Add Sparse Geodesic Cost Support

[selmanozleyen]

Here are the steps I planned. I first want to ensure the tests work with this version and I am currently on that step.

• [x] make sure it works on the new commit of ottjax (here: https://github.com/ott-jax/ott/commit/51a658aaa026528a3b9702e3d25c8f7af598cef0)
• [x] don't densify sparse arrays for geodesic costs
• [x] adjust and add tests

In order to comply to new version:

• [x] created new solution files because loaded objects in test_regression_testing had corrupted format.
• [ ] https://github.com/theislab/moscot/issues/678
• [x] https://github.com/ott-jax/ott/issues/509
• [x] https://github.com/theislab/moscot/pull/686
• [x] https://github.com/theislab/moscot/pull/688 (already included in this PR) ping: @MUCDK , @giovp
• [ ] https://github.com/ott-jax/ott/issues/519

[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

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[MUCDK]

in the failing tests, set tau_a, tau_b > 0.5

[giovp]

• try increase the taus for the failing tests for FGW/GW problems
• default to None the n iterations

[selmanozleyen]

I tried all of your suggestions and it only worked when I set the tau's to be 1.0 which is balanced. I checked again and it fails after this https://github.com/ott-jax/ott/commit/41906a2a1ade19aa154189fabd7c159a160c9bf3 commit specifically. I created a PR separately for the setting the defaults to None https://github.com/theislab/moscot/pull/686

[giovp]

ok then i think we need to raise this to @michalk8 because it is not expected

[MUCDK]

agree, can you maybe try to run the example without moscot, but directly with ott-jax @selmanozleyen ? This might help @michalk8

[selmanozleyen]

agree, can you maybe try to run the example without moscot, but directly with ott-jax @selmanozleyen ? This might help @michalk8

@MUCDK ok I created it here https://github.com/ott-jax/ott/issues/519