Python 确定多项式拟合/回归的阶数实例

import numpy as npimport matplotlib.pyplot as pltfrom sklearn.preprocessing import PolynomialFeaturesfrom sklearn.linear_model import LinearRegression,Perceptronfrom sklearn.metrics import mean_squared_error,r2_scorefrom sklearn.model_selection import train_test_split X = np.array([-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10]).reshape(-1, 1)y = np.array(2*(X**4) + X**2 + 9*X + 2)#y = np.array([300,500,0,-10,0,20,200,300,1000,800,4000,5000,10000,9000,22000]).reshape(-1, 1) x_train, x_test, y_train, y_test = train_test_split(X, y, test_size=0.3)rmses = []degrees = np.arange(1, 10)min_rmse, min_deg,score = 1e10, 0 ,0 for deg in degrees:	# 生成多项式特征集(如根据degree=3 ,生成 [[x,x**2,x**3]] )	poly = PolynomialFeatures(degree=deg, include_bias=False)	x_train_poly = poly.fit_transform(x_train) 	# 多项式拟合	poly_reg = LinearRegression()	poly_reg.fit(x_train_poly, y_train)	#print(poly_reg.coef_,poly_reg.intercept_) #系数及常数		# 测试集比较	x_test_poly = poly.fit_transform(x_test)	y_test_pred = poly_reg.predict(x_test_poly)		#mean_squared_error(y_true, y_pred) #均方误差回归损失,越小越好。	poly_rmse = np.sqrt(mean_squared_error(y_test, y_test_pred))	rmses.append(poly_rmse)	# r2 范围[0，1]，R2越接近1拟合越好。	r2score = r2_score(y_test, y_test_pred)		# degree交叉验证	if min_rmse > poly_rmse:		min_rmse = poly_rmse		min_deg = deg		score = r2score	print('degree = %s, RMSE = %.2f ,r2_score = %.2f' % (deg, poly_rmse,r2score))		fig = plt.figure()ax = fig.add_subplot(111)ax.plot(degrees, rmses)ax.set_yscale('log')ax.set_xlabel('Degree')ax.set_ylabel('RMSE')ax.set_title('Best degree = %s, RMSE = %.2f, r2_score = %.2f' %(min_deg, min_rmse,score)) plt.show()

y = np.array([300,500,0,-10,0,20,200,300,1000,800,4000,5000,10000,9000,22000]).reshape(-1, 1)