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Title: User guide — POT Python Optimal Transport 0.9.6 documentation

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Domain: PythonOT.github.io

Links:

POT Python Optimal Transport https://PythonOT.github.io/index.html
POT: Python Optimal Transporthttps://PythonOT.github.io/index.html
Quickstart Guidehttps://PythonOT.github.io/auto_examples/plot_quickstart_guide.html
Examples galleryhttps://PythonOT.github.io/auto_examples/index.html
User guidehttps://PythonOT.github.io/user_guide.html
Why Optimal Transport ?https://PythonOT.github.io/user_guide.html#why-optimal-transport
When to use OThttps://PythonOT.github.io/user_guide.html#when-to-use-ot
Wasserstein distance between distributionshttps://PythonOT.github.io/user_guide.html#wasserstein-distance-between-distributions
OT for mapping estimationhttps://PythonOT.github.io/user_guide.html#ot-for-mapping-estimation
When to use POThttps://PythonOT.github.io/user_guide.html#when-to-use-pot
When not to use POThttps://PythonOT.github.io/user_guide.html#when-not-to-use-pot
Optimal transport and Wasserstein distancehttps://PythonOT.github.io/user_guide.html#optimal-transport-and-wasserstein-distance
Solving optimal transporthttps://PythonOT.github.io/user_guide.html#solving-optimal-transport
Examples of use for ot.emdhttps://PythonOT.github.io/user_guide.html#examples-of-use-for-ot-emd
Computing Wasserstein distancehttps://PythonOT.github.io/user_guide.html#computing-wasserstein-distance
Examples of use for ot.emd2https://PythonOT.github.io/user_guide.html#examples-of-use-for-ot-emd2
Special caseshttps://PythonOT.github.io/user_guide.html#special-cases
Regularized Optimal Transporthttps://PythonOT.github.io/user_guide.html#regularized-optimal-transport
Entropic regularized OThttps://PythonOT.github.io/user_guide.html#entropic-regularized-ot
Examples of use for Sinkhorn algorithmhttps://PythonOT.github.io/user_guide.html#examples-of-use-for-sinkhorn-algorithm
Other regularizationshttps://PythonOT.github.io/user_guide.html#other-regularizations
Quadratic regularizationhttps://PythonOT.github.io/user_guide.html#quadratic-regularization
Examples of use of quadratic regularizationhttps://PythonOT.github.io/user_guide.html#examples-of-use-of-quadratic-regularization
Group Lasso regularizationhttps://PythonOT.github.io/user_guide.html#group-lasso-regularization
Examples of group Lasso regularizationhttps://PythonOT.github.io/user_guide.html#examples-of-group-lasso-regularization
Generic solvershttps://PythonOT.github.io/user_guide.html#generic-solvers
Examples of the generic solvershttps://PythonOT.github.io/user_guide.html#examples-of-the-generic-solvers
Wasserstein Barycentershttps://PythonOT.github.io/user_guide.html#wasserstein-barycenters
Barycenters with fixed supporthttps://PythonOT.github.io/user_guide.html#barycenters-with-fixed-support
Examples of Wasserstein and regularized Wasserstein barycentershttps://PythonOT.github.io/user_guide.html#examples-of-wasserstein-and-regularized-wasserstein-barycenters
An example of convolutional barycenter (ot.bregman.convolutional_barycenter2d) computationhttps://PythonOT.github.io/user_guide.html#an-example-of-convolutional-barycenter-ot-bregman-convolutional-barycenter2d-computation
Barycenters with free supporthttps://PythonOT.github.io/user_guide.html#barycenters-with-free-support
Examples of free support barycenter estimationhttps://PythonOT.github.io/user_guide.html#examples-of-free-support-barycenter-estimation
Monge mapping and Domain adaptationhttps://PythonOT.github.io/user_guide.html#monge-mapping-and-domain-adaptation
Monge Mapping estimationhttps://PythonOT.github.io/user_guide.html#monge-mapping-estimation
Domain adaptation classeshttps://PythonOT.github.io/user_guide.html#domain-adaptation-classes
Examples of the use of OTDA classeshttps://PythonOT.github.io/user_guide.html#examples-of-the-use-of-otda-classes
Unbalanced and partial OThttps://PythonOT.github.io/user_guide.html#unbalanced-and-partial-ot
Unbalanced optimal transporthttps://PythonOT.github.io/user_guide.html#unbalanced-optimal-transport
Examples of Unbalanced OThttps://PythonOT.github.io/user_guide.html#examples-of-unbalanced-ot
Unbalanced Barycentershttps://PythonOT.github.io/user_guide.html#unbalanced-barycenters
Examples of Unbalanced OT barycentershttps://PythonOT.github.io/user_guide.html#examples-of-unbalanced-ot-barycenters
Partial optimal transporthttps://PythonOT.github.io/user_guide.html#partial-optimal-transport
Examples of Partial OThttps://PythonOT.github.io/user_guide.html#examples-of-partial-ot
Gromov Wasserstein and extensionshttps://PythonOT.github.io/user_guide.html#gromov-wasserstein-and-extensions
Gromov Wasserstein(GW)https://PythonOT.github.io/user_guide.html#gromov-wasserstein-gw
Examples of computation of GW, regularized G and FGWhttps://PythonOT.github.io/user_guide.html#examples-of-computation-of-gw-regularized-g-and-fgw
