python - 如何使用 Lasso 和 RobustScalar 构建预测函数？

Question

我试图弄清楚如何在不使用 Sklearn 提供的 .predict 函数的情况下使用 LASSO 回归来预测值。这基本上只是为了加深我对 LASSO 内部工作原理的理解。我在Cross Validated上问了一个问题关于 LASSO 回归如何工作，其中一条评论提到预测函数如何与线性回归中的工作方式相同。正因为如此，我想尝试制作自己的函数来做到这一点。

我能够在更简单的示例中成功地重新创建预测函数，但是当我尝试将其与 RobustScaler 结合使用时，我不断得到不同的输出。在这个例子中，我使用 Sklearn 得到的预测为 4.33，使用我自己的函数得到的预测为 6.18。我在这里缺少什么？我最后没有正确地对预测进行逆变换吗？

import pandas as pd
from sklearn.preprocessing import RobustScaler
from sklearn.linear_model import Lasso
import numpy as np

df = pd.DataFrame({'Y':[5, -10, 10, .5, 2.5, 15], 'X1':[1., -2.,  2., .1, .5, 3], 'X2':[1, 1, 2, 1, 1, 1], 
              'X3':[6, 6, 6, 5, 6, 4], 'X4':[6, 5, 4, 3, 2, 1]})

X = df[['X1','X2','X3','X4']]
y = df[['Y']]

#Scaling 
transformer_x = RobustScaler().fit(X)
transformer_y = RobustScaler().fit(y) 
X_scal = transformer_x.transform(X)
y_scal = transformer_y.transform(y)

#LASSO
lasso = Lasso()
lasso = lasso.fit(X_scal, y_scal)

#LASSO info
print('Score: ', lasso.score(X_scal,y_scal))
print('Raw Intercept: ', lasso.intercept_.round(2)[0]) 
intercept = transformer_y.inverse_transform([lasso.intercept_])[0][0]
print('Unscaled Intercept: ', intercept) 
print('\nCoefficients Used: ')
coeff_array = lasso.coef_
inverse_coeff_array = transformer_x.inverse_transform(lasso.coef_.reshape(1,-1))[0]
for i,j,k in zip(X.columns, coeff_array, inverse_coeff_array):
    if j != 0:
        print(i, j.round(2), k.round(2))

#Predictions
example = [[3,1,1,1]]
pred = lasso.predict(example)
pred_scal = transformer_y.inverse_transform(pred.reshape(-1, 1))
print('\nRaw Prediction where X1 = 3: ', pred[0])
print('Unscaled Prediction where X1 = 3: ', pred_scal[0][0])

#Predictions without using the .predict function 
def lasso_predict_value_(X1,X2,X3,X4): 
    print('intercept: ', intercept)
    print('coef: ', inverse_coeff_array[0])
    print('X1: ', X1)
    preds = intercept + inverse_coeff_array[0]*X1
    print('Your predicted value is: ', preds)

lasso_predict_value_(3,1,1,1)

Answer 1

经过训练的Lasso没有任何给定数据点是否被调用的信息。因此，您进行预测的手动方法不应采用缩放方面的方法。

如果我去掉你对模型系数的处理，我们就可以得到sklearn模型的结果

example = [[3,1,1,1]]
lasso.predict(example)

# array([0.07533937])


#Predictions without using the .predict function 
def lasso_predict_value_(X1,X2,X3,X4): 
    x_test = np.array([X1,X2, X3, X4])
    preds = lasso.intercept_ + sum(x_test*lasso.coef_)
    print('Your predicted value is: ', preds)


lasso_predict_value_(3,1,1,1)

# Your predicted value is:  [0.07533937]

更新 2:

Once I use LASSO, I then need to see what my predictions were in their original units. My dependent variable is in dollar amounts, and if I don't inverse transform it back, I'm unable to see how many dollars I need for the prediction.

这是一个非常有效的场景。您需要应用 transformer_y.inverse_transform 来获取未调用的美元金额值。无需干扰模型权重。

更新的示例

example = [[3,1,1,1]]
scaled_pred = lasso.predict(transformer_x.transform(example))
transformer_y.inverse_transform([scaled_pred])
# array([[4.07460407]])

#Predictions without using the .predict function 
def lasso_predict_value_(X1,X2,X3,X4): 
    x_test = transformer_x.transform(np.array([X1,X2, X3, X4]).reshape(1,-1))[0]
    preds = lasso.intercept_ + sum(x_test*lasso.coef_)
    print('Your predicted value is: ', preds)
    print('Your unscaled predicted value is: ', 
          transformer_y.inverse_transform([scaled_pred]))


lasso_predict_value_(3,1,1,1)
# Your predicted value is:  [0.0418844]    
# Your unscaled predicted value is:  [[4.07460407]]