Stabilize singular empirical covariance precision

[sylvesterkaczmarek]

Closes #8566

Summary

• use a dtype-aware cutoff when computing the covariance pseudoinverse
• apply the same cutoff to stored and on-demand precision matrices
• add regression coverage for singular float32 covariance and Mahalanobis distances

Validation

• python3 -m py_compile python/cuml/cuml/covariance/empirical_covariance.py python/cuml/tests/test_empirical_covariance.py
• git diff --check

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• python/cuml/tests/test_empirical_covariance.py

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• python/cuml/tests/test_empirical_covariance.py

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📝 Summary

Summary by CodeRabbit

• Bug Fixes

  • Improved precision calculations for covariance matrices across supported data types, including rank-deficient and singular matrices.
  • Improved consistency of Mahalanobis distance results for float32 covariance data.
  • Improved numerical reliability when calculating precision matrices from singular covariance inputs.

• Tests

  • Added regression coverage comparing precision and Mahalanobis distance results with scikit-learn for singular covariance matrices in multiple precision-storage configurations.

Walkthrough

Changes

Empirical covariance stability

Layer / File(s)	Summary
Dtype-aware pseudoinverse integration python/cuml/cuml/covariance/empirical_covariance.py	Adds _pinv with a dtype-specific tolerance. fit and get_precision use it to compute precision matrices.
Singular covariance regression coverage python/cuml/tests/test_empirical_covariance.py	Adds parametrized comparisons with scikit-learn for singular float32 covariance input and both precision-storage configurations.

Estimated code review effort: 2 (Simple) | ~10 minutes

Severity of issue fixed: Medium

Merge Risk: ⚪ Minimal · up to b9e98

This change stabilizes singular covariance precision and Mahalanobis distances with dtype-aware behavior and regression coverage. No actionable merge-blocking risk is identified.

🚥 Pre-merge checks | ✅ 4 | ❌ 1

❌ Failed checks (1 warning)

Check name	Status	Explanation	Resolution
Docstring Coverage	⚠️ Warning	Docstring coverage is 66.67% which is insufficient. The required threshold is 80.00%. Docstring coverage is scoped to functions touched by this diff. Analyzed 9 functions across 2 files.	Write docstrings for the functions missing them to satisfy the coverage threshold.

✅ Passed checks (4 passed)

Check name	Status	Explanation
Title check	✅ Passed	The title clearly and concisely describes the primary change: stabilizing precision computation for singular empirical covariance matrices.
Description check	✅ Passed	The description directly explains the dtype-aware pseudoinverse cutoff, its application to precision matrices, and the regression tests for singular float32 covariance.
Linked Issues check	✅ Passed	The changes address issue #8566 by using a dtype-aware pseudoinverse cutoff for stable precision matrices and by adding regression coverage for Mahalanobis distances on singular covariance data.
Out of Scope Changes check	✅ Passed	The implementation and test changes are limited to the singular covariance precision fix, related Mahalanobis regression coverage, and attribution updates. No unrelated code changes are evident.

✨ Finishing Touches 💡 1

🛠️ Fix failing CI checks 💡

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[csadorf]

Looks good. I ran all 44 EmpiricalCovariance tests and found no meaningful performance regression. I pushed the required pre-commit fix to this PR. Please run the pre-commit hooks for future commits.

[csadorf]

I’d suggest investigating a Hermitian-specific pseudoinverse based on cp.linalg.eigh in a follow-up. That would also match scikit-learn’s use of scipy.linalg.pinvh. I ran some quick tests, and performance looked promising. This fix looks good, so we can merge as-is.

[csadorf]

CI is only blocked by the known libcuml wheel repair failure tracked in #8603. All four wheel jobs fail because auditwheel cannot locate libkvikio.so; the same failures occur on main. All relevant build, test, style, and documentation checks passed.

[csadorf]

/ok to test b9e981f