Explicit Feature Map Approximations of Kernel Functions

[EthanJamesLew]

I've been using explicit feature map approximations of kernels (based on references below). I've made my own implementations for the work so far, but it would be nice to see some of these common methods--i.e., random fourier features, quadrature methods---land in a polished package like GPy and plug seamlessly into the GP methods. Some questions

• does these kernels exist somewhere?
• If the answer to the above is no: would having these kernels be of interest to the GPy team or the community?

If there is interest, I can contribute these kernels; I see there are some development instructions in the main README.md. I imagine that this would involved adding kernels to GPy.kern with some methods to approximate existing kernels like RBF to an explicit form.

References

Rahimi, A., & Recht, B. (2007). Random features for large-scale kernel machines. Advances in neural information processing systems, 20.

Li, K., & Principe, J. C. (2019). No-trick (treat) kernel adaptive filtering using deterministic features. arXiv preprint arXiv:1912.04530.

Dao, T., De Sa, C. M., & Ré, C. (2017). Gaussian quadrature for kernel features. Advances in neural information processing systems, 30.