File size: 2,830 Bytes
fc329a3 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 | """Model-bias DGP: predictor misspecification beyond pure local scale."""
import numpy as np
from .base import BaseDGP, DGPSample
from .pure_scale import PureScaleDGP
from ..utils.simplex import ilr, ilr_inv, entropy, aitchison_dist
class ModelBiasDGP(PureScaleDGP):
"""Predictor bias that cannot be summarized by a scalar local scale alone.
The data-generating truth still follows the pure-scale construction, but the
predictor is shifted in ILR space by a location-dependent bias field.
Depending on `bias_type`, this field can rotate with prediction-space angle
or vary smoothly with the covariates. This creates residual distributions
whose heterogeneity is not purely radial.
"""
def __init__(self, K: int = 3, sigma_min: float = 0.1, c: float = 0.5,
d_x: int = 2, bias_scale: float = 0.15, bias_type: str = "smooth"):
super().__init__(K=K, sigma_min=sigma_min, c=c, d_x=d_x)
self.bias_scale = bias_scale
self.bias_type = bias_type
self._B = None # linear bias weights
def _init_bias(self, rng: np.random.Generator):
if self._B is None:
self._B = rng.standard_normal((self.d_x, self.K - 1)) * 0.5
def _bias(self, X: np.ndarray, Z_mu: np.ndarray) -> np.ndarray:
"""Location-dependent predictor bias in ILR space."""
if self.bias_type == "linear":
return self.bias_scale * (X @ self._B)
if self.bias_type == "smooth":
return self.bias_scale * np.sin(X @ self._B)
if self.bias_type == "rotational":
bias = np.zeros_like(Z_mu)
z0 = Z_mu[:, 0]
z1 = Z_mu[:, 1] if Z_mu.shape[1] > 1 else np.zeros_like(z0)
phase = np.arctan2(z1, z0 + 1e-8)
radius = np.sqrt(z0 ** 2 + z1 ** 2)
amp = self.bias_scale * (0.5 + np.tanh(radius))
bias[:, 0] = amp * np.cos(2.0 * phase)
if Z_mu.shape[1] > 1:
bias[:, 1] = amp * np.sin(2.0 * phase)
if Z_mu.shape[1] > 2:
bias[:, 2:] = 0.35 * self.bias_scale * np.sin(1.7 * Z_mu[:, 2:])
return bias
raise ValueError(f"Unknown bias_type: {self.bias_type}")
def sample(self, n: int, rng: np.random.Generator) -> DGPSample:
self._init_weights(rng)
self._init_bias(rng)
X = rng.standard_normal((n, self.d_x))
mu = self._mu(X)
sigma = self._sigma(mu)
# True Y: same as DGP 1
Z_mu = ilr(mu)
eps = rng.standard_normal((n, self.K - 1))
Z_y = Z_mu + sigma[:, None] * eps
Y = ilr_inv(Z_y, K=self.K)
# Biased predictor
b = self._bias(X, Z_mu)
U = ilr_inv(Z_mu + b, K=self.K)
R = aitchison_dist(Y, U)
return DGPSample(X=X, Y=Y, U=U, R=R, sigma_true=sigma)
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