Gromov Wasserstein barycentershttps://PythonOT.github.io/user_guide.html#gromov-wasserstein-barycenters
Examples of GW, regularized G and FGW barycentershttps://PythonOT.github.io/user_guide.html#examples-of-gw-regularized-g-and-fgw-barycenters
Other applicationshttps://PythonOT.github.io/user_guide.html#other-applications
Wasserstein Discriminant Analysishttps://PythonOT.github.io/user_guide.html#wasserstein-discriminant-analysis
Examples of the use of WDAhttps://PythonOT.github.io/user_guide.html#examples-of-the-use-of-wda
Solving OT with Multiple backends on CPU/GPUhttps://PythonOT.github.io/user_guide.html#solving-ot-with-multiple-backends-on-cpu-gpu
How it workshttps://PythonOT.github.io/user_guide.html#how-it-works
GPU accelerationhttps://PythonOT.github.io/user_guide.html#gpu-acceleration
List of compatible Backendshttps://PythonOT.github.io/user_guide.html#list-of-compatible-backends
FAQhttps://PythonOT.github.io/user_guide.html#faq
Referenceshttps://PythonOT.github.io/user_guide.html#references
API and moduleshttps://PythonOT.github.io/all.html
Releaseshttps://PythonOT.github.io/releases.html
Contributorshttps://PythonOT.github.io/contributors.html
Contributing to POThttps://PythonOT.github.io/contributing.html
Code of conducthttps://PythonOT.github.io/code_of_conduct.html
POT Python Optimal Transporthttps://PythonOT.github.io/index.html
https://PythonOT.github.io/index.html
View page sourcehttps://PythonOT.github.io/_sources/user_guide.rst.txt
https://PythonOT.github.io/user_guide.html#user-guide
the bookhttps://arxiv.org/pdf/1803.00567.pdf
[15]https://PythonOT.github.io/user_guide.html#id66
OTML tutorialhttps://remi.flamary.com/cours/tuto_otml.html
Backend sectionhttps://PythonOT.github.io/user_guide.html#solving-ot-with-multiple-backends
https://PythonOT.github.io/user_guide.html#why-optimal-transport
https://PythonOT.github.io/user_guide.html#when-to-use-ot
Solving optimal transporthttps://PythonOT.github.io/user_guide.html#kantorovitch-solve
https://PythonOT.github.io/user_guide.html#wasserstein-distance-between-distributions
Generative Adversarial Networks (GANs)https://arxiv.org/pdf/1701.07875.pdf
discriminanthttps://arxiv.org/pdf/1608.08063.pdf
robusthttps://arxiv.org/pdf/1901.08949.pdf
similarity between word embeddings of documentshttp://proceedings.mlr.press/v37/kusnerb15.pdf
signalshttps://www.math.ucdavis.edu/~saito/data/acha.read.s19/kolouri-etal_optimal-mass-transport.pdf
spectrahttps://arxiv.org/pdf/1609.09799.pdf
https://PythonOT.github.io/user_guide.html#ot-for-mapping-estimation
color transfer between imageshttps://arxiv.org/pdf/1307.5551.pdf
domain adaptationhttps://arxiv.org/pdf/1507.00504.pdf
word embeddingshttps://arxiv.org/pdf/1809.00013.pdf
https://PythonOT.github.io/user_guide.html#when-to-use-pot
ot.optim.cghttps://PythonOT.github.io/gen_modules/ot.optim.html#id0
[30]https://PythonOT.github.io/user_guide.html#id80
https://PythonOT.github.io/user_guide.html#when-not-to-use-pot
GeomLosshttps://www.kernel-operations.io/geomloss/
Wasserstein GANhttps://arxiv.org/pdf/1701.07875.pdf
statistical propertieshttps://arxiv.org/pdf/1910.04091.pdf
https://PythonOT.github.io/user_guide.html#optimal-transport-and-wasserstein-distance
ot.emdhttps://PythonOT.github.io/all.html#ot.emd
ot.emd2https://PythonOT.github.io/all.html#ot.emd2
https://PythonOT.github.io/user_guide.html#solving-optimal-transport
ot.emdhttps://PythonOT.github.io/all.html#ot.emd
[1]https://PythonOT.github.io/user_guide.html#id53
ot.emdhttps://PythonOT.github.io/all.html#ot.emd
https://PythonOT.github.io/user_guide.html#examples-of-use-for-ot-emd
Different gradient computations for regularized optimal transporthttps://PythonOT.github.io/auto_examples/backends/plot_Sinkhorn_gradients.html#sphx-glr-auto-examples-backends-plot-sinkhorn-gradients-py
Solving Many Optimal Transport Problems in Parallelhttps://PythonOT.github.io/auto_examples/backends/plot_ot_batch.html#sphx-glr-auto-examples-backends-plot-ot-batch-py
Optimal Transport between empirical distributionshttps://PythonOT.github.io/auto_examples/plot_OT_2D_samples.html#sphx-glr-auto-examples-plot-ot-2d-samples-py
Quickstart Guidehttps://PythonOT.github.io/auto_examples/plot_quickstart_guide.html#sphx-glr-auto-examples-plot-quickstart-guide-py
Optimal Transport solvers comparisonhttps://PythonOT.github.io/auto_examples/plot_solve_variants.html#sphx-glr-auto-examples-plot-solve-variants-py
https://PythonOT.github.io/user_guide.html#computing-wasserstein-distance
ot.emd2https://PythonOT.github.io/all.html#ot.emd2
Wasserstein distancehttps://en.wikipedia.org/wiki/Wasserstein_metric
ot.emd2https://PythonOT.github.io/all.html#ot.emd2
ot.emd2https://PythonOT.github.io/all.html#ot.emd2
ot.emd2https://PythonOT.github.io/all.html#ot.emd2
https://PythonOT.github.io/user_guide.html#examples-of-use-for-ot-emd2
Different gradient computations for regularized optimal transporthttps://PythonOT.github.io/auto_examples/backends/plot_Sinkhorn_gradients.html#sphx-glr-auto-examples-backends-plot-sinkhorn-gradients-py
