【机器学习sklearn实战】计算偏差和方差

采用mlxtend可以很方便的计算Bias-Variance误差分解，下面是回归决策树方法的偏差-方差分解。

from mlxtend.evaluate import bias_variance_decomp
from sklearn.tree import DecisionTreeRegressor
from mlxtend.data import boston_housing_data
from sklearn.model_selection import train_test_split

X, y = boston_housing_data()
X_train, X_test, y_train, y_test = train_test_split(X, y,
                                                    test_size=0.3,
                                                    random_state=123,
                                                    shuffle=True)

tree = DecisionTreeRegressor(random_state=123)

avg_expected_loss, avg_bias, avg_var = bias_variance_decomp(
        tree, X_train, y_train, X_test, y_test, 
        loss='mse',
        random_seed=123)

print('Average expected loss: %.3f' % avg_expected_loss)
print('Average bias: %.3f' % avg_bias)
print('Average variance: %.3f' % avg_var)

输出结果为：

Average expected loss: 31.536
Average bias: 14.096
Average variance: 17.440

作为对比，下面是Bagging方法的偏差-方差，可以看出采用Bagging方法可以降低variance。

from sklearn.ensemble import BaggingRegressor

tree = DecisionTreeRegressor(random_state=123)
bag = BaggingRegressor(estimator=tree,
                       n_estimators=100,
                       random_state=123)

avg_expected_loss, avg_bias, avg_var = bias_variance_decomp(
        bag, X_train, y_train, X_test, y_test, 
        loss='mse',
        random_seed=123)

print('Average expected loss: %.3f' % avg_expected_loss)
print('Average bias: %.3f' % avg_bias)
print('Average variance: %.3f' % avg_var)

输出结果为：

Average expected loss: 18.620
Average bias: 15.460
Average variance: 3.159