ott.geometry.costs.ElasticSTVS

class ott.geometry.costs.ElasticSTVS(scaling_reg=1.0, matrix=None, orthogonal=False)

Cost with soft thresholding operator with vanishing shrinkage (STVS) [Schreck et al., 2016] regularization.

\[\frac{1}{2} \|\cdot\|_2^2 + \text{scaling_reg}^2\mathbf{1}_d^T\left(\sigma(\cdot) - \frac{1}{2} \exp\left(-2\sigma(\cdot)\right) + \frac{1}{2}\right)\]

where \(\sigma(\cdot) := \text{asinh}\left(\frac{\cdot} {2\text{scaling_reg}}\right)\)

Parameters:

• scaling_reg (float) – Strength of the regularization.

• matrix (Optional[Array]) – \(p \times d\) projection matrix with orthogonal rows.

• orthogonal (bool) – Whether to regularize in the orthogonal complement to promote displacements in the span of matrix.

Methods

all_pairs(x, y)	Compute matrix of all pairwise costs, including the norms.
all_pairs_pairwise(x, y)	Compute matrix of all pairwise costs, excluding the norms.
barycenter(weights, xs)	Output barycenter of vectors.
h(z)	TI function acting on difference of \(x-y\) to output cost.
h_legendre(z)	Legendre transform of h() when it is convex.
h_transform(f, **kwargs)	Compute the h-transform of a concave function.
pairwise(x, y)	Compute cost as evaluation of h() on \(x-y\).
prox_legendre_reg(z[, tau])	Proximal operator of the Legendre transform of reg().
prox_reg(z[, tau])	Proximal operator of reg().
reg(z)	Regularization function.
twist_operator(vec, dual_vec, variable)	Twist inverse operator of the cost function.

Attributes

norm