Solving Many Optimal Transport Problems in Parallelhttps://PythonOT.github.io/auto_examples/backends/plot_ot_batch.html#sphx-glr-auto-examples-backends-plot-ot-batch-py
Optimal Transport between empirical distributionshttps://PythonOT.github.io/auto_examples/plot_OT_2D_samples.html#sphx-glr-auto-examples-plot-ot-2d-samples-py
Quickstart Guidehttps://PythonOT.github.io/auto_examples/plot_quickstart_guide.html#sphx-glr-auto-examples-plot-quickstart-guide-py
Optimal Transport solvers comparisonhttps://PythonOT.github.io/auto_examples/plot_solve_variants.html#sphx-glr-auto-examples-plot-solve-variants-py
https://PythonOT.github.io/user_guide.html#special-cases
ot.emd_1dhttps://PythonOT.github.io/all.html#ot.emd_1d
ot.emd2_1dhttps://PythonOT.github.io/all.html#ot.emd2_1d
ot.emd_1dhttps://PythonOT.github.io/all.html#ot.emd_1d
ot.wasserstein_1dhttps://PythonOT.github.io/all.html#ot.wasserstein_1d
[15]https://PythonOT.github.io/user_guide.html#id66
ot.gaussian.bures_wasserstein_mappinghttps://PythonOT.github.io/gen_modules/ot.gaussian.html#id39
ot.solve_samplehttps://PythonOT.github.io/all.html#ot.solve_sample
https://PythonOT.github.io/user_guide.html#regularized-optimal-transport
https://PythonOT.github.io/user_guide.html#entropic-regularized-ot
[2]https://PythonOT.github.io/user_guide.html#id54
[2]https://PythonOT.github.io/user_guide.html#id54
ot.smoothhttps://PythonOT.github.io/gen_modules/ot.smooth.html#module-ot.smooth
ot.sinkhornhttps://PythonOT.github.io/all.html#ot.sinkhorn
ot.sinkhorn2https://PythonOT.github.io/all.html#ot.sinkhorn2
ot.sinkhornhttps://PythonOT.github.io/all.html#ot.sinkhorn
ot.bregman.sinkhorn_knopphttps://PythonOT.github.io/gen_modules/ot.bregman.html#ot.bregman.sinkhorn_knopp
[2]https://PythonOT.github.io/user_guide.html#id54
ot.bregman.sinkhorn_loghttps://PythonOT.github.io/gen_modules/ot.bregman.html#ot.bregman.sinkhorn_log
[2]https://PythonOT.github.io/user_guide.html#id54
ot.bregman.sinkhorn_stabilizedhttps://PythonOT.github.io/gen_modules/ot.bregman.html#ot.bregman.sinkhorn_stabilized
[9]https://PythonOT.github.io/user_guide.html#id60
ot.bregman.sinkhorn_epsilon_scalinghttps://PythonOT.github.io/gen_modules/ot.bregman.html#ot.bregman.sinkhorn_epsilon_scaling
[9]https://PythonOT.github.io/user_guide.html#id60
ot.bregman.greenkhornhttps://PythonOT.github.io/gen_modules/ot.bregman.html#ot.bregman.greenkhorn
[22]https://PythonOT.github.io/user_guide.html#id73
ot.bregman.screenkhornhttps://PythonOT.github.io/gen_modules/ot.bregman.html#ot.bregman.screenkhorn
[26]https://PythonOT.github.io/user_guide.html#id77
ot.smoothhttps://PythonOT.github.io/gen_modules/ot.smooth.html#module-ot.smooth
scipy.optimize.minimizehttps://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html#scipy.optimize.minimize
ot.smooth.smooth_ot_dualhttps://PythonOT.github.io/gen_modules/ot.smooth.html#id27
ot.smooth.smooth_ot_semi_dualhttps://PythonOT.github.io/gen_modules/ot.smooth.html#id32
ot.bregman.sinkhorn_stabilizedhttps://PythonOT.github.io/gen_modules/ot.bregman.html#ot.bregman.sinkhorn_stabilized
ot.bregman.sinkhorn_epsilon_scalinghttps://PythonOT.github.io/gen_modules/ot.bregman.html#ot.bregman.sinkhorn_epsilon_scaling
ot.bregman.greenkhornhttps://PythonOT.github.io/gen_modules/ot.bregman.html#ot.bregman.greenkhorn
ot.bregman.screenkhornhttps://PythonOT.github.io/gen_modules/ot.bregman.html#ot.bregman.screenkhorn
ot.bregman.sinkhorn_loghttps://PythonOT.github.io/gen_modules/ot.bregman.html#ot.bregman.sinkhorn_log
[23]https://PythonOT.github.io/user_guide.html#id74
ot.bregman.empirical_sinkhorn_divergencehttps://PythonOT.github.io/gen_modules/ot.bregman.html#ot.bregman.empirical_sinkhorn_divergence
ot.bregman.empirical_sinkhornhttps://PythonOT.github.io/gen_modules/ot.bregman.html#ot.bregman.empirical_sinkhorn
ot.bregman.empirical_sinkhorn2https://PythonOT.github.io/gen_modules/ot.bregman.html#ot.bregman.empirical_sinkhorn2
ot.stochastichttps://PythonOT.github.io/gen_modules/ot.stochastic.html#module-ot.stochastic
[18]https://PythonOT.github.io/user_guide.html#id69
[19]https://PythonOT.github.io/user_guide.html#id70
[18]https://PythonOT.github.io/user_guide.html#id69
[19]https://PythonOT.github.io/user_guide.html#id70
https://PythonOT.github.io/user_guide.html#examples-of-use-for-sinkhorn-algorithm
OT for multi-source target shifthttps://PythonOT.github.io/auto_examples/domain-adaptation/plot_otda_jcpot.html#sphx-glr-auto-examples-domain-adaptation-plot-otda-jcpot-py
Nyström approximation for OThttps://PythonOT.github.io/auto_examples/lowrank/plot_nystroem_approximation.html#sphx-glr-auto-examples-lowrank-plot-nystroem-approximation-py
Stochastic exampleshttps://PythonOT.github.io/auto_examples/others/plot_stochastic.html#sphx-glr-auto-examples-others-plot-stochastic-py
Introduction to Optimal Transport with Pythonhttps://PythonOT.github.io/auto_examples/plot_Intro_OT.html#sphx-glr-auto-examples-plot-intro-ot-py
