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#7 Open

Implement periodic kernel (isotropic and ARD).

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  1. kiudee

This is the first implementation of the periodic kernel proposed in issue #5:


Testing it with a few periodic test functions utilizing the mcmc sampler, the kernel fits them often perfectly after having observed a few (~15 in 1D) datapoints. But often the predicted function can vary wildly in the beginning. I would guess that this behaviour results from the low amount of samples the mcmc sampler collects.

I chose to provide the following parameters:

  • The periodicity p (ISO: params(1), ARD: params(0) to params(n_inputs - 1)) and
  • The length scale l (ISO: params(0), ARD: params(n_inputs) to params(2 * n_inputs - 1))

Let me know if you find something which could be improved.

Comments (1)

  1. Ruben Martinez-Cantin repo owner

    Thanks for the contribution!

    Looking at the literature, the most common way of periodic kernel is equation (4.31) of Rassmusen and Williams http://www.gaussianprocess.org/gpml/chapters/RW.pdf That's a totally different kernel. This one is stationary (although your implementation miss the norm part) and RW is non-stationary.

    Just a couple of details of implementation: - The order of parameters should be consistent. For 1D, ARD and ISO should be equivalent. For consistency with other kernels, the scale should go always first. - The parameter should be l, not l^2. - This is a header file. Put the constant pi in a local scope (e.g.: inside the operator) and never outside the namespace. - I haven't found a periodic kernel with ARD in any paper, but having a different "p" and "l" per dimension can be problematic. RW version is trivial to implement as ARD because it's a just modified SE kernel.