@@ -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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-
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-
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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
@@ -417,7 +415,27 @@ operators. We provide an implementation of this algorithm in function
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Barycenters with free support
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- ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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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+
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+ .. math ::
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+ \min _\{ x_i\} \quad \sum _{k} w_kW(\mu ,\mu _k)
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+
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+ s.t. \quad \mu =\sum _{i=1 }^n a_i\delta _{x_i}
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+
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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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@@ -438,7 +456,7 @@ Gromov-Wasserstein
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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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