Optimal Transport for fixed supporthttps://PythonOT.github.io/auto_examples/plot_OT_1D.html#sphx-glr-auto-examples-plot-ot-1d-py
Optimal Transport between empirical distributionshttps://PythonOT.github.io/auto_examples/plot_OT_2D_samples.html#sphx-glr-auto-examples-plot-ot-2d-samples-py
Geometry of OT distanceshttps://PythonOT.github.io/auto_examples/plot_compute_emd.html#sphx-glr-auto-examples-plot-compute-emd-py
Quickstart Guidehttps://PythonOT.github.io/auto_examples/plot_quickstart_guide.html#sphx-glr-auto-examples-plot-quickstart-guide-py
https://PythonOT.github.io/user_guide.html#other-regularizations
ot.optimhttps://PythonOT.github.io/gen_modules/ot.optim.html#module-ot.optim
https://PythonOT.github.io/user_guide.html#quadratic-regularization
[17]https://PythonOT.github.io/user_guide.html#id68
ot.smoothhttps://PythonOT.github.io/gen_modules/ot.smooth.html#module-ot.smooth
ot.smooth.smooth_ot_dualhttps://PythonOT.github.io/gen_modules/ot.smooth.html#id27
ot.smooth.smooth_ot_semi_dualhttps://PythonOT.github.io/gen_modules/ot.smooth.html#id32
https://PythonOT.github.io/user_guide.html#examples-of-use-of-quadratic-regularization
Optimal Transport for fixed supporthttps://PythonOT.github.io/auto_examples/plot_OT_1D.html#sphx-glr-auto-examples-plot-ot-1d-py
Regularized OT with generic solverhttps://PythonOT.github.io/auto_examples/plot_optim_OTreg.html#sphx-glr-auto-examples-plot-optim-otreg-py
Quickstart Guidehttps://PythonOT.github.io/auto_examples/plot_quickstart_guide.html#sphx-glr-auto-examples-plot-quickstart-guide-py
https://PythonOT.github.io/user_guide.html#group-lasso-regularization
[5]https://PythonOT.github.io/user_guide.html#id56
[5]https://PythonOT.github.io/user_guide.html#id56
ot.sinkhorn_lpl1_mmhttps://PythonOT.github.io/all.html#ot.sinkhorn_lpl1_mm
[7]https://PythonOT.github.io/user_guide.html#id58
ot.da.sinkhorn_l1l2_glhttps://PythonOT.github.io/gen_modules/ot.da.html#id137
https://PythonOT.github.io/user_guide.html#examples-of-group-lasso-regularization
OT for domain adaptationhttps://PythonOT.github.io/auto_examples/domain-adaptation/plot_otda_classes.html#sphx-glr-auto-examples-domain-adaptation-plot-otda-classes-py
OT for domain adaptation on empirical distributionshttps://PythonOT.github.io/auto_examples/domain-adaptation/plot_otda_d2.html#sphx-glr-auto-examples-domain-adaptation-plot-otda-d2-py
https://PythonOT.github.io/user_guide.html#generic-solvers
ot.optim.cghttps://PythonOT.github.io/gen_modules/ot.optim.html#id0
[6]https://PythonOT.github.io/user_guide.html#id57
ot.emdhttps://PythonOT.github.io/all.html#ot.emd
[7]https://PythonOT.github.io/user_guide.html#id58
ot.optim.gcghttps://PythonOT.github.io/gen_modules/ot.optim.html#id22
ot.sinkhornhttps://PythonOT.github.io/all.html#ot.sinkhorn
https://PythonOT.github.io/user_guide.html#examples-of-the-generic-solvers
Regularized OT with generic solverhttps://PythonOT.github.io/auto_examples/plot_optim_OTreg.html#sphx-glr-auto-examples-plot-optim-otreg-py
Quickstart Guidehttps://PythonOT.github.io/auto_examples/plot_quickstart_guide.html#sphx-glr-auto-examples-plot-quickstart-guide-py
https://PythonOT.github.io/user_guide.html#wasserstein-barycenters
[16]https://PythonOT.github.io/user_guide.html#id67
https://PythonOT.github.io/user_guide.html#barycenters-with-fixed-support
ot.lp.barycenter()https://PythonOT.github.io/gen_modules/ot.lp.html#ot.lp.barycenter
scipy.optimize.linproghttps://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linprog.html#scipy.optimize.linprog
[3]https://PythonOT.github.io/user_guide.html#id55
ot.bregman.barycenterhttps://PythonOT.github.io/gen_modules/ot.bregman.html#ot.bregman.barycenter
ot.barycenterhttps://PythonOT.github.io/all.html#ot.barycenter
[21]https://PythonOT.github.io/user_guide.html#id72
ot.bregman.convolutional_barycenter2dhttps://PythonOT.github.io/gen_modules/ot.bregman.html#ot.bregman.convolutional_barycenter2d
https://PythonOT.github.io/user_guide.html#examples-of-wasserstein-and-regularized-wasserstein-barycenters
1D Wasserstein barycenter demohttps://PythonOT.github.io/auto_examples/barycenters/plot_barycenter_1D.html#sphx-glr-auto-examples-barycenters-plot-barycenter-1d-py
1D Wasserstein barycenter: exact LP vs entropic regularizationhttps://PythonOT.github.io/auto_examples/barycenters/plot_barycenter_lp_vs_entropic.html#sphx-glr-auto-examples-barycenters-plot-barycenter-lp-vs-entropic-py
Debiased Sinkhorn barycenter demohttps://PythonOT.github.io/auto_examples/barycenters/plot_debiased_barycenter.html#sphx-glr-auto-examples-barycenters-plot-debiased-barycenter-py
Computing 1-dimensional Barycenters via d-MMOThttps://PythonOT.github.io/auto_examples/others/plot_dmmot.html#sphx-glr-auto-examples-others-plot-dmmot-py
ot.bregman.convolutional_barycenter2dhttps://PythonOT.github.io/gen_modules/ot.bregman.html#ot.bregman.convolutional_barycenter2d
https://PythonOT.github.io/user_guide.html#an-example-of-convolutional-barycenter-ot-bregman-convolutional-barycenter2d-computation
