馃殌 Feature
Add UnifOrtho sampling of slicing directions for Sliced Wasserstein --
recommended in the recent literature as the best choice in high
dimensions, complementing the QSW/RQSW (d=3-only) sampling added in #838.
Motivation
QSW/RQSW (generalized spiral points, #838) only supports d=3. A recent,
dedicated variance analysis [2] gives an explicit recommendation for
higher dimensions:
"Our final recommendation for the computation of the sliced
Wasserstein distance is to use randomized quasi-Monte Carlo in low
dimensions and UnifOrtho in large dimensions." -- Petrovic, Bardenet &
Desolneux (2025)
UnifOrtho is the orthogonal Monte Carlo estimator introduced by
Rowland et al. (2019) [1]; [2] specifically analyses why it succeeds in
large dimensions and confirms it as the recommended choice there.
Pitch
Add sampling from UnifOrt(S^{d-1}; N) [1]: N mutually orthogonal
directions, each marginally uniform on the sphere, obtained as N rows of
a Haar-random orthogonal matrix (concatenating independent draws when
N > d). No dimension restriction, unlike QSW/RQSW.
Additional context
[1] Rowland, M., Hron, J., Tang, Y., Choromanski, K., Sarlos, T., &
Weller, A. (2019). "Orthogonal Estimation of Wasserstein Distances."
AISTATS 2019, PMLR 89.
[2] Petrovic, V., Bardenet, R., & Desolneux, A. (2025). "Repulsive
Monte Carlo on the sphere for the sliced Wasserstein distance."
arXiv:2509.10166 (under review at TMLR).
Follow-up to #838.
I'd like to work on this myself and will follow up with a PR.
馃殌 Feature
Add
UnifOrthosampling of slicing directions for Sliced Wasserstein --recommended in the recent literature as the best choice in high
dimensions, complementing the QSW/RQSW (d=3-only) sampling added in #838.
Motivation
QSW/RQSW (generalized spiral points, #838) only supports d=3. A recent,
dedicated variance analysis [2] gives an explicit recommendation for
higher dimensions:
UnifOrthois the orthogonal Monte Carlo estimator introduced byRowland et al. (2019) [1]; [2] specifically analyses why it succeeds in
large dimensions and confirms it as the recommended choice there.
Pitch
Add sampling from
UnifOrt(S^{d-1}; N)[1]: N mutually orthogonaldirections, each marginally uniform on the sphere, obtained as N rows of
a Haar-random orthogonal matrix (concatenating independent draws when
N > d). No dimension restriction, unlike QSW/RQSW.
Additional context
[1] Rowland, M., Hron, J., Tang, Y., Choromanski, K., Sarlos, T., &
Weller, A. (2019). "Orthogonal Estimation of Wasserstein Distances."
AISTATS 2019, PMLR 89.
[2] Petrovic, V., Bardenet, R., & Desolneux, A. (2025). "Repulsive
Monte Carlo on the sphere for the sliced Wasserstein distance."
arXiv:2509.10166 (under review at TMLR).
Follow-up to #838.
I'd like to work on this myself and will follow up with a PR.