随机梯度下降算法及其注释

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# -*- coding:utf8 -*-

import math
import matplotlib.pyplot as plt

def f(w, x):
N = len(w)
i = 0
y = 0
while i < N - 1:
y += w[i] * x[i]
i += 1
y += w[N - 1] # 常数项
return y

def gradient(data, w, j):
M = len(data) # 样本数
N = len(data[0])
i = 0
g = 0 # 当前维度的梯度
while i < M:
y = f(w, data[i])
if (j != N - 1):
g += (data[i][N - 1] - y) * data[i][j]
else:
g += data[i][N - 1] - y
i += 1
return g / M

def gradientStochastic(data, w, j):
N = len(data) # 维度
y = data[N - 1] - f(w, data)
if (j != N - 1):
return y * data[j]
return y # 常数项

def isSame(a, b):
n = len(a)
i = 0
while i < n:
if abs(a[i] - b[i]) > 0.01:
return False
i += 1
return True

def fw(w, data):
M = len(data) # 样本数
N = len(data[0])
i = 0
s = 0
while i < M:
y = data[i][N - 1] - f(w, data[i])
s += y ** 2
i += 1
return s / 2

def fwStochastic(w, data):
y = data[len(data) - 1] - f(w, data)
y **= 2
return y / 2

def numberProduct(n, vec, w):
N = len(vec)
i = 0
while i < N:
w[i] += vec[i] * n
i += 1

def assign(a):
L = []
for x in a:
L.append(x)
return L

# a = b
def assign2(a, b):
i = 0
while i < len(a):
a[i] = b[i]
i += 1

def dotProduct(a, b):
N = len(a)
i = 0
dp = 0
while i < N:
dp += a[i] * b[i]
i += 1
return dp

# w当前值；g当前梯度方向；a当前学习率；data数据
def calcAlpha(w, g, a, data):
c1 = 0.3
now = fw(w, data)
wNext = assign(w) #复制一份w
numberProduct(a, g, wNext) #利用w = w + alpha(y-f(x))x 更新 w
next = fw(wNext, data) # 计算整个1000个样本的loss
# 寻找足够大的a，使得h(a)>0
count = 30
while next < now:
a *= 2
wNext = assign(w)
numberProduct(a, g, wNext)
next = fw(wNext, data)
count -= 1
if count == 0:
break

# 寻找合适的学习率a
count = 50
while next > now - c1*a*dotProduct(g, g):
a /= 2
wNext = assign(w)
numberProduct(a, g, wNext)
next = fw(wNext, data)

count -= 1
if count == 0:
break
return a

# w当前值；g当前梯度方向；a当前学习率；data数据
def calcAlphaStochastic(w, g, a, data):
c1 = 0.01 # 因为是每个样本都下降，所以参数运行度大些，即：激进一些
now = fwStochastic(w, data) #计算当前的全体样本的LOSS
wNext = assign(w) #重新复制一份W
numberProduct(a, g, wNext) #利用w = w + alpha*(y-f(x))*x 计算更新W
next = fwStochastic(wNext, data) #利用更新后的W 计算全体样本LOSS
# 寻找足够大的a，使得h(a)>0
count = 30
while next < now:
if a < 1e-10:
a = 0.01
else:
a *= 2
wNext = assign(w)
numberProduct(a, g, wNext)
next = fwStochastic(wNext, data)
count -= 1
if count == 0:
break

# 寻找合适的学习率a
count = 50
while next > now - c1*a*dotProduct(g, g):
a /= 2
wNext = assign(w)
numberProduct(a, g, wNext)
next = fwStochastic(wNext, data)

count -= 1
if count == 0:
break
return a

def normalize(g):
s = 0
for x in g:
s += x * x
s = math.sqrt(s)
i = 0
N = len(g)
while i < N:
g[i] /= s
i += 1

def calcCoefficient(data, listA, listW, listLostFunction):
M = len(data) # 样本数目
N = len(data[0]) # 维度
w = [0 for i in range(N)]
wNew = [0 for i in range(N)]
g = [0 for i in range(N)]

times = 0
alpha = 100.0 # 学习率随意初始化
same = False
while times < 10000:
i = 0
while i < M:
j = 0
while j < N:
g[j] = gradientStochastic(data[i], w, j)
j += 1
normalize(g) # 正则化梯度
alpha = calcAlphaStochastic(w, g, alpha, data[i])
#alpha = 0.01
numberProduct(alpha, g, wNew)

print "times,i, alpha,fw,w,g:\t", times, i, alpha, fw(w, data), w, g
if isSame(w, wNew):
if times > 5: #防止训练次数过少
same = True
break
assign2(w, wNew) # 更新权值

listA.append(alpha)
listW.append(assign(w))
listLostFunction.append(fw(w, data))

i += 1
if same:
break
times += 1
return w

if __name__ == "__main__":
fileData = open("d8.txt")
data = []
for line in fileData:
d = map(float, line.split(‘,‘))
data.append(d)
fileData.close()

listA = [] # 每一步的学习率
listW = [] # 每一步的权值
listLostFunction = [] # 每一步的损失函数值
w = calcCoefficient(data, listA, listW, listLostFunction)

# 绘制学习率
plt.plot(listA, ‘r-‘, linewidth=2)
plt.plot(listA, ‘go‘)
plt.xlabel(‘Times‘)
plt.ylabel(‘Ratio/Step‘)
plt.show()

# 绘制损失
listLostFunction = listLostFunction[0:100]
listLostFunction[0] /= 2
plt.plot(listLostFunction, ‘r-‘, linewidth=2)
plt.plot(listLostFunction, ‘gv‘, alpha = 0.75)
plt.xlabel(‘Times‘)
plt.ylabel(‘Loss Value‘)
plt.grid(True)
plt.show()

# 绘制权值
X = []
Y = []
for d in data:
X.append(d[0])
Y.append(d[1])
plt.plot(X, Y, ‘cp‘, label=u‘Original Data‘, alpha=0.75)
x = [min(X), max(X)]
y = [w[0] * x[0] + w[1], w[0] * x[1] + w[1]]
plt.plot(x, y, ‘r-‘, linewidth=3, label=‘Regression Curve‘)
plt.legend(loc=‘upper left‘)
plt.grid(True)
plt.show()

随机梯度下降算法及其注释

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原文地址：http://www.cnblogs.com/mxc2/p/5839434.html