OptimalTransport.jl

This package provides some Julia implementations of algorithms for computational optimal transport, including the Earth-Mover's (Wasserstein) distance, Sinkhorn algorithm for entropically regularized optimal transport as well as some variants or extensions.

Notably, OptimalTransport.jl provides GPU acceleration through CUDA.jl and NNlibCUDA.jl.

This package is inspired by the Python Optimal Transport package.

Example

using OptimalTransport
using Distances

# uniform histograms
μ = fill(1/250, 250)
ν = fill(1/200, 200)

# random cost matrix
C = pairwise(SqEuclidean(), rand(1, 250), rand(1, 200); dims=2)

# regularization parameter
ε = 0.01

# solve entropically regularized optimal transport problem
sinkhorn(μ, ν, C, ε)

Please see the documentation pages for further information.

Related packages

• ExactOptimalTransport.jl: Julia implementation of algorithms for exact unregularized (Kantorovich) optimal transport problems.
• PythonOT.jl: Julia interface for the Python Optimal Transport (POT) package.
• StochasticOptimalTransport.jl: Julia implementation of stochastic optimization algorithms for large-scale optimal transport.

Contributing

Contributions are more than welcome! Please feel free to submit an issue or pull request in this repository.

Acknowledgements

Contributors include:

• Tim Matsumoto (UBC)
• David Widmann (Uppsala)
• Davi Barreira (FGV)
• Stephen Zhang (UBC)

References

• Peyré, G. and Cuturi, M., 2019. Computational optimal transport. Foundations and Trends® in Machine Learning, 11(5-6), pp.355-607.
• Lorenz, D.A., Manns, P. and Meyer, C., 2019. Quadratically regularized optimal transport. Applied Mathematics & Optimization, pp.1-31.
• Rémi Flamary and Nicolas Courty, POT Python Optimal Transport library, https://pythonot.github.io/, 2017
• Chizat, L., Peyré, G., Schmitzer, B. and Vialard, F.X., 2016. Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816.
• Schmitzer, B., 2019. Stabilized sparse scaling algorithms for entropy regularized transport problems. SIAM Journal on Scientific Computing, 41(3), pp.A1443-A1481.