回归（多项式回归）

例子：回归（多项式回归）

训练数据：text.csv

x,y
235,591
216,539
148,413
35,310
85,308
204,519
49,325
25,332
173,498
191,498
134,392
99,334
117,385
112,387
162,425
272,659
159,400
159,427
59,319
198,522

import numpy as np
import matplotlib.pyplot as plt

#读入训练数据
train = np.loadtxt('text.csv',delimiter=',',skiprows=1)
train_x = train[:,0]
train_y = train[:,1]

#展示训练数据
#plt.plot(train_x,train_y,'o')
#plt.show()

#标准化数据
mu = train_x.mean()
sigma = train_x.std()
def standardize(x):
    return (x - mu)/sigma

train_z = standardize(train_x)
#plt.plot(train_z,train_y,'o')
#plt.show()

#均方误差
#在停止重复的条件里用上
def MSE(x,y):
    return (1/x.shape[0])*np.sum((y-f(x)) ** 2)

#生成三个随机数 代表三个参数 theta是参数列表
theta = np.random.rand(3)

#均方误差的历史记录
errors = []

#创建训练数据的矩阵
#因为训练数据很多 把它们都放在一个矩阵里
#直接和theta相乘
#theta0 + theta1*x1 + theta2*x2
def to_matrix(x):
    return np.vstack([np.ones(x.shape[0]),x,x**2]).T

X = to_matrix(train_z)

#预测函数
#theta0 + theta1*x1 + theta2*x2
#dot:矩阵乘法
def f(x):
    return np.dot(x,theta)

#目标函数 error误差 最小二乘法
def E(x,y):
    return 0.5*np.sum((y-f(x))**2)

#learning rate 学习率
ETA = 1e-3

#误差的差值
diff = 1;

#重复学习
errors.append(MSE(X,train_y))
error = E(X,train_y)
while diff>1e-2:
    #更新参数
    theta = theta - ETA*np.dot(f(X)-train_y,X)

    #计算差值
    errors.append(MSE(X,train_y))
    current_error = E(X,train_y)
    diff = errors[-2] - errors[-1]
    #不用均方误差的diff
    #diff = error - current_error
    error = current_error

'''
图表拟合展示
x = np.linspace(-3,3,100)
plt.plot(train_z,train_y,'o')
plt.plot(x,f(to_matrix(x)))
plt.show()
'''

#绘制误差变化图
x = np.arange(len(errors))
plt.plot(x,errors)
plt.show()