Convolutional Wasserstein Barycenter examplehttps://PythonOT.github.io/auto_examples/barycenters/plot_convolutional_barycenter.html#sphx-glr-auto-examples-barycenters-plot-convolutional-barycenter-py
Debiased Sinkhorn barycenter demohttps://PythonOT.github.io/auto_examples/barycenters/plot_debiased_barycenter.html#sphx-glr-auto-examples-barycenters-plot-debiased-barycenter-py
https://PythonOT.github.io/user_guide.html#barycenters-with-free-support
[20]https://PythonOT.github.io/user_guide.html#id71
ot.lp.free_support_barycenterhttps://PythonOT.github.io/gen_modules/ot.lp.html#ot.lp.free_support_barycenter
https://PythonOT.github.io/user_guide.html#examples-of-free-support-barycenter-estimation
2D free support Wasserstein barycenters of distributionshttps://PythonOT.github.io/auto_examples/barycenters/plot_free_support_barycenter.html#sphx-glr-auto-examples-barycenters-plot-free-support-barycenter-py
https://PythonOT.github.io/user_guide.html#monge-mapping-and-domain-adaptation
theoremhttps://who.rocq.inria.fr/Jean-David.Benamou/demiheure.pdf
ot.dahttps://PythonOT.github.io/gen_modules/ot.da.html#module-ot.da
https://PythonOT.github.io/user_guide.html#monge-mapping-estimation
[14]https://PythonOT.github.io/user_guide.html#id65
ot.gaussian.bures_wasserstein_mappinghttps://PythonOT.github.io/gen_modules/ot.gaussian.html#id39
[6]https://PythonOT.github.io/user_guide.html#id57
ot.da.EMDTransporthttps://PythonOT.github.io/gen_modules/ot.da.html#id53
ot.dahttps://PythonOT.github.io/gen_modules/ot.da.html#module-ot.da
[8]https://PythonOT.github.io/user_guide.html#id59
https://PythonOT.github.io/user_guide.html#domain-adaptation-classes
[5]https://PythonOT.github.io/user_guide.html#id56
ot.da.BaseTransporthttps://PythonOT.github.io/gen_modules/ot.da.html#id0
ot.da.BaseTransport.fithttps://PythonOT.github.io/gen_modules/ot.da.html#id38
ot.da.BaseTransport.transformhttps://PythonOT.github.io/gen_modules/ot.da.html#id42
ot.da.BaseTransport.inverse_transformhttps://PythonOT.github.io/gen_modules/ot.da.html#id40
ot.da.EMDTransporthttps://PythonOT.github.io/gen_modules/ot.da.html#id53
ot.da.BaseTransporthttps://PythonOT.github.io/gen_modules/ot.da.html#id0
ot.da.EMDTransporthttps://PythonOT.github.io/gen_modules/ot.da.html#id53
ot.da.SinkhornTransporthttps://PythonOT.github.io/gen_modules/ot.da.html#id113
ot.da.SinkhornL1l2Transporthttps://PythonOT.github.io/gen_modules/ot.da.html#id98
[5]https://PythonOT.github.io/user_guide.html#id56
ot.da.SinkhornLpl1Transporthttps://PythonOT.github.io/gen_modules/ot.da.html#id106
[5]https://PythonOT.github.io/user_guide.html#id56
ot.da.LinearTransporthttps://PythonOT.github.io/gen_modules/ot.da.html#id76
[14]https://PythonOT.github.io/user_guide.html#id65
ot.da.MappingTransporthttps://PythonOT.github.io/gen_modules/ot.da.html#id83
[8]https://PythonOT.github.io/user_guide.html#id59
https://PythonOT.github.io/user_guide.html#examples-of-the-use-of-otda-classes
OT for domain adaptationhttps://PythonOT.github.io/auto_examples/domain-adaptation/plot_otda_classes.html#sphx-glr-auto-examples-domain-adaptation-plot-otda-classes-py
OT for image color adaptationhttps://PythonOT.github.io/auto_examples/domain-adaptation/plot_otda_color_images.html#sphx-glr-auto-examples-domain-adaptation-plot-otda-color-images-py
OT for domain adaptation on empirical distributionshttps://PythonOT.github.io/auto_examples/domain-adaptation/plot_otda_d2.html#sphx-glr-auto-examples-domain-adaptation-plot-otda-d2-py
OT for multi-source target shifthttps://PythonOT.github.io/auto_examples/domain-adaptation/plot_otda_jcpot.html#sphx-glr-auto-examples-domain-adaptation-plot-otda-jcpot-py
OT with Laplacian regularization for domain adaptationhttps://PythonOT.github.io/auto_examples/domain-adaptation/plot_otda_laplacian.html#sphx-glr-auto-examples-domain-adaptation-plot-otda-laplacian-py
Linear OT mapping estimationhttps://PythonOT.github.io/auto_examples/domain-adaptation/plot_otda_linear_mapping.html#sphx-glr-auto-examples-domain-adaptation-plot-otda-linear-mapping-py
OT for image color adaptation with mapping estimationhttps://PythonOT.github.io/auto_examples/domain-adaptation/plot_otda_mapping_colors_images.html#sphx-glr-auto-examples-domain-adaptation-plot-otda-mapping-colors-images-py
OTDA unsupervised vs semi-supervised settinghttps://PythonOT.github.io/auto_examples/domain-adaptation/plot_otda_semi_supervised.html#sphx-glr-auto-examples-domain-adaptation-plot-otda-semi-supervised-py
https://PythonOT.github.io/user_guide.html#unbalanced-and-partial-ot
https://PythonOT.github.io/user_guide.html#unbalanced-optimal-transport
[25]https://PythonOT.github.io/user_guide.html#id76
[10]https://PythonOT.github.io/user_guide.html#id61
[10]https://PythonOT.github.io/user_guide.html#id61
ot.unbalancedhttps://PythonOT.github.io/gen_modules/ot.unbalanced.html#module-ot.unbalanced
ot.sinkhorn_unbalancedhttps://PythonOT.github.io/all.html#ot.sinkhorn_unbalanced
