交叉验证给出负 R2？
Cross-validation gives Negative R2?
为了简单起见，我将 500 个样本划分为 10,000 多行数据集。请将 X 和 y 复制并粘贴到您的 IDE.
X=
array([ -8.93, -0.17, 1.47, -6.13, -4.06, -2.22, -2.11, -0.25,
0.25, 0.49, 1.7 , -0.77, 1.07, 5.61, -11.95, -3.8 ,
-3.42, -2.55, -2.44, -1.99, -1.7 , -0.98, -0.91, -0.91,
-0.25, 1.7 , 2.88, -6.9 , -4.07, -1.35, -0.33, 0.63,
0.98, -3.31, -2.61, -2.61, -2.17, -1.38, -0.77, -0.25,
-0.08, -1.2 , -3.1 , -1.07, -0.7 , -0.41, -0.33, 0.41,
0.77, 0.77, 1.14, 2.17, -7.92, -3.8 , -2.11, -2.06,
-1.2 , -1.14, 0. , 0.56, 1.47, -1.99, -0.17, 2.44,
-5.87, -3.74, -3.37, -2.88, -0.49, -0.25, -0.08, 0.33,
0.33, 0.84, 1.64, 2.06, 2.88, -4.58, -1.82, -1.2 ,
0.25, 0.25, 0.63, 2.61, -5.36, -1.47, -0.63, 0. ,
0.63, 1.99, 1.99, -10.44, -2.55, 0.33, -8.93, -5.87,
-5.1 , -2.78, -0.25, 1.47, 1.93, 2.17, -5.36, -5.1 ,
-3.48, -2.44, -2.06, -2.06, -1.82, -1.58, -1.58, -0.63,
-0.33, 0. , 0.17, -3.31, -0.25, -5.1 , -3.8 , -2.55,
-1.99, -1.7 , -0.98, -0.91, -0.63, -0.25, 0.77, 0.91,
0.91, -9.43, -8.42, -2.72, -2.55, -1.26, 0.7 , 0.77,
1.07, 1.47, 1.7 , -1.82, -1.47, 0.17, 1.26, -5.36,
-1.52, -1.47, -0.17, -3.48, -3.31, -2.06, -1.47, 0.17,
0.25, 1.7 , 2.5 , -9.94, -6.08, -5.87, -3.37, -2.44,
-2.17, -1.87, -0.98, -0.7 , -0.49, 0.41, 1.47, 2.28,
-14.95, -12.44, -6.39, -4.33, -3.8 , -2.72, -2.17, -1.2 ,
0.41, 0.77, 0.84, 2.51, -1.99, -1.7 , -1.47, -1.2 ,
0.49, 0.63, 0.84, 0.98, 1.14, 2.5 , -2.06, -1.26,
-0.33, 0.17, 4.58, -7.41, -5.87, 1.2 , 1.38, 1.58,
1.82, 1.99, -6.39, -2.78, -2.67, -1.87, -1.58, -1.47,
0.84, -10.44, -7.41, -3.05, -2.17, -1.07, -1.07, -0.91,
0.25, 1.82, 2.88, -6.9 , -1.47, 0.33, -8.42, -3.8 ,
-1.99, -1.47, -1.47, -0.56, 0.17, 0.17, 0.25, 0.56,
4.58, -3.48, -2.61, -2.44, -0.7 , 0.63, 1.47, 1.82,
-13.96, -9.43, -2.67, -1.38, -0.08, 0. , 1.82, 3.05,
-4.58, -3.31, -0.98, -0.91, -0.7 , 0.77, -0.7 , -0.33,
0.56, 1.58, 1.7 , 2.61, -4.84, -4.84, -4.32, -2.88,
-1.38, -0.98, -0.17, 0.17, 0.49, 2.44, 4.32, -3.48,
-3.05, 0.56, -8.42, -3.48, -2.61, -2.61, -2.06, -1.47,
-0.98, 0. , 0.08, 1.38, 1.93, -9.94, -2.72, -1.87,
-1.2 , -1.07, 1.58, 4.58, -6.64, -2.78, -0.77, -0.7 ,
-0.63, 0.49, 1.07, -8.93, -4.84, -1.7 , 1.76, 3.31,
-11.95, -3.16, -3.05, -1.82, -0.49, -0.41, 0.56, 1.58,
-13.96, -3.05, -2.78, -2.55, -1.7 , -1.38, -0.91, -0.33,
1.2 , 1.32, 1.47, -2.06, -1.82, -7.92, -6.33, -4.32,
-3.8 , -1.93, -1.52, -0.98, -0.49, -0.33, 0.7 , 1.52,
1.76, -8.93, -7.41, -2.88, -2.61, -2.33, -1.99, -1.82,
-1.64, -0.84, 1.07, 2.06, -3.96, -2.44, -1.58, 0. ,
-3.31, -2.61, -1.58, -0.25, 0.33, 0.56, 0.84, 1.07,
-1.58, -0.25, 1.35, -1.99, -1.7 , -1.47, -1.47, -0.84,
-0.7 , -0.56, -0.33, 0.56, 0.63, 1.32, 2.28, 2.28,
-2.72, -0.25, 0.41, -6.9 , -4.42, -4.32, -1.76, -1.2 ,
-1.14, -1.07, 0.56, 1.32, 1.52, -14.97, -7.41, -5.1 ,
-2.61, -1.93, -0.98, 0.17, 0.25, 0.41, -4.42, -2.61,
-0.91, -0.84, 2.39, -2.61, -1.32, 0.41, -6.9 , -5.61,
-4.06, -3.31, -1.47, -0.91, -0.7 , -0.63, 0.33, 1.38,
2.61, -2.29, 3.06, 4.44, -10.94, -4.32, -3.42, -2.17,
-1.7 , -1.47, -1.32, -1.07, -0.7 , 0. , 0.77, 1.07,
-3.31, -2.88, -2.61, -1.47, -1.38, -0.63, -0.49, 1.07,
1.52, -3.8 , -1.58, -0.91, -0.7 , 0.77, 3.42, -8.42,
-2.88, -1.76, -1.76, -0.63, -0.25, 0.49, 0.63, -6.9 ,
-4.06, -1.82, -1.76, -1.76, -1.38, -0.91, -0.7 , 0.17,
