joint_normal, p, noise=False)

Joint Normal simulation.

Joint Normal \((X, Y) \in \mathbb{R}^p \times \mathbb{R}^p\): Let \(\rho = \frac{1}{2} p\), \(I_p\) be the identity matrix of size \(p \times p\), \(J_p\) be the matrix of ones of size \(p \times p\) and \(\Sigma = \begin{bmatrix} I_p & \rho J_p \\ \rho J_p & (1 + 0.5\kappa) I_p \end{bmatrix}\). Then,

\[(X, Y) \sim \mathcal{N}(0, \Sigma)\]
  • 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.


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.