From 64693f98c22775048222f61f5e495849844e0135 Mon Sep 17 00:00:00 2001 From: Rémi Flamary Date: Tue, 2 Jul 2019 11:09:50 +0200 Subject: quickstart wasserstein barycenter done --- docs/source/quickstart.rst | 26 ++++++++++++++++++++++---- 1 file changed, 22 insertions(+), 4 deletions(-) (limited to 'docs') diff --git a/docs/source/quickstart.rst b/docs/source/quickstart.rst index 7cbc962..8cce1c9 100644 --- a/docs/source/quickstart.rst +++ b/docs/source/quickstart.rst @@ -217,8 +217,6 @@ More details about the algorithm used is given in the following note. choose entropic/Kullbach Leibler regularization. - - Recently [23]_ introduced the sinkhorn divergence that build from entropic regularization to compute fast and differentiable geometric divergence between empirical distributions. Note that we provide a function that compute directly @@ -417,7 +415,27 @@ operators. We provide an implementation of this algorithm in function Barycenters with free support -^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Estimating the Wassresein barycenter with free support but fixed weights +corresponds to solving the following optimization problem: + +.. math:: + \min_\{x_i\} \quad \sum_{k} w_kW(\mu,\mu_k) + + s.t. \quad \mu=\sum_{i=1}^n a_i\delta_{x_i} + +WE provide an alternating solver based on [20]_ in +:any:`ot.lp.free_support_barycenter`. This function minimize the problem and +return an optimal support :math:`\{x_i\}` for uniform or given weights +:math:`a`. + + .. hint:: + + Example of the fee support barycenter estimation is available + in the following example: + + - :any:`auto_examples/plot_free_support_barycenter` @@ -438,7 +456,7 @@ Gromov-Wasserstein GPU acceleration ----------------- +^^^^^^^^^^^^^^^^ We provide several implementation of our OT solvers in :any:`ot.gpu`. Those implementation use the :code:`cupy` toolbox. -- cgit v1.2.3