jacobrgardner
commented
4 years ago In general, the nu=integer+1/2 Matern kernels are a lot nicer to work with because they don't require us to evaluate fairly expensive functions like modified Bessel functions, as these kernels reduce to a product of an exponential and a polynomial. The worry is that they basically might become outrageously expensive to evaluate, so people in ML often tend to stick to the int+1/2 setting.
I'm in general not opposed to a general implementation, but it'd require having to implement both the forward and backward pass manually, since I doubt PyTorch supports some of the special functions involved natively.
dhruvbalwada
gpleiss
shc443
🚀 Feature Request
Have a general matern kernel as an option, in addition to the current version which takes in values of nu=1/2, 3/2 and 5/2.
Motivation
I am trying to use GP modeling to estimate spectral properties of (and sometimes also map) 2D or 3D scalar fields from scattered or patchy observations. My understanding is that the Matern kernel (or its combinations) is a good way to approach this problem (https://arxiv.org/abs/1605.01684). For example, a matern kernel with nu=1/2, 3/2 and 5/2 corresponds to a spectral slope of -2, -4 and -6 at high wavenumber. In oceanography, however, it common to find fields where the spectral slopes might be different from these (e.g -5/3 or -3 are more common) or are sometimes a combination (e.g. -3 at some intermediate wavenumber and -5/3 at high wavenumber).
I was wondering if there is a reason why a general kernel has not been implemented (maybe it is very hard to optimize for the value of nu)? or if it is just not there because most communities doing GP modeling don't have a use for it?
Additional context
I am very new to GPs, so any thoughts or guidance would be appreciated.