[WIP] Add debiased barycenter (Sinkhorn + convolutional sinkhorn)

[hichamjanati]

Types of changes

• Add debiased barycenter
• Add debiased convolutional barycenter
• Add convolutional barycenter wrapper
• Test "debiased" arg
• Remove while loops -> for loops + break
• Example for debiased barycenters

[agramfort]

just a first set of comments

please pay attention to public API

[agramfort]

so barycenter_sinkhorn_debiased is also a new public function?

[rflamary]

should we put it here? It is not another algorithm to solve the baycenter, it solve a different problem with a diferent solution.

Maybe we should use a debiased parameter in the new API but for now a new public function seems OK.

[hichamjanati]

since it's a new function, and the default 'method' is 'sinkhorn', UX won't change if we make the specific methods funcs private, it's done in the last push.

[codecov]

Codecov Report

Merging #291 (6bd076b) into master (61340d5) will increase coverage by 0.08%.
The diff coverage is n/a.

@@            Coverage Diff             @@
##           master     #291      +/-   ##
==========================================
+ Coverage   93.29%   93.37%   +0.08%     
==========================================
  Files          21       21              
  Lines        4502     4799     +297     
==========================================
+ Hits         4200     4481     +281     
- Misses        302      318      +16     

[agramfort]

pushed some stuff on example. I would need to do a pass on bregman.py maybe too

…

[hichamjanati]

Jax doesn't support item assignment in arrays which is needed in sinkhorn_log functions (for e.g here https://github.com/hichamjanati/POT/blob/5297495058d662a5f4eee779c5b33dd20343cb30/ot/bregman.py#L1499) to avoid using lists.

any obvious workaround for this ? I'm thinking adding a method nx.assign that does a normal subscription with np and torch and the specific .at().set() for jax. WDYT ?

[rflamary]

barycenters are done with a relatively small number of distributions in practice so using lists is not much of a problem here (you can stack after the loop). I agree this is a pain so either you use list (maybe test to see the overhead in practice but it should be small) or you raise a not implemented for jax.

[rflamary]

This is great but we have a bade coverage due to all the parameters. could you put verbose=True on some test and also test for the warning when numItermax is very small?