ott.experimental.mmsinkhorn.MMSinkhornOutput

class ott.experimental.mmsinkhorn.MMSinkhornOutput(potentials, errors, x_s=None, a_s=None, cost_fns=None, epsilon=None, ent_reg_cost=None, threshold=None, converged=None, inner_iterations=None)

Output of the MMSinkhorn solver used on \(k\) point clouds.

This class contains both solutions and problem definition of a regularized MM-OT problem involving \(k\) weighted point clouds of varying sizes, along with methods and properties that can use or describe the solution.

Parameters:

• potentials (Tuple[Array, ...]) – Tuple of \(k\) optimal dual variables, vectors of sizes equal to the number of points in each of the \(k\) point clouds.

• errors (Array) – Vector of errors, along iterations. This vector is of size max_iterations // inner_iterations where those were the parameters passed on to the MMSinkhorn solver. Follows the conventions used in errors

• x_s (Optional[Tuple[Array, ...]]) – Tuple of \(k\) point clouds, x_s[i] is a matrix of size \(n_i \times d\) where d is common to all point clouds.

• a_s (Optional[Tuple[Array, ...]]) – Tuple of \(k\) probability vectors, each of size \(n_i\).

• cost_fns (Union[CostFn, Tuple[CostFn, ...], None]) – Cost function, or a tuple of \(k(k-1)/2\) such instances.

• epsilon (Optional[float]) – Entropic regularization used to solve the multimarginal Sinkhorn problem.

• ent_reg_cost (Optional[Array]) – The regularized optimal transport cost, the linear contribution (dot product between optimal tensor and cost) minus entropy times epsilon.

• threshold (Optional[Array]) – Convergence threshold used to control the termination of the algorithm.

• converged (Optional[bool]) – Whether the output corresponds to a solution whose error is below the convergence threshold.

• inner_iterations (Optional[int]) – Number of iterations that were run between two computations of errors.

Methods

count(value, /)	Return number of occurrences of value.
index(value[, start, stop])	Return first index of value.
marginal(k)	Return the marginal probability weight vector at slice \(k\).
set(**kwargs)	Return a copy of self, with potential overwrites.

Attributes

a_s	Alias for field number 3
converged	Alias for field number 8
cost_fns	Alias for field number 4
cost_t	Cost tensor.
ent_reg_cost	Alias for field number 6
epsilon	Alias for field number 5
errors	Alias for field number 1
inner_iterations	Alias for field number 9
marginals	\(k\) marginal probability weight vectors.
n_iters	Total number of iterations that were needed to terminate.
n_marginals	Number of marginals.
potentials	Alias for field number 0
shape	Shape of the transport tensor.
tensor	Transport tensor.
threshold	Alias for field number 7
transport_mass	Sum of transport tensor.
x_s	Alias for field number 2