Classification Modeling

分类建模

概述

分类建模用于预测类别型目标值，根据输入特征将观测值分配到离散的类别或分类中。

适用场景

• 预测二元结果，例如客户流失、贷款违约或电子邮件垃圾邮件
• 将项目划分为多个类别，例如产品类型或情感类别
• 构建信用评分模型或风险评估系统
• 根据患者数据识别疾病诊断或医疗状况
• 预测客户购买可能性或对营销活动的响应
• 检测生产系统中的欺诈、异常或质量缺陷

分类类型

• 二元分类：两个类别（是/否、成功/失败）
• 多分类：两个以上类别
• 多标签分类：每个观测值可对应多个类别

常用算法

• 逻辑回归：线性分类
• 决策树：基于规则的非线性分类
• 随机森林：由多棵决策树组成的集成
• 梯度提升：顺序构建决策树
• SVM：支持向量机
• 朴素贝叶斯：概率分类器

关键指标

• 准确率：预测正确的总体比例
• 精确率：真正例 /（真正例 + 假正例）
• 召回率：真正例 /（真正例 + 假负例）
• F1 分数：精确率与召回率的调和平均值
• AUC-ROC：受试者工作特征曲线下的面积

使用 Python 实现

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split, cross_val_score
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LogisticRegression
from sklearn.tree import DecisionTreeClassifier
from sklearn.ensemble import RandomForestClassifier, GradientBoostingClassifier
from sklearn.metrics import (
    confusion_matrix, classification_report, roc_auc_score, roc_curve,
    precision_recall_curve, f1_score, accuracy_score
)
import seaborn as sns

# Generate sample binary classification data
np.random.seed(42)
from sklearn.datasets import make_classification

X, y = make_classification(
    n_samples=1000, n_features=20, n_informative=10,
    n_redundant=5, random_state=42
)

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

# Standardize features
scaler = StandardScaler()
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)

# Logistic Regression
lr_model = LogisticRegression(max_iter=1000)
lr_model.fit(X_train_scaled, y_train)
y_pred_lr = lr_model.predict(X_test_scaled)
y_proba_lr = lr_model.predict_proba(X_test_scaled)[:, 1]

print("Logistic Regression:")
print(classification_report(y_test, y_pred_lr))
print(f"AUC-ROC: {roc_auc_score(y_test, y_proba_lr):.4f}\n")

# Decision Tree
dt_model = DecisionTreeClassifier(max_depth=10, random_state=42)
dt_model.fit(X_train, y_train)
y_pred_dt = dt_model.predict(X_test)
y_proba_dt = dt_model.predict_proba(X_test)[:, 1]

print("Decision Tree:")
print(classification_report(y_test, y_pred_dt))
print(f"AUC-ROC: {roc_auc_score(y_test, y_proba_dt):.4f}\n")

# Random Forest
rf_model = RandomForestClassifier(n_estimators=100, max_depth=10, random_state=42)
rf_model.fit(X_train, y_train)
y_pred_rf = rf_model.predict(X_test)
y_proba_rf = rf_model.predict_proba(X_test)[:, 1]

print("Random Forest:")
print(classification_report(y_test, y_pred_rf))
print(f"AUC-ROC: {roc_auc_score(y_test, y_proba_rf):.4f}\n")

# Gradient Boosting
gb_model = GradientBoostingClassifier(n_estimators=100, max_depth=5, random_state=42)
gb_model.fit(X_train, y_train)
y_pred_gb = gb_model.predict(X_test)
y_proba_gb = gb_model.predict_proba(X_test)[:, 1]

print("Gradient Boosting:")
print(classification_report(y_test, y_pred_gb))
print(f"AUC-ROC: {roc_auc_score(y_test, y_proba_gb):.4f}\n")

# Confusion matrices
fig, axes = plt.subplots(2, 2, figsize=(12, 10))

models = [
    (y_pred_lr, 'Logistic Regression'),
    (y_pred_dt, 'Decision Tree'),
    (y_pred_rf, 'Random Forest'),
    (y_pred_gb, 'Gradient Boosting'),
]

for idx, (y_pred, title) in enumerate(models):
    cm = confusion_matrix(y_test, y_pred)
    ax = axes[idx // 2, idx % 2]
    sns.heatmap(cm, annot=True, fmt='d', cmap='Blues', ax=ax)
    ax.set_title(title)
    ax.set_ylabel('True Label')
    ax.set_xlabel('Predicted Label')

plt.tight_layout()
plt.show()

