python - 在 SciKit Learn 算法中将数据放入 DataFrame 会产生不同的结果

Question

我刚刚注意到 Sci-Kit Learn 的线性回归算法将一些不同的结果加载到 pandas 数据帧中，而不是仅在原始状态下使用它们。

我不明白为什么会出现这种情况。

考虑以下线性回归示例:

from sklearn.datasets import load_boston
from sklearn.linear_model import LinearRegression
boston     = load_boston()
X1         = pd.DataFrame(boston.data)
X1.columns = boston.feature_names
X2         = boston.data
y2         = boston.target
y1         = boston.target
lreg       = LinearRegression()
X1         = (X1 - X1.mean()) / X1.std()
X2         = (X2 - X2.mean()) / X2.std()

生成的模型给出了相同的 R^2 值和预测值，但系数和截距的结果却截然不同。

演示:

intcpt1 = lreg.fit(X1, y1).intercept_
intcpt2 = lreg.fit(X2, y2).intercept_
f"Intercept for model with dataframe: {intcpt1}, model with numpy array: {intcpt2}"

给予:

'Intercept for model with dataframe: 22.53280632411069, model with numpay array: -941.8009906279219'

同样，系数也非常不同:

coef1 = lreg.fit(X1, y1).coef_[:3]
coef2 = lreg.fit(X2, y2).coef_[:3]
f"First the coeffs for model with dataframe: {coef1}, modely with numpy array: {coef2}"

给出:

'First the coeffs for model with dataframe: [-0.92906457  1.08263896  0.14103943], modely with numpy array: [-15.67844685   6.73818665   2.98419849]'

但是得分和预测是相同的:

score1 = lreg.fit(X1, y1).score(X1, y1)
score2 = lreg.fit(X2, y2).score(X2, y2)
f"Score for model with dataframe: {score1}, model with numpy array: {score2}"

产量:

'Score for model with dataframe: 0.7406426641094094, model with numpy array: 0.7406426641094073'

对于系数也是如此:

pred1 = lreg.fit(X1, y1).predict(X1)[:3]
pred2 = lreg.fit(X2, y2).predict(X2)[:3]
f"First 3 predictions with dataframe: {pred1}, with numpy array: {pred2}"

提供:

'First 3 predictions with dataframe: [30.00384338 25.02556238 30.56759672], with numpy array: [30.00384338 25.02556238 30.56759672]'

boston.data 的格式如下:

array([[6.3200e-03, 1.8000e+01, 2.3100e+00, ..., 1.5300e+01, 3.9690e+02,
    4.9800e+00],
   [2.7310e-02, 0.0000e+00, 7.0700e+00, ..., 1.7800e+01, 3.9690e+02,
    9.1400e+00],
   [2.7290e-02, 0.0000e+00, 7.0700e+00, ..., 1.7800e+01, 3.9283e+02,
    4.0300e+00],
   ...,
   [6.0760e-02, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9690e+02,
    5.6400e+00],
   [1.0959e-01, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9345e+02,
    6.4800e+00],
   [4.7410e-02, 0.0000e+00, 1.1930e+01, ..., 2.1000e+01, 3.9690e+02,
    7.8800e+00]])

而数据框输出的数据如下:

     CRIM        ZN     INDUS      CHAS       NOX        RM       AGE  \
0   -0.419367  0.284548 -1.286636 -0.272329 -0.144075  0.413263 -0.119895   
1   -0.416927 -0.487240 -0.592794 -0.272329 -0.739530  0.194082  0.366803   
2   -0.416929 -0.487240 -0.592794 -0.272329 -0.739530  1.281446 -0.265549   
3   -0.416338 -0.487240 -1.305586 -0.272329 -0.834458  1.015298 -0.809088   
4   -0.412074 -0.487240 -1.305586 -0.272329 -0.834458  1.227362 -0.510674   
5   -0.416631 -0.487240 -1.305586 -0.272329 -0.834458  0.206892 -0.350810

我不清楚为什么 LinearRegression 算法在每种情况下都会以不同的方式解释信息。

Answer 1

这是因为你的转变:

X1 = (X1 - X1.mean()) / X1.std()
X2 = (X2 - X2.mean()) / X2.std()

Pandas 将计算各列的平均值和标准差。要对 numpy 执行此操作，请将 axis 参数添加到 mean 和 std:

X2 = (X2 - X2.mean(axis=0)) / X2.std(axis=0)