https://www.analyticsvidhya.com/blog/2017/06/a-comprehensive-guide-for-linear-ridge-and-lasso-regression/

“Everything should be made simple as possible, but not simpler – Albert Einstein”

from sklearn.linear_model import Ridge

## training the model

ridgeReg = Ridge(alpha=0.05, normalize=True)

ridgeReg.fit(x_train,y_train)

pred = ridgeReg.predict(x_cv)

calculating mse

mse = np.mean((pred_cv - y_cv)**2)

mse 1348171.96 ## calculating score ridgeReg.score(x_cv,y_cv) 0.5691

普通最小二乘，没有阿尔法值 alpha为0.5 alpha值为5 阿尔法值为10

可以看到：

随着alpha值的增加，系数的数量也在减小，向零靠近。

计算R-2值，发现等alpha为0.05时，R-2值最大。应当选误差平方和最小的。

改变alpha值就是改变惩罚项，alpha值越大，惩罚项越大从而系数也越来越小。 

要点：

1. 岭回归It shrinks the parameters, therefore it is mostly used to prevent multicollinearity.

2. It reduces the model complexity by coefficient shrinkage.

3. It uses L2 regularization technique. (which I will discussed later in this article)