逻辑回归：从分类概率到决策阈值

import numpy as np

scores = np.array([-3.0, -1.0, 0.0, 1.0, 3.0])
probabilities = 1 / (1 + np.exp(-scores))
print(np.round(probabilities, 3))

import numpy as np
from sklearn.datasets import make_classification
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import precision_score, recall_score
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import make_pipeline

X, y = make_classification(
    n_samples=1000, n_features=6, n_informative=4,
    weights=[0.8, 0.2], class_sep=1.0, random_state=7,
)
X_train, X_valid, y_train, y_valid = train_test_split(
    X, y, test_size=0.3, stratify=y, random_state=42,
)
model = make_pipeline(StandardScaler(), LogisticRegression(max_iter=1000))
model.fit(X_train, y_train)
probability = model.predict_proba(X_valid)[:, 1]

for threshold in (0.3, 0.5, 0.7):
    prediction = (probability >= threshold).astype(int)
    print(
        threshold,
        "precision=", round(precision_score(y_valid, prediction, zero_division=0), 3),
        "recall=", round(recall_score(y_valid, prediction), 3),
    )

import pandas as pd

rows = []
false_negative_cost = 8
false_positive_cost = 1

for threshold in np.arange(0.15, 0.86, 0.05):
    prediction = (probability >= threshold).astype(int)
    false_negative = int(((y_valid == 1) & (prediction == 0)).sum())
    false_positive = int(((y_valid == 0) & (prediction == 1)).sum())
    rows.append({
        "threshold": round(float(threshold), 2),
        "alerts": int(prediction.sum()),
        "precision": precision_score(y_valid, prediction, zero_division=0),
        "recall": recall_score(y_valid, prediction, zero_division=0),
        "cost": false_negative * false_negative_cost + false_positive * false_positive_cost,
    })

threshold_report = pd.DataFrame(rows)
print(threshold_report.sort_values("cost").head())

from sklearn.calibration import calibration_curve

observed, predicted = calibration_curve(
    y_valid, probability, n_bins=8, strategy="quantile"
)
for mean_prediction, positive_rate in zip(predicted, observed):
    print(round(mean_prediction, 3), round(positive_rate, 3))