Draft: Implementation Diffusive Gibbs kernel

[jcopo]

Draft PR for #744

Algorithm is implemented. What would be relevant tests to incorporate to this PR?

A few important guidelines and requirements before we can merge your PR:

• If I add a new sampler, there is an issue discussing it already;
• We should be able to understand what the PR does from its title only;
• There is a high-level description of the changes;
• There are links to all the relevant issues, discussions and PRs;
• The branch is rebased on the latest main commit;
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• The code respects the current naming conventions;
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• There are tests covering the changes;
• [ x] The doc is up-to-date;
• If I add a new sampler* I added/updated related examples

Consider opening a Draft PR if your work is still in progress but you would like some feedback from other contributors.

[junpenglao]

Algorithm is implemented. What would be relevant tests to incorporate to this PR?

The test should go in tests/mcmc/test_sampling.py for simple convergent testing, here is an example of adding a new sampler #596

[AdrienCorenflos]

@junpenglao I am a bit dubious we want this algo in the library exactly as it is: at the end of the day it's just MALA for an auxiliary model with an increasing step size.
I am more in favour of implementing a meta proximal-sampler algorithm, which this is an instance of.

[AdrienCorenflos]

I seem to not be the only one thinking the link to proximal samplers is pretty tight.

[junpenglao]

thanks @AdrienCorenflos - i have not read the details or review the implementation, but this is a great early feedback!