ot.sinkhorn_unbalanced2https://PythonOT.github.io/all.html#ot.sinkhorn_unbalanced2
ot.sinkhorn_unbalancedhttps://PythonOT.github.io/all.html#ot.sinkhorn_unbalanced
ot.unbalanced.sinkhorn_knopp_unbalancedhttps://PythonOT.github.io/gen_modules/ot.unbalanced.html#ot.unbalanced.sinkhorn_knopp_unbalanced
[25]https://PythonOT.github.io/user_guide.html#id76
[10]https://PythonOT.github.io/user_guide.html#id61
ot.unbalanced.sinkhorn_stabilized_unbalancedhttps://PythonOT.github.io/gen_modules/ot.unbalanced.html#ot.unbalanced.sinkhorn_stabilized_unbalanced
[10]https://PythonOT.github.io/user_guide.html#id61
https://PythonOT.github.io/user_guide.html#examples-of-unbalanced-ot
Quickstart Guidehttps://PythonOT.github.io/auto_examples/plot_quickstart_guide.html#sphx-glr-auto-examples-plot-quickstart-guide-py
1D Unbalanced optimal transporthttps://PythonOT.github.io/auto_examples/unbalanced-partial/plot_UOT_1D.html#sphx-glr-auto-examples-unbalanced-partial-plot-uot-1d-py
Translation Invariant Sinkhorn for Unbalanced Optimal Transporthttps://PythonOT.github.io/auto_examples/unbalanced-partial/plot_conv_sinkhorn_ti.html#sphx-glr-auto-examples-unbalanced-partial-plot-conv-sinkhorn-ti-py
2D examples of exact and entropic unbalanced optimal transporthttps://PythonOT.github.io/auto_examples/unbalanced-partial/plot_unbalanced_OT.html#sphx-glr-auto-examples-unbalanced-partial-plot-unbalanced-ot-py
https://PythonOT.github.io/user_guide.html#unbalanced-barycenters
ot.barycenter_unbalancedhttps://PythonOT.github.io/all.html#ot.barycenter_unbalanced
ot.barycenter_unbalancedhttps://PythonOT.github.io/all.html#ot.barycenter_unbalanced
[10]https://PythonOT.github.io/user_guide.html#id61
ot.unbalanced.barycenter_unbalanced_stabilizedhttps://PythonOT.github.io/gen_modules/ot.unbalanced.html#ot.unbalanced.barycenter_unbalanced_stabilized
[10]https://PythonOT.github.io/user_guide.html#id61
https://PythonOT.github.io/user_guide.html#examples-of-unbalanced-ot-barycenters
1D Wasserstein barycenter demo for Unbalanced distributionshttps://PythonOT.github.io/auto_examples/unbalanced-partial/plot_UOT_barycenter_1D.html#sphx-glr-auto-examples-unbalanced-partial-plot-uot-barycenter-1d-py
https://PythonOT.github.io/user_guide.html#partial-optimal-transport
[28]https://PythonOT.github.io/user_guide.html#id78
[29]https://PythonOT.github.io/user_guide.html#id79
ot.partialhttps://PythonOT.github.io/gen_modules/ot.partial.html#module-ot.partial
ot.partial.partial_wassersteinhttps://PythonOT.github.io/gen_modules/ot.partial.html#ot.partial.partial_wasserstein
ot.partial.partial_wasserstein2https://PythonOT.github.io/gen_modules/ot.partial.html#ot.partial.partial_wasserstein2
ot.partial.entropic_partial_wassersteinhttps://PythonOT.github.io/gen_modules/ot.partial.html#ot.partial.entropic_partial_wasserstein
[3]https://PythonOT.github.io/user_guide.html#id55
ot.partial.partial_gromov_wassersteinhttps://PythonOT.github.io/gen_modules/ot.partial.html#ot.partial.partial_gromov_wasserstein
ot.partial.entropic_partial_gromov_wassersteinhttps://PythonOT.github.io/gen_modules/ot.partial.html#ot.partial.entropic_partial_gromov_wasserstein
https://PythonOT.github.io/user_guide.html#examples-of-partial-ot
Quickstart Guidehttps://PythonOT.github.io/auto_examples/plot_quickstart_guide.html#sphx-glr-auto-examples-plot-quickstart-guide-py
Partial Wasserstein and Gromov-Wasserstein examplehttps://PythonOT.github.io/auto_examples/unbalanced-partial/plot_partial_wass_and_gromov.html#sphx-glr-auto-examples-unbalanced-partial-plot-partial-wass-and-gromov-py
2D examples of exact and entropic unbalanced optimal transporthttps://PythonOT.github.io/auto_examples/unbalanced-partial/plot_unbalanced_OT.html#sphx-glr-auto-examples-unbalanced-partial-plot-unbalanced-ot-py
https://PythonOT.github.io/user_guide.html#gromov-wasserstein-and-extensions
https://PythonOT.github.io/user_guide.html#gromov-wasserstein-gw
[13]https://PythonOT.github.io/user_guide.html#id64
[13]https://PythonOT.github.io/user_guide.html#id64
ot.gromov.gromov_wassersteinhttps://PythonOT.github.io/gen_modules/ot.gromov.html#ot.gromov.gromov_wasserstein
[12]https://PythonOT.github.io/user_guide.html#id63
ot.gromov.entropic_gromov_wassersteinhttps://PythonOT.github.io/gen_modules/ot.gromov.html#ot.gromov.entropic_gromov_wasserstein
https://PythonOT.github.io/user_guide.html#examples-of-computation-of-gw-regularized-g-and-fgw
Gromov-Wasserstein examplehttps://PythonOT.github.io/auto_examples/gromov/plot_gromov.html#sphx-glr-auto-examples-gromov-plot-gromov-py
Quickstart Guidehttps://PythonOT.github.io/auto_examples/plot_quickstart_guide.html#sphx-glr-auto-examples-plot-quickstart-guide-py
https://PythonOT.github.io/user_guide.html#gromov-wasserstein-barycenters
ot.gromov.gromov_barycentershttps://PythonOT.github.io/gen_modules/ot.gromov.html#ot.gromov.gromov_barycenters
ot.gromov.entropic_gromov_barycentershttps://PythonOT.github.io/gen_modules/ot.gromov.html#ot.gromov.entropic_gromov_barycenters
