- Author:
- Michael W. Mahoney
Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, largely since matrices are popular structures with which to model data drawn from a wide range of application domains, and the success of this line of work opens the possibility of performing matrix-based computations with truly massive data sets. Originating within theoretical computer science, this work was subsequently extended and applied in important ways by researchers from numerical linear algebra, statistics, applied mathematics, data analysis, and machine learning, as well as domain scientists. Randomized Algorithms for Matrices and Data provides a detailed overview, appropriate for both students and researchers from all of these areas, of recent work on the theory of randomized matrix algorithms as well as the application of those ideas to the solution of practical problems in large-scale data analysis. By focusing on ubiquitous and fundamental problems such as least squares approximation and low-rank matrix approximation that have been at the center of recent developments, an emphasis is placed on a few simple core ideas that underlie not only recent theoretical advances but also the usefulness of these algorithmic tools in large-scale data applications.
Cited By
- Zhang Z, Ji T, Shi H, Li C, Huang Y and Yang L (2023). A Self-Supervised Learning-Based Channel Estimation for IRS-Aided Communication Without Ground Truth, IEEE Transactions on Wireless Communications, 22:8, (5446-5460), Online publication date: 1-Aug-2023.
- Saibaba A, Alexanderian A and Ipsen I (2017). Randomized matrix-free trace and log-determinant estimators, Numerische Mathematik, 137:2, (353-395), Online publication date: 1-Oct-2017.
- Yang J, Chow Y, Ré C and Mahoney M (2017). Weighted SGD for ℓp regression with randomized preconditioning, The Journal of Machine Learning Research, 18:1, (7811-7853), Online publication date: 1-Jan-2017.
- Xu P, Yang J, Roosta-Khorasani F, Ré C and Mahoney M Sub-sampled Newton methods with non-uniform sampling Proceedings of the 30th International Conference on Neural Information Processing Systems, (3008-3016)
- Yang J, Chow Y, Ré C and Mahoney M Weighted SGD for ℓ regression with randomized preconditioning Proceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms, (558-569)
- Ma P, Mahoney M and Yu B (2015). A statistical perspective on algorithmic leveraging, The Journal of Machine Learning Research, 16:1, (861-911), Online publication date: 1-Jan-2015.
Kaltofen E and Yang Z Sparse multivariate function recovery with a high error rate in the evaluations Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation, (280-287)- Meng X and Mahoney M Low-distortion subspace embeddings in input-sparsity time and applications to robust linear regression Proceedings of the forty-fifth annual ACM symposium on Theory of Computing, (91-100)
- Clarkson K, Drineas P, Magdon-Ismail M, Mahoney M, Meng X and Woodruff D The fast cauchy transform and faster robust linear regression Proceedings of the twenty-fourth annual ACM-SIAM symposium on Discrete algorithms, (466-477)
- Mahoney M Approximate computation and implicit regularization for very large-scale data analysis Proceedings of the 31st ACM SIGMOD-SIGACT-SIGAI symposium on Principles of Database Systems, (143-154)
- Chen S, Varma R, Singh A and Kovačcević J A statistical perspective of sampling scores for linear regression 2016 IEEE International Symposium on Information Theory (ISIT), (1556-1560)
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