Unbalance FGW full rank marginal normalization issue

[giovp]

xlink #686

[selmanozleyen]

Ok just to update this issue waits for ott-jax/ott#519 to be closed and then we'd need to unskip the test related in

class TestSpatioTemporalProblem:
...
@pytest.mark.skip(reason="unbalanced does not work yet: https://github.com/ott-jax/ott/issues/519")
    def test_solve_unbalanced(self, adata_spatio_temporal: AnnData):

[MUCDK]

Hi @selmanozleyen ,

What's the current state on this?

[selmanozleyen]

@MUCDK its still the same, it is an error from the ott-jax side and the issue is linked above

[HarryZhang1224]

Hi @MUCDK @selmanozleyen,

Is unbalanced FGW still not supported?

Thanks

[MUCDK]

Hi @HarryZhang1224 ,

Unfortunately, this is an issue inherent to entropic FGW, see ott-jax/ott#519.
Hence, you can run it in an unbalanced way, but make sure that the marginals sum up to 1.0.

[HarryZhang1224]

Hi @HarryZhang1224 ,

Unfortunately, this is an issue inherent to entropic FGW, see ott-jax/ott#519. Hence, you can run it in an unbalanced way, but make sure that the marginals sum up to 1.0.

@MUCDK Thanks for the quick reply! Specifying the marginals a and b to sum to 1 worked. Is there a numerical instability issue with unbalanced + entropic FGW? For large values of fused penalty, the returned coupling has all nan, and sometimes it also seems to interact with epsilon.

[MUCDK]

Yes, unfortunately, GW and FGW are sometimes hard to optimise. Normally, increasing epsilon would help, as this turns the problem near-convex, see

Gabriel Rioux, Ziv Goldfeld, and Kengo Kato. Entropic gromov-wasserstein distances: Stability,
algorithms, and distributional limits. arXiv preprint arXiv:2306.00182, 2023. 4