Implement whitened parametrisation

[willtebbutt]

Closes #60

@theogf I've beaten you to making a PR!

[codecov]

Codecov Report

Merging #71 (c1babe5) into master (8b4d798) will increase coverage by 0.12%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master      #71      +/-   ##
==========================================
+ Coverage   90.65%   90.78%   +0.12%     
==========================================
  Files           4        4              
  Lines         246      282      +36     
==========================================
+ Hits          223      256      +33     
- Misses         23       26       +3     

Impacted Files	Coverage Δ
src/sparse_variational.jl	96.84% <100.00%> (-3.16%)	⬇️

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[st--]

Could we not have the whitened/non-whitened q(u) parametrisation as a type parametrisation on SparseVariationalApproximation? It feels weird to have it be an entirely separate type...

[willtebbutt]

Could we not have the whitened/non-whitened q(u) parametrisation as a type parametrisation on SparseVariationalApproximation? It feels weird to have it be an entirely separate type...

Hmmm having both types subtype AbstractSparseVariationalApproximation felt reasonable to me, but I can also see adding a type parameter to SparseVariationalApproximation making sense. Could you elaborate a bit on why you feel it's weird having it as a separate type?

[st--]

Could we not have the whitened/non-whitened q(u) parametrisation as a type parametrisation on SparseVariationalApproximation? It feels weird to have it be an entirely separate type...

Hmmm having both types subtype AbstractSparseVariationalApproximation felt reasonable to me, but I can also see adding a type parameter to SparseVariationalApproximation making sense. Could you elaborate a bit on why you feel it's weird having it as a separate type?

See https://github.com/JuliaGaussianProcesses/ApproximateGPs.jl/pull/71/files#r744641359

I'm also wondering if we could remove a bunch of the code duplication in whitened_/sparse_variational.jl ...

[theogf]

Let's merge conflicts and get that merged?

[willtebbutt]

@theogf please let me know if there's anything else that needs doing.

[theogf]

Sorry I found additional comments. Especially about "Representation"

[willtebbutt]

Docs are failing to build -- for some reason it can't find the docstrings for Centered and NonCentered (I've renamed to use American English locally). Any idea what might be going on?

[theogf]

Are the docs building locally?

[willtebbutt]

Unfortunately not :(

[theogf]

Ok I think I got the right fix for the docs (and pushed it)

[theogf]

The whole reason is that

raw"""
"""
function

looks like it does not properly attribute docs, you need to do:

@doc raw"""
"""
function

for it to work

[willtebbutt]

@st-- @theogf are one of you happy to approve now? I think I've covered all of your suggestions.