Non-Stationary GPs

[willtebbutt]

There are a number of non-stationary kernels that are mentioned in the textbook p260, but which this package doesn't implement:

• Wiener process
• Wiener velocity
• Polynomial

There are also a couple of extra non-stationary kernels discussed in [1] which might be nice to have. I've not gone through the paper in depth though.

Currently this package only implements stationary kernels, but this there aren't really any restrictions in place that require stationarity, it's just that no non-stationary kernels have been implemented yet.

To implement a non-stationary kernel, one would just need to implement an appropriate method of lgssm_components

[1] - https://arxiv.org/pdf/1601.01544.pdf

[mvsoom]

Can a Mercer-expanded kernel k(t,t') = ∑ₘ aₘ ϕₘ(t) ϕₘ(t') be easily converted to a space-state model?

Regression and optimization with the Mercer expansion of order M (i.e. a degenerate GP of rank M) is already linear in the number of observation points N. But the D parameter associated with state-space methods might be much smaller than the M required for a good approximation.

[mvsoom]

I guess what I'm trying to get at is whether the state-space view can yield automatic speedups for Bayesian linear regression with a finite number of basis functions, in the case of 1D inputs (i.e. time). Sorry if I'm too much off-topic!