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Table 1 Examples of popular shift-invariant kernels and the corresponding sampling distributions

From: SDRNF: generating scalable and discriminative random nonlinear features from data

Kernel name k() p(w)
Gaussian \(\mathrm {e}^{\left (-\frac {||\bigtriangleup ||^{2}_{2}}{2}\right)}\) \((2\pi)^{-\frac {D}{2}}\mathrm {e}^{\left (-\frac {||w||^{2}_{2}}{2}\right)}\)
Laplacian \(\mathrm {e}^{\left (-||\bigtriangleup ||_{1}\right)}\) \(\prod _{d} \frac {1}{\pi \left (1+{w^{2}_{d}}\right)}\)