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author | Rémi Flamary <remi.flamary@gmail.com> | 2019-07-02 11:09:50 +0200 |
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committer | Rémi Flamary <remi.flamary@gmail.com> | 2019-07-02 11:09:50 +0200 |
commit | 64693f98c22775048222f61f5e495849844e0135 (patch) | |
tree | 6f5e0e4a12c764c1b6027c454d6269e31b238bd5 | |
parent | b250212448ed3c1d023a6412abf4a3395d5585fb (diff) |
quickstart wasserstein barycenter done
-rw-r--r-- | docs/source/quickstart.rst | 26 |
1 files changed, 22 insertions, 4 deletions
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. |