# ROC Curves
plt.figure(figsize=(10, 8))

probas = [
    (y_proba_lr, 'Logistic Regression'),
    (y_proba_dt, 'Decision Tree'),
    (y_proba_rf, 'Random Forest'),
    (y_proba_gb, 'Gradient Boosting'),
]

for y_proba, label in probas:
    fpr, tpr, _ = roc_curve(y_test, y_proba)
    auc = roc_auc_score(y_test, y_proba)
    plt.plot(fpr, tpr, label=f'{label} (AUC={auc:.4f})')

plt.plot([0, 1], [0, 1], 'k--', label='Random Classifier')
plt.xlabel('False Positive Rate')
plt.ylabel('True Positive Rate')
plt.title('ROC Curves Comparison')
plt.legend()
plt.grid(True, alpha=0.3)
plt.show()

# Precision-Recall Curves
plt.figure(figsize=(10, 8))

for y_proba, label in probas:
    precision, recall, _ = precision_recall_curve(y_test, y_proba)
    f1 = f1_score(y_test, (y_proba > 0.5).astype(int))
    plt.plot(recall, precision, label=f'{label} (F1={f1:.4f})')

plt.xlabel('Recall')
plt.ylabel('Precision')
plt.title('Precision-Recall Curves')
plt.legend()
plt.grid(True, alpha=0.3)
plt.show()

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

# Tree-based feature importance
feature_importance_rf = pd.Series(
    rf_model.feature_importances_, index=range(X.shape[1])
).sort_values(ascending=False)

axes[0].barh(range(10), feature_importance_rf.values[:10])
axes[0].set_yticks(range(10))
axes[0].set_yticklabels([f'Feature {i}' for i in feature_importance_rf.index[:10]])
axes[0].set_title('Random Forest - Top 10 Features')
axes[0].set_xlabel('Importance')

# Logistic regression coefficients
lr_coef = pd.Series(lr_model.coef_[0], index=range(X.shape[1])).abs().sort_values(ascending=False)
axes[1].barh(range(10), lr_coef.values[:10])
axes[1].set_yticks(range(10))
axes[1].set_yticklabels([f'Feature {i}' for i in lr_coef.index[:10]])
axes[1].set_title('Logistic Regression - Top 10 Features (abs coef)')
axes[1].set_xlabel('Absolute Coefficient')

plt.tight_layout()
plt.show()

# Model comparison
results = pd.DataFrame({
    'Model': ['Logistic Regression', 'Decision Tree', 'Random Forest', 'Gradient Boosting'],
    'Accuracy': [
        accuracy_score(y_test, y_pred_lr),
        accuracy_score(y_test, y_pred_dt),
        accuracy_score(y_test, y_pred_rf),
        accuracy_score(y_test, y_pred_gb),
    ],
    'AUC-ROC': [
        roc_auc_score(y_test, y_proba_lr),
        roc_auc_score(y_test, y_proba_dt),
        roc_auc_score(y_test, y_proba_rf),
        roc_auc_score(y_test, y_proba_gb),
    ],
    'F1-Score': [
        f1_score(y_test, y_pred_lr),
        f1_score(y_test, y_pred_dt),
        f1_score(y_test, y_pred_rf),
        f1_score(y_test, y_pred_gb),
    ]
})

print("Model Comparison:")
print(results)

# Cross-validation
cv_scores = cross_val_score(
    RandomForestClassifier(n_estimators=100, random_state=42),
    X_train, y_train, cv=5, scoring='roc_auc'
)
print(f"\nCross-validation AUC scores: {cv_scores}")
print(f"Mean CV AUC: {cv_scores.mean():.4f} (+/- {cv_scores.std():.4f})")

# Probability calibration
from sklearn.calibration import calibration_curve

prob_true, prob_pred = calibration_curve(y_test, y_proba_rf, n_bins=10)

plt.figure(figsize=(8, 6))
plt.plot(prob_pred, prob_true, 'o-', label='Random Forest')
plt.plot([0, 1], [0, 1], 'k--', label='Perfect Calibration')
plt.xlabel('Mean Predicted Probability')
plt.ylabel('Fraction of Positives')
plt.title('Calibration Curve')
plt.legend()
plt.grid(True, alpha=0.3)
plt.show()

处理类别不平衡

• 过采样：增加少数类样本
• 欠采样：减少多数类样本
• SMOTE：合成少数类过采样
• 类别权重：对少数类误分类进行惩罚

阈值选择

• 默认值（0.5）：误分类成本相同
• 自定义阈值：根据业务需求设定
• 最优阈值：最大化 F1 分数或 AUC

交付内容

• 分类指标（准确率、精确率、召回率、F1 分数）
• 所有模型的混淆矩阵
• ROC 曲线和精确率-召回率曲线
• 特征重要性分析
• 模型对比表
• 最佳模型建议
• 概率校准图