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author | Oleksii Kachaiev <kachayev@gmail.com> | 2023-05-03 10:36:09 +0200 |
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committer | GitHub <noreply@github.com> | 2023-05-03 10:36:09 +0200 |
commit | 2aeb591be6b19a93f187516495ed15f1a47be925 (patch) | |
tree | 9a6f759856a3f6b2d7c6db3514927ba3e5af10b5 /docs/source | |
parent | 8a7035bdaa5bb164d1c16febbd83650d1fb6d393 (diff) |
[DOC] Corrected spelling errors (#467)
* Fix typos in docstrings and examples
* A few more fixes
* Fix ref for `center_ot_dual` function
* Another typo
* Fix titles formatting
* Explicit empty line after math blocks
* Typo: asymmetric
* Fix code cell formatting for 1D barycenters
* Empirical
* Fix indentation for references
* Fixed all WARNINGs about title formatting
* Fix empty lines after math blocks
* Fix whitespace line
* Update changelog
* Consistent Gromov-Wasserstein
* More Gromov-Wasserstein consistency
---------
Co-authored-by: Rémi Flamary <remi.flamary@gmail.com>
Diffstat (limited to 'docs/source')
-rw-r--r-- | docs/source/quickstart.rst | 34 |
1 files changed, 17 insertions, 17 deletions
diff --git a/docs/source/quickstart.rst b/docs/source/quickstart.rst index 1dc9f71..cd41a95 100644 --- a/docs/source/quickstart.rst +++ b/docs/source/quickstart.rst @@ -151,7 +151,7 @@ case you are only solving an approximation of the Wasserstein distance because the 1-Lipschitz constraint on the dual cannot be enforced exactly (approximated through filter thresholding or regularization). Finally note that in order to avoid solving large scale OT problems, a number of recent approached minimized -the expected Wasserstein distance on minibtaches that is different from the +the expected Wasserstein distance on minibatches that is different from the Wasserstein but has better computational and `statistical properties <https://arxiv.org/pdf/1910.04091.pdf>`_. @@ -164,8 +164,8 @@ Optimal transport and Wasserstein distance In POT, most functions that solve OT or regularized OT problems have two versions that return the OT matrix or the value of the optimal solution. For instance :any:`ot.emd` returns the OT matrix and :any:`ot.emd2` returns the - Wassertsein distance. This approach has been implemented in practice for all - solvers that return an OT matrix (even Gromov-Wasserstsein). + Wasserstein distance. This approach has been implemented in practice for all + solvers that return an OT matrix (even Gromov-Wasserstein). .. _kantorovitch_solve: @@ -349,9 +349,9 @@ More details about the algorithms used are given in the following note. classic algorithm [2]_. + :code:`method='sinkhorn_log'` calls :any:`ot.bregman.sinkhorn_log` the sinkhorn algorithm in log space [2]_ that is more stable but can be - slower in numpy since `logsumexp` is not implmemented in parallel. + slower in numpy since `logsumexp` is not implemented in parallel. It is the recommended solver for applications that requires - differentiability with a small number of iterations. + differentiability with a small number of iterations. + :code:`method='sinkhorn_stabilized'` calls :any:`ot.bregman.sinkhorn_stabilized` the log stabilized version of the algorithm [9]_. + :code:`method='sinkhorn_epsilon_scaling'` calls @@ -368,7 +368,7 @@ More details about the algorithms used are given in the following note. function to solve the smooth problem with :code:`L-BFGS-B` algorithm. Tu use this solver, use functions :any:`ot.smooth.smooth_ot_dual` or :any:`ot.smooth.smooth_ot_semi_dual` with parameter :code:`reg_type='kl'` to - choose entropic/Kullbach Leibler regularization. + choose entropic/Kullbach-Leibler regularization. **Choosing a Sinkhorn solver** @@ -378,7 +378,7 @@ More details about the algorithms used are given in the following note. :any:`ot.bregman.sinkhorn_stabilized` solver that will avoid numerical errors. This last solver can be very slow in practice and might not even converge to a reasonable OT matrix in a finite time. This is why - :any:`ot.bregman.sinkhorn_epsilon_scaling` that relie on iterating the value + :any:`ot.bregman.sinkhorn_epsilon_scaling` that relies on iterating the value of the regularization (and using warm start) sometimes leads to better solutions. Note that the greedy version of the Sinkhorn :any:`ot.bregman.greenkhorn` can also lead to a speedup and the screening @@ -546,7 +546,7 @@ where :math:`b_k` are also weights in the simplex. In the non-regularized case, the problem above is a classical linear program. In this case we propose a solver :meth:`ot.lp.barycenter` that relies on generic LP solvers. By default the function uses :any:`scipy.optimize.linprog`, but more efficient LP solvers from -cvxopt can be also used by changing parameter :code:`solver`. Note that this problem +`cvxopt` can be also used by changing parameter :code:`solver`. Note that this problem requires to solve a very large linear program and can be very slow in practice. @@ -812,7 +812,7 @@ 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 from the two distributions. [13]_ proposed instead to realign the metric spaces -by computing a transport between distance matrices. The Gromow Wasserstein +by computing a transport between distance matrices. The Gromov Wasserstein alignment between two distributions can be expressed as the one minimizing: .. math:: @@ -837,7 +837,7 @@ There also exists an entropic regularized variant of GW that has been proposed i :heading-level: " Gromov Wasserstein barycenters -^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Note that similarly to Wasserstein distance GW allows for the definition of GW barycenters that can be expressed as @@ -1134,7 +1134,7 @@ References .. [23] Genevay, A., Peyré, G., Cuturi, M., `Learning Generative Models with Sinkhorn Divergences <https://arxiv.org/abs/1706.00292>`__, Proceedings - of the Twenty-First International Conference on Artficial Intelligence + of the Twenty-First International Conference on Artificial Intelligence and Statistics, (AISTATS) 21, 2018 .. [24] Vayer, T., Chapel, L., Flamary, R., Tavenard, R. and Courty, N. @@ -1187,18 +1187,18 @@ References In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. 10648-10656). .. [36] Liutkus, A., Simsekli, U., Majewski, S., Durmus, A., & Stöter, F. R. - (2019, May). `Sliced-Wasserstein flows: Nonparametric generative modeling via - optimal transport and diffusions - <http://proceedings.mlr.press/v97/liutkus19a/liutkus19a.pdf>`_. In International - Conference on Machine Learning (pp. 4104-4113). PMLR. + (2019, May). `Sliced-Wasserstein flows: Nonparametric generative modeling via + optimal transport and diffusions + <http://proceedings.mlr.press/v97/liutkus19a/liutkus19a.pdf>`_. In International + Conference on Machine Learning (pp. 4104-4113). PMLR. .. [37] Janati, H., Cuturi, M., Gramfort, A. `Debiased sinkhorn barycenters <http://proceedings.mlr.press/v119/janati20a/janati20a.pdf>`_ Proceedings of the 37th International Conference on Machine Learning, PMLR 119:4692-4701, 2020 .. [38] C. Vincent-Cuaz, T. Vayer, R. Flamary, M. Corneli, N. Courty, `Online - Graph Dictionary Learning <https://arxiv.org/pdf/2102.06555.pdf>`_\ , - International Conference on Machine Learning (ICML), 2021. + Graph Dictionary Learning <https://arxiv.org/pdf/2102.06555.pdf>`_\ , + International Conference on Machine Learning (ICML), 2021. .. [39] Gozlan, N., Roberto, C., Samson, P. M., & Tetali, P. (2017). `Kantorovich duality for general transport costs and applications |