Model Calibration — Are Probabilities Trustworthy?

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split, cross_val_score
from sklearn.ensemble import RandomForestClassifier, GradientBoostingClassifier
from sklearn.linear_model import LogisticRegression
from sklearn.naive_bayes import GaussianNB
from sklearn.calibration import CalibratedClassifierCV, CalibrationDisplay
from sklearn.metrics import brier_score_loss

np.random.seed(42)
X, y = make_classification(n_samples=5000, n_features=20, random_state=42)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
X_train_base, X_cal, y_train_base, y_cal = train_test_split(X_train, y_train, test_size=0.3, random_state=42)

# MODELS WITH DIFFERENT CALIBRATION CHARACTERISTICS
models = {
    "Logistic Regression":   LogisticRegression(max_iter=1000, random_state=42),
    "Random Forest":         RandomForestClassifier(n_estimators=100, random_state=42),
    "Gradient Boosting":     GradientBoostingClassifier(n_estimators=100, random_state=42),
    "Naive Bayes":           GaussianNB(),
}

fig, axes = plt.subplots(1, 2, figsize=(14, 6))

# CALIBRATION CURVES
for name, model in models.items():
    model.fit(X_train, y_train)
    CalibrationDisplay.from_estimator(model, X_test, y_test, n_bins=10, ax=axes[0], name=name)
    bs = brier_score_loss(y_test, model.predict_proba(X_test)[:, 1])
    print(f"  {name:22s}: Brier score = {bs:.4f}  (lower = better calibration + accuracy)")

axes[0].set_title("Calibration Curves\n(Diagonal = perfectly calibrated)")

# FIX CALIBRATION: Platt Scaling (sigmoid) or Isotonic Regression
rf_uncal = RandomForestClassifier(n_estimators=100, random_state=42)
rf_uncal.fit(X_train_base, y_train_base)

rf_platt    = CalibratedClassifierCV(RandomForestClassifier(n_estimators=100, random_state=42), method="sigmoid",  cv=5)
rf_isotonic = CalibratedClassifierCV(RandomForestClassifier(n_estimators=100, random_state=42), method="isotonic", cv=5)

for cal_model, cal_name in [(rf_uncal, "RF Uncalibrated"), (rf_platt, "RF + Platt"), (rf_isotonic, "RF + Isotonic")]:
    cal_model.fit(X_train, y_train)
    CalibrationDisplay.from_estimator(cal_model, X_test, y_test, n_bins=10, ax=axes[1], name=cal_name)
    bs = brier_score_loss(y_test, cal_model.predict_proba(X_test)[:, 1])
    print(f"  {cal_name:22s}: Brier score = {bs:.4f}")

axes[1].set_title("Calibration: RF Before/After Calibration")
plt.tight_layout()
plt.savefig("calibration_curves.png", dpi=100, bbox_inches="tight")
plt.show()

print("\nWhen calibration matters:")
use_cases = [
    "Insurance pricing: probabilities directly map to premium calculations",
    "Medical risk scoring: 30% risk score means different treatment than 60%",
    "Ranking/sorting: if only comparing predictions, ROC-AUC matters, not calibration",
    "Decision threshold: if just predicting class labels, calibration less critical",
]
for case in use_cases:
    print(f"  -> {case}")