ott.geometry.costs.ElasticSTVS#
- class ott.geometry.costs.ElasticSTVS(gamma=1.0)[source]#
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