Add Gradient based sampler for latent Gaussian models

[AdrienCorenflos]

This is a clean up of the commit history of #228, implementing the marginal sampler of https://rss.onlinelibrary.wiley.com/doi/full/10.1111/rssb.12269.

[codecov]

Codecov Report

Merging #247 (8cd5cc0) into main (e9f8bbe) will increase coverage by 0.07%.
The diff coverage is 100.00%.

❗ Current head 8cd5cc0 differs from pull request most recent head 877bbe8. Consider uploading reports for the commit 877bbe8 to get more accurate results

@@            Coverage Diff             @@
##             main     #247      +/-   ##
==========================================
+ Coverage   98.33%   98.40%   +0.07%     
==========================================
  Files          41       42       +1     
  Lines        1621     1693      +72     
==========================================
+ Hits         1594     1666      +72     
  Misses         27       27              

Impacted Files	Coverage Δ
blackjax/__init__.py	100.00% <ø> (ø)
blackjax/kernels.py	99.43% <100.00%> (+0.02%)	⬆️
blackjax/mcmc/__init__.py	100.00% <100.00%> (ø)
blackjax/mcmc/marginal_latent_gaussian.py	100.00% <100.00%> (ø)
blackjax/optimizers/lbfgs.py	100.00% <0.00%> (ø)
blackjax/vi/pathfinder.py	94.44% <0.00%> (+0.32%)	⬆️

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[junpenglao]

Should we just go with mGrad like in the paper?

[AdrienCorenflos]

It's not very standard...

[AdrienCorenflos]

That being said, if you want to change the name, please do. I'm not attached to it.

[rlouf]

Renamed to mgrad_gaussian. Good to merge, we'll have to revisit the PyTree situation later.