Explicit Approximations of the Gaussian Kernel
By Andrew Cotter, Joseph Keshet, Nati Srebro. 2011
68 citations recorded by the source corpus.
We investigate training and using Gaussian kernel SVMs by approximating the kernel with an explicit finite- dimensional polynomial feature representation based on the Taylor expansion of the exponential. Although not as efficient as the recently-proposed random Fourier features [Rahimi and Recht, 2007] in terms of the number of features, we show how this polynomial representation can provide a better approximation in terms of the computational cost involved. This makes our "Taylor features" especially attractive for use on very large data sets, in conjunction with online or stochastic training.
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Citations in the corpus
- Memory Efficient Kernel Approximation (2014, methodology): “…independently min where c = 1 , . . . , k , α ( c ) denotes the subvector After computing all the subproblem solutions, we concatenate them to form an approximate solution for the whole problem ¯ α = [ ¯ α (1) , . . . , ¯ α ( k ) ], where ¯ α ( c ) is the optimal solution for the c -th subproblem.”
- Subspace Robust Wasserstein distances (2019, methodology): “(2018b) to approximate Gaussian kernel matrices appearing in the regularized OT problem with Nyström-type factorizations (or exact features using a Taylor expansion (Cotter et al., 2011) as in (Altschuler et al.”