### 添加置信区间的部分依赖图 为了在Python中为部分依赖图(Partial Dependence Plot, PDP)添加置信区间，可以采用多次重采样方法来估计不确定性。具体实现可以通过`sklearn.inspection.permutation_importance`函数以及自定义代码完成。 下面是一个完整的例子，展示如何基于给定数据集创建带有置信区间的PDP： ```python import numpy as np import pandas as pd from sklearn.datasets import make_friedman1 from sklearn.model_selection import train_test_split from sklearn.ensemble import GradientBoostingRegressor from matplotlib import pyplot as plt from sklearn.inspection import partial_dependence, plot_partial_dependence # 创建样本数据并训练模型 X, y = make_friedman1(n_samples=500, noise=1.0, random_state=42) model = GradientBoostingRegressor(random_state=42).fit(X, y) # 定义计算置信区间的方法 def compute_pdp_with_ci(model, X, features, num_iter=100): results = [] for i in range(num_iter): # 使用bootstrap抽样的方式获取子样本 indices = np.random.choice(range(len(X)), size=len(X), replace=True) sample_X = X.iloc[indices] # 计算单次迭代的部分依赖关系 result = partial_dependence( model, target=features, grid_resolution=50, percentiles=(0.05, 0.95), kind="average", X=sample_X ) results.append(result['average'][0]) mean_result = np.mean(results, axis=0) std_deviation = np.std(results, axis=0) return { 'mean': mean_result, 'ci_lower': mean_result - 1.96 * std_deviation / np.sqrt(num_iter), 'ci_upper': mean_result + 1.96 * std_deviation / np.sqrt(num_iter) } # 应用上述方法到实际的数据集中 pdp_results = compute_pdp_with_ci(model=model, X=pd.DataFrame(X), features=[0]) fig, ax = plt.subplots() ax.fill_between(pdp_results['grid_values'], pdp_results['ci_lower'], pdp_results['ci_upper'], alpha=.25) ax.plot(pdp_results['grid_values'], pdp_results['mean']) plt.show() ``` 此代码片段展示了如何通过重复抽样构建置信区间，并将其可视化于图表之上[^3]。