Make ∂H∂r consistent with ∂H∂θ

[ErikQQY]

Fix: #173

While ∂H∂θ return a DualValue containing log density and its gradient, this PR makes ∂H∂r consistent with ∂H∂θ and return a DualValue containing negative energy and momentum.

This PR also change the weird argumnet order of neg_energy(h, r, θ) to neg_energy(h, θ, r), which is more commonly used in this package, e.g. phasepoint(h, θ, r),

[github-actions]

AdvancedHMC.jl documentation for PR #458 is available at:
https://TuringLang.github.io/AdvancedHMC.jl/previews/PR458/

[codecov]

Codecov Report

Attention: Patch coverage is 25.00000% with 6 lines in your changes missing coverage. Please review.

Project coverage is 75.42%. Comparing base (5a562e0) to head (41c04ab).

Files with missing lines	Patch %	Lines
src/riemannian/hamiltonian.jl	0.00%	3 Missing ⚠️
src/riemannian/integrator.jl	0.00%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #458      +/-   ##
==========================================
- Coverage   75.44%   75.42%   -0.03%     
==========================================
  Files          21       21              
  Lines        1230     1233       +3     
==========================================
+ Hits          928      930       +2     
- Misses        302      303       +1     

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[yebai]

Looks good, @ErikQQY. Let's mark this as a breaking release with a clear item in HISTORY.md, since some downstream pages might depend on neg_energy.

[ErikQQY]

HISTORY is updated and a minor version is bumped!

[yebai]

We need to remove these too.

AdvancedHMC.jl/src/riemannian/hamiltonian.jl

Lines 106 to 108 in 5a562e0

	# TODO Make the order of θ and r consistent with neg_energy
	∂H∂θ(h::Hamiltonian, θ::AbstractVecOrMat, r::AbstractVecOrMat) = ∂H∂θ(h, θ)
	∂H∂r(h::Hamiltonian, θ::AbstractVecOrMat, r::AbstractVecOrMat) = ∂H∂r(h, r)

[yebai]

This computes neg_energy but doesn't use it, which has performance implications. Maybe use a different name for functions that returns DualValue, eg: neg_energy_and_∂H∂r.

[ErikQQY]

Ohh, I suddenly realize the riemannian manifold HMC is not included in AdvancedHMC yet, this file is not included in the package, see

AdvancedHMC.jl/src/AdvancedHMC.jl

Line 50 in 5a562e0

include("riemannian/integrator.jl")

I think we might start with #439, which is ready to get in now.

[nsiccha]

This is mainly reshuffling some internal logic, isn't it?

[nsiccha]

I think it actually makes more sense to have ∂H∂θ not return a DualValue. It's kind of fine for Euclidean HMC, where you can get away with this by just saying "oh, ∂H∂θ is actually ∂ℓπ∂θ, and it's returning both the log density and its gradient" - but this doesn't work for Riemannian HMC, as ∂H∂θ != ∂ℓπ∂θ.

[nsiccha]

That being said, it's actually doubly confusing because even in the Euclidean setting, ∂H∂θ is not actually ∂ℓπ∂θ.

Instead, ∂H∂θ returns the log density and its negative gradient, see

AdvancedHMC.jl/src/hamiltonian.jl

Lines 44 to 48 in 41c04ab

	# `∂H∂θ` now returns `(logprob, -∂ℓπ∂θ)`
	function ∂H∂θ(h::Hamiltonian, θ::AbstractVecOrMat)
	res = h.∂ℓπ∂θ(θ)
	return DualValue(res[1], -res[2])
	end

[nsiccha]

I don't think this is a change which decreases the the confusingness of AdvancedHMC - see #483. I'd close this PR in favour of a more exhaustive refactor.