ott.geometry.costs.Bures.barycenter#

Bures.barycenter(weights, xs, **kwargs)[source]#

Compute the Bures barycenter of weighted Gaussian distributions.

Implements the fixed point approach proposed in [Álvarez-Esteban et al., 2016] for the computation of the mean and the covariance of the barycenter of weighted Gaussian distributions.

Parameters:

  • weights (Array) – The barycentric weights.

  • xs (Array) – The points to be used in the computation of the barycenter, where each point is described by a concatenation of the mean and the covariance (raveled).

  • kwargs (Any) – Passed on to covariance_fixpoint_iter(), and by extension to ott.math.matrix_square_root.sqrtm(). Note that tolerance is used for the fixed-point iteration of the barycenter, whereas threshold will apply to the fixed point iteration of Newton-Schulz iterations.

Return type:

Array

Returns:

A concatenation of the mean and the raveled covariance of the barycenter.