python 实现梯度下降

浏览数：25 / 时间：2015年06月08日

在多元线性回归中会用到梯度下降来计算参数值。这里我用python实现一个梯度下降版本。

这里多元线性方程为 y = A0+A1*x1+...+An* xn

数据输入格式，y表示

1	`y \t x1 \t x2 \t .... xn`

代码如下：

import 
os
import 
sys
 
theta = 
[]
training_data = 
[]
h_value = 
[]
alpha = 
0.0000009
 
def load(path):
    f = 
open(path,‘r‘)
    for 
x in 
f:
        x = 
x.strip(‘\r\n‘)
        field = 
x.split(‘\t‘)
        v_list = 
[]
        for 
v in 
field:
            v_list.append(int(v))
        training_data.append(v_list)
    f.close()
    for 
x in 
training_data:
        h_value.append(0.0)
 
def 
init(path,theta_num):
    for 
x in 
range(theta_num):
        theta.append(1.0)
    load(path);
 
def 
gradient():
    i = 
0
    loss = 
100.0
    theta_num = 
len(theta)
    data_num = 
len(training_data)
    while 
i < 3000 
and loss > 0.0001:
        #compute hvalue
        for 
index in 
range(data_num):
            hv = 
theta[0]
            for 
k in 
range(1,theta_num):
                hv += 
theta[k]*training_data[index][k]
            h_value[index] = 
hv
        #update theta
        for 
index in 
range(theta_num):
            s = 
0.0
            for 
k in 
range(data_num):
                if 
index == 
0:
                    s += 
(h_value[k] - 
training_data[k][0])*1
                else:
                    s += 
(h_value[k] - 
training_data[k][0])*training_data[k][index]
            theta[index] = 
theta[index] - 
alpha * 
1/data_num * 
(s)
        #compute loss
        loss = 
0.0
        for 
index in 
range(data_num):
            hv = 
theta[0] / 
(2*data_num)
            for 
k in 
range(1,theta_num):
                hv += 
theta[k]*training_data[index][k]
            loss +=  
pow((hv - 
training_data[index][0]),2)/(2*data_num)
        print 
loss
        i += 
1
    for 
x in 
theta:
       print 
x,
 
if __name__==‘__main__‘:
    path = 
sys.argv[1]
    init(path,int(sys.argv[2]))
    gradient()
    sys.exit(0)
    