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• W3029333834 abstract "We generalize random Fourier features, that usually require kernel functions to be both stationary and positive definite (PD), to a more general range of non-stationary or/and non-PD kernels, e.g., dot-product kernels on the unit sphere and a linear combination of positive definite kernels. Specifically, we find that the popular neural tangent kernel in two-layer ReLU network, a typical dot-product kernel, is shift-invariant but not positive definite if we consider $ell_2$-normalized data. By introducing the signed measure, we propose a general framework that covers the above kernels by associating them with specific finite Borel measures, i.e., probability distributions. In this manner, we are able to provide the first random features algorithm to obtain unbiased estimation of these kernels. Experiments on several benchmark datasets verify the effectiveness of our algorithm over the existing methods. Last but not least, our work provides a sufficient and necessary condition, which is also computationally implementable, to solve a long-lasting open question: does any indefinite kernel have a positive decomposition?" @default.
• W3029333834 created "2020-06-05" @default.
• W3029333834 creator A5016703530 @default.
• W3029333834 creator A5018369444 @default.
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• W3029333834 date "2020-05-30" @default.
• W3029333834 modified "2023-09-27" @default.
• W3029333834 title "Generalizing Random Fourier Features via Generalized Measures." @default.
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• W3029333834 hasPublicationYear "2020" @default.
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