线性回归问题 自写拟合函数

二次回归拟合

#生成数据点
import numpy as np 
import matplotlib.pyplot as plt 

xx = np.random.normal(0, 1, [1000]) 
dd = xx**2 + xx + np.random.normal(0, 0.3, [1000]) #产生样本

plt.scatter(xx, dd) 
plt.show()

转换数据

xx = np.array(xx)
dd = np.array(dd)
xx = xx.reshape(-1,1)
dd = dd.reshape(-1,1)

一阶线性回归

from sklearn.linear_model import LinearRegression
LR1 = LinearRegression()
LR1.fit(xx,dd)
y_predict= LR1.predict(xx)
print(y_predict)

画图

ig_reslut = plt.figure(figsize = (8,5))
plt.scatter(xx,dd)
plt.plot(xx,y_predict,"r")
plt.show()

二次回归

from sklearn.preprocessing import PolynomialFeatures
quadratic_featurizer = PolynomialFeatures(degree=2)
X_train_quadratic = quadratic_featurizer.fit_transform(xx)
regressor_quadratic = LinearRegression()
regressor_quadratic.fit(X_train_quadratic, dd)
xx_l = np.linspace(-4, 4, 1000)#给出一些点，并画出线性回归的曲线
xx_quadratic = quadratic_featurizer.transform(xx_l.reshape(xx_l.shape[0], 1))
fig_reslut = plt.figure(figsize = (8,5))
plt.scatter(xx,dd)
plt.plot(xx_l,regressor_quadratic.predict(xx_quadratic),"r")#根据需求点预测结果点
plt.show()

自写拟合函数

import numpy as np 
import matplotlib.pyplot as plt 

xx = np.random.normal(0, 1, [1000]) 
dd = xx**2 + xx + np.random.normal(0, 0.3, [1000]) #产生样本作用，实际不知道

# x,y是数据，样本点
plt.scatter(xx, dd) 
plt.show()

def model(x, a, b, c):
    # 构建的模型 
    y = a * x ** 2 + b * x + c
    return y 
def gradL(x, d, a, b, c):
    # dL/dy 
    y = model(x, a, b, c)
    dldy = 2 * (y - d) 
    dlda = np.mean(dldy * x ** 2) # dl/dy * dy/da
    dldb = np.mean(dldy * x)
    dldc = np.mean(dldy * 1)
    return dlda, dldb, dldc, np.mean((y-d)**2)

a, b, c = 0, 0, 0 # 初始值 
eta = 0.1   # 学习率，步长 
loss = []
batch_size = 100 #批学习
for step in range(100):
    idx = np.random.randint(0, 1000, [batch_size])
    inx = xx[idx]
    ind = dd[idx]
    ga, gb, gc, ls = gradL(inx, ind, a, b, c) # 计算梯度 
    loss.append(ls)
    a = a - eta * ga 
    b = b - eta * gb 
    c = c - eta * gc
plt.plot(loss)
plt.show()
x_plot = np.linspace(-3, 3, 1000) 
y_plot = model(x_plot, a, b, c)
plt.plot(x_plot, y_plot, lw=3, c="r")
plt.scatter(xx, dd)
plt.show()
1000) 
y_plot = model(x_plot, a, b, c)
plt.plot(x_plot, y_plot, lw=3, c="r")
plt.scatter(xx, dd)
plt.show()