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Fast Sketching of Polynomial Kernels of Polynomial Degree
Zhao Song · David Woodruff · Zheng Yu · Lichen Zhang

Thu Jul 22 07:25 PM -- 07:30 PM (PDT) @
Kernel methods are fundamental in machine learning, and faster algorithms for kernel approximation provide direct speedups for many core tasks in machine learning. The polynomial kernel is especially important as other kernels can often be approximated by the polynomial kernel via a Taylor series expansion. Recent techniques in oblivious sketching reduce the dependence in the running time on the degree $q$ of the polynomial kernel from exponential to polynomial, which is useful for the Gaussian kernel, for which $q$ can be chosen to be polylogarithmic. However, for more slowly growing kernels, such as the neural tangent and arc cosine kernels, $q$ needs to be polynomial, and previous work incurs a polynomial factor slowdown in the running time. We give a new oblivious sketch which greatly improves upon this running time, by removing the dependence on $q$ in the leading order term. Combined with a novel sampling scheme, we give the fastest algorithms for approximating a large family of slow-growing kernels.

Author Information

Zhao Song (UT-Austin & University of Washington)
David Woodruff (Carnegie Mellon University)
Zheng Yu (Princeton University)
Lichen Zhang (Carnegie Mellon University)

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