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@pytest.mark.parametrize(
    "method, lmbda",
    [
        ("box-cox", 0.1),
        ("box-cox", 0.5),
        ("yeo-johnson", 0.1),
        ("yeo-johnson", 0.5),
        ("yeo-johnson", 1.0),
    ],
)
def test_optimization_power_transformer(method, lmbda):
    # Test the optimization procedure:
    # - set a predefined value for lambda
    # - apply inverse_transform to a normal dist (we get X_inv)
    # - apply fit_transform to X_inv (we get X_inv_trans)
    # - check that X_inv_trans is roughly equal to X

    rng = np.random.RandomState(0)
    n_samples = 20000
    X = rng.normal(loc=0, scale=1, size=(n_samples, 1))

    pt = PowerTransformer(method=method, standardize=False)
    pt.lambdas_ = [lmbda]
    X_inv = pt.inverse_transform(X)

    pt = PowerTransformer(method=method, standardize=False)
    X_inv_trans = pt.fit_transform(X_inv)

    assert_almost_equal(0, np.linalg.norm(X - X_inv_trans) / n_samples, decimal=2)
    assert_almost_equal(0, X_inv_trans.mean(), decimal=1)
    assert_almost_equal(1, X_inv_trans.std(), decimal=1)

I think we need to reconsider the test above since some values of X are not possible with the preset lambda.

Recall that Box-Cox transformation requires $x>0$, therefore $\lambda y + 1 = x^\lambda > 0$, where $y=(x^\lambda-1)/\lambda$. However, when $y<-2$, which is possible for random generated data, $\lambda y + 1<0$ for $\lambda=0.5$.

And the build error is during computing the inverse.

lmbda = 0.5
x = -2.1
print((x * lmbda + 1) ** (1 / lmbda)) # 0.0025000000000000044 (scikit-learn's inverse of box-cox)
print(np.exp(np.log1p(lmbda * x) / lmbda)) # nan (scipy's inverse of box-cox)

In the original PR #10210, inv_boxcox was used (780baf7) and then later removed (df2b372), and I'm not sure why.

Maybe @glemaitre would remember? @jjerphan might also have an idea here.

Sorry, I don't have any idea nor time to have a look at it at the moment. 😕

@xuefeng-xu you're right regarding the test as well. It would be nice if you could fix the test for this change as well and improve the test. We can also add a test to make sure if input is not resonable, we output nan, and we add a bug fix entry in the changelog.

In the original PR #10210, inv_boxcox was used (780baf7) and then later removed (df2b372)

It seems that the minimum supported scipy doesn't have special.inv_boxcox at that time, that's why we implemeted ourself?
See the discussion between these two commits #6781 (comment) and #6781 (comment)

I have fixed the broken test and added a new one.