如何使用PolynomialFeatures选择最合适的度数参数？

Question

我有生成线性和二次趋势的时间序列代码。我很困惑要为degree参数选择什么。我看到了如下定义：

Within scikit-learn's PolynomialFeatures, when the argument degree is passed, all terms up to that degree are created.

我只是不理解这个定义。有没有使用简单数学的解释？我如何确保我使用最好的学位？

这是我的代码，如果你想要它的样本。

import pandas as pd 
import numpy as np 
import matplotlib.pyplot as plt 
import statsmodels.api as sm                               

import statsmodels.formula.api as smf                             

import statsmodels.tsa.api as smt 
import random 
from sklearn.linear_model import LinearRegression 
from sklearn.linear_model import Ridge 
from sklearn.preprocessing import PolynomialFeatures 
from sklearn.pipeline import make_pipeline 


y = [5*np.random.normal() for j in range(50)] + [30 + 5 * np.random.normal() for j in range(50)] + [50 + 5 * np.random.normal() for j in range(50)] + [20 + 5 * np.random.normal() for j in range(50)] 
X = [x for x in range(len(y))] 
X = np.reshape(X, (len(X), 1)) 

model = LinearRegression() 
model.fit(X, y) 
trend = model.predict(X) 

model = make_pipeline(PolynomialFeatures(2), Ridge()) 
model.fit(X, y) 
quadratic = model.predict(X) 

fig = plt.figure(1, figsize=(15, 9)) 
ax = fig.add_subplot(111) 
ax.plot(trend, label="Linear Trend") 
ax.plot(quadratic, label="Quadratic Trend") 
ax.plot(X, y, label='Time Series') 
ax.legend() 
plt.show() 

Answer 1

您使用为度;线性分量将被包含在二次方程中。例如，如果计算的线性分量为2x - 5，二次方程为3x^2 + x + 1，那么从函数返回的值将是总和3x^2 + 3x + 4。