Probabilistic methods of linear algebra and Big Data
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Drineas P., Mahoney M. W., Muthukrishnan S., Sarlos T. Faster Least Squares Approximation https://arxiv.org/abs/0710.1435
Avron H., Maymounkov P., Toledo S. Blendenpik: Supercharging LAPACK's Least-Squares Solver https://doi.org/10.1137/090767911
Mahoney M. W. Randomized algorithms for matrices and data https://arxiv.org/abs/1104.5557
N. Benjamin Erichson, Peng Zheng, Krithika Manohar, Steven L. Brunton, J. Nathan Kutz, Aleksandr Y. Aravkin. Sparse Principal Component Analysis via Variable Projection. https://arxiv.org/abs/1804.00341
J. A. Tropp, A. Yurtsever, M. Udell, and V. Cevher. “Fixed-rank approximation of a positive-semidefinite matrix from streaming data”. In: Advances in Neural Information Processing Systems. Ed. by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett. Vol. 30. https://arxiv.org/abs/1706.05736
S. Voronin and P.-G. Martinsson. “Efficient algorithms for CUR and interpolative matrix decompositions”. In: Advances in Computational Mathematics 43.3 (Nov. 2016), pp. 495–516. https://arxiv.org/abs/1412.8447
Y. Dong and P.-G. Martinsson. Simpler is better: A comparative study of randomized algorithms for computing the CUR decomposition. 2021. https://arxiv.org/abs/2104.05877
N. Halko, P. G. Martinsson, and J. A. Tropp. Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions. https://arxiv.org/abs/0909.4061
Erichson N. B., Voronin S., Brunton S. L., Kutz J. N. Randomized Matrix Decompositions Using R. https://arxiv.org/abs/1608.02148
Ootomo H., Yokota R. Mixed-Precision Random Projection for RandNLA on Tensor Cores https://arxiv.org/abs/2304.04612
Filip Hanzely, Konstantin Mishchenko, and Peter Richtárik. SEGA: Variance reduction via gradient sketching. Advances in Neural Information Processing Systems, 31, 2018. https://arxiv.org/abs/1809.03054
Daniel Rothchild, Ashwinee Panda, Enayat Ullah, Nikita Ivkin, Ion Stoica, Vladimir Braverman, Joseph Gonzalez, and Raman Arora. Fetchsgd: Communication-efficient federated learning with sketching. In International Conference on Machine Learning, pages 8253–8265. PMLR, 2020. https://arxiv.org/abs/2007.07682
Deanna Needell, Rachel Ward, and Nati Srebro. Gradient descent, weighted sampling, and the randomized Kaczmarz algorithm. Advances in neural information processing systems. https://arxiv.org/abs/1310.5715
Alon Gonen, Francesco Orabona, and Shai Shalev-Shwartz. Solving ridge regression using sketched preconditioned SVRG. https://arxiv.org/abs/1602.02350
Robert Gower, Nicolas Le Roux, and Francis Bach. Tracking the gradients using the Hessian: A new look at variance reducing stochastic methods. In International Conference on Artificial Intelligence and Statistics, pages 707–715. PMLR, 2018. https://arxiv.org/abs/1710.07462
Murray R., Demmel J., Mahoney M. W., Erichson N. B., Melnichenko M., Malik O. A., Grigori L., Luszczek P., Dereziński M., Lopes M. E., Liang T., Luo H., Dongarra J. Randomized Numerical Linear Algebra: A Perspective on the Field With an Eye to Software. https://arxiv.org/abs/2302.11474
T. Sarlos. “Improved approximation algorithms for large matrices via random projections”. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS). FOCS ’06. USA: IEEE Computer Society, 2006, pp. 143–152. isbn: 0769527205. DOI: 10.1109/FOCS.2006.37
Hitczenko P., Kwapień S. On the Rademacher series. Probability in Banach Spaces. Progress in Probability. Т. 35. С. 31–36. DOI: 10.1007/978-1-4612-0253-0_2
D. P. Woodruff. “Sketching as a tool for numerical linear algebra”. In: Found. Trends Theor. Comput. Sci. 10.1–2 (Oct. 2014), pp. 1–157. https://arxiv.org/abs/1411.4357
V. Rokhlin and M. Tygert. “A fast randomized algorithm for overdetermined linear least-squares regression”. In: Proceedings of the National Academy of Sciences 105.36 (Sept. 2008), pp. 13212–13217. DOI: 10.1073/pnas.080486910
A. Ben-Israel and T.N.E. Greville. Generalized Inverses: Theory and Applications. SpringerVerlag, New York, 2003. DOI: 10.1007/b97366
M. E. Lopes, S. Wang, and M. Mahoney. “Error estimation for randomized least-squares algorithms via the bootstrap”. In: Proceedings of the 35th International Conference on Machine Learning (ICML). Ed. by J. Dy and A. Krause. Vol. 80. Proceedings of Machine Learning Research. PMLR, July 2018, pp. 3217–3226. https://arxiv.org/abs/1803.08021
D. M. Kane and J. Nelson. “Sparser Johnson-Lindenstrauss Transforms”. In: Proceedings of the 2012 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). https://arxiv.org/abs/1012.1577
Lloyd N. Trefethen и David Bau III. “Numerical Linear Algebra”. (1997) DOI: https://doi.org/10.1137/1.9780898719574
C. C. Paige and M. A. Saunders. “LSQR: an algorithm for sparse linear equations and sparse least squares”. In: ACM Trans. Math. Softw. 8.1 (Mar. 1982), pp. 43–71. DOI: 10.1145/355984.355989
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