cleaunup gromov + stat guide

2 files changed, 142 insertions, 16 deletions

diff --git a/docs/source/index.rst b/docs/source/index.rst
index 03943e8..9078d35 100644
--- a/docs/source/index.rst
+++ b/docs/source/index.rst
@@ -10,7 +10,7 @@ Contents
 --------
 
 .. toctree::
-   :maxdepth: 3
+   :maxdepth: 2
 
    self
    quickstart
diff --git a/docs/source/quickstart.rst b/docs/source/quickstart.rst
index ac96f26..d8d4838 100644
--- a/docs/source/quickstart.rst
+++ b/docs/source/quickstart.rst
@@ -1,8 +1,6 @@
 
-Quick start
-===========
-
-
+Quick start guide
+=================
 
 In the following we provide some pointers about which functions and classes 
 to use for different problems related to optimal transport (OT).
@@ -11,6 +9,11 @@ to use for different problems related to optimal transport (OT).
 Optimal transport and Wasserstein distance
 ------------------------------------------
 
+.. note::
+    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` return the OT matrix and :any:`ot.emd2` return the
+    Wassertsein distance.
 
 Solving optimal transport
 ^^^^^^^^^^^^^^^^^^^^^^^^^
@@ -36,6 +39,10 @@ that will return the optimal transport matrix :math:`\gamma^*`:
     # M is the ground cost matrix
     T=ot.emd(a,b,M) # exact linear program
 
+The method used for solving the OT problem is the network simplex, it is
+implemented in C from  [1]_. It has a complexity of :math:`O(n^3)` but the
+solver is quite efficient and uses sparsity of the solution.
+
 .. hint::
     Examples of use for :any:`ot.emd` are available in the following examples:
 
@@ -73,16 +80,19 @@ properties. It can computed from an already estimated OT matrix with
     - :any:`auto_examples/plot_compute_emd`
  
 
-.. note::
-    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. Fir
-    instance :any:`ot.emd` return the OT matrix and :any:`ot.emd2` return the
-    Wassertsein distance.
-
-
 Regularized Optimal Transport
 -----------------------------
 
+Entropic regularized OT
+^^^^^^^^^^^^^^^^^^^^^^^
+
+
+Other regularization
+^^^^^^^^^^^^^^^^^^^^
+
+Stochastic gradient decsent
+^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
 Wasserstein Barycenters
 -----------------------
 
@@ -99,8 +109,8 @@ GPU acceleration
 
 
 
-How to?
--------
+FAQ
+---
 
 
 
