[MRG]Add UnifOrtho sampling of slicing directions for Sliced Wasserstein - #853
Open
Samuel-Vangu wants to merge 5 commits into
Open
Samuel-Vangu wants to merge 5 commits into
Samuel-Vangu wants to merge 5 commits into
Conversation
Contributor
Author
Codecov Report✅ All modified and coverable lines are covered by tests. Additional details and impacted files@@ Coverage Diff @@
## master #853 +/- ##
========================================
Coverage 96.86% 96.86%
========================================
Files 128 128
Lines 26181 26289 +108
========================================
+ Hits 25359 25465 +106
- Misses 822 824 +2 🚀 New features to boost your workflow:
|
rflamary
requested review from
clbonet
and
a lite review from Copilot
and removed request for
Copilot
September 16, 2026 11:41
clbonet
reviewed
Sep 16, 2026
clbonet
left a comment
clbonet
left a comment
Collaborator
There was a problem hiding this comment.
Thank you @Samuel-Vangu for this PR. The code looks very good, I only have few minor comments.
Comment on lines
+84
to
+107
| ax1.set_title("Uniform (Monte Carlo)") | ||
|
|
||
| ax2 = fig.add_subplot(1, 2, 2, projection="3d") | ||
| block_ids = np.repeat(np.arange(n_blocks), d) | ||
| ax2.scatter( | ||
| theta_uniortho[0], | ||
| theta_uniortho[1], | ||
| theta_uniortho[2], | ||
| c=block_ids, | ||
| cmap="tab10", | ||
| s=25, | ||
| alpha=0.9, | ||
| ) | ||
| ax2.set_title("UnifOrtho (one color per orthogonal block)") | ||
|
|
||
| for ax in (ax1, ax2): | ||
| ax.set_box_aspect([1, 1, 1]) | ||
| ax.view_init(elev=20, azim=45) | ||
| ax.set_xticks([]) | ||
| ax.set_yticks([]) | ||
| ax.set_zticks([]) | ||
|
|
||
| pl.tight_layout() | ||
| pl.show() |
Collaborator
There was a problem hiding this comment.
Add a sphere for better visualization?
| than independent draws would. | ||
|
|
||
| We first visualize this block structure on the ordinary 3D sphere, purely | ||
| for intuition -- dimension 3 is precisely where QSW/RQSW should be |
Collaborator
There was a problem hiding this comment.
You could maybe add this baseline in the 3D example to show that QMC is better than UnifOrtho in this case.
| return radius * x_azimuth / nx.sqrt(norm2) | ||
|
|
||
|
|
||
| def get_projections_uniortho(d, n_projections, seed=None, backend=None, type_as=None): |
| # directions (see get_random_rotations for the QR-based construction | ||
| # and its Mezzadri (2007) sign correction, which is what makes the | ||
| # rotation genuinely Haar-uniform rather than merely orthogonal). | ||
| rotations = get_random_rotations(d, k, seed=seed, backend=nx, type_as=type_as) |
| .. [95] Nguyen, K., Bariletto, N., & Ho, N. (2024). "Quasi-Monte Carlo for 3D Sliced Wasserstein." International Conference on Learning Representations (ICLR). | ||
| .. [96] Rakhmanov, E. A., Saff, E. B., & Zhou, Y. M. (1994). "Minimal Discrete Energy on the Sphere." Mathematical Research Letters, 1(6), 647-662. | ||
| .. [97] Rowland, M., Hron, J., Tang, Y., Choromanski, K., Sarlos, T., & Weller, A. (2019). "Orthogonal Estimation of Wasserstein Distances." Proceedings of the 22nd International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 89. | ||
| .. [98] Petrovic, V., Bardenet, R., & Desolneux, A. (2025). "Repulsive Monte Carlo on the sphere for the sliced Wasserstein distance." arXiv:2509.10166. |
Collaborator
There was a problem hiding this comment.
This is a TMLR paper, add the right citation
Collaborator
There was a problem hiding this comment.
I guess you can also cite https://openreview.net/forum?id=ECBepTWAFG which also studies methods to draw directions and tested the UnifOrth
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
3 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Types of changes
Motivation and context / Related issue
The Sliced Wasserstein distance only supports a low-discrepancy sampling
alternative to plain Monte Carlo (QSW/RQSW, PR #838) for
dim == 3. Thisleaves no principled alternative in higher dimension, where variance
reduction matters most.
Adds UnifOrtho sampling: independent blocks of mutually orthogonal
directions, drawn from the Haar measure on
O(dim), defined for anydimand recommended specifically for large dimension by a recentnumerical and theoretical study. Reuses the existing
get_random_rotationsdirectly, requiring no new randomization primitive.
Closes #850 .
How has this been tested (if it applies)
within a block, correctness for arbitrary dimensions (including
non-multiples of
dim), seed reproducibility, cross-backend consistency(NumPy, PyTorch, JAX, TensorFlow), and reduced approximation error
compared to uniform sampling in high dimension against a closed-form
reference distance.
plot_uniortho.py) demonstrating both theorthogonal block structure and the convergence gain in high dimension.
PR checklist