfaces and Modeling - SBIM '09  
We address the problem of large scale sketch based image retrieval, searching in a database of over a million images.  ...  The proposed descriptor is constructed such that both the full color image and the sketch undergo exactly the same preprocessing steps.  ...  As x T guv attains a maximum if x guv we pose the definition of x as the following optimization x = arg max x =1 ∑ (u,v)∈Ci j x T guv 2 . (6) Figure 2 : The tensor descriptor subdivides the image into  ... 
doi:10.1145/1572741.1572747 fatcat:33s4g4se5nhrbd7qduv2ad7gue

Parallel algorithms for computing the tensor-train decomposition [article]

Tianyi Shi, Maximilian Ruth, Alex Townsend
2021 arXiv   pre-print
The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in molecular simulations, high-order correlation functions, and optimization.  ...  For example, for a d-dimension tensor in ℝ^n×...× n, a two-sided sketching algorithm PSTT2 is shown to have a memory complexity of 𝒪(n^⌊ d/2 ⌋), improving upon 𝒪(n^d-1) from previous algorithms.  ...  This criterion can be satisfied when the TT rank of X is optimal.  ... 
arXiv:2111.10448v1 fatcat:5wkv6t2ar5dxxpk4sv7g27uuy4

Fast and scalable polynomial kernels via explicit feature maps

Ninh Pham, Rasmus Pagh
2013 Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '13  
Empirically, Tensor Sketching achieves higher accuracy and often runs orders of magnitude faster than the state-of-the-art approach for large-scale real-world datasets.  ...  Sketching, for approximating any polynomial kernel in O(n(d + D log D)) time.  ...  So we have to use large D for almost orthogonal data points to achieve a good approximation.  ... 
doi:10.1145/2487575.2487591 dblp:conf/kdd/PhamP13 fatcat:ixrmgagtsbfcfifa6ysrgjzmle

Efficient Exploration of Hamiltonian Parameter Space for Optimal Control of Non-Markovian Open Quantum Systems

Gerald E. Fux, Eoin P. Butler, Paul R. Eastham, Brendon W. Lovett, Jonathan Keeling
2021 Physical Review Letters  
We present a general method to efficiently design optimal control sequences for non-Markovian open quantum systems, and illustrate it by optimizing the shape of a laser pulse to prepare a quantum dot in  ...  The optimization of control procedures for quantum systems with strong coupling to structured environments-where time-local descriptions fail-is a computationally challenging task.  ...  Pollock for insightful discussions on the process tensor framework. G. E. F. acknowledges support from EPSRC (EP/L015110/1). B. W. L. and J. K. acknowledge support from EPSRC (EP/T014032/1). E. P.  ... 
doi:10.1103/physrevlett.126.200401 pmid:34110219 fatcat:ufan2of2vvayjeaghts6qawx4a

Low-rank nonnegative tensor approximation via alternating projections and sketching [article]

Azamat Sultonov, Sergey Matveev, Stanislav Budzinskiy
2022 arXiv   pre-print
randomized sketching.  ...  We show how to construct nonnegative low-rank approximations of nonnegative tensors in Tucker and tensor train formats.  ...  Some optimality properties of this best-approximation formulation were studied in [20] , viewed as a more general low-rank optimization problem with convex constraints [21, 22] .  ... 
arXiv:2209.02060v1 fatcat:rguezbaegvgsfljpayvjqtcdea

High thermoelectric figure of merit and thermopower in layered perovskite oxides

Vincenzo Fiorentini, Roberta Farris, Edoardo Argiolas, Maria Barbara Maccioni
2019 PHYSICAL REVIEW MATERIALS  
The Seebeck thermopower coefficient is between 200 and 300 μV/K at optimal doping, but can reach nearly 1 mV/K at low doping.  ...  The figure of merit ZT computed with a temperature-dependent relaxation time increases monotonically from just above 1 at room temperature to over 2.5 at 1200 K, at an optimal carrier density of around  ...  FIG. 6 . 6 Components of the ZT , Seebeck (absolute value), electrical conductivity, and electronic thermal conductivity tensors vs. T at optimal n-doping for each T .  ... 
doi:10.1103/physrevmaterials.3.022401 fatcat:j5ioaoky6zc5pec2yg6os6omae

Generative Modeling via Tree Tensor Network States [article]

Xun Tang, Yoonhaeng Hur, Yuehaw Khoo, Lexing Ying
2022 arXiv   pre-print
The proposed method consists of determining the tree topology with Chow-Liu algorithm, and obtaining a linear system of equations that defines the tensor-network components via sketching techniques.  ...  In this paper, we present a density estimation framework based on tree tensor-network states.  ...  In [2, 10, 13] , nonconvex optimization approaches are applied to determine the tensor cores.  ... 
arXiv:2209.01341v1 fatcat:t65ac4qmdbgkbnhthoo3vnc3b4
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