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
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y \t x1 \t x2 \t .... xn |
代码如下：
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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)
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