ott.geometry.costs.ElasticSTVS

class ott.geometry.costs.ElasticSTVS(gamma=1.0)

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

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

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

Parameters:

gamma (float) – Strength of the STVS regularization, \(> 0\).

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)	Barycentric operator.
h(z)	TI function acting on difference of \(x-y\) to output cost.
h_legendre(z)	Legendre transform of h() when it is convex.
pairwise(x, y)	Compute cost as evaluation of h() on \(x-y\).
prox_reg(z)	Proximal operator of reg().
reg(z)	Regularization function.

Attributes

norm