线性回归和梯度下降代码demo

程序所用文件：https://files.cnblogs.com/files/henuliulei/%E5%9B%9E%E5%BD%92%E5%88%86%E7%B1%BB%E6%95%B0%E6%8D%AE.zip

线性回归

决定系数越接近一那么预测效果越好

对于多元线性回归和一元线性回归推导理论是一致的，只不过参数是多个参数而已

梯度下降

梯度下降法存在局部最小值

太小迭代次数多，太大将无法迭代到最优质

梯度下降发容易到达局部最小值

凸函数使用局部下降法一定可以到全部最小值，所以不存在局部最小值才可以

下面两个demo是一元函数的拟合

1使用梯度下降法的数学公式进行的机器学习代码

 import numpy as np

 from matplotlib import  pyplot as plt

 #读取数据

 data = np.genfromtxt('data.csv',delimiter=',')

 x_data = data[:, ]

 y_data = data[:, ]

 #plt.scatter(x_data, y_data)

 #plt.show()

 lr = 0.0001

 k =

 b =

 epochs =

 def compute_loss(x_data, y_data, b, k):#计算损失函数

     m = float(len(x_data))

     sum =

     for i in range(, len(x_data)):

         sum += (y_data[i] - (k*x_data[i] + b))**

     return sum/(*m)

 def gradient(x_data, y_data, k, b, lr, epochs):#进行梯度下降

     m = float(len(x_data))

     for i in range(,epochs):

         k_gradient =

         b_gradiet =

         for j in range(,len(x_data)):

             k_gradient += (/m)*((x_data[j] * k + b) - y_data[j])

             b_gradiet += (/m)*((x_data[j] * k + b) - y_data[j]) * x_data[j]

         k -= lr * k_gradient

         b -= lr * b_gradiet

         if i %  == :

             print(i)

             plt.plot(x_data, y_data, 'b.')

             plt.plot(x_data, k*x_data + b, 'r')

             plt.show()

     return k, b

 k,b = gradient(x_data, y_data, , , lr, epochs)

 plt.plot(x_data, k * x_data + b, 'r')

 plt.plot(x_data, y_data, 'b.')

 print('loss =:',compute_loss(x_data, y_data, b, k),'b =:',b,'k =:',k)

 plt.show()

2 使用Python的sklearn库

 import numpy as np

 from matplotlib import  pyplot as plt

 from sklearn.linear_model import LinearRegression

 #读取数据

 data = np.genfromtxt('data.csv',delimiter=',')

 x_data = data[:, ]

 y_data = data[:, ]

 plt.scatter(x_data, y_data)

 plt.show()

 x_data = data[:, , np.newaxis]#使一位数据编程二维数据

 y_data = data[:, , np.newaxis]

 model =LinearRegression()

 model.fit(x_data, y_data)#传进的参数必须是二维的

 plt.plot(x_data, y_data, 'b.')

 plt.plot(x_data, model.predict(x_data), 'r')#画出预测的线条

 plt.show()

3使用梯度下降法完成多元线性回归（以二元为例）

 import numpy as np

 from numpy import genfromtxt

 import matplotlib.pyplot as plt

 from mpl_toolkits.mplot3d import Axes3D #用来画3D图的包

 # 读入数据

 data = genfromtxt(r"Delivery.csv",delimiter=',')

 print(data)

 # 切分数据

 x_data = data[:,:-]

 y_data = data[:,-]

 print(x_data)

 print(y_data)

 # 学习率learning rate

 lr = 0.0001

 # 参数

 theta0 =

 theta1 =

 theta2 =

 # 最大迭代次数

 epochs =

 # 最小二乘法

 def compute_error(theta0, theta1, theta2, x_data, y_data):

     totalError =

     for i in range(, len(x_data)):

         totalError += (y_data[i] - (theta1 * x_data[i,] + theta2*x_data[i,] + theta0)) **

     return totalError / float(len(x_data))

 def gradient_descent_runner(x_data, y_data, theta0, theta1, theta2, lr, epochs):

     # 计算总数据量

     m = float(len(x_data))

     # 循环epochs次

     for i in range(epochs):

         theta0_grad =

         theta1_grad =

         theta2_grad =

         # 计算梯度的总和再求平均

         for j in range(, len(x_data)):

             theta0_grad += (/m) * ((theta1 * x_data[j,] + theta2*x_data[j,] + theta0) - y_data[j])

             theta1_grad += (/m) * x_data[j,] * ((theta1 * x_data[j,] + theta2*x_data[j,] + theta0) - y_data[j])

             theta2_grad += (/m) * x_data[j,] * ((theta1 * x_data[j,] + theta2*x_data[j,] + theta0) - y_data[j])

