Selecting the features for the Friedman-1 regression problem

The Friedman-1 regression problem, which was created by Friedman and Breiman, describes a single output value, y , which is a function of five input values, x 0, x 1, x 2, x 3, x 4, and randomly generated noise, according to the following formula:

y(x 0, x 1, x 2, x 3, x 4)

= 10 ∙ sin(π ∙ x 0 ∙ x 1) + 20 (x 2 − 0.5) 2 + 10 x 3 + 5 x 4 + noise

∙ N(0, 1)

The input variables, x 0 . .x 4, are independent, and uniformly distributed over the interval [0, 1]. The last component in the formula is the randomly generated noise. The noise is normally distributed and multiplied by the constant noise, which determines its level.

In Python, the scikit-learn (sklearn) library provides us with the make_friedman1() function, which can be used to generate a dataset containing the desired number...