# Learning Gaussian processes which map functions to functions

December 7, 2020 — February 25, 2022

Gaussian

generative

geometry

Hilbert space

how do science

kernel tricks

machine learning

PDEs

physics

regression

spatial

stochastic processes

time series

In which I discover how to learn operators via GPs. I suspect a lot of things break; What is a usable gaussian distribution over a mapping between functions?

It might be handy here to revisit the notation for Bayesian nonparametrics, since we don’t get the same kind of setup as when the distributions in question are finitely parameterised. TBC

## 1 Universal Kriging

Does universal kriging fit in this notebook? (Menafoglio, Secchi, and Rosa 2013) In this setting our observations are function-valued and we wish to spatially interpolate them. TBC. Keyword: Hilbert-Kriging. See Júlio Hoffimann’s Hilbert-Kriging lecture.

## 2 Hilbert-space valued GPs

TBC

## 3 References

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