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Leverage Score Sampling for Tensor Product Matrices in Input Sparsity Time. (arXiv:2202.04515v2 [cs.LG] UPDATED)
June 27, 2022, 1:11 a.m. | David P. Woodruff, Amir Zandieh
cs.LG updates on arXiv.org arxiv.org
We propose an input sparsity time sampling algorithm that can spectrally
approximate the Gram matrix corresponding to the $q$-fold column-wise tensor
product of $q$ matrices using a nearly optimal number of samples, improving
upon all previously known methods by poly$(q)$ factors. Furthermore, for the
important special case of the $q$-fold self-tensoring of a dataset, which is
the feature matrix of the degree-$q$ polynomial kernel, the leading term of our
method's runtime is proportional to the size of the input dataset …
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