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quickstart wasserstein barycenter done
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docs/source/quickstart.rst

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@@ -217,8 +217,6 @@ More details about the algorithm used is given in the following note.
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choose entropic/Kullbach Leibler regularization.
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Recently [23]_ introduced the sinkhorn divergence that build from entropic
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regularization to compute fast and differentiable geometric divergence between
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empirical distributions. Note that we provide a function that compute directly
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Barycenters with free support
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^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Estimating the Wassresein barycenter with free support but fixed weights
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corresponds to solving the following optimization problem:
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.. math::
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\min_\{x_i\} \quad \sum_{k} w_kW(\mu,\mu_k)
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s.t. \quad \mu=\sum_{i=1}^n a_i\delta_{x_i}
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WE provide an alternating solver based on [20]_ in
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:any:`ot.lp.free_support_barycenter`. This function minimize the problem and
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return an optimal support :math:`\{x_i\}` for uniform or given weights
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:math:`a`.
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.. hint::
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Example of the fee support barycenter estimation is available
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in the following example:
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- :any:`auto_examples/plot_free_support_barycenter`
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GPU acceleration
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----------------
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^^^^^^^^^^^^^^^^
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We provide several implementation of our OT solvers in :any:`ot.gpu`. Those
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implementation use the :code:`cupy` toolbox.

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