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@@ -15,13 +15,16 @@ It provides the following solvers: * OT Network Flow solver for the linear program/ Earth Movers Distance [1]. * Entropic regularization OT solver with Sinkhorn Knopp Algorithm [2] and stabilized version [9][10] with optional GPU implementation (requires cudamat). -* Non regularized Wasserstein barycenters [16] with LP solver. +* Smooth optimal transport solvers (dual and semi-dual) for KL and squared L2 regularizations [17]. +* Non regularized Wasserstein barycenters [16] with LP solver (only small scale). +* Non regularized free support Wasserstein barycenters [20]. * Bregman projections for Wasserstein barycenter [3] and unmixing [4]. * Optimal transport for domain adaptation with group lasso regularization [5] * Conditional gradient [6] and Generalized conditional gradient for regularized OT [7]. * Linear OT [14] and Joint OT matrix and mapping estimation [8]. * Wasserstein Discriminant Analysis [11] (requires autograd + pymanopt). * Gromov-Wasserstein distances and barycenters ([13] and regularized [12]) +* Stochastic Optimization for Large-scale Optimal Transport (semi-dual problem [18] and dual problem [19]) Some demonstrations (both in Python and Jupyter Notebook format) are available in the examples folder. @@ -29,10 +32,11 @@ Some demonstrations (both in Python and Jupyter Notebook format) are available i If you use this toolbox in your research and find it useful, please cite POT using the following bibtex reference: ``` -@article{flamary2017pot, - title={POT Python Optimal Transport library}, - author={Flamary, R{\'e}mi and Courty, Nicolas}, - year={2017} +@misc{flamary2017pot, +title={POT Python Optimal Transport library}, +author={Flamary, R{'e}mi and Courty, Nicolas}, +url={https://github.com/rflamary/POT}, +year={2017} } ``` @@ -160,6 +164,7 @@ The contributors to this library are: * [Stanislas Chambon](https://slasnista.github.io/) * [Antoine Rolet](https://arolet.github.io/) * Erwan Vautier (Gromov-Wasserstein) +* [Kilian Fatras](https://kilianfatras.github.io/) (Stochastic optimization) This toolbox benefit a lot from open source research and we would like to thank the following persons for providing some code (in various languages): @@ -215,3 +220,11 @@ You can also post bug reports and feature requests in Github issues. Make sure t [15] Peyré, G., & Cuturi, M. (2018). [Computational Optimal Transport](https://arxiv.org/pdf/1803.00567.pdf) . [16] Agueh, M., & Carlier, G. (2011). [Barycenters in the Wasserstein space](https://hal.archives-ouvertes.fr/hal-00637399/document). SIAM Journal on Mathematical Analysis, 43(2), 904-924. + +[17] Blondel, M., Seguy, V., & Rolet, A. (2018). [Smooth and Sparse Optimal Transport](https://arxiv.org/abs/1710.06276). Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics (AISTATS). + +[18] Genevay, A., Cuturi, M., Peyré, G. & Bach, F. (2016) [Stochastic Optimization for Large-scale Optimal Transport](arXiv preprint arxiv:1605.08527). Advances in Neural Information Processing Systems (2016). + +[19] Seguy, V., Bhushan Damodaran, B., Flamary, R., Courty, N., Rolet, A.& Blondel, M. [Large-scale Optimal Transport and Mapping Estimation](https://arxiv.org/pdf/1711.02283.pdf). International Conference on Learning Representation (2018) + +[20] Cuturi, M. and Doucet, A. (2014) [Fast Computation of Wasserstein Barycenters](http://proceedings.mlr.press/v32/cuturi14.html). International Conference in Machine Learning
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