Plotting CQR with symmetric argument

An example plot of MapieQuantileRegressor illustrating the impact of the symmetry parameter.

import numpy as np
from matplotlib import pyplot as plt
from sklearn.datasets import make_regression
from sklearn.ensemble import GradientBoostingRegressor

from mapie.metrics import regression_coverage_score
from mapie.quantile_regression import MapieQuantileRegressor

random_state = 2

We generate a synthetic data.

X, y = make_regression(n_samples=500, n_features=1, noise=20, random_state=59)

# Define alpha level
alpha = 0.2

# Fit a Gradient Boosting Regressor for quantile regression
gb_reg = GradientBoostingRegressor(
    loss="quantile", alpha=0.5, random_state=random_state
)

# MAPIE Quantile Regressor
mapie_qr = MapieQuantileRegressor(estimator=gb_reg, alpha=alpha)
mapie_qr.fit(X, y, random_state=random_state)
y_pred_sym, y_pis_sym = mapie_qr.predict(X, symmetry=True)
y_pred_asym, y_pis_asym = mapie_qr.predict(X, symmetry=False)
y_qlow = mapie_qr.estimators_[0].predict(X)
y_qup = mapie_qr.estimators_[1].predict(X)

# Calculate coverage scores
coverage_score_sym = regression_coverage_score(
    y, y_pis_sym[:, 0], y_pis_sym[:, 1]
)
coverage_score_asym = regression_coverage_score(
    y, y_pis_asym[:, 0], y_pis_asym[:, 1]
)

# Sort the values for plotting
order = np.argsort(X[:, 0])
X_sorted = X[order]
y_pred_sym_sorted = y_pred_sym[order]
y_pis_sym_sorted = y_pis_sym[order]
y_pred_asym_sorted = y_pred_asym[order]
y_pis_asym_sorted = y_pis_asym[order]
y_qlow = y_qlow[order]
y_qup = y_qup[order]

Out:

/home/docs/checkouts/readthedocs.org/user_builds/mapie/conda/latest/lib/python3.10/site-packages/sklearn/utils/deprecation.py:66: FutureWarning: Class MapieQuantileRegressor is deprecated; WARNING: Deprecated path to import MapieQuantileRegressor. Please prefer the new path: [from mapie.regression import MapieQuantileRegressor].
  warnings.warn(msg, category=FutureWarning)
INFO:root:The predictions are ill-sorted.
INFO:root:The predictions are ill-sorted.
INFO:root:The predictions are ill-sorted.

We will plot the predictions and prediction intervals for both symmetric and asymmetric intervals. The line represents the predicted values, the dashed lines represent the prediction intervals, and the shaded area represents the symmetric and asymmetric prediction intervals.

plt.figure(figsize=(14, 7))

plt.subplot(1, 2, 1)
plt.xlabel("x")
plt.ylabel("y")
plt.scatter(X, y, alpha=0.3)
plt.plot(X_sorted, y_qlow, color="C1")
plt.plot(X_sorted, y_qup, color="C1")
plt.plot(X_sorted, y_pis_sym_sorted[:, 0], color="C1", ls="--")
plt.plot(X_sorted, y_pis_sym_sorted[:, 1], color="C1", ls="--")
plt.fill_between(
    X_sorted.ravel(),
    y_pis_sym_sorted[:, 0].ravel(),
    y_pis_sym_sorted[:, 1].ravel(),
    alpha=0.2,
)
plt.title(
    f"Symmetric Intervals\n"
    f"Target and effective coverages for "
    f"alpha={alpha:.2f}: ({1-alpha:.3f}, {coverage_score_sym:.3f})"
)

# Plot asymmetric prediction intervals
plt.subplot(1, 2, 2)
plt.xlabel("x")
plt.ylabel("y")
plt.scatter(X, y, alpha=0.3)
plt.plot(X_sorted, y_qlow, color="C2")
plt.plot(X_sorted, y_qup, color="C2")
plt.plot(X_sorted, y_pis_asym_sorted[:, 0], color="C2", ls="--")
plt.plot(X_sorted, y_pis_asym_sorted[:, 1], color="C2", ls="--")
plt.fill_between(
    X_sorted.ravel(),
    y_pis_asym_sorted[:, 0].ravel(),
    y_pis_asym_sorted[:, 1].ravel(),
    alpha=0.2,
)
plt.title(
    f"Asymmetric Intervals\n"
    f"Target and effective coverages for "
    f"alpha={alpha:.2f}: ({1-alpha:.3f}, {coverage_score_asym:.3f})"
)
plt.tight_layout()
plt.show()

The symmetric intervals (symmetry=True) use a combined set of residuals for both bounds, while the asymmetric intervals use distinct residuals for each bound, allowing for more flexible and accurate intervals that reflect the heteroscedastic nature of the data. The resulting effective coverages demonstrate the theoretical guarantee of the target coverage level 1 - α.