如何从多项式拟合中提取方程？

Question

我的目标是将一些数据拟合到多项式函数,并获得包括拟合参数值的实际方程.

我将此示例应用于我的数据,结果如预期.

这是我的代码:

import numpy as np
import matplotlib.pyplot as plt

from sklearn.linear_model import Ridge
from sklearn.preprocessing import PolynomialFeatures
from sklearn.pipeline import make_pipeline


x = np.array([0., 4., 9., 12., 16., 20., 24., 27.])
y = np.array([2.9,4.3,66.7,91.4,109.2,114.8,135.5,134.2])

x_plot = np.linspace(0, max(x), 100)
# create matrix versions of these arrays
X = x[:, np.newaxis]
X_plot = x_plot[:, np.newaxis]

plt.scatter(x, y, label="training points")

for degree in np.arange(3, 6, 1):
    model = make_pipeline(PolynomialFeatures(degree), Ridge())
    model.fit(X, y)
    y_plot = model.predict(X_plot)
    plt.plot(x_plot, y_plot, label="degree %d" % degree)

plt.legend(loc='lower left')

plt.show()

但是,我现在不知道在哪里提取实际方程和适合各个拟合的参数值.我在哪里可以访问实际拟合方程？

编辑:

该变量model具有以下属性:

model.decision_function  model.fit_transform      model.inverse_transform  model.predict            model.predict_proba      model.set_params         model.transform          
model.fit                model.get_params         model.named_steps        model.predict_log_proba  model.score              model.steps

model.get_params 不存储所需的参数.

Answer 1

线性模型的系数被存储在intercept_与coeff_该模型的属性.

通过调低正则化和输入已知模型,您可以更清楚地看到这一点; 例如

import numpy as np
from sklearn.linear_model import Ridge
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import PolynomialFeatures

x = 10 * np.random.random(100)
y = -4 + 2 * x - 3 * x ** 2

model = make_pipeline(PolynomialFeatures(2), Ridge(alpha=1E-8, fit_intercept=False))
model.fit(x[:, None], y)
ridge = model.named_steps['ridge']
print(ridge.coef_)
# array([-4.,  2., -3.])

另请注意,PolynomialFeatures默认情况下包含一个偏置项,因此拟合截距Ridge对于小型来说将是多余的alpha.