ott.solvers.quadratic.lower_bound.third_lower_bound#

ott.solvers.quadratic.lower_bound.third_lower_bound(prob, distrib_cost=None, epsilon=None, **kwargs)[source]#

Computes the third lower bound distance from [Mémoli, 2011], def. 6.3.

Parameters:

prob (QuadraticProblem) – Quadratic OT problem.
distrib_cost (Optional[UnivariateWasserstein]) – Univariate Wasserstein cost used to compare two point clouds in different spaces. Each point is seen as its distribution of costs to other points in its respective point cloud.
epsilon (Optional[float]) – Entropy regularization.
kwargs (Any) – Keyword arguments for solve().

Return type:

SinkhornOutput

Returns:

An approximation of the GW coupling that can be used to initialize the solution of the quadratic OT problem.

ott.solvers.quadratic.lower_bound.third_lower_bound