带有sklearn的numpy多项式线性回归

Question

我正在尝试将多项式的线性系统拟合到数据中。 numpy 的polynomial 模块包含拟合功能，完美运行。当我尝试使用sklearn 线性求解器拟合模型时，拟合效果非常糟糕！我不明白出了什么问题。我构造了一个矩阵 X，其中 x_{ij} 对应于ith 观察到的输入和jth 多项式。我知道 X 矩阵没问题，因为当我找到 numpy 的系数时，数据非常适合。我使用 sklearn 的 fit 函数（我尝试了几个线性求解器），但它求解的系数（coef_ 对象）是错误的。我究竟做错了什么？如何使sklearn 线性求解器找到的系数与numpy 找到的系数相匹配？

import numpy as np
from sklearn import linear_model
from sklearn.linear_model import OrthogonalMatchingPursuit
import matplotlib.pyplot as plt

# accept x and polynomial order, return basis of that order
def legs(x, c):
   s = np.zeros(c + 1)
   s[-1] = 1
   return np.polynomial.legendre.legval(x, s)

# Generate normalized samples   
samples = np.random.uniform(2, 3, 5)
evals = samples ** 2
xnorm = (samples - 2) * 2 / (3 - 2) - 1

# instantiate linear regressor
omp = linear_model.LinearRegression()
#omp = linear_model.Lasso(alpha=0.000001)
#omp = OrthogonalMatchingPursuit(n_nonzero_coefs=2)

# construct X matrix. Each row is an observed value. 
#  Each column is a different polynomial.
X = np.array([[legs(xnorm[jj], ii) for ii in range(5)] for jj in range(xnorm.size)])

# Perform the fit. Why isn't this working?
omp.fit(X, evals)

# Plot the truth data
plt.scatter(xnorm, evals, label='data', s=15, marker='x')

# Dot the coefficients found with sklearn against X
plt.scatter(xnorm, omp.coef_.dot(X.T), label='linear regression')

# Dot the coefficients found with numpy against X
plt.scatter(xnorm, np.polynomial.legendre.legfit(xnorm, evals, 4).dot(X.T), label='Numpy regression')

# complete the plot
plt.legend(ncol=3, prop={'size':3})
plt.savefig('simpleExample')
plt.clf()

Answer 1

您的omp.coef_.dot(X.T) 不包括拦截；手动添加或直接使用omp.predict。

即：

plt.scatter(xnorm, omp.coef_.dot(X.T) + omp.intercept_, label='linear regression')
plt.scatter(xnorm, evals, label='data', s=15, marker='x')

或

plt.scatter(xnorm, omp.predict(X), label='linear regression')
plt.scatter(xnorm, evals, label='data', s=15, marker='x')