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Stabilize singular empirical covariance precision #8606

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Stabilize singular empirical covariance precision #8606

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b84de5c
Stabilize singular empirical covariance precision
sylvesterkaczmarek Sep 10, 2026
2611612
Fix copyright notice
csadorf Sep 10, 2026
5064106
Merge upstream main into PR branch
sylvesterkaczmarek Sep 10, 2026
b9e981f
Merge branch 'main' into bug-empirical-covariance-pinv
csadorf Sep 11, 2026
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10 changes: 8 additions & 2 deletions python/cuml/cuml/covariance/empirical_covariance.py
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Original file line number Diff line number Diff line change
Expand Up @@ -23,6 +23,12 @@ def _empirical_covariance(X, assume_centered=False):
return cp.dot(X_centered.T, X_centered) / X.shape[0]


def _pinv(covariance):

@csadorf csadorf Sep 10, 2026

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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.

"""Compute a dtype-aware Moore-Penrose pseudoinverse."""
rcond = max(covariance.shape) * cp.finfo(covariance.dtype).eps
return cp.linalg.pinv(covariance, rcond=rcond)


def _log_likelihood(emp_cov, precision):
"""Compute the sample mean log-likelihood under a covariance model."""
sign, log_det_precision = cp.linalg.slogdet(precision)
Expand Down Expand Up @@ -188,7 +194,7 @@ def fit(self, X, y=None) -> "EmpiricalCovariance":
self.covariance_ = covariance

if self.store_precision:
self.precision_ = cp.linalg.pinv(covariance)
self.precision_ = _pinv(covariance)
else:
self.precision_ = None

Expand All @@ -207,7 +213,7 @@ def get_precision(self):

if self.store_precision:
return self.precision_
return cp.linalg.pinv(self.covariance_)
return _pinv(self.covariance_)

@mlfunc(convert_output=False)
def score(self, X_test, y=None) -> float:
Expand Down
22 changes: 21 additions & 1 deletion python/cuml/tests/test_empirical_covariance.py
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Original file line number Diff line number Diff line change
@@ -1,5 +1,5 @@
#
# SPDX-FileCopyrightText: Copyright (c) 2026, NVIDIA CORPORATION.
# SPDX-FileCopyrightText: Copyright (c) 2026, NVIDIA CORPORATION & AFFILIATES. All rights reserved.
# SPDX-License-Identifier: Apache-2.0
#

Expand Down Expand Up @@ -244,6 +244,26 @@ def test_mahalanobis_matches_sklearn():
)


@pytest.mark.parametrize("store_precision", [True, False])
def test_singular_covariance_matches_sklearn(store_precision):
X = np.array([[1, 2], [3, 4], [5, 6]], dtype=np.float32)
cu_cov = EmpiricalCovariance(store_precision=store_precision).fit(X)
sk_cov = SklearnEmpiricalCovariance(store_precision=store_precision).fit(X)

np.testing.assert_allclose(
np.asarray(cu_cov.get_precision()),
sk_cov.get_precision(),
rtol=1e-5,
atol=1e-6,
)
np.testing.assert_allclose(
np.asarray(cu_cov.mahalanobis(X[:2])),
sk_cov.mahalanobis(X[:2]),
rtol=1e-5,
atol=1e-6,
)


def test_error_norm_frobenius_matches_sklearn():
X = _make_random_data()
cu_cov = EmpiricalCovariance().fit(X)
Expand Down
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