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Diffstat (limited to 'docs/source/quickstart.rst')
| -rw-r--r-- | docs/source/quickstart.rst | 98 |
1 files changed, 48 insertions, 50 deletions
diff --git a/docs/source/quickstart.rst b/docs/source/quickstart.rst index b4cc8ab..1dc9f71 100644 --- a/docs/source/quickstart.rst +++ b/docs/source/quickstart.rst @@ -127,14 +127,6 @@ been used to solve both graph Laplacian regularization OT and Gromov Wasserstein [30]_. -.. note:: - - POT is originally designed to solve OT problems with Numpy interface and - is not yet compatible with Pytorch API. We are currently working on a torch - submodule that will provide OT solvers and losses for the most common deep - learning configurations. - - When not to use POT """"""""""""""""""" @@ -279,7 +271,7 @@ distributions. In this case there exists a close form solution given in Remark 2.29 in [15]_ and the Monge mapping is an affine function and can be also computed from the covariances and means of the source and target distributions. In the case when the finite sample dataset is supposed Gaussian, -we provide :any:`ot.da.OT_mapping_linear` that returns the parameters for the +we provide :any:`ot.gaussian.bures_wasserstein_mapping` that returns the parameters for the Monge mapping. @@ -628,7 +620,7 @@ approximate a Monge mapping from finite distributions. First note that when the source and target distributions are supposed to be Gaussian distributions, there exists a close form solution for the mapping and its an affine function [14]_ of the form :math:`T(x)=Ax+b` . In this case we provide the function -:any:`ot.da.OT_mapping_linear` that returns the operator :math:`A` and vector +:any:`ot.gaussian.bures_wasserstein_mapping` that returns the operator :math:`A` and vector :math:`b`. Note that if the number of samples is too small there is a parameter :code:`reg` that provides a regularization for the covariance matrix estimation. @@ -640,7 +632,7 @@ method proposed in [8]_ that estimates a continuous mapping approximating the barycentric mapping is provided in :any:`ot.da.joint_OT_mapping_linear` for linear mapping and :any:`ot.da.joint_OT_mapping_kernel` for non-linear mapping. -.. minigallery:: ot.da.joint_OT_mapping_linear ot.da.joint_OT_mapping_linear ot.da.OT_mapping_linear +.. minigallery:: ot.da.joint_OT_mapping_linear ot.da.joint_OT_mapping_linear ot.gaussian.bures_wasserstein_mapping :add-heading: Examples of Monge mapping estimation :heading-level: " @@ -692,42 +684,8 @@ A list of the provided implementation is given in the following note. :heading-level: " -Other applications ------------------- - -We discuss in the following several OT related problems and tools that has been -proposed in the OT and machine learning community. - -Wasserstein Discriminant Analysis -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ - -Wasserstein Discriminant Analysis [11]_ is a generalization of `Fisher Linear Discriminant -Analysis <https://en.wikipedia.org/wiki/Linear_discriminant_analysis>`__ that -allows discrimination between classes that are not linearly separable. It -consists in finding a linear projector optimizing the following criterion - -.. math:: - P = \text{arg}\min_P \frac{\sum_i OT_e(\mu_i\#P,\mu_i\#P)}{\sum_{i,j\neq i} - OT_e(\mu_i\#P,\mu_j\#P)} - -where :math:`\#` is the push-forward operator, :math:`OT_e` is the entropic OT -loss and :math:`\mu_i` is the -distribution of samples from class :math:`i`. :math:`P` is also constrained to -be in the Stiefel manifold. WDA can be solved in POT using function -:any:`ot.dr.wda`. It requires to have installed :code:`pymanopt` and -:code:`autograd` for manifold optimization and automatic differentiation -respectively. Note that we also provide the Fisher discriminant estimator in -:any:`ot.dr.fda` for easy comparison. - -.. warning:: - - Note that due to the hard dependency on :code:`pymanopt` and - :code:`autograd`, :any:`ot.dr` is not imported by default. If you want to - use it you have to specifically import it with :code:`import ot.dr` . - -.. minigallery:: ot.dr.wda - :add-heading: Examples of the use of WDA - :heading-level: " +Unbalanced and partial OT +------------------------- @@ -845,10 +803,11 @@ regularization of the problem. :heading-level: " +Gromov Wasserstein and extensions +--------------------------------- - -Gromov-Wasserstein -^^^^^^^^^^^^^^^^^^ +Gromov Wasserstein(GW) +^^^^^^^^^^^^^^^^^^^^^^ Gromov Wasserstein (GW) is a generalization of OT to distributions that do not lie in the same space [13]_. In this case one cannot compute distance between samples @@ -877,6 +836,8 @@ There also exists an entropic regularized variant of GW that has been proposed i :add-heading: Examples of computation of GW, regularized G and FGW :heading-level: " +Gromov Wasserstein barycenters +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Note that similarly to Wasserstein distance GW allows for the definition of GW barycenters that can be expressed as @@ -905,6 +866,43 @@ The implementations of FGW and FGW barycenter is provided in functions :heading-level: " +Other applications +------------------ + +We discuss in the following several OT related problems and tools that has been +proposed in the OT and machine learning community. + +Wasserstein Discriminant Analysis +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Wasserstein Discriminant Analysis [11]_ is a generalization of `Fisher Linear Discriminant +Analysis <https://en.wikipedia.org/wiki/Linear_discriminant_analysis>`__ that +allows discrimination between classes that are not linearly separable. It +consists in finding a linear projector optimizing the following criterion + +.. math:: + P = \text{arg}\min_P \frac{\sum_i OT_e(\mu_i\#P,\mu_i\#P)}{\sum_{i,j\neq i} + OT_e(\mu_i\#P,\mu_j\#P)} + +where :math:`\#` is the push-forward operator, :math:`OT_e` is the entropic OT +loss and :math:`\mu_i` is the +distribution of samples from class :math:`i`. :math:`P` is also constrained to +be in the Stiefel manifold. WDA can be solved in POT using function +:any:`ot.dr.wda`. It requires to have installed :code:`pymanopt` and +:code:`autograd` for manifold optimization and automatic differentiation +respectively. Note that we also provide the Fisher discriminant estimator in +:any:`ot.dr.fda` for easy comparison. + +.. warning:: + + Note that due to the hard dependency on :code:`pymanopt` and + :code:`autograd`, :any:`ot.dr` is not imported by default. If you want to + use it you have to specifically import it with :code:`import ot.dr` . + +.. minigallery:: ot.dr.wda + :add-heading: Examples of the use of WDA + :heading-level: " + Solving OT with Multiple backends on CPU/GPU -------------------------------------------- |