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Found 10 papers, 7 papers with code
Mirror and Preconditioned Gradient Descent in Wasserstein Space
As the problem of minimizing functionals on the Wasserstein space encompasses many applications in machine learning, different optimization algorithms on $\mathbb{R}^d$ have received their counterpart analog on the Wasserstein space.
Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifolds
On Euclidean spaces, a popular alternative is the Sliced-Wasserstein distance, which leverages a closed-form solution of the Wasserstein distance in one dimension, but which is not readily available on manifolds.
Leveraging Optimal Transport via Projections on Subspaces for Machine Learning Applications
Back to the original Euclidean Sliced-Wasserstein distance between probability measures, we study the dynamic of gradient flows when endowing the space with this distance in place of the usual Wasserstein distance.
Fast Optimal Transport through Sliced Wasserstein Generalized Geodesics
Wasserstein distance (WD) and the associated optimal transport plan have been proven useful in many applications where probability measures are at stake.
Unbalanced Optimal Transport meets Sliced-Wasserstein
In parallel, unbalanced OT was designed to allow comparisons of more general positive measures, while being more robust to outliers.
Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signals
When dealing with electro or magnetoencephalography records, many supervised prediction tasks are solved by working with covariance matrices to summarize the signals.
Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projections
It has been shown beneficial for many types of data which present an underlying hierarchical structure to be embedded in hyperbolic spaces.
Spherical Sliced-Wasserstein
Many variants of the Wasserstein distance have been introduced to reduce its original computational burden.
Subspace Detours Meet Gromov-Wasserstein
In the context of optimal transport methods, the subspace detour approach was recently presented by Muzellec and Cuturi (2019).
Efficient Gradient Flows in Sliced-Wasserstein Space
However, it requires solving a nested optimization problem at each iteration, and is known for its computational challenges, especially in high dimension.