@@ -128,5 +138,121 @@ How to?
 2. **Compute a Wasserstein distance**
 
 
-
-
+References
+----------
+
+.. [1] Bonneel, N., Van De Panne, M., Paris, S., & Heidrich, W. (2011,
+    December). `Displacement  nterpolation using Lagrangian mass transport
+    <https://people.csail.mit.edu/sparis/publi/2011/sigasia/Bonneel_11_Displacement_Interpolation.pdf>`__.
+    In ACM Transactions on Graphics (TOG) (Vol. 30, No. 6, p. 158). ACM. 
+
+.. [2] Cuturi, M. (2013). `Sinkhorn distances: Lightspeed computation of
+    optimal transport <https://arxiv.org/pdf/1306.0895.pdf>`__. In Advances
+    in Neural Information Processing Systems (pp. 2292-2300).
+
+.. [3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G.
+    (2015). `Iterative Bregman projections for regularized transportation
+    problems <https://arxiv.org/pdf/1412.5154.pdf>`__. SIAM Journal on
+    Scientific Computing, 37(2), A1111-A1138.
+
+.. [4] S. Nakhostin, N. Courty, R. Flamary, D. Tuia, T. Corpetti,
+    `Supervised planetary unmixing with optimal
+    transport <https://hal.archives-ouvertes.fr/hal-01377236/document>`__,
+    Whorkshop on Hyperspectral Image and Signal Processing : Evolution in
+    Remote Sensing (WHISPERS), 2016.
+
+.. [5] N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy, `Optimal Transport
+    for Domain Adaptation <https://arxiv.org/pdf/1507.00504.pdf>`__, in IEEE
+    Transactions on Pattern Analysis and Machine Intelligence , vol.PP,
+    no.99, pp.1-1
+
+.. [6] Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014).
+    `Regularized discrete optimal
+    transport <https://arxiv.org/pdf/1307.5551.pdf>`__. SIAM Journal on
+    Imaging Sciences, 7(3), 1853-1882.
+
+.. [7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). `Generalized
+    conditional gradient: analysis of convergence and
+    applications <https://arxiv.org/pdf/1510.06567.pdf>`__. arXiv preprint
+    arXiv:1510.06567.
+
+.. [8] M. Perrot, N. Courty, R. Flamary, A. Habrard (2016), `Mapping
+    estimation for discrete optimal
+    transport <http://remi.flamary.com/biblio/perrot2016mapping.pdf>`__,
+    Neural Information Processing Systems (NIPS).
+
+.. [9] Schmitzer, B. (2016). `Stabilized Sparse Scaling Algorithms for
+    Entropy Regularized Transport
+    Problems <https://arxiv.org/pdf/1610.06519.pdf>`__. arXiv preprint
+    arXiv:1610.06519.
+
+.. [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016).
+    `Scaling algorithms for unbalanced transport
+    problems <https://arxiv.org/pdf/1607.05816.pdf>`__. arXiv preprint
+    arXiv:1607.05816.
+
+.. [11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016).
+    `Wasserstein Discriminant
+    Analysis <https://arxiv.org/pdf/1608.08063.pdf>`__. arXiv preprint
+    arXiv:1608.08063.
+
+.. [12] Gabriel Peyré, Marco Cuturi, and Justin Solomon (2016),
+    `Gromov-Wasserstein averaging of kernel and distance
+    matrices <http://proceedings.mlr.press/v48/peyre16.html>`__
+    International Conference on Machine Learning (ICML).
+
+.. [13] Mémoli, Facundo (2011). `Gromov–Wasserstein distances and the
+    metric approach to object
+    matching <https://media.adelaide.edu.au/acvt/Publications/2011/2011-Gromov%E2%80%93Wasserstein%20Distances%20and%20the%20Metric%20Approach%20to%20Object%20Matching.pdf>`__.
+    Foundations of computational mathematics 11.4 : 417-487.
+
+.. [14] Knott, M. and Smith, C. S. (1984).`On the optimal mapping of
+    distributions <https://link.springer.com/article/10.1007/BF00934745>`__,
+    Journal of Optimization Theory and Applications Vol 43.
+
+.. [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 <https://arxiv.org/abs/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
+
+.. [21] Solomon, J., De Goes, F., Peyré, G., Cuturi, M., Butscher, A.,
+    Nguyen, A. & Guibas, L. (2015). `Convolutional wasserstein distances:
+    Efficient optimal transportation on geometric
+    domains <https://dl.acm.org/citation.cfm?id=2766963>`__. ACM
+    Transactions on Graphics (TOG), 34(4), 66.
+
+.. [22] J. Altschuler, J.Weed, P. Rigollet, (2017) `Near-linear time
+    approximation algorithms for optimal transport via Sinkhorn
+    iteration <https://papers.nips.cc/paper/6792-near-linear-time-approximation-algorithms-for-optimal-transport-via-sinkhorn-iteration.pdf>`__,
+    Advances in Neural Information Processing Systems (NIPS) 31
+
+.. [23] Aude, G., 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
+    and Statistics, (AISTATS) 21, 2018
+
+.. [24] Vayer, T., Chapel, L., Flamary, R., Tavenard, R. and Courty, N.
+    (2019). `Optimal Transport for structured data with application on
+    graphs <http://proceedings.mlr.press/v97/titouan19a.html>`__ Proceedings
+    of the 36th International Conference on Machine Learning (ICML).
\ No newline at end of file