ott.solvers.quadratic.lower_bound.third_lower_bound

ott.solvers.quadratic.lower_bound.third_lower_bound#

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

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

Parameters:

  • prob (QuadraticProblem) – Quadratic OT problem.

  • distrib_cost (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.

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