1.38, 1.47, 1.47, -11.95, -0.98, -0.56, -14.97, -9.43,
-8.93, -2.72, -2.61, -1.64, -1.32, -0.56, -0.49, 0.91,
1.2 , 1.47, -3.8 , -3.06, -2.51, -1.04, -0.33, -0.33,
-3.31, -3.16, -3.05, -2.61, -1.47, -1.07, 2.17, 3.1 ,
-2.61, -0.25, -3.85, -2.44])
y =
array([1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0,
1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1,
0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1,
1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0,
0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1,
1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1,
1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0,
0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1,
0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1,
1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1,
1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0,
0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1,
1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0,
1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0,
1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1,
1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1,
0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0,
0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0,
0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0,
0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0,
1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1])
初始化和训练：
from sklearn.linear_model import LogisticRegression
model = LogisticRegression()
model.fit(X, y)
交叉验证：
from sklearn.model_selection import cross_val_score
cross_val_score(model, X, y, cv=10, scoring='r2').mean()
-0.3339677563815496 (Negative R2?)
看看它是否接近模型的真实 R2。我这样做了：
from sklearn.metrics import r2_score
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.20, random_state=None, shuffle=False)
r2_score(y_test, model.predict_proba(X_test)[:,1], multioutput='variance_weighted')
0.32642659661798396
这个 R2 对于模型的拟合优度更有意义，看起来两个 R2 只是一个 +/- 符号开关，但事实并非如此。在我使用更大样本的模型中，R2 cross-val 为 -0.24，R2 test 为 0.18。而且，当我添加一个似乎有利于模型的特征时，R2 测试上升，R2 交叉验证下降
此外，如果将 LogisticRegression 切换为 LinearRegression，R2 cross-val 现在为正并且接近 R2 检验。是什么导致了这个问题？
R2有可能为负。以下段落来自 "Coefficient of determination"
的 wikipedia 页
There are cases where the computational definition of R2 can yield negative values, depending on the definition used. This can arise when the predictions that are being compared to the corresponding outcomes have not been derived from a model-fitting procedure using those data. Even if a model-fitting procedure has been used, R2 may still be negative, for example when linear regression is conducted without including an intercept, or when a non-linear function is used to fit the data. In cases where negative values arise, the mean of the data provides a better fit to the outcomes than do the fitted function values, according to this particular criterion. Since the most general definition of the coefficient of determination is also known as the Nash–Sutcliffe model efficiency coefficient, this last notation is preferred in many fields, because denoting a goodness-of-fit indicator that can vary from -infinity to 1 (i.e., it can yield negative values) with a squared letter is confusing.
