Adding Gaussian Process Covariance Functions


#21

This gets a little philosophical – in some sense the question is whether or not there are other processes (probability distributions over Hilbert spaces) with covariance functions K(x1, x2) that marginalize to corresponding probability distributions with the covariance matrices K_{ij} = (x_i, x_j). I believe that only Gaussian processes have this property in which case mathematically we would indeed only ever use these functions for GPs. Even if there are some exceptions, however, I can’t think of a practical use of them otherwise.

Do other people have thoughts?


#23

My understanding is that this is true of any elliptical distribution - it is discussed a bit in Shah et al. 2014, with a reference to Fang et al., to which I don’t have easy access.

My apologies if this is dragging up a dead thread - I saw it on my feed as modified a few days ago even though the last post seems to be from 2/10…


#24

Hi all -

I think this is a good place to post this. Had a good conversation with @syclik today. I’m going to work on developing these covariance functions.

First ARD prior, in the primitives. I’ll first add support for real length_scale[N] and vector[N] length scale arguments, then update rev's cov_exp_quad.hpp, for the length scale arguments for better performance/speed.

If you all have ideas about what I should tackle, suggestions are appreciated!