Minimizing a fitted gaussian process

Question

I fitted a computational model with scikit's gaussian process. I would like to find the minimum of the fitted gaussian process.

Davoud

Answer 1

A gaussian process (GP) is a probability distribution over an infinite number functions with an infinite number minima. That is the beauty of a GP, although perhaps in your view a downfall.

What I believe you mean to say is what is the minima of the mean function of a GP. This, unfortunately, is not something we can write down in closed from and hence is probably why scikit would not have it built into the framework.

If you really want to find it I suggest taking a linespace over your input space to sample and try to find a minima (if your input space is low dimensional) or expand the expression for the mean function and differentiate with respect to your input space to try and find the extreme points and global minima (not much use when you have many observations).