| """Pure-scale heterogeneity with heavy-tailed ILR noise.""" |
| import numpy as np |
|
|
| from .base import DGPSample |
| from .pure_scale import PureScaleDGP |
| from ..utils.simplex import aitchison_dist, ilr, ilr_inv |
|
|
|
|
| class HeavyTailDGP(PureScaleDGP): |
| """D2 with Student-t noise in ILR space.""" |
|
|
| def __init__( |
| self, |
| K: int = 3, |
| sigma_min: float = 0.1, |
| c: float = 0.5, |
| d_x: int = 2, |
| df: float = 3.0, |
| ): |
| super().__init__(K=K, sigma_min=sigma_min, c=c, d_x=d_x) |
| self.df = df |
|
|
| def sample(self, n: int, rng: np.random.Generator) -> DGPSample: |
| self._init_weights(rng) |
| X = rng.standard_normal((n, self.d_x)) |
| mu = self._mu(X) |
| sigma = self._sigma(mu) |
|
|
| Z_mu = ilr(mu) |
| scale = np.sqrt(self.df / (self.df - 2.0)) if self.df > 2 else 1.0 |
| eps = rng.standard_t(df=self.df, size=(n, self.K - 1)) / scale |
| Y = ilr_inv(Z_mu + sigma[:, None] * eps, K=self.K) |
|
|
| U = mu |
| R = aitchison_dist(Y, U) |
| return DGPSample(X=X, Y=Y, U=U, R=R, sigma_true=sigma) |
|
|
