Python实现随机梯度下降法：原理与代码详解

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import axes3d
from matplotlib import style
 
 
#构造数据
def get_data(sample_num=1000):
 """
 拟合函数为
 y = 5*x1 + 7*x2
 :return:
 """
 x1 = np.linspace(0, 9, sample_num)
 x2 = np.linspace(4, 13, sample_num)
 x = np.concatenate(([x1], [x2]), axis=0).T
 y = np.dot(x, np.array([5, 7]).T) 
 return x, y
#梯度下降法
def SGD(samples, y, step_size=2, max_iter_count=1000):
 """
 :param samples: 样本
 :param y: 结果value
 :param step_size: 每一接迭代的步长
 :param max_iter_count: 最大的迭代次数
 :param batch_size: 随机选取的相对于总样本的大小
 :return:
 """
 #确定样本数量以及变量的个数初始化theta值
 
 m, var = samples.shape
 theta = np.zeros(2)
 y = y.flatten()
 #进入循环内
 loss = 1
 iter_count = 0
 iter_list=[]
 loss_list=[]
 theta1=[]
 theta2=[]
 #当损失精度大于0.01且迭代此时小于最大迭代次数时，进行
 while loss > 0.01 and iter_count < max_iter_count:
 loss = 0
 #梯度计算
 theta1.append(theta[0])
 theta2.append(theta[1]) 
 #样本维数下标
 rand1 = np.random.randint(0,m,1)
 h = np.dot(theta,samples[rand1].T)
 #关键点，只需要一个样本点来更新权值
 for i in range(len(theta)):
 theta[i] =theta[i] - step_size*(1/m)*(h - y[rand1])*samples[rand1,i]
 #计算总体的损失精度，等于各个样本损失精度之和
 for i in range(m):
 h = np.dot(theta.T, samples[i])
 #每组样本点损失的精度
 every_loss = (1/(var*m))*np.power((h - y[i]), 2)
 loss = loss + every_loss
 
 print("iter_count: ", iter_count, "the loss:", loss)
 
 iter_list.append(iter_count)
 loss_list.append(loss)
 
 iter_count += 1
 plt.plot(iter_list,loss_list)
 plt.xlabel("iter")
 plt.ylabel("loss")
 plt.show()
 return theta1,theta2,theta,loss_list
 
def painter3D(theta1,theta2,loss):
 style.use('ggplot')
 fig = plt.figure()
 ax1 = fig.add_subplot(111, projection='3d')
 x,y,z = theta1,theta2,loss
 ax1.plot_wireframe(x,y,z, rstride=5, cstride=5)
 ax1.set_xlabel("theta1")
 ax1.set_ylabel("theta2")
 ax1.set_zlabel("loss")
 plt.show()
 
if __name__ == '__main__':
 samples, y = get_data()
 theta1,theta2,theta,loss_list = SGD(samples, y)
 print(theta) # 会很接近[5, 7]
 
 painter3D(theta1,theta2,loss_list)