1.简介
理论知识回顾
逻辑回归的主要公式罗列如下：
sigmoid(x)=1+e(−x)1
y^(i)=a(i)=sigmoid(z(i))=sigmoid(wTx(i)+b)\hat{y}^{(i)} = a^{(i)} = sigmoid(z^{(i)}) = sigmoid(w^Tx^{(i)} + b)y^(i)=a(i)=sigmoid(z(i))=sigmoid(wTx(i)+b)
损失函数（cost function）：
J=m1∑i=1mL(a(i),y(i))
其中
L(a(i),y(i))=−y(i)log(a(i))−(1−y(i))log(1−a(i))
损失函数求偏导（derivative cost function）：
∂w∂J=m1X(A−Y)T
∂b∂J=m1∑i=1m(a(i)−y(i))
2.训练模型
数据准备
扫描二维码关注公众号，回复：
718794 查看本文章
首先我们需要先下载MNIST的数据集。使用以下的命令进行下载：
wget http://tensorflow-1253902462.cosgz.myqcloud.com/mnist_cnn/t10k-images-idx3-ubyte.gz wget http://tensorflow-1253902462.cosgz.myqcloud.com/mnist_cnn/t10k-labels-idx1-ubyte.gz wget http://tensorflow-1253902462.cosgz.myqcloud.com/mnist_cnn/train-images-idx3-ubyte.gz wget http://tensorflow-1253902462.cosgz.myqcloud.com/mnist_cnn/train-labels-idx1-ubyte.gz
创建代码
现在您可以在 /home/ubuntu 目录下创建源文件 logistic_regression.py，内容可参考：
#-*- coding:utf-8 -*-
import time
import numpy as np
import tensorflow as tf
from tensorflow.examples.tutorials.mnist import input_data
MNIST = input_data.read_data_sets("./", one_hot=True)
learning_rate = 0.01
batch_size = 128
n_epochs = 25
X = tf.placeholder(tf.float32, [batch_size, 784])
Y = tf.placeholder(tf.float32, [batch_size, 10])
w = tf.Variable(tf.random_normal(shape=[784,10], stddev=0.01), name="weights")
b = tf.Variable(tf.zeros([1, 10]), name="bias")
logits = tf.matmul(X, w) + b
entropy = tf.nn.softmax_cross_entropy_with_logits(labels=Y, logits=logits)
loss = tf.reduce_mean(entropy)
optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate).minimize(loss)
init = tf.global_variables_initializer()
with tf.Session() as sess:
sess.run(init)
n_batches = int(MNIST.train.num_examples/batch_size)
for i in range(n_epochs):
for j in range(n_batches):
X_batch, Y_batch = MNIST.train.next_batch(batch_size)
_, loss_ = sess.run([optimizer, loss], feed_dict={ X: X_batch, Y: Y_batch})
print "Loss of epochs[{0}] batch[{1}]: {2}".format(i, j, loss_)
执行代码
python logistic_regression.py
运行过程中，如果出现网络错误，请重试。
运行输出：
Loss of epochs[0] batch[0]: 2.28968191147 Loss of epochs[0] batch[1]: 2.30224704742 Loss of epochs[0] batch[2]: 2.26435565948 Loss of epochs[0] batch[3]: 2.26956915855 Loss of epochs[0] batch[4]: 2.25983452797 Loss of epochs[0] batch[5]: 2.2572259903 ...... Loss of epochs[24] batch[420]: 0.393310219049 Loss of epochs[24] batch[421]: 0.309725940228 Loss of epochs[24] batch[422]: 0.378903746605 Loss of epochs[24] batch[423]: 0.472946226597 Loss of epochs[24] batch[424]: 0.259472459555 Loss of epochs[24] batch[425]: 0.290799200535 Loss of epochs[24] batch[426]: 0.256865829229 Loss of epochs[24] batch[427]: 0.250789999962 Loss of epochs[24] batch[428]: 0.328135550022
3.测试模型
示例代码编辑源文件 logistic_regression.py，内容可参考：
#-*- coding:utf-8 -*-
import time
import numpy as np
import tensorflow as tf
from tensorflow.examples.tutorials.mnist import input_data
MNIST = input_data.read_data_sets("./", one_hot=True)
learning_rate = 0.01
batch_size = 128
n_epochs = 25
X = tf.placeholder(tf.float32, [batch_size, 784])
Y = tf.placeholder(tf.float32, [batch_size, 10])
w = tf.Variable(tf.random_normal(shape=[784,10], stddev=0.01), name="weights")
b = tf.Variable(tf.zeros([1, 10]), name="bias")
logits = tf.matmul(X, w) + b
entropy = tf.nn.softmax_cross_entropy_with_logits(labels=Y, logits=logits)
loss = tf.reduce_mean(entropy)
optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate).minimize(loss)
init = tf.global_variables_initializer()
with tf.Session() as sess:
sess.run(init)
n_batches = int(MNIST.train.num_examples/batch_size)
for i in range(n_epochs):
for j in range(n_batches):
X_batch, Y_batch = MNIST.train.next_batch(batch_size)
_, loss_ = sess.run([optimizer, loss], feed_dict={ X: X_batch, Y: Y_batch})
print "Loss of epochs[{0}] batch[{1}]: {2}".format(i, j, loss_)
n_batches = int(MNIST.test.num_examples/batch_size)
total_correct_preds = 0
for i in range(n_batches):
X_batch, Y_batch = MNIST.test.next_batch(batch_size)
preds = tf.nn.softmax(tf.matmul(X_batch, w) + b)
correct_preds = tf.equal(tf.argmax(preds, 1), tf.argmax(Y_batch, 1))
accuracy = tf.reduce_sum(tf.cast(correct_preds, tf.float32))
total_correct_preds += sess.run(accuracy)
print "Accuracy {0}".format(total_correct_preds/MNIST.test.num_examples)
执行代码
python logistic_regression.py
运行输出：
Accuracy 0.9108
4.完成实验
实验内容已完成