看来预测比横线还差
TLDR：R2 可能为负，您误解了 train_test_split 结果。
我将在下面解释这两种说法。
cross_val_score error 和 loss 指标的符号翻转
从 docs 中，您可以看到 cross_val_score 实际上翻转了某些指标的符号。但仅适用于 error 或 loss 指标（越低越好），不适用于 score 指标（越高越好）：
All scorer objects follow the convention that higher return values are better than lower return values. Thus metrics which measure the distance between the model and the data, like metrics.mean_squared_error, are available as neg_mean_squared_error which return the negated value of the metric.
由于 r2 是一个 score 度量标准，因此它不会翻转符号。您在交叉验证中得到 -0.33。请注意，这是正常的。来自 r2_score docs:
Best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a R^2 score of 0.0.
因此这将我们引向第二部分：为什么使用 CV 和 train/test 拆分会得到如此不同的结果？
CV与train/test分割结果的区别
使用 train_test_split 获得更好结果的原因有两个。
根据概率而不是 类 评估 r2（您使用 predict_proba 而不是 predict 可以减少错误的危害：
print(r2_score(y_test, model.predict_proba(X_test)[:,1], multioutput='variance_weighted'))
0.19131536389654913
同时：
print(r2_score(y_test, model.predict(X_test)))
-0.364200082678793
取 10 倍 cv 的平均值，不检查方差，这是高的。如果检查方差和结果的详细信息，您会发现方差很大：
scores = cross_val_score(model, X, y, cv=10, scoring='r2')
scores
array([-0.67868339, -0.03918495, 0.04075235, -0.47783251, -0.23152709,
-0.39573071, -0.72413793, -0.66666667, 0. , -0.16666667])
scores.mean(), scores.std() * 2
(-0.3339677563815496, 0.5598543351649792)
希望对您有所帮助！
为了简单起见，我将 500 个样本划分为 10,000 多行数据集。请将 X 和 y 复制并粘贴到您的 IDE.
X=
array([ -8.93, -0.17, 1.47, -6.13, -4.06, -2.22, -2.11, -0.25,
0.25, 0.49, 1.7 , -0.77, 1.07, 5.61, -11.95, -3.8 ,
-3.42, -2.55, -2.44, -1.99, -1.7 , -0.98, -0.91, -0.91,
-0.25, 1.7 , 2.88, -6.9 , -4.07, -1.35, -0.33, 0.63,
0.98, -3.31, -2.61, -2.61, -2.17, -1.38, -0.77, -0.25,
-0.08, -1.2 , -3.1 , -1.07, -0.7 , -0.41, -0.33, 0.41,
0.77, 0.77, 1.14, 2.17, -7.92, -3.8 , -2.11, -2.06,
-1.2 , -1.14, 0. , 0.56, 1.47, -1.99, -0.17, 2.44,
-5.87, -3.74, -3.37, -2.88, -0.49, -0.25, -0.08, 0.33,
0.33, 0.84, 1.64, 2.06, 2.88, -4.58, -1.82, -1.2 ,
0.25, 0.25, 0.63, 2.61, -5.36, -1.47, -0.63, 0. ,
0.63, 1.99, 1.99, -10.44, -2.55, 0.33, -8.93, -5.87,
-5.1 , -2.78, -0.25, 1.47, 1.93, 2.17, -5.36, -5.1 ,
-3.48, -2.44, -2.06, -2.06, -1.82, -1.58, -1.58, -0.63,
-0.33, 0. , 0.17, -3.31, -0.25, -5.1 , -3.8 , -2.55,
-1.99, -1.7 , -0.98, -0.91, -0.63, -0.25, 0.77, 0.91,
0.91, -9.43, -8.42, -2.72, -2.55, -1.26, 0.7 , 0.77,
1.07, 1.47, 1.7 , -1.82, -1.47, 0.17, 1.26, -5.36,
-1.52, -1.47, -0.17, -3.48, -3.31, -2.06, -1.47, 0.17,
0.25, 1.7 , 2.5 , -9.94, -6.08, -5.87, -3.37, -2.44,
-2.17, -1.87, -0.98, -0.7 , -0.49, 0.41, 1.47, 2.28,
-14.95, -12.44, -6.39, -4.33, -3.8 , -2.72, -2.17, -1.2 ,
0.41, 0.77, 0.84, 2.51, -1.99, -1.7 , -1.47, -1.2 ,
0.49, 0.63, 0.84, 0.98, 1.14, 2.5 , -2.06, -1.26,
-0.33, 0.17, 4.58, -7.41, -5.87, 1.2 , 1.38, 1.58,
1.82, 1.99, -6.39, -2.78, -2.67, -1.87, -1.58, -1.47,
0.84, -10.44, -7.41, -3.05, -2.17, -1.07, -1.07, -0.91,
0.25, 1.82, 2.88, -6.9 , -1.47, 0.33, -8.42, -3.8 ,
-1.99, -1.47, -1.47, -0.56, 0.17, 0.17, 0.25, 0.56,
4.58, -3.48, -2.61, -2.44, -0.7 , 0.63, 1.47, 1.82,
-13.96, -9.43, -2.67, -1.38, -0.08, 0. , 1.82, 3.05,
-4.58, -3.31, -0.98, -0.91, -0.7 , 0.77, -0.7 , -0.33,
