Simulating Gaussian processes

March 17, 2022 — March 17, 2022

Gaussian
Hilbert space
kernel tricks
Lévy processes
nonparametric
regression
spatial
stochastic processes
time series

Assumed audience:

ML people

How can I simulate a Gaussian Processes with a given covariance? Handy in GP regression, especially GP functional regression and spatial statistics.

Historical overview in Liu et al. (2019).

Figure 1

1 Krylov subspace methods

The Lanczos trick works here.

TBC

2 Random projection

TBC

3 Langevin dynamics

See GP samplings via Langevin dynamics

4 Lattice tricks

On lattices, we can make some computational shortcuts. See GP simulation on lattices.

5 Basis tricks

TBD

6 Simulating from posterior GPs

Probably many tricks, but I know of pathwise GPs.

7 Incoming

8 References

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