multiplicative_noise

hyppo.tools.multiplicative_noise(n, p)

Multiplicative Noise simulation.

Multiplicative Noise \((X, Y) \in \mathbb{R}^p \times \mathbb{R}^p\): \(\U \sim \mathcal{N}(0, I_p)\),

\[\begin{split}X &\sim \mathcal{N}(0, I_p) \\ Y_{|d|} &= U_{|d|} X_{|d|}\ \mathrm{for}\ d = 1, ..., p\end{split}\]

Parameters

• n (int) -- The number of samples desired by the simulation (>= 5).

• p (int) -- The number of dimensions desired by the simulation (>= 1).

Returns

x,y (ndarray) -- Simulated data matrices. x` and ``y have shapes (n, p) and (n, p) where n is the number of samples and p is the number of dimensions.