[24]https://PythonOT.github.io/user_guide.html#id75
ot.gromov.fused_gromov_wassersteinhttps://PythonOT.github.io/gen_modules/ot.gromov.html#ot.gromov.fused_gromov_wasserstein
ot.gromov.fgw_barycentershttps://PythonOT.github.io/gen_modules/ot.gromov.html#ot.gromov.fgw_barycenters
https://PythonOT.github.io/user_guide.html#examples-of-gw-regularized-g-and-fgw-barycenters
Barycenter of labeled graphs with FGWhttps://PythonOT.github.io/auto_examples/gromov/plot_barycenter_fgw.html#sphx-glr-auto-examples-gromov-plot-barycenter-fgw-py
https://PythonOT.github.io/user_guide.html#other-applications
https://PythonOT.github.io/user_guide.html#wasserstein-discriminant-analysis
[11]https://PythonOT.github.io/user_guide.html#id62
Fisher Linear Discriminant Analysishttps://en.wikipedia.org/wiki/Linear_discriminant_analysis
ot.dr.wdahttps://PythonOT.github.io/gen_modules/ot.dr.html#id15
ot.dr.fdahttps://PythonOT.github.io/gen_modules/ot.dr.html#id7
ot.drhttps://PythonOT.github.io/gen_modules/ot.dr.html#module-ot.dr
https://PythonOT.github.io/user_guide.html#examples-of-the-use-of-wda
Wasserstein Discriminant Analysishttps://PythonOT.github.io/auto_examples/others/plot_WDA.html#sphx-glr-auto-examples-others-plot-wda-py
https://PythonOT.github.io/user_guide.html#solving-ot-with-multiple-backends-on-cpu-gpu
https://PythonOT.github.io/user_guide.html#how-it-works
ot.emdhttps://PythonOT.github.io/all.html#ot.emd
ot.emd2https://PythonOT.github.io/all.html#ot.emd2
numpy.arrayhttps://numpy.org/doc/stable/reference/generated/numpy.array.html#numpy.array
torch.tensorhttps://docs.pytorch.org/docs/stable/generated/torch.tensor.html#torch.tensor
jax.numpy.arrayhttps://docs.jax.dev/en/latest/_autosummary/jax.numpy.array.html#jax.numpy.array
https://PythonOT.github.io/user_guide.html#gpu-acceleration
ot.emdhttps://PythonOT.github.io/all.html#ot.emd
ot.emd2https://PythonOT.github.io/all.html#ot.emd2
ot.gromov_wassersteinhttps://PythonOT.github.io/all.html#ot.gromov_wasserstein
ot.gromov_wasserstein2https://PythonOT.github.io/all.html#ot.gromov_wasserstein2
ot.optim.cghttps://PythonOT.github.io/gen_modules/ot.optim.html#id0
https://PythonOT.github.io/user_guide.html#list-of-compatible-backends
Numpyhttps://numpy.org/
Pytorchhttps://pytorch.org/
Jaxhttps://github.com/google/jax
Tensorflowhttps://www.tensorflow.org/
Cupyhttps://cupy.dev/
https://PythonOT.github.io/user_guide.html#faq
ot.emdhttps://PythonOT.github.io/all.html#ot.emd
ot.sinkhornhttps://PythonOT.github.io/all.html#ot.sinkhorn
Optimal Transport between empirical distributionshttps://PythonOT.github.io/auto_examples/plot_OT_2D_samples.html
Issue #59https://github.com/rflamary/POT/issues/59
[22]https://PythonOT.github.io/user_guide.html#id73
https://PythonOT.github.io/user_guide.html#references
1https://PythonOT.github.io/user_guide.html#id3
Displacement nterpolation using Lagrangian mass transporthttps://people.csail.mit.edu/sparis/publi/2011/sigasia/Bonneel_11_Displacement_Interpolation.pdf
1https://PythonOT.github.io/user_guide.html#id5
2https://PythonOT.github.io/user_guide.html#id6
3https://PythonOT.github.io/user_guide.html#id7
4https://PythonOT.github.io/user_guide.html#id8
Sinkhorn distances: Lightspeed computation of optimal transporthttps://arxiv.org/pdf/1306.0895.pdf
1https://PythonOT.github.io/user_guide.html#id25
2https://PythonOT.github.io/user_guide.html#id46
Iterative Bregman projections for regularized transportation problemshttps://arxiv.org/pdf/1412.5154.pdf
1https://PythonOT.github.io/user_guide.html#id19
2https://PythonOT.github.io/user_guide.html#id20
3https://PythonOT.github.io/user_guide.html#id31
4https://PythonOT.github.io/user_guide.html#id32
5https://PythonOT.github.io/user_guide.html#id33
Optimal Transport for Domain Adaptationhttps://arxiv.org/pdf/1507.00504.pdf
1https://PythonOT.github.io/user_guide.html#id22
2https://PythonOT.github.io/user_guide.html#id29
Regularized discrete optimal transporthttps://arxiv.org/pdf/1307.5551.pdf
1https://PythonOT.github.io/user_guide.html#id21
2https://PythonOT.github.io/user_guide.html#id23
Generalized conditional gradient: analysis of convergence and applicationshttps://arxiv.org/pdf/1510.06567.pdf
1https://PythonOT.github.io/user_guide.html#id30
2https://PythonOT.github.io/user_guide.html#id35
Mapping estimation for discrete optimal transporthttp://remi.flamary.com/biblio/perrot2016mapping.pdf
1https://PythonOT.github.io/user_guide.html#id9
2https://PythonOT.github.io/user_guide.html#id10
Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problemshttps://arxiv.org/pdf/1610.06519.pdf
1https://PythonOT.github.io/user_guide.html#id37
2https://PythonOT.github.io/user_guide.html#id38
3https://PythonOT.github.io/user_guide.html#id40
4https://PythonOT.github.io/user_guide.html#id41
5https://PythonOT.github.io/user_guide.html#id42
6https://PythonOT.github.io/user_guide.html#id43
Scaling algorithms for unbalanced transport problemshttps://arxiv.org/pdf/1607.05816.pdf