0.56, 1.58, 1.7 , 2.61, -4.84, -4.84, -4.32, -2.88,
-1.38, -0.98, -0.17, 0.17, 0.49, 2.44, 4.32, -3.48,
-3.05, 0.56, -8.42, -3.48, -2.61, -2.61, -2.06, -1.47,
-0.98, 0. , 0.08, 1.38, 1.93, -9.94, -2.72, -1.87,
-1.2 , -1.07, 1.58, 4.58, -6.64, -2.78, -0.77, -0.7 ,
-0.63, 0.49, 1.07, -8.93, -4.84, -1.7 , 1.76, 3.31,
-11.95, -3.16, -3.05, -1.82, -0.49, -0.41, 0.56, 1.58,
-13.96, -3.05, -2.78, -2.55, -1.7 , -1.38, -0.91, -0.33,
1.2 , 1.32, 1.47, -2.06, -1.82, -7.92, -6.33, -4.32,
-3.8 , -1.93, -1.52, -0.98, -0.49, -0.33, 0.7 , 1.52,
1.76, -8.93, -7.41, -2.88, -2.61, -2.33, -1.99, -1.82,
-1.64, -0.84, 1.07, 2.06, -3.96, -2.44, -1.58, 0. ,
-3.31, -2.61, -1.58, -0.25, 0.33, 0.56, 0.84, 1.07,
-1.58, -0.25, 1.35, -1.99, -1.7 , -1.47, -1.47, -0.84,
-0.7 , -0.56, -0.33, 0.56, 0.63, 1.32, 2.28, 2.28,
-2.72, -0.25, 0.41, -6.9 , -4.42, -4.32, -1.76, -1.2 ,
-1.14, -1.07, 0.56, 1.32, 1.52, -14.97, -7.41, -5.1 ,
-2.61, -1.93, -0.98, 0.17, 0.25, 0.41, -4.42, -2.61,
-0.91, -0.84, 2.39, -2.61, -1.32, 0.41, -6.9 , -5.61,
-4.06, -3.31, -1.47, -0.91, -0.7 , -0.63, 0.33, 1.38,
2.61, -2.29, 3.06, 4.44, -10.94, -4.32, -3.42, -2.17,
-1.7 , -1.47, -1.32, -1.07, -0.7 , 0. , 0.77, 1.07,
-3.31, -2.88, -2.61, -1.47, -1.38, -0.63, -0.49, 1.07,
1.52, -3.8 , -1.58, -0.91, -0.7 , 0.77, 3.42, -8.42,
-2.88, -1.76, -1.76, -0.63, -0.25, 0.49, 0.63, -6.9 ,
-4.06, -1.82, -1.76, -1.76, -1.38, -0.91, -0.7 , 0.17,
1.38, 1.47, 1.47, -11.95, -0.98, -0.56, -14.97, -9.43,
-8.93, -2.72, -2.61, -1.64, -1.32, -0.56, -0.49, 0.91,
1.2 , 1.47, -3.8 , -3.06, -2.51, -1.04, -0.33, -0.33,
-3.31, -3.16, -3.05, -2.61, -1.47, -1.07, 2.17, 3.1 ,
-2.61, -0.25, -3.85, -2.44])
y =
array([1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0,
1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1,
0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1,
1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0,
0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1,
1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1,
1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0,
0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1,
0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1,
1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1,
1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0,
0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1,
1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0,
1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0,
1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1,
1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1,
0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0,
0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0,
0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0,
0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0,
1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1])
初始化和训练：
from sklearn.linear_model import LogisticRegression
model = LogisticRegression()
model.fit(X, y)
交叉验证：
from sklearn.model_selection import cross_val_score
cross_val_score(model, X, y, cv=10, scoring='r2').mean()
-0.3339677563815496 (Negative R2?)
