w_shaped¶
-
hyppo.tools.w_shaped(n, p, noise=False, low=- 1, high=1)¶ W-Shaped simulation.
W-Shaped \((X, Y) \in \mathbb{R}^p \times \mathbb{R}\): \(\mathcal{U}(-1, 1)^p\),
\[\begin{split}X &\sim \mathcal{U}(-1, 1)^p \\ Y &= \left[ \left( (w^T X)^2 - \frac{1}{2} \right)^2 + \frac{w^T U}{500} \right] + 0.5 \kappa \epsilon\end{split}\]- 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 (
ndarray) -- 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.