11https://PythonOT.github.io/user_guide.html#id51
Wasserstein Discriminant Analysishttps://arxiv.org/pdf/1608.08063.pdf
12https://PythonOT.github.io/user_guide.html#id49
Gromov-Wasserstein averaging of kernel and distance matriceshttp://proceedings.mlr.press/v48/peyre16.html
1https://PythonOT.github.io/user_guide.html#id47
2https://PythonOT.github.io/user_guide.html#id48
Gromov–Wasserstein distances and the metric approach to object matchinghttps://media.adelaide.edu.au/acvt/Publications/2011/2011-Gromov%E2%80%93Wasserstein%20Distances%20and%20the%20Metric%20Approach%20to%20Object%20Matching.pdf
1https://PythonOT.github.io/user_guide.html#id28
2https://PythonOT.github.io/user_guide.html#id34
On the optimal mapping of distributionshttps://link.springer.com/article/10.1007/BF00934745
1https://PythonOT.github.io/user_guide.html#id1
2https://PythonOT.github.io/user_guide.html#id4
Computational Optimal Transporthttps://arxiv.org/pdf/1803.00567.pdf
16https://PythonOT.github.io/user_guide.html#id24
Barycenters in the Wasserstein spacehttps://hal.archives-ouvertes.fr/hal-00637399/document
17https://PythonOT.github.io/user_guide.html#id18
Smooth and Sparse Optimal Transporthttps://arxiv.org/abs/1710.06276
1https://PythonOT.github.io/user_guide.html#id14
2https://PythonOT.github.io/user_guide.html#id16
Stochastic Optimization for Large-scale Optimal Transporthttps://arxiv.org/abs/1605.08527
1https://PythonOT.github.io/user_guide.html#id15
2https://PythonOT.github.io/user_guide.html#id17
Large-scale Optimal Transport and Mapping Estimationhttps://arxiv.org/pdf/1711.02283.pdf
20https://PythonOT.github.io/user_guide.html#id27
Fast Computation of Wasserstein Barycentershttp://proceedings.mlr.press/v32/cuturi14.html
21https://PythonOT.github.io/user_guide.html#id26
Convolutional wasserstein distances: Efficient optimal transportation on geometric domainshttps://dl.acm.org/citation.cfm?id=2766963
1https://PythonOT.github.io/user_guide.html#id11
2https://PythonOT.github.io/user_guide.html#id52
Near-linear time approximation algorithms for optimal transport via Sinkhorn iterationhttps://papers.nips.cc/paper/6792-near-linear-time-approximation-algorithms-for-optimal-transport-via-sinkhorn-iteration.pdf
23https://PythonOT.github.io/user_guide.html#id13
Learning Generative Models with Sinkhorn Divergenceshttps://arxiv.org/abs/1706.00292
24https://PythonOT.github.io/user_guide.html#id50
Optimal Transport for structured data with application on graphshttp://proceedings.mlr.press/v97/titouan19a.html
1https://PythonOT.github.io/user_guide.html#id36
2https://PythonOT.github.io/user_guide.html#id39
26https://PythonOT.github.io/user_guide.html#id12
https://papers.nips.cc/paper/9386-screening-sinkhorn-algorithm-for-regularized-optimal-transporthttps://papers.nips.cc/paper/9386-screening-sinkhorn-algorithm-for-regularized-optimal-transport
28https://PythonOT.github.io/user_guide.html#id44
http://www.math.toronto.edu/~mccann/papers/annals2010.pdfhttp://www.math.toronto.edu/~mccann/papers/annals2010.pdf
29https://PythonOT.github.io/user_guide.html#id45
https://arxiv.org/abs/2002.08276https://arxiv.org/abs/2002.08276
30https://PythonOT.github.io/user_guide.html#id2
Sliced and radon wasserstein barycenters of measureshttps://perso.liris.cnrs.fr/nicolas.bonneel/WassersteinSliced-JMIV.pdf
A Riemannian Block Coordinate Descent Method for Computing the Projection Robust Wasserstein Distancehttp://proceedings.mlr.press/v139/huang21e.html
Sampled Gromov Wassersteinhttps://hal.archives-ouvertes.fr/hal-03232509/document
Interpolating between optimal transport and MMD using Sinkhorn divergenceshttp://proceedings.mlr.press/v89/feydy19a/feydy19a.pdf
Max-sliced wasserstein distance and its use for ganshttps://openaccess.thecvf.com/content_CVPR_2019/papers/Deshpande_Max-Sliced_Wasserstein_Distance_and_Its_Use_for_GANs_CVPR_2019_paper.pdf
Sliced-Wasserstein flows: Nonparametric generative modeling via optimal transport and diffusionshttp://proceedings.mlr.press/v97/liutkus19a/liutkus19a.pdf
Debiased sinkhorn barycentershttp://proceedings.mlr.press/v119/janati20a/janati20a.pdf
Online Graph Dictionary Learninghttps://arxiv.org/pdf/2102.06555.pdf
Kantorovich duality for general transport costs and applicationshttps://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.712.1825&rep=rep1&type=pdf
Statistical optimal transport via factored couplingshttp://proceedings.mlr.press/v89/forrow19a/forrow19a.pdf
Scalable Gromov-Wasserstein learning for graph partitioning and matchinghttps://arxiv.org/abs/1906.03666
Previoushttps://PythonOT.github.io/auto_examples/others/plot_stochastic.html
Next https://PythonOT.github.io/all.html
Sphinxhttps://www.sphinx-doc.org/
themehttps://github.com/readthedocs/sphinx_rtd_theme
Read the Docshttps://readthedocs.org
Releasehttps://pythonot.github.io/
Developmenthttps://pythonot.github.io/master
Codehttps://github.com/PythonOT/POT

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