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[WIP] Implementation of FUGW and UCOOT #617

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@6Ulm 6Ulm commented Apr 4, 2024

Types of changes

This PR is dedicated to the implementation of Fused Unbalanced GW and (Fused) Unbalanced COOT.
Since their structures, it is enough to write a common template, then write a wrapper for each divergence.
More precisely, we create a method called fused_unbalanced_cross_spaces_divergence , in which

  • reg_type="independent" corresponds to (Fused) UCOOT. This yields fused_unbalanced_co_optimal_transport method.
  • reg_type="joint" corresponds to FUGW. This yields fused_unbalanced_gromov_wasserstein method.

We also allow for unregularized approximation of FUGW and UCOOT, i.e. $\varepsilon = 0$, thanks to the Majorization-Minization ot.unbalanced.mm_unbalanced and ot.unbalanced.lbfgsb_unbalanced L-BFGS-B methods.

This implementation also allows for $2$ types of marginal penalization: Kullback-Leibler divergence and squared L2 norm. We also allow the cost to be sub-differentiable w.r.t the input matrices and reference distributions. This is implemented in fused_unbalanced_co_optimal_transport2 and fused_unbalanced_gromov_wasserstein methods.

Motivation and context / Related issue

TO DO: write tests and illustrations.

How has this been tested (if it applies)

There are still many missing tests.

PR checklist

  • [ x] I have read the CONTRIBUTING document.
  • [ x] The documentation is up-to-date with the changes I made (check build artifacts).
  • All tests passed, and additional code has been covered with new tests.
  • I have added the PR and Issue fix to the RELEASES.md file.

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