         # 更新b和k

         theta0 = theta0 - (lr*theta0_grad)

         theta1 = theta1 - (lr*theta1_grad)

         theta2 = theta2 - (lr*theta2_grad)

     return theta0, theta1, theta2

 print("Starting theta0 = {0}, theta1 = {1}, theta2 = {2}, error = {3}".

       format(theta0, theta1, theta2, compute_error(theta0, theta1, theta2, x_data, y_data)))

 print("Running...")

 theta0, theta1, theta2 = gradient_descent_runner(x_data, y_data, theta0, theta1, theta2, lr, epochs)

 print("After {0} iterations theta0 = {1}, theta1 = {2}, theta2 = {3}, error = {4}".

       format(epochs, theta0, theta1, theta2, compute_error(theta0, theta1, theta2, x_data, y_data)))

 ax = Axes3D(plt.figure())#和下面的代码功能一样

 #ax = plt.figure().add_subplot(, projection='3d')#plt.figure().add_subplot和plt.subplot的作用是一致的

 ax.scatter(x_data[:, ], x_data[:, ], y_data, c='r', marker='o', s=)  # 点为红色三角形

 x0 = x_data[:, ]

 x1 = x_data[:, ]

 # 生成网格矩阵

 x0, x1 = np.meshgrid(x0, x1)#生成一个网格矩阵，矩阵的每个点的第一个轴的取值来自于x0范围内，第二个坐标轴的取值来自于x1范围内

 z = theta0 + x0 * theta1 + x1 * theta2

 # 画3D图

 ax.plot_surface(x0, x1, z)

 # 设置坐标轴

 ax.set_xlabel('Miles')

 ax.set_ylabel('Num of Deliveries')

 ax.set_zlabel('Time')

 # 显示图像

 plt.show()

4：使用Python的sklearn库完成多元线性回归

import numpy as np

from numpy import genfromtxt

from sklearn import linear_model

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

# 读入数据

data = genfromtxt(r"Delivery.csv",delimiter=',')

print(data)

# 切分数据

x_data = data[:,:-]

y_data = data[:,-]

print(x_data)

print(y_data)

# 创建模型

model = linear_model.LinearRegression()

model.fit(x_data, y_data)

# 系数

print("coefficients:",model.coef_)

# 截距

print("intercept:",model.intercept_)

# 测试

x_test = [[,]]

predict = model.predict(x_test)

print("predict:",predict)

ax = plt.figure().add_subplot(, projection='3d')

ax.scatter(x_data[:, ], x_data[:, ], y_data, c='r', marker='o', s=)  # 点为红色三角形

x0 = x_data[:, ]

x1 = x_data[:, ]

# 生成网格矩阵

x0, x1 = np.meshgrid(x0, x1)

z = model.intercept_ + x0*model.coef_[] + x1*model.coef_[]

# 画3D图

ax.plot_surface(x0, x1, z)#参数是二维的，而model.prodict(x_data)是一维的。

# 设置坐标轴

ax.set_xlabel('Miles')

ax.set_ylabel('Num of Deliveries')

ax.set_zlabel('Time')

# 显示图像

plt.show()

5 多项式回归拟合

 import numpy as np

 import matplotlib.pyplot as plt

 from sklearn.preprocessing import PolynomialFeatures#多项式

 from sklearn.linear_model import LinearRegression

 # 载入数据

 data = np.genfromtxt("job.csv", delimiter=",")

 x_data = data[:,]

 y_data = data[:,]

 plt.scatter(x_data,y_data)

 plt.show()

 x_data

 x_data = x_data[:,np.newaxis]

 y_data = y_data[:,np.newaxis]

 x_data

 # 创建并拟合模型

 model = LinearRegression()

 model.fit(x_data, y_data)

 # 画图

 plt.plot(x_data, y_data, 'b.')

 plt.plot(x_data, model.predict(x_data), 'r')

 plt.show()

 # 定义多项式回归,degree的值可以调节多项式的特征

 poly_reg  = PolynomialFeatures(degree=)

 # 特征处理

 x_poly = poly_reg.fit_transform(x_data)

 # 定义回归模型

 lin_reg = LinearRegression()

 # 训练模型

 lin_reg.fit(x_poly, y_data)

 # 画图

 plt.plot(x_data, y_data, 'b.')

 plt.plot(x_data, lin_reg.predict(poly_reg.fit_transform(x_data)), c='r')

 plt.title('Truth or Bluff (Polynomial Regression)')

 plt.xlabel('Position level')

 plt.ylabel('Salary')

 plt.show()

 # 画图

 plt.plot(x_data, y_data, 'b.')

 x_test = np.linspace(,,)

 x_test = x_test[:,np.newaxis]

 plt.plot(x_test, lin_reg.predict(poly_reg.fit_transform(x_test)), c='r')

 plt.title('Truth or Bluff (Polynomial Regression)')

 plt.xlabel('Position level')

 plt.ylabel('Salary')

 plt.show()