From e0c935a865a57bc4603144b27f1b58cbfba87760 Mon Sep 17 00:00:00 2001 From: Hicham Janati Date: Wed, 4 Sep 2019 10:28:04 +0200 Subject: improve doc --- docs/source/quickstart.rst | 10 ++++------ 1 file changed, 4 insertions(+), 6 deletions(-) (limited to 'docs') diff --git a/docs/source/quickstart.rst b/docs/source/quickstart.rst index 9729664..978eaff 100644 --- a/docs/source/quickstart.rst +++ b/docs/source/quickstart.rst @@ -577,10 +577,10 @@ Unbalanced optimal transport Unbalanced OT is a relaxation of the entropy regularized OT problem where the violation of the constraint on the marginals is added to the objective of the optimization -problem. The unbalanced OT metric between two histograms a and b is defined as [25]_ [10]_: +problem. The unbalanced OT metric between two unbalanced histograms a and b is defined as [25]_ [10]_: .. math:: - W_u(a, b) = \min_\gamma \quad \sum_{i,j}\gamma_{i,j}M_{i,j} + reg\cdot\Omega(\gamma) + \alpha KL(\gamma 1, a) + \alpha KL(\gamma^T 1, b) + W_u(a, b) = \min_\gamma \quad \sum_{i,j}\gamma_{i,j}M_{i,j} + reg\cdot\Omega(\gamma) + reg_m KL(\gamma 1, a) + reg_m KL(\gamma^T 1, b) s.t. \quad \gamma\geq 0 @@ -593,13 +593,11 @@ in :any:`ot.unbalanced`. Computing the optimal transport plan or the transport cost is similar to the balanced case. The Sinkhorn-Knopp algorithm is implemented in :any:`ot.sinkhorn_unbalanced` and :any:`ot.sinkhorn_unbalanced2` that return respectively the OT matrix and the value of the -linear term. Note that the regularization parameter :math:`\alpha` in the -equation above is given to those functions with the parameter :code:`reg_m`. - +linear term. .. note:: The main function to solve entropic regularized UOT is :any:`ot.sinkhorn_unbalanced`. - This function is a wrapper and the parameter :code:`method` help you select + This function is a wrapper and the parameter :code:`method` helps you select the actual algorithm used to solve the problem: + :code:`method='sinkhorn'` calls :any:`ot.unbalanced.sinkhorn_knopp_unbalanced` -- cgit v1.2.3