LinearRegression is sometimes not deterministic

LinearRegression is sometimes not deterministic, as shown by the following test:

from sklearn.linear_model import LinearRegression
from sklearn.utils.testing import assert_array_equal
from sklearn.tests.test_multioutput import generate_multilabel_dataset_with_correlations

def test_investigate_linear_regression_indeterminacy():
    # Is LinearRegression deterministic?
    X, Y = generate_multilabel_dataset_with_correlations()
    y = Y[:, 1]
    ref = LinearRegression().fit(X, y).coef_
    for i in range(1000):
        coef = LinearRegression().fit(X, y).coef_
        assert_array_equal(ref, coef, 'iter %d' % i)

test_investigate_linear_regression_indeterminacy()

which failed at iteration 18 in this Travis job. I can’t reproduce locally. It only occurs on one Travis platform (Linux + python 3.6.2), only sometimes (iteration 18 in this test case).

Failure spotted initially in https://github.com/scikit-learn/scikit-learn/pull/9257#issuecomment-350111442

[rth]

Thanks @maxsargent !

+1 for closing, due to,

• assert_array_equal being too strict for floating point comparison (as compared to assert_allclose) an can lead to false positives (as discussed in the linked scipy issue BLAS implementations can be non-deterministic within the float eps tolerance).
• difficulties to reproduce locally even with assert_array_equal
• in a similar issue https://github.com/scikit-learn/scikit-learn/issues/12724 the coefficients are the same with 10 significant digits, which should be enough in practice I think?

the discussion in the corresponding scipy issue https://github.com/scipy/scipy/issues/8208 is insightful (and remains open).

Please comment/reopen in case of disagreement.

[maxsargentdev]

This issue has come to me through a triage email.

From a brief look at Travis this issue is no longer occurring, I have tried this code with the Python version mentioned (3.6.2) and it is not reproducible outside of Travis.

Due to the extended period of time this issue has been open and the fact it cant reproduced I am suggesting it is closed out.