make_friedman2

sklearn.datasets.make_friedman2(n_samples=100, *, noise=0.0, random_state=None)[source]

Generate the “Friedman #2” regression problem.

This dataset is described in Friedman [1] and Breiman [2].

Inputs X are 4 independent features uniformly distributed on the intervals:

0 <= X[:, 0] <= 100,
40 * pi <= X[:, 1] <= 560 * pi,
0 <= X[:, 2] <= 1,
1 <= X[:, 3] <= 11.

The output y is created according to the formula:

y(X) = (X[:, 0] ** 2 + (X[:, 1] * X[:, 2]  - 1 / (X[:, 1] * X[:, 3])) ** 2) ** 0.5 + noise * N(0, 1).

Read more in the User Guide.

Parameters:

n_samplesint, default=100

The number of samples.

noisefloat, default=0.0

The standard deviation of the gaussian noise applied to the output.

random_stateint, RandomState instance or None, default=None

Determines random number generation for dataset noise. Pass an int for reproducible output across multiple function calls. See Glossary.

Returns:

Xndarray of shape (n_samples, 4)

The input samples.

yndarray of shape (n_samples,)

The output values.

References

[1]

J. Friedman, “Multivariate adaptive regression splines”, The Annals of Statistics 19 (1), pages 1-67, 1991.

[2]

L. Breiman, “Bagging predictors”, Machine Learning 24, pages 123-140, 1996.

Examples

>>> from sklearn.datasets import make_friedman2
>>> X, y = make_friedman2(random_state=42)
>>> X.shape
(100, 4)
>>> y.shape
(100,)
>>> list(y[:3])
[np.float64(1229.4...), np.float64(27.0...), np.float64(65.6...)]