Implementation of Low Rank Gromov-Wasserstein

[laudavid]

Types of changes

This PR is for the implementation of the Low Rank Gromov-Wasserstein solver.

Paper reference:
Scetbon, M., Peyré, G. & Cuturi, M. (2022).
"Linear-Time GromovWasserstein Distances using Low Rank Couplings and Costs".
In International Conference on Machine Learning (ICML), 2022.

Changes made:

• Created the lowrank_gromov_wasserstein function in ot/lowrank.py
• Created the _flat_product_operator function in ot/lowrank.py since it is needed for the low rank GW solver
• Added tests for each new functions in test\lowrank.py
• Added the lowrank_gromov_wasserstein solver in __init__.py
• Added the paper reference in READ.me
• Created an example for Low Rank GW (plot_lowrank_GW.py) in examples/others

Motivation and context / Related issue

Adding a new low rank solver for gromov-wasserstein.
No existing issue is linked to this PR.

How has this been tested (if it applies)

Tests for each function are available in test_lowrank.py.
The Low Rank GW solver has also been tested by reproducing Figure 2 from the paper.

PR checklist

• I have read the CONTRIBUTING document.
• 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.

[codecov]

Codecov Report

Attention: Patch coverage is 97.19101% with 5 lines in your changes are missing coverage. Please review.

Project coverage is 96.78%. Comparing base (81d7631) to head (a960b28).

Additional details and impacted files

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  Coverage   96.78%   96.78%            
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  Files          81       83     +2     
  Lines       16142    16320   +178     
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+ Hits        15623    15796   +173     
- Misses        519      524     +5     

[cedricvincentcuaz]

Hello @laudavid,
thank you for your nice PR.
Before I go into a detailed review of your code, could you please resolve conflicts with the current master branch and move low-rank GW functions to a new file ot/gromov/_lowrank.py and adjust your code accordingly ?

Best,
Cédric

[laudavid]

Hello @laudavid, thank you for your nice PR. Before I go into a detailed review of your code, could you please resolve conflicts with the current master branch and move low-rank GW functions to a new file ot/gromov/_lowrank.py and adjust your code accordingly ?

Best, Cédric

Hello Cédric,
Thank you for your comment.
I resolved the conflits with the current master branch and moved lr GW to "ot/gromov/_lowrank.py".

Have a nice day,
Laurène.

[cedricvincentcuaz]

Thank you again for this nice PR :)
Here are some remarks to complete your work and clarify few elements.

[cedricvincentcuaz]

Thank you for these updates :) The PR is ready imo, we recently fixed POT testing mechanism. Could you pull the last version of the master branch so that we can proceed with the merge ?