[MRG] HD Gaussian empirical bures

CITATION.cff

@@ -81,6 +81,9 @@ authors:
   - given-names: David
     family-names: Coeurjolly
     affiliation: CNRS, LIRIS
+  - given-names: Marco
+    family-names: Corneli
+    affiliation: Université Côte d'Azur
 
 identifiers:
   - type: url

README.md

@@ -464,3 +464,7 @@ Artificial Intelligence.
 [86] Tanguy, E., Chapel, L., Delon, J. (2025). [Sliced Transport Plans](https://arxiv.org/abs/2508.01243) arXiv preprint 2506.03661.
 
 [87] Liu, X., Diaz Martin, R., Bai Y., Shahbazi A., Thorpe M., Aldroubi A., Kolouri, S. (2024). [Expected Sliced Transport Plans](https://openreview.net/forum?id=P7O1Vt1BdU). International Conference on Learning Representations.
+
+[88] Bouveyron, C. & Corneli, M. (2026).  [Scaling optimal transport to high-dimensional Gaussian distributions with application to domain adaptation](https://hal.science/hal-04930868v4/file/Article-OT-HDGauss-v4.pdf). Statistics and Computing 36.2 (2026): 88.
+
+[89] Tipping, M.E. & Bishop, C.M. (1999). [Probabilistic principal component analysis]. Journal of the Royal Statistical Society Series B: Statistical Methodology 61.3 (1999): 611-622.

RELEASES.md

@@ -29,6 +29,8 @@ This new release adds support for sparse cost matrices and a new lazy EMD solver
 - Add a numerically stable log-domain solver for entropic partial Wasserstein, selectable via the new `method` parameter of `entropic_partial_wasserstein` (`method='sinkhorn_log'`) or directly through `entropic_partial_wasserstein_logscale` (Issue #723)
 - Add cost functions between linear operators following [A Spectral-Grassmann Wasserstein metric for operator representations of dynamical systems](https://arxiv.org/pdf/2509.24920),  implemented in `ot.sgot` (PR #792)
 - Build wheels on ubuntu ARM to avoid QEMU emulation (PR #818)
+- Add new methods to compute the linear transport map and the related 2-Wasserstein distance betweeen high-dimensional (HD) Gaussian distributions as described in [88], implemented in  `ot.gaussian.bures_wasserstein_mapping_hd` and `ot.gaussian.bures_wasserstein_distance_hd`, respectively. Two additional methods estimate the same quantities from the source and destination observed data and are implemented in `ot.gaussian.empirical_bures_wasserstein_mapping_hd` and `ot.gaussian.empirical_bures_wasserstein_distance_hd`, respectively (PR #814)   
+
 
 #### Closed issues
 

ot/datasets.py

@@ -8,6 +8,7 @@
 
 import numpy as np
 import scipy as sp
+from scipy.stats import ortho_group, multivariate_normal
 from .utils import check_random_state, deprecated
 
 
@@ -180,3 +181,97 @@ def make_data_classif(dataset, n, nz=0.5, theta=0, p=0.5, random_state=None, **k
 def get_data_classif(dataset, n, nz=0.5, theta=0, random_state=None, **kwargs):
     """Deprecated see  make_data_classif"""
     return make_data_classif(dataset, n, nz=0.5, theta=0, random_state=None, **kwargs)
+
+
+def make_gauss_hd(
+    ns, nt, p=100, dim=5, m_diff=3.0, a=(10.0, 15.0), b=(3.0, 3.0), sub_the_same=False
+):
+    """Generation of source and target domains from Gaussian HD distributions
+
+    Parameters
+    ----------
+    ns      : int
+            number of samples (source)
+    nt      : int
+            number of samples (target)
+    p       : int
+            dimension of the ambient space the data live in
+    dim     : (int,int) or int
+            the intrinsic dimensions of the source and target Gaussian HD distriutions. If a single int the intrinsic dimension is assumed to be the same
+    m_diff  : float
+            the shift in the first coordinate of the means of the Gaussian HD distributions, i.e. ms_0 and mt_0, respectively (see code)
+    a       : (float, float)
+            positive floating numbers corresponding to the isotropic variances in the principal subspace, for the source and target distributions, respectively. The same as \delta in :ref:`[1] <references-make_gauss-hd>`, Proposition 2.2
+    b       : (float, float)
+            positive floating numbers corresponding to the isotropic variance outside the principal subspace for the source and target distributions, respectively.
+    sub_the_same : bool
+              should the source/target Gaussian HD distributions live in the same principal subspace?
+
+    Returns
+    -------
+    Xs   : ndarray, shape (ns, p)
+        `ns` observations of size `p` (source)
+    Xt   : ndarray, shape (nt, p)
+        `nt` observations of size `p` (destination)
+    pmts : list
+         a list containing the parameters of the Gaussian HD distributions
+
+    .. _references-make_gauss_hd:
+    References
+    ----------
+
+    .. [1] Bouveyron, C. & Corneli, M. ("Scaling Optimal Transport to High-Dimensional Gaussian Distributions")
+
+    """
+    d = (dim, dim) if isinstance(dim, int) else dim
+    mu = np.zeros((2, p))
+    S = []
+    mu[1, 0] = m_diff
+    Q = [ortho_group.rvs(p) for _ in range(2)]
+
+    if sub_the_same:
+        Q[1] = Q[0]
+
+    S.append(
+        Q[0]
+        @ np.diag(np.hstack((np.full(d[0], a[0]), np.full(p - d[0], b[0]))))
+        @ Q[0].T
+    )
+    S.append(
+        Q[1]
+        @ np.diag(np.hstack((np.full(d[1], a[1]), np.full(p - d[1], b[1]))))
+        @ Q[1].T
+    )
+
+    Xs = multivariate_normal.rvs(mean=mu[0], cov=S[0], size=ns)
+    Xt = multivariate_normal.rvs(mean=mu[1], cov=S[1], size=ns)
+
+    ms = mu[0]
+    mt = mu[1]
+    ds = d[0]
+    dt = d[1]
+    sigma2_s = np.array(b[0])
+    sigma2_t = np.array(b[1])
+    ls = np.repeat(a[0], ds) - sigma2_s
+    lt = np.repeat(a[1], dt) - sigma2_t
+    Us = Q[0][:, :ds]
+    Ut = Q[1][:, :dt]
+    ds = np.array([ds])
+    dt = np.array([dt])
+
+    prmts = {
+        "ms": ms,
+        "mt": mt,
+        "sigma2_s": sigma2_s,
+        "sigma2_t": sigma2_t,
+        "ls": ls,
+        "lt": lt,
+        "Us": Us,
+        "Ut": Ut,
+        "ds": ds,
+        "dt": dt,
+        "Cs": S[0],
+        "Ct": S[1],
+    }
+
+    return Xs, Xt, prmts