Redesign of mean function / kernel / cross-kernel evaluation

[willtebbutt]

Problem

There are currently specialised implementations of mean for each MeanFunction, cov and xcov for each Kernel and CrossKernel, potentially for a variety of scenarios. This proposal is aims to sort out the interface to move towards a standard interface for new mean functions and kernels to implement which is more intuitive, and potentially removes some of the duplication in the code base at the minute.

Specification and Implementation

MeanFunctions / Kernels / CrossKernels must implement the following interface:

• be callable. If you have a mean function, you should be able to invoke it on whatever it considers to be a single input (e.g. a Real)
• colwise (a la Distances.jl) functionality.
• pairwise (a la Distances.jl) functionality.

There will be fallbacks implemented for colwise and pairwise which just iterate over the data provided and require only that the mean function / kernel / cross-kernel is callable. It will be possible for any particular mean function / kernel / cross-kernel to override this functionality by implementing a custom version of colwise and / or pairwise. Indeed, it will often be preferable that a (cross-)kernel override the default pairwise implementation (e.g. EQ kernel).

mean, cov, and xcov will then simply have generic implementations in terms of the above. Additionally, it will be trivial to, for example, get only the diagonal / first row of a covariance matrix by the appropriate use of colwise.

[willtebbutt]

This was resolved by a recent merge.