Machine Learning: 逻辑回归 — 分类问题入门与电商用户行为预测指南

from sklearn.linear_model import LogisticRegression
from sklearn.metrics import classification_report

model = LogisticRegression(class_weight="balanced")
model.fit(X_train, y_train)
y_pred = model.predict(X_test)
print(classification_report(y_test, y_pred, target_names=["Retained", "Churned"]))

import numpy as np
import matplotlib.pyplot as plt

z = np.linspace(-8, 8, 100)
sigmoid = 1 / (1 + np.exp(-z))

fig, ax = plt.subplots(figsize=(8, 5))
ax.plot(z, sigmoid, linewidth=2, color="#2196F3")
ax.axhline(0.5, color="red", linestyle="--", alpha=0.5, label="Decision boundary")
ax.axvline(0, color="gray", linestyle="--", alpha=0.3)
ax.set_xlabel("z (linear combination)")
ax.set_ylabel("σ(z) = P(y=1)")
ax.set_title("Sigmoid Function")
ax.legend()
ax.grid(True, alpha=0.3)
plt.tight_layout()
plt.savefig("sigmoid.png", dpi=150)

# 执行成功

from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.pipeline import Pipeline
from sklearn.metrics import accuracy_score, confusion_matrix, classification_report
import numpy as np

rng = np.random.default_rng(42)
n = 1000
X = rng.standard_normal((n, 4))  # [browsing_time, pages_viewed, cart_value, visit_count]
y = (X[:, 0] * 0.5 + X[:, 1] * 1.2 + X[:, 2] * 2.0 + rng.normal(0, 0.5, n) > 1.5).astype(int)

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42, stratify=y)

pipe = Pipeline([
    ("scaler", StandardScaler()),
    ("model", LogisticRegression(random_state=42)),
])
pipe.fit(X_train, y_train)
y_pred = pipe.predict(X_test)
y_prob = pipe.predict_proba(X_test)[:, 1]  # Probability of class 1

print(f"Accuracy: {accuracy_score(y_test, y_pred):.4f}")
print(f"\nConfusion Matrix:\n{confusion_matrix(y_test, y_pred)}")
print(f"\nClassification Report:\n{classification_report(y_test, y_pred)}")
print(f"\nSample probabilities: {y_prob[:5].round(3)}")

# 执行成功

from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import roc_auc_score, precision_recall_fscore_support
import pandas as pd
import numpy as np

rng = np.random.default_rng(42)
n = 5000
df = pd.DataFrame({
    "tenure_months": rng.integers(1, 60, n),
    "monthly_usage_hours": rng.exponential(20, n),
    "support_tickets": rng.poisson(2, n),
    "payment_delay_days": rng.integers(0, 30, n),
    "plan_tier": rng.choice([1, 2, 3], n, p=[0.5, 0.35, 0.15]),
})

# Churn logic: short tenure + low usage + many tickets + delays
churn_score = (
    -0.05 * df["tenure_months"]
    - 0.1 * df["monthly_usage_hours"]
    + 0.5 * df["support_tickets"]
    + 0.1 * df["payment_delay_days"]
    + rng.normal(0, 1, n)
)
df["churned"] = (churn_score > 2).astype(int)
print(f"Churn rate: {df['churned'].mean():.1%}")

# Train with class_weight="balanced" for imbalanced data
X = df.drop(columns=["churned"])
y = df["churned"]
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42, stratify=y)

model = LogisticRegression(class_weight="balanced", max_iter=500, random_state=42)
model.fit(X_train, y_train)

y_pred = model.predict(X_test)
y_prob = model.predict_proba(X_test)[:, 1]
auc = roc_auc_score(y_test, y_prob)
precision, recall, f1, _ = precision_recall_fscore_support(y_test, y_pred, average="binary")

print(f"AUC-ROC: {auc:.4f}")
print(f"Precision: {precision:.4f}, Recall: {recall:.4f}, F1: {f1:.4f}")

# 执行成功

from sklearn.linear_model import LogisticRegression
from sklearn.datasets import load_iris
from sklearn.model_selection import cross_val_score

X, y = load_iris(return_X_y=True)

# One-vs-Rest (default)
ovr_model = LogisticRegression(multi_class="ovr", max_iter=200)
ovr_scores = cross_val_score(ovr_model, X, y, cv=5, scoring="accuracy")

# Softmax (Multinomial)
softmax_model = LogisticRegression(multi_class="multinomial", max_iter=200)
softmax_scores = cross_val_score(softmax_model, X, y, cv=5, scoring="accuracy")

print(f"One-vs-Rest:  {ovr_scores.mean():.4f} +/- {ovr_scores.std():.4f}")
print(f"Softmax:      {softmax_scores.mean():.4f} +/- {softmax_scores.std():.4f}")

# 执行成功

from sklearn.metrics import roc_curve, auc, precision_recall_curve
import matplotlib.pyplot as plt
import numpy as np

# Assume y_test and y_prob from previous example
rng = np.random.default_rng(42)
y_test = rng.choice([0, 1], 500, p=[0.85, 0.15])
y_prob = np.clip(y_test * 0.8 + rng.normal(0, 0.3, 500), 0, 1)

fig, axes = plt.subplots(1, 2, figsize=(14, 5))

# ROC Curve
fpr, tpr, _ = roc_curve(y_test, y_prob)
roc_auc = auc(fpr, tpr)
axes[0].plot(fpr, tpr, color="#2196F3", lw=2, label=f"AUC = {roc_auc:.3f}")
axes[0].plot([0, 1], [0, 1], "r--", alpha=0.5)
axes[0].set_xlabel("False Positive Rate")
axes[0].set_ylabel("True Positive Rate")
axes[0].set_title("ROC Curve")
axes[0].legend()

# PR Curve
precision_vals, recall_vals, _ = precision_recall_curve(y_test, y_prob)
axes[1].plot(recall_vals, precision_vals, color="#4CAF50", lw=2)
axes[1].set_xlabel("Recall")
axes[1].set_ylabel("Precision")
axes[1].set_title("Precision-Recall Curve")

plt.tight_layout()
plt.savefig("roc_pr_curves.png", dpi=150)

# 执行成功