logarithmic

hyppo.tools.logarithmic(n, p, noise=False)

Logarithmic simulation.

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

\[\begin{split}X &\sim \mathcal{N}(0, I_p) \\ Y_{|d|} &= 2 \log_2 (|X_{|d|}|) + 3 \kappa \epsilon_{|d|} \ \mathrm{for}\ d = 1, ..., p\end{split}\]

Parameters

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

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

• noise (bool, default: False) -- Whether or not to include noise in the simulation.

Returns

x,y (ndarray of float) -- 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.