ott.tools.sinkhorn_divergence.sinkhorn_divergence#

ott.tools.sinkhorn_divergence.sinkhorn_divergence(geom, *args, a=None, b=None, sinkhorn_kwargs=mappingproxy({}), static_b=False, share_epsilon=True, symmetric_sinkhorn=True, **kwargs)[source]#

Compute Sinkhorn divergence defined by a geometry, weights, parameters.

Parameters:

  • geom (Type[Geometry]) – Type of the geometry.

  • args (Any) – Positional arguments to prepare_divergences() that are specific to each geometry.

  • a (Optional[Array]) – the weight of each input point. The sum of all elements of a must match that of b to converge.

  • b (Optional[Array]) – the weight of each target point. The sum of all elements of b must match that of a to converge.

  • sinkhorn_kwargs (Mapping[str, Any]) – keywords arguments for Sinkhorn that is called twice if static_b = True else 3 times.

  • static_b (bool) – if True, divergence of measure b against itself is not computed.

  • share_epsilon (bool) – if True, enforces that the same epsilon regularizer is shared for all 2 or 3 terms of the Sinkhorn divergence. In that case, the epsilon will be by default that used when comparing x to y (contained in the first geometry). This flag is set to True by default, because in the default setting, the epsilon regularization is a function of the mean of the cost matrix.

  • symmetric_sinkhorn (bool) – Use Sinkhorn updates in Eq. 25 of [Feydy et al., 2019] for symmetric terms comparing x/x and y/y.

  • kwargs (Any) – keywords arguments to the generic class. This is specific to each geometry.

Return type:

SinkhornDivergenceOutput

Returns:

Sinkhorn divergence value, three pairs of potentials, three costs.