[MRG] Docs updates (#298)

* bregman docs

* sliced docs

* docs partial

* unbalanced docs

* stochastic docs

* plot docs

* datasets docs

* utils docs

* dr docs

* dr docs corrected

* smooth docs

* docs da

* pep8

* docs gromov

* more space after min and argmin

* docs lp

* bregman docs

* bregman docs mistake corrected

* pep8

Co-authored-by: Rémi Flamary <remi.flamary@gmail.com>

1 files changed, 20 insertions, 15 deletions

diff --git a/ot/gromov.py b/ot/gromov.py
index a0fbf48..465693d 100644
--- a/ot/gromov.py
+++ b/ot/gromov.py
@@ -327,7 +327,8 @@ def gromov_wasserstein(C1, C2, p, q, loss_fun, log=False, armijo=False, **kwargs
     The function solves the following optimization problem:

 

     .. math::

-        \mathbf{GW} = \mathop{\arg \min}_\mathbf{T} \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l}

+        \mathbf{GW} = \mathop{\arg \min}_\mathbf{T} \quad \sum_{i,j,k,l}

+        L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l}

 

     Where :

 

@@ -410,7 +411,8 @@ def gromov_wasserstein2(C1, C2, p, q, loss_fun, log=False, armijo=False, **kwarg
     The function solves the following optimization problem:

 

     .. math::

-        GW = \min_\mathbf{T} \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l}

+        GW = \min_\mathbf{T} \quad \sum_{i,j,k,l}

+        L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l}

 

     Where :

 

@@ -487,8 +489,8 @@ def fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5,
     Computes the FGW transport between two graphs (see :ref:`[24] <references-fused-gromov-wasserstein>`)

 

     .. math::

-        \gamma = \mathop{\arg \min}_\gamma (1 - \alpha) <\gamma, \mathbf{M}>_F + \alpha \sum_{i,j,k,l}

-        L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l}

+        \gamma = \mathop{\arg \min}_\gamma \quad (1 - \alpha) \langle \gamma, \mathbf{M} \rangle_F +

+        \alpha \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l}

 

         s.t. \ \mathbf{\gamma} \mathbf{1} &= \mathbf{p}

 

@@ -569,7 +571,7 @@ def fused_gromov_wasserstein2(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5
     Computes the FGW distance between two graphs see (see :ref:`[24] <references-fused-gromov-wasserstein2>`)

 

     .. math::

-        \min_\gamma (1 - \alpha) <\gamma, \mathbf{M}>_F + \alpha \sum_{i,j,k,l}

+        \min_\gamma \quad (1 - \alpha) \langle \gamma, \mathbf{M} \rangle_F + \alpha \sum_{i,j,k,l}

         L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l}

 

         s.t. \ \mathbf{\gamma} \mathbf{1} &= \mathbf{p}

@@ -591,9 +593,9 @@ def fused_gromov_wasserstein2(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5
     M : array-like, shape (ns, nt)

         Metric cost matrix between features across domains

     C1 : array-like, shape (ns, ns)

-        Metric cost matrix respresentative of the structure in the source space.

+        Metric cost matrix representative of the structure in the source space.

     C2 : array-like, shape (nt, nt)

-        Metric cost matrix espresentative of the structure in the target space.

+        Metric cost matrix representative of the structure in the target space.

     p :  array-like, shape (ns,)

         Distribution in the source space.

     q :  array-like, shape (nt,)

@@ -612,8 +614,8 @@ def fused_gromov_wasserstein2(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5
 

     Returns

     -------

-    gamma : array-like, shape (ns, nt)

-        Optimal transportation matrix for the given parameters.

+    fgw-distance : float

+        Fused gromov wasserstein distance for the given parameters.

     log : dict

         Log dictionary return only if log==True in parameters.

 

@@ -780,7 +782,8 @@ def pointwise_gromov_wasserstein(C1, C2, p, q, loss_fun,
     The function solves the following optimization problem:

 

     .. math::

-        \mathbf{GW} = \mathop{\arg \min}_\mathbf{T} \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l}

+        \mathbf{GW} = \mathop{\arg \min}_\mathbf{T} \quad \sum_{i,j,k,l}

+        L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l}

 

         s.t. \ \mathbf{T} \mathbf{1} &= \mathbf{p}

 

@@ -901,7 +904,8 @@ def sampled_gromov_wasserstein(C1, C2, p, q, loss_fun,
     The function solves the following optimization problem:

 

     .. math::

-        \mathbf{GW} = \mathop{\arg \min}_\mathbf{T} \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l}

+        \mathbf{GW} = \mathop{\arg \min}_\mathbf{T} \quad \sum_{i,j,k,l}

+        L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l}

 

         s.t. \ \mathbf{T} \mathbf{1} &= \mathbf{p}

 

@@ -1052,7 +1056,7 @@ def entropic_gromov_wasserstein(C1, C2, p, q, loss_fun, epsilon,
     The function solves the following optimization problem:

 

     .. math::

-        \mathbf{GW} = \mathop{\arg\min}_\mathbf{T} \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} - \epsilon(H(\mathbf{T}))

+        \mathbf{GW} = \mathop{\arg\min}_\mathbf{T} \quad \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} - \epsilon(H(\mathbf{T}))

 

         s.t. \ \mathbf{T} \mathbf{1} &= \mathbf{p}

 

@@ -1157,7 +1161,8 @@ def entropic_gromov_wasserstein2(C1, C2, p, q, loss_fun, epsilon,
     The function solves the following optimization problem:

 

     .. math::

-        GW = \min_\mathbf{T} \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l}) \mathbf{T}_{i,j} \mathbf{T}_{k,l} - \epsilon(H(\mathbf{T}))

+        GW = \min_\mathbf{T} \quad \sum_{i,j,k,l} L(\mathbf{C_1}_{i,k}, \mathbf{C_2}_{j,l})

+        \mathbf{T}_{i,j} \mathbf{T}_{k,l} - \epsilon(H(\mathbf{T}))

 

     Where :

 

@@ -1223,7 +1228,7 @@ def entropic_gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun, epsilon,
 

     .. math::

 

-        \mathbf{C} = \mathop{\arg \min}_{\mathbf{C}\in \mathbb{R}^{N \times N}} \sum_s \lambda_s \mathrm{GW}(\mathbf{C}, \mathbf{C}_s, \mathbf{p}, \mathbf{p}_s)

+        \mathbf{C} = \mathop{\arg \min}_{\mathbf{C}\in \mathbb{R}^{N \times N}} \quad \sum_s \lambda_s \mathrm{GW}(\mathbf{C}, \mathbf{C}_s, \mathbf{p}, \mathbf{p}_s)

 

     Where :

 

@@ -1336,7 +1341,7 @@ def gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun,
 

     .. math::

 

-        \mathbf{C} = \mathop{\arg \min}_{\mathbf{C}\in \mathbb{R}^{N \times N}} \sum_s \lambda_s \mathrm{GW}(\mathbf{C}, \mathbf{C}_s, \mathbf{p}, \mathbf{p}_s)

+        \mathbf{C} = \mathop{\arg \min}_{\mathbf{C}\in \mathbb{R}^{N \times N}} \quad \sum_s \lambda_s \mathrm{GW}(\mathbf{C}, \mathbf{C}_s, \mathbf{p}, \mathbf{p}_s)

 

     Where :