如果有一个包含数十个甚至数百个特征的数据集，每个特征都可能对你的机器学习模型的性能有所贡献。但是并不是所有的特征都是一样的。有些可能是冗余的或不相关的，这会增加建模的复杂性并可能导致过拟合。特征重要性分析可以识别并关注最具信息量的特征，从而带来以下几个优势:

改进的模型性能
减少过度拟合
更快的训练和推理
增强的可解释性

下面我们深入了解在Python中的一些特性重要性分析的方法。

特征重要性分析方法

1、排列重要性 PermutationImportance

该方法会随机排列每个特征的值，然后监控模型性能下降的程度。如果获得了更大的下降意味着特征更重要。

from sklearn.datasets import load_breast_cancer
from sklearn.ensemble import RandomForestClassifier
from sklearn.inspection import permutation_importance
from sklearn.model_selection import train_test_split
import matplotlib.pyplot as plt
 
cancer = load_breast_cancer()
 
X_train, X_test, y_train, y_test = train_test_split(cancer.data, cancer.target, random_state=1)
 
rf = RandomForestClassifier(n_estimators=100, random_state=1)
rf.fit(X_train, y_train)
 
baseline = rf.score(X_test, y_test)
result = permutation_importance(rf, X_test, y_test, n_repeats=10, random_state=1, scoring='accuracy')
 
importances = result.importances_mean
 
# Visualize permutation importances
plt.bar(range(len(importances)), importances)
plt.xlabel('Feature Index')
plt.ylabel('Permutation Importance')
plt.show()

2、内置特征重要性(coef_或feature_importances_)

一些模型，如线性回归和随机森林，可以直接输出特征重要性分数。这些显示了每个特征对最终预测的贡献。

from sklearn.datasets import load_breast_cancer
from sklearn.ensemble import RandomForestClassifier
 
X, y = load_breast_cancer(return_X_y=True)
 
rf = RandomForestClassifier(n_estimators=100, random_state=1)
rf.fit(X, y)
 
importances = rf.feature_importances_
 
# Plot importances
plt.bar(range(X.shape[1]), importances)
plt.xlabel('Feature Index')
plt.ylabel('Feature Importance')
plt.show()

3、Leave-one-out

迭代地每次删除一个特征并评估准确性。

from sklearn.datasets import load_breast_cancer
 from sklearn.model_selection import train_test_split
 from sklearn.ensemble import RandomForestClassifier
 from sklearn.metrics import accuracy_score
 import matplotlib.pyplot as plt
 import numpy as np
 
 # Load sample data
 X, y = load_breast_cancer(return_X_y=True)
 
 # Split data into train and test sets
 X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=1)
 
 # Train a random forest model
 rf = RandomForestClassifier(n_estimators=100, random_state=1)
 rf.fit(X_train, y_train)
 
 # Get baseline accuracy on test data
 base_acc = accuracy_score(y_test, rf.predict(X_test))
 
 # Initialize empty list to store importances
 importances = []
 
 # Iterate over all columns and remove one at a time
 for i in range(X_train.shape[1]):
    X_temp = np.delete(X_train, i, axis=1)
    rf.fit(X_temp, y_train)
    acc = accuracy_score(y_test, rf.predict(np.delete(X_test, i, axis=1)))
    importances.append(base_acc - acc)
     
 # Plot importance scores    
 plt.bar(range(len(importances)), importances)
 plt.show()

4、相关性分析

计算各特征与目标变量之间的相关性。相关性越高的特征越重要。

import pandas as pd
from sklearn.datasets import load_breast_cancer
 
X, y = load_breast_cancer(return_X_y=True)
df = pd.DataFrame(X, columns=range(30))
df['y'] = y
 
correlations = df.corrwith(df.y).abs()
correlations.sort_values(ascending=False, inplace=True)
 
correlations.plot.bar()

5、递归特征消除 Recursive Feature Elimination

递归地删除特征并查看它如何影响模型性能。删除时会导致更大下降的特征更重要。

from sklearn.ensemble import RandomForestClassifier
 from sklearn.feature_selection import RFE
 import pandas as pd
 from sklearn.datasets import load_breast_cancer
 import matplotlib.pyplot as plt
 
 X, y = load_breast_cancer(return_X_y=True)
 df = pd.DataFrame(X, columns=range(30))
 df['y'] = y
 
 rf = RandomForestClassifier()
 
 rfe = RFE(rf, n_features_to_select=10)
 rfe.fit(X, y)
 
 print(rfe.ranking_)

输出为[6 4 11 12 7 11 18 21 8 16 10 3 15 14 19 17 20 13 11 11 12 9 11 5 11]

6、XGBoost特性重要性

计算一个特性用于跨所有树拆分数据的次数。更多的分裂意味着更重要。

import xgboost as xgb
 import pandas as pd
 from sklearn.datasets import load_breast_cancer
 import matplotlib.pyplot as plt
 
 X, y = load_breast_cancer(return_X_y=True)
 df = pd.DataFrame(X, columns=range(30))
 df['y'] = y
 
 model = xgb.XGBClassifier()
 model.fit(X, y)
 
 importances = model.feature_importances_
 importances = pd.Series(importances, index=range(X.shape[1]))
 importances.plot.bar()

7、主成分分析 PCA

对特征进行主成分分析，并查看每个主成分的解释方差比。在前几个组件上具有较高负载的特性更为重要。

from sklearn.decomposition import PCA
 import pandas as pd
 from sklearn.datasets import load_breast_cancer
 import matplotlib.pyplot as plt
 
 X, y = load_breast_cancer(return_X_y=True)
 df = pd.DataFrame(X, columns=range(30))
 df['y'] = y
 
 pca = PCA()
 pca.fit(X)
 
 plt.bar(range(pca.n_components_), pca.explained_variance_ratio_)
 plt.xlabel('PCA components')
 plt.ylabel('Explained Variance')

8、方差分析 ANOVA

使用f_classif()获得每个特征的方差分析f值。f值越高，表明特征与目标的相关性越强。

from sklearn.feature_selection import f_classif
 import pandas as pd
 from sklearn.datasets import load_breast_cancer
 import matplotlib.pyplot as plt
 
 X, y = load_breast_cancer(return_X_y=True)
 df = pd.DataFrame(X, columns=range(30))
 df['y'] = y
 
 fval = f_classif(X, y)
 fval = pd.Series(fval[0], index=range(X.shape[1]))
 fval.plot.bar()

9、卡方检验

使用chi2()获得每个特征的卡方统计信息。得分越高的特征越有可能独立于目标。

from sklearn.feature_selection import chi2
 import pandas as pd
 from sklearn.datasets import load_breast_cancer
 import matplotlib.pyplot as plt
 
 X, y = load_breast_cancer(return_X_y=True)
 df = pd.DataFrame(X, columns=range(30))
 df['y'] = y
 
 chi_scores = chi2(X, y)
 chi_scores = pd.Series(chi_scores[0], index=range(X.shape[1]))
 chi_scores.plot.bar()