fourth_root¶
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hyppo.tools.fourth_root(n, p, noise=False, low=- 1, high=1)¶ Fourth Root simulation.
Fourth Root \((X, Y) \in \mathbb{R}^p \times \mathbb{R}\):
\[\begin{split}X &\sim \mathcal{U}(-1, 1)^p \\ Y &= |w^T X|^\frac{1}{4} + \frac{\kappa}{4} \epsilon\end{split}\]- Parameters
n (
int) -- The number of samples desired by the simulation (>= 5).p (
int) -- The number of dimensions desired by the simulation (>= 1).noise (
bool, default:False) -- Whether or not to include noise in the simulation.low (
float, default:-1) -- The lower limit of the uniform distribution simulated from.high (
float, default:1) -- The upper limit of the uniform distribution simulated from.
- Returns
x,y (
ndarrayoffloat) -- Simulated data matrices.x` and ``yhave shapes(n, p)and(n, 1)where n is the number of samples and p is the number of dimensions.