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To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation.
Positive definite functions on spheres
Schoenberg, I · 1988
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An elementary proof of a theorem of johnson and lindenstrauss
Dasgupta, S. and Gupta, A · 2003
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Approximate nearest neighbors and the fast johnson-lindenstrauss transform
Ailon, N. and Chazelle, B · 2006
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Random features for large-scale kernel machines
Rahimi, A. and Recht, B · 2008
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Improved analysis of the subsampled randomized hadamard transform
Tropp, J. A · 2011
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Sharp analysis of low-rank kernel matrix approximations
Bach, F · 2013
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Concentration inequalities: A nonasymptotic theory of independence
Boucheron, S., Lugosi, G., and Massart, P · 2013
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Fastfood-approximating kernel expansions in loglinear time
Le, Q., Sarlós, T., and Smola, A · 2013
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Fast and scalable polynomial kernels via explicit feature maps
Pham, N. and Pagh, R · 2013
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Subspace embeddings for the polynomial kernel
Avron, H., Nguyen, H., and Woodruff, D · 2014
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Sparser johnson-lindenstrauss transforms
Kane, D. M. and Nelson, J · 2014
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Single pass spectral sparsification in dynamic streams
Kapralov, M., Lee, Y. T., Musco, C., Musco, C., and Sidford, A · 2014
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Fast randomized kernel ridge regression with statistical guarantees
Alaoui, A. and Mahoney, M. W · 2015
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Cohen, M. B., Musco, C., and Pachocki, J · 2016
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Input sparsity time low-rank approximation via ridge leverage score sampling
Cohen, M. B., Musco, C., and Musco, C · 2017
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Recursive sampling for the nystrom method
Musco, C. and Musco, C · 2017
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Oblivious sketching of high-degree polynomial kernels
Ahle, T. D., Kapralov, M., Knudsen, J. B., Pagh, R., Velingker, A., Woodruff, D. P., and Zandieh, A · 2020
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Scaling up kernel ridge regression via locality sensitive hashing
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Faster kernel ridge regression using sketching and preconditioning
Avron, H., Clarkson, K. L., and Woodruff, D. P
Cited in the paper.
Random fourier features for kernel ridge regression: Approximation bounds and statistical guarantees
Avron, H., Kapralov, M., Musco, C., Musco, C., Velingker, A., and Zandieh, A
Cited in the paper.
Zandieh, A., Nouri, N., Velingker, A., Kapralov, M., and Razenshteyn, I · 2020
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