[WIP] CO-Optimal Transport

Author: 6Ulm

README.md

@@ -292,4 +292,6 @@ Dictionary Learning](https://arxiv.org/pdf/2102.06555.pdf), International Confer
 
 [42] Delon, J., Gozlan, N., and Saint-Dizier, A. [Generalized Wasserstein barycenters between probability measures living on different subspaces](https://arxiv.org/pdf/2105.09755). arXiv preprint arXiv:2105.09755, 2021.
 
-[43]  Álvarez-Esteban, Pedro C., et al. [A fixed-point approach to barycenters in Wasserstein space.](https://arxiv.org/pdf/1511.05355.pdf) Journal of Mathematical Analysis and Applications 441.2 (2016): 744-762.
+[43] Álvarez-Esteban, Pedro C., et al. [A fixed-point approach to barycenters in Wasserstein space.](https://arxiv.org/pdf/1511.05355.pdf) Journal of Mathematical Analysis and Applications 441.2 (2016): 744-762.
+
+[44] Redko, I., Vayer, T., Flamary, R., and Courty, N. (2020). [CO-Optimal Transport](https://proceedings.neurips.cc/paper/2020/file/cc384c68ad503482fb24e6d1e3b512ae-Paper.pdf). Advances in Neural Information Processing Systems, 33.

RELEASES.md

@@ -10,6 +10,7 @@
 - New API for OT solver using function `ot.solve` (PR #388)
 - Backend version of `ot.partial` and `ot.smooth` (PR #388)
 - Added argument for warmstart of dual vectors in Sinkhorn-based methods in `ot.bregman` (PR #437)
+- Added CO-Optimal Transport solver and example (PR #)
 
 #### Closed issues
 

ot/__init__.py

@@ -36,6 +36,7 @@
 from . import factored
 from . import solvers
 from . import gaussian
+from . import coot
 
 # OT functions
 from .lp import emd, emd2, emd_1d, emd2_1d, wasserstein_1d
@@ -49,6 +50,7 @@
 from .weak import weak_optimal_transport
 from .factored import factored_optimal_transport
 from .solvers import solve
+from .coot import co_optimal_transport, co_optimal_transport2
 
 # utils functions
 from .utils import dist, unif, tic, toc, toq
@@ -64,4 +66,4 @@
            'gromov_wasserstein', 'gromov_wasserstein2', 'gromov_barycenters', 'fused_gromov_wasserstein', 'fused_gromov_wasserstein2',
             'max_sliced_wasserstein_distance', 'weak_optimal_transport',
             'factored_optimal_transport', 'solve',
-           'smooth', 'stochastic', 'unbalanced', 'partial', 'regpath', 'solvers']
+            'smooth', 'stochastic', 'unbalanced', 'partial', 'regpath', 'solvers', 'coot', 'co_optimal_transport', 'co_optimal_transport2']