tensorflow--Logistics Regression

import tensorflow as tf

# Import MNIST data
from tensorflow.examples.tutorials.mnist import input_data
mnist = input_data.read_data_sets("/tmp/data/", one_hot=True) # one_hot是一种编码方式，在MNIST中，标签为2的编码为00000010

# Parameters
learning_rate = 0.01
training_epochs = 25
batch_size = 100
display_step = 1

# tf Graph Input
x = tf.placeholder(tf.float32, [None, 784]) # mnist data image of shape 28*28=784
y = tf.placeholder(tf.float32, [None, 10]) # 0-9 digits recognition => 10 classes

# Set model weights
W = tf.Variable(tf.zeros([784, 10]))
b = tf.Variable(tf.zeros([10]))

# Construct model
pred = tf.nn.softmax(tf.matmul(x, W) + b) # Softmax 多分类器

# Minimize error using cross entropy
cost = tf.reduce_mean(-tf.reduce_sum(y*tf.log(pred), axis=1))
# Gradient Descent
optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)

# Initialize the variables (i.e. assign their default value)
init = tf.global_variables_initializer()

# Start training
with tf.Session() as sess:

    # Run the initializer
    sess.run(init)

    # Training cycle
    for epoch in range(training_epochs):
        avg_cost = 0.
        total_batch = int(mnist.train.num_examples/batch_size)
        # Loop over all batches
        for i in range(total_batch):
            batch_xs, batch_ys = mnist.train.next_batch(batch_size)
            # Run optimization op (backprop) and cost op (to get loss value)
            _, c = sess.run([optimizer, cost], feed_dict={x: batch_xs,
                                                          y: batch_ys})
            # Compute average loss
            avg_cost += c / total_batch
        # Display logs per epoch step
        if (epoch+1) % display_step == 0:
            print("Epoch:", '%04d' % (epoch+1), "cost=", "{:.9f}".format(avg_cost))

    print("Optimization Finished!")

    # Test model
    correct_prediction = tf.equal(tf.argmax(pred, 1), tf.argmax(y, 1))
    # Calculate accuracy
    accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
    print("Accuracy:", accuracy.eval({x: mnist.test.images, y: mnist.test.labels}))

tf.nn.softmax(
    logits,
    axis=None,
    name=None,
    dim=None #弃用参数
) 

softmax = tf.exp(logits) / tf.reduce_sum(tf.exp(logits), axis)

上图来自李宏毅的《一天读懂深度学习》，很好地解释了softmax如何实现多分类任务

交叉熵（cross entropy loss）公式：H(p,q)=−∑i=1np(xi)logq(xi)，p, q即为实际值和预测值H(p,q)=−∑i=1np(xi)log⁡q(xi)

tf.reduce_mean求均值，用法和tf.reduce_sum类似

tf.argmax(
    input,
    axis=None,
    name=None,
    dimension=None,
    output_type=tf.int64
)# 找到沿axis轴的最大的那个数的下标并返回

tf.equal(
    x,
    y,
    name=None
)# 比较x和y的所有元素，x和y具有相同的shape，函数返回该shape的bool tensor，x和y对应位置上的元素若相等，则返回值该位置上为True，否则为False

tf.cast(
    x,
    dtype,
    name=None
)# 类型转换，在此做bool类型转换，转换为数值后，求均值即为准确率

eval(
    feed_dict=None,
    session=None
)# tensor的成员函数，调用此函数会执行该tensor包含的所有图计算和操作，前提是此前必须有Session