ott.geometry.costs.ElasticL1#
- class ott.geometry.costs.ElasticL1(scaling_reg=1.0, matrix=None, orthogonal=False)[source]#
Cost inspired by elastic net [Zou and Hastie, 2005] regularization.
\[\frac{1}{2} \|\cdot\|_2^2 + \text{scaling_reg} \|\text{matrix} \cdot\|_1\]- Parameters
scaling_reg (
float
) – Strength of theregularization
.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 ofmatrix
.
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.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.
Attributes