python实现梯度下降法

本文实例为大家分享了python实现梯度下降法的具体代码,供大家参考,具体内容如下

使用工具:Python(x,y) 2.6.6

运行环境:Windows10

问题:求解y=2*x1+x2+3,即使用梯度下降法求解y=a*x1+b*x2+c中参数a,b,c的最优值(监督学习)

训练数据:

x_train=[1, 2], [2, 1],[2, 3], [3, 5], [1,3], [4, 2], [7, 3], [4, 5], [11, 3], [8, 7]

y_train=[7, 8, 10, 14, 8, 13, 20, 16, 28,26]

测试数据:

x_test = [1, 4],[2, 2],[2, 5],[5, 3],[1,5],[4, 1]

# -*- coding: utf-8 -*-

"""

Created on Wed Nov 16 09:37:03 2016

@author: Jason

"""

import numpy as np

import matplotlib.pyplot as plt

# y=2 * (x1) + (x2) + 3

rate = 0.001

x_train = np.array([[1, 2], [2, 1],[2, 3], [3, 5], [1, 3], [4, 2], [7, 3], [4, 5], [11, 3], [8, 7] ])

y_train = np.array([7, 8, 10, 14, 8, 13, 20, 16, 28, 26])

x_test = np.array([[1, 4],[2, 2],[2, 5],[5, 3],[1, 5],[4, 1]])

a = np.random.normal()

b = np.random.normal()

c = np.random.normal()

def h(x):

return a*x[0]+b*x[1]+c

for i in range(100):

sum_a=0

sum_b=0

sum_c=0

for x, y in zip(x_train, y_train):

for xi in x:

sum_a = sum_a+ rate*(y-h(x))*xi

sum_b = sum_b+ rate*(y-h(x))*xi

#sum_c = sum_c + rate*(y-h(x)) *1

a = a + sum_a

b = b + sum_b

c = c + sum_c

plt.plot([h(xi) for xi in x_test])

print(a)

print(b)

print(c)

result=[h(xi) for xi in x_train]

print(result)

result=[h(xi) for xi in x_test]

print(result)

plt.show()

运行结果:

结论:线段是在逐渐逼近的,训练数据越多,迭代次数越多就越逼近真实值。

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