WIP: Feature: Wasserstein Barycenter Transport

[eddardd]

Related to Issue #291

This PR adds the algorithm Wasserstein Barycenter Transport [29] to the SKADA benchmark. I also took the liberty of implementing a linearized version using affine OT mappings as proposed by [7]. Besides these 2 algorithms, I added 2 examples,

• plot_joint_wasserstein_barycenter.py, which focuses exclusively on the computation of joint Wasserstein barycenters as in [38]
• plot_multi_source_da, which compares the linearlized and empirical versions of WBT in the context of multi-source domain adaptation.

I also added references to two papers [38, 39], which are related to the computation of barycenters of Gaussian measures and feature-label joint empirical measures

Need for help

Before merging, I need to fix a few issues, notably concerning the documentation. I faced the following errors while running make html on skada/docs,

..\..\examples\plot_method_comparison.py unexpectedly failed to execute correctly:

    Traceback (most recent call last):
      File "C:\Users\eduar\Documents\repos\skada\examples\plot_method_comparison.py", line 193, in <module>
        clf.fit(X, y, sample_domain=sample_domain)
      File "C:\Users\eduar\.conda\envs\OptimalTransport\lib\site-packages\sklearn\base.py", line 1152, in wrapper
        return fit_method(estimator, *args, **kwargs)
      File "C:\Users\eduar\.conda\envs\OptimalTransport\lib\site-packages\sklearn\pipeline.py", line 422, in fit
        fit_params_steps = self._check_fit_params(**fit_params)
      File "C:\Users\eduar\.conda\envs\OptimalTransport\lib\site-packages\sklearn\pipeline.py", line 341, in _check_fit_params
        raise ValueError(
    ValueError: Pipeline.fit does not accept the sample_domain parameter. You can pass parameters to specific steps of your pipeline using the stepname__parameter format, e.g. `Pipeline.fit(X, y, logisticregression__sample_weight=sample_weight)`.

These errors were reproduced on nearly every instance where LogisticRegression is called with sample_domain.

References

[7] Flamary, R., Lounici, K., & Ferrari, A. (2019). Concentration bounds for linear monge mapping estimation and optimal transport domain adaptation. arXiv preprint arXiv:1905.10155.

[29] Montesuma, Eduardo Fernandes, and Fred Maurice Ngole Mboula. "Wasserstein barycenter for multi-source domain adaptation." In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 16785-16793. 2021.

[38] Álvarez-Esteban, Pedro C., et al. A fixed-point approach to barycenters in Wasserstein space. Journal of Mathematical Analysis and Applications 441.2 (2016): 744-762

[39] Montesuma, Eduardo, Fred Maurice Ngole Mboula, and Antoine Souloumiac. Multi-source domain adaptation through dataset dictionary learning in wasserstein space. ECAI 2023. IOS Press, 2023. 1739-1746.

[tgnassou]

Hi @eddardd , I'm happy to see your PR! Let me know if you need help or anything. I can do a review whenever you want;)

[tgnassou]

For the CI, your new example multi_source_da misses docstrings at the beginning of the files. Look at the other examples if you need help.

I think you have some linter problem, did you use pre commit ?

And don't forget to add test for your new methods !

[rflamary]

Hello @eddardd

The Linear Mapping DA is already implemented in:
https://scikit-adaptation.github.io/gen_modules/skada.LinearOTMappingAdapter.html#skada.LinearOTMappingAdapter

[rflamary]

also the multi sourcer case with gaussian barycenter is already mplemented here:

skada/skada/_mapping.py

Line 552 in 14f20fe

class MultiLinearMongeAlignmentAdapter(BaseAdapter):