使用TensorFlow的一个优势是,它可以维护操作状态和基于反向传播自动地更新模型变量。
TensorFlow通过计算图来更新变量和最小化损失函数来反向传播误差的。这步将通过声明优化函数(optimization function)来实现。一旦声明好优化函数,TensorFlow将通过它在所有的计算图中解决反向传播的项。当我们传入数据,最小化损失函数,TensorFlow会在计算图中根据状态相应的调节变量。
回归算法的例子从均值为1、标准差为0.1的正态分布中抽样随机数,然后乘以变量A,损失函数为L2正则损失函数。理论上,A的最优值是10,因为生成的样例数据均值是1。
二个例子是一个简单的二值分类算法。从两个正态分布(N(-1,1)和N(3,1))生成100个数。所有从正态分布N(-1,1)生成的数据标为目标类0;从正态分布N(3,1)生成的数据标为目标类1,模型算法通过sigmoid函数将这些生成的数据转换成目标类数据。换句话讲,模型算法是sigmoid(x+A),其中,A是要拟合的变量,理论上A=-1。假设,两个正态分布的均值分别是m1和m2,则达到A的取值时,它们通过-(m1+m2)/2转换成到0等距的值。后面将会在TensorFlow中见证怎样取到相应的值。
同时,指定一个合适的学习率对机器学习算法的收敛是有帮助的。优化器类型也需要指定,前面的两个例子会使用标准梯度下降法,它在TensorFlow中的实现是GradientDescentOptimizer()函数。
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
|
# 反向传播
#----------------------------------
#
# 以下Python函数主要是展示回归和分类模型的反向传播
import matplotlib.pyplot as plt
import numpy as np
import tensorflow as tf
from tensorflow.python.framework import ops
ops.reset_default_graph()
# 创建计算图会话
sess = tf.Session()
# 回归算法的例子:
# We will create sample data as follows:
# x-data: 100 random samples from a normal ~ N(1, 0.1)
# target: 100 values of the value 10.
# We will fit the model:
# x-data * A = target
# Theoretically, A = 10.
# 生成数据,创建占位符和变量A
x_vals = np.random.normal( 1 , 0.1 , 100 )
y_vals = np.repeat( 10. , 100 )
x_data = tf.placeholder(shape = [ 1 ], dtype = tf.float32)
y_target = tf.placeholder(shape = [ 1 ], dtype = tf.float32)
# Create variable (one model parameter = A)
A = tf.Variable(tf.random_normal(shape = [ 1 ]))
# 增加乘法操作
my_output = tf.multiply(x_data, A)
# 增加L2正则损失函数
loss = tf.square(my_output - y_target)
# 在运行优化器之前,需要初始化变量
init = tf.global_variables_initializer()
sess.run(init)
# 声明变量的优化器
my_opt = tf.train.GradientDescentOptimizer( 0.02 )
train_step = my_opt.minimize(loss)
# 训练算法
for i in range ( 100 ):
rand_index = np.random.choice( 100 )
rand_x = [x_vals[rand_index]]
rand_y = [y_vals[rand_index]]
sess.run(train_step, feed_dict = {x_data: rand_x, y_target: rand_y})
if (i + 1 ) % 25 = = 0 :
print ( 'Step #' + str (i + 1 ) + ' A = ' + str (sess.run(A)))
print ( 'Loss = ' + str (sess.run(loss, feed_dict = {x_data: rand_x, y_target: rand_y})))
# 分类算法例子
# We will create sample data as follows:
# x-data: sample 50 random values from a normal = N(-1, 1)
# + sample 50 random values from a normal = N(1, 1)
# target: 50 values of 0 + 50 values of 1.
# These are essentially 100 values of the corresponding output index
# We will fit the binary classification model:
# If sigmoid(x+A) < 0.5 -> 0 else 1
# Theoretically, A should be -(mean1 + mean2)/2
# 重置计算图
ops.reset_default_graph()
# Create graph
sess = tf.Session()
# 生成数据
x_vals = np.concatenate((np.random.normal( - 1 , 1 , 50 ), np.random.normal( 3 , 1 , 50 )))
y_vals = np.concatenate((np.repeat( 0. , 50 ), np.repeat( 1. , 50 )))
x_data = tf.placeholder(shape = [ 1 ], dtype = tf.float32)
y_target = tf.placeholder(shape = [ 1 ], dtype = tf.float32)
# 偏差变量A (one model parameter = A)
A = tf.Variable(tf.random_normal(mean = 10 , shape = [ 1 ]))
# 增加转换操作
# Want to create the operstion sigmoid(x + A)
# Note, the sigmoid() part is in the loss function
my_output = tf.add(x_data, A)
# 由于指定的损失函数期望批量数据增加一个批量数的维度
# 这里使用expand_dims()函数增加维度
my_output_expanded = tf.expand_dims(my_output, 0 )
y_target_expanded = tf.expand_dims(y_target, 0 )
# 初始化变量A
init = tf.global_variables_initializer()
sess.run(init)
# 声明损失函数 交叉熵(cross entropy)
xentropy = tf.nn.sigmoid_cross_entropy_with_logits(logits = my_output_expanded, labels = y_target_expanded)
# 增加一个优化器函数 让TensorFlow知道如何更新和偏差变量
my_opt = tf.train.GradientDescentOptimizer( 0.05 )
train_step = my_opt.minimize(xentropy)
# 迭代
for i in range ( 1400 ):
rand_index = np.random.choice( 100 )
rand_x = [x_vals[rand_index]]
rand_y = [y_vals[rand_index]]
sess.run(train_step, feed_dict = {x_data: rand_x, y_target: rand_y})
if (i + 1 ) % 200 = = 0 :
print ( 'Step #' + str (i + 1 ) + ' A = ' + str (sess.run(A)))
print ( 'Loss = ' + str (sess.run(xentropy, feed_dict = {x_data: rand_x, y_target: rand_y})))
# 评估预测
predictions = []
for i in range ( len (x_vals)):
x_val = [x_vals[i]]
prediction = sess.run(tf. round (tf.sigmoid(my_output)), feed_dict = {x_data: x_val})
predictions.append(prediction[ 0 ])
accuracy = sum (x = = y for x,y in zip (predictions, y_vals)) / 100.
print ( '最终精确度 = ' + str (np. round (accuracy, 2 )))
|
输出:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
|
Step #25 A = [ 6.12853956]
Loss = [ 16.45088196]
Step #50 A = [ 8.55680943]
Loss = [ 2.18415046]
Step #75 A = [ 9.50547695]
Loss = [ 5.29813051]
Step #100 A = [ 9.89214897]
Loss = [ 0.34628963]
Step #200 A = [ 3.84576249]
Loss = [[ 0.00083012]]
Step #400 A = [ 0.42345378]
Loss = [[ 0.01165466]]
Step #600 A = [-0.35141727]
Loss = [[ 0.05375391]]
Step #800 A = [-0.74206048]
Loss = [[ 0.05468176]]
Step #1000 A = [-0.89036471]
Loss = [[ 0.19636908]]
Step #1200 A = [-0.90850282]
Loss = [[ 0.00608062]]
Step #1400 A = [-1.09374011]
Loss = [[ 0.11037558]]
最终精确度 = 1.0
|
以上就是本文的全部内容,希望对大家的学习有所帮助,也希望大家多多支持服务器之家。
原文链接:http://blog.csdn.net/lilongsy/article/details/79258470