看看它是否接近模型的真实 R2。我这样做了：
from sklearn.metrics import r2_score
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.20, random_state=None, shuffle=False)
r2_score(y_test, model.predict_proba(X_test)[:,1], multioutput='variance_weighted')
0.32642659661798396
这个 R2 对于模型的拟合优度更有意义，看起来两个 R2 只是一个 +/- 符号开关，但事实并非如此。在我使用更大样本的模型中，R2 cross-val 为 -0.24，R2 test 为 0.18。而且，当我添加一个似乎有利于模型的特征时，R2 测试上升，R2 交叉验证下降
此外，如果将 LogisticRegression 切换为 LinearRegression，R2 cross-val 现在为正并且接近 R2 检验。是什么导致了这个问题？
R2有可能为负。以下段落来自 "Coefficient of determination"
的 wikipedia 页There are cases where the computational definition of R2 can yield negative values, depending on the definition used. This can arise when the predictions that are being compared to the corresponding outcomes have not been derived from a model-fitting procedure using those data. Even if a model-fitting procedure has been used, R2 may still be negative, for example when linear regression is conducted without including an intercept, or when a non-linear function is used to fit the data. In cases where negative values arise, the mean of the data provides a better fit to the outcomes than do the fitted function values, according to this particular criterion. Since the most general definition of the coefficient of determination is also known as the Nash–Sutcliffe model efficiency coefficient, this last notation is preferred in many fields, because denoting a goodness-of-fit indicator that can vary from -infinity to 1 (i.e., it can yield negative values) with a squared letter is confusing.
看来预测比横线还差
TLDR：R2 可能为负，您误解了 train_test_split 结果。
我将在下面解释这两种说法。
cross_val_score error 和 loss 指标的符号翻转
从 docs 中，您可以看到 cross_val_score 实际上翻转了某些指标的符号。但仅适用于 error 或 loss 指标（越低越好），不适用于 score 指标（越高越好）：
All scorer objects follow the convention that higher return values are better than lower return values. Thus metrics which measure the distance between the model and the data, like metrics.mean_squared_error, are available as neg_mean_squared_error which return the negated value of the metric.
由于 r2 是一个 score 度量标准，因此它不会翻转符号。您在交叉验证中得到 -0.33。请注意，这是正常的。来自 r2_score docs:
Best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a R^2 score of 0.0.
因此这将我们引向第二部分：为什么使用 CV 和 train/test 拆分会得到如此不同的结果？
CV与train/test分割结果的区别
使用 train_test_split 获得更好结果的原因有两个。
根据概率而不是 类 评估 r2（您使用 predict_proba 而不是 predict 可以减少错误的危害：
print(r2_score(y_test, model.predict_proba(X_test)[:,1], multioutput='variance_weighted'))
0.19131536389654913
同时：
print(r2_score(y_test, model.predict(X_test)))
-0.364200082678793
取 10 倍 cv 的平均值，不检查方差，这是高的。如果检查方差和结果的详细信息，您会发现方差很大：
scores = cross_val_score(model, X, y, cv=10, scoring='r2')
scores
array([-0.67868339, -0.03918495, 0.04075235, -0.47783251, -0.23152709,
-0.39573071, -0.72413793, -0.66666667, 0. , -0.16666667])
scores.mean(), scores.std() * 2
(-0.3339677563815496, 0.5598543351649792)
希望对您有所帮助！