tensorflow初学之SGD

在开始本任务之前，确保已经完成了之前的notMNIST的步骤，点击查看notMNIST

提示：训练随机梯度下降（SGD）花费的时间应给明显少于简单的梯度下降（GD）.

1.检查包

首先，检查本次学习要用到的包，确保都已经正确导入，输入以下代码，点击“run cell”，运行不报错即可

#在学习之前确保以下包已经正确导入
from __future__ import print_function
import numpy as np
import tensorflow as tf
from six.moves import cPickle as pickle
from six.moves import range

2.导入pickle

导入之前生成的notMNIST.pickle文件（链接在本文开头）

pickle_file = 'notMNIST.pickle'

with open(pickle_file, 'rb') as f:
  save = pickle.load(f)
  train_dataset = save['train_dataset']
  train_labels = save['train_labels']
  valid_dataset = save['valid_dataset']
  valid_labels = save['valid_labels']
  test_dataset = save['test_dataset']
  test_labels = save['test_labels']
  del save  # hint to help gc free up memory
  print('Training set', train_dataset.shape, train_labels.shape)
  print('Validation set', valid_dataset.shape, valid_labels.shape)
  print('Test set', test_dataset.shape, test_labels.shape)

结果如下：

Training set (200000, 28, 28) (200000,)
Validation set (10000, 28, 28) (10000,)
Test set (18724, 28, 28) (18724,)

3.数据处理

将数据重新处理为更适合接下来模型学习的格式：

数据作为平面矩阵；标签用One-Hot编码处理.

image_size = 28
num_labels = 10

def reformat(dataset, labels):
  dataset = dataset.reshape((-1, image_size * image_size)).astype(np.float32)
  # Map 0 to [1.0, 0.0, 0.0 ...], 1 to [0.0, 1.0, 0.0 ...]
  labels = (np.arange(num_labels) == labels[:,None]).astype(np.float32)
  return dataset, labels
train_dataset, train_labels = reformat(train_dataset, train_labels)
valid_dataset, valid_labels = reformat(valid_dataset, valid_labels)
test_dataset, test_labels = reformat(test_dataset, test_labels)
print('Training set', train_dataset.shape, train_labels.shape)
print('Validation set', valid_dataset.shape, valid_labels.shape)
print('Test set', test_dataset.shape, test_labels.shape)

结果：

Training set (200000, 784) (200000, 10)
Validation set (10000, 784) (10000, 10)
Test set (10000, 784) (10000, 10)

4.简单的梯度下降（GD）

我们首先使用简单的梯度下降训练多项Logistic回归。

tensorflow工作流程：

首先描述你想要在输入，变量和操作上执行的计算方式，它们通过计算图的方式创建为一个节点。此描述全部包含在以下内容中：

with graph.as_default():

然后可以通过session.run()，在计算图上运行多次你想要的操作，从返回的图中提取提供输出。此运行时操作全部包含在以下块中：

with tf.Session(graph=graph) as session:

我们将所有数据加载到TensorFlow中，构建对应于我们培训的计算图：

# With gradient descent training, even this much data is prohibitive.
# Subset the training data for faster turnaround.
train_subset = 10000

graph = tf.Graph()
with graph.as_default():

  # Input data.
  # Load the training, validation and test data into constants that are
  # attached to the graph.
  tf_train_dataset = tf.constant(train_dataset[:train_subset, :])
  tf_train_labels = tf.constant(train_labels[:train_subset])
  tf_valid_dataset = tf.constant(valid_dataset)
  tf_test_dataset = tf.constant(test_dataset)

  # Variables.
  # These are the parameters that we are going to be training. The weight
  # matrix will be initialized using random values following a (truncated)
  # normal distribution. The biases get initialized to zero.
  weights = tf.Variable(
    tf.truncated_normal([image_size * image_size, num_labels]))
  biases = tf.Variable(tf.zeros([num_labels]))

  # Training computation.
  # We multiply the inputs with the weight matrix, and add biases. We compute
  # the softmax and cross-entropy (it's one operation in TensorFlow, because
  # it's very common, and it can be optimized). We take the average of this
  # cross-entropy across all training examples: that's our loss.
  logits = tf.matmul(tf_train_dataset, weights) + biases
  loss = tf.reduce_mean(
    tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits))

  # Optimizer.
  # We are going to find the minimum of this loss using gradient descent.
  optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)

  # Predictions for the training, validation, and test data.
  # These are not part of training, but merely here so that we can report
  # accuracy figures as we train.
  train_prediction = tf.nn.softmax(logits)
  valid_prediction = tf.nn.softmax(
    tf.matmul(tf_valid_dataset, weights) + biases)
  test_prediction = tf.nn.softmax(tf.matmul(tf_test_dataset, weights) + biases)

我们来运行这个计算并迭代：

num_steps = 801

def accuracy(predictions, labels):
  return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1))
          / predictions.shape[0])

with tf.Session(graph=graph) as session:
  # This is a one-time operation which ensures the parameters get initialized as
  # we described in the graph: random weights for the matrix, zeros for the
  # biases. 
  tf.global_variables_initializer().run()
  print('Initialized')
  for step in range(num_steps):
    # Run the computations. We tell .run() that we want to run the optimizer,
    # and get the loss value and the training predictions returned as numpy
    # arrays.
    _, l, predictions = session.run([optimizer, loss, train_prediction])
    if (step % 100 == 0):
      print('Loss at step %d: %f' % (step, l))
      print('Training accuracy: %.1f%%' % accuracy(
        predictions, train_labels[:train_subset, :]))
      # Calling .eval() on valid_prediction is basically like calling run(), but
      # just to get that one numpy array. Note that it recomputes all its graph
      # dependencies.
      print('Validation accuracy: %.1f%%' % accuracy(
        valid_prediction.eval(), valid_labels))
  print('Test accuracy: %.1f%%' % accuracy(test_prediction.eval(), test_labels))

结果：

Initialized
Loss at step 0: 16.442284
Training accuracy: 7.8%
Validation accuracy: 11.4%
Loss at step 100: 2.226995
Training accuracy: 72.3%
Validation accuracy: 70.9%
Loss at step 200: 1.799694
Training accuracy: 75.2%
Validation accuracy: 73.5%
Loss at step 300: 1.574350
Training accuracy: 76.3%
Validation accuracy: 74.3%
Loss at step 400: 1.420926
Training accuracy: 77.2%
Validation accuracy: 74.9%
Loss at step 500: 1.305450
Training accuracy: 77.9%
Validation accuracy: 75.2%
Loss at step 600: 1.214321
Training accuracy: 78.5%
Validation accuracy: 75.4%
Loss at step 700: 1.140065
Training accuracy: 78.9%
Validation accuracy: 75.3%
Loss at step 800: 1.078110
Training accuracy: 79.4%
Validation accuracy: 75.5%
Test accuracy: 82.9%

5.随机梯度下降（SGD）

现在我们来改用随机梯度下降训练，这样快得多。

计算图是类似的，除了不是将所有训练数据保存到恒定节点中，我们创建了一个占位符节点，每次通过session.run()来馈送实际数据.

batch_size = 128

graph = tf.Graph()
with graph.as_default():

  # Input data. For the training data, we use a placeholder that will be fed
  # at run time with a training minibatch.
  tf_train_dataset = tf.placeholder(tf.float32,
                                    shape=(batch_size, image_size * image_size))
  tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))
  tf_valid_dataset = tf.constant(valid_dataset)
  tf_test_dataset = tf.constant(test_dataset)

  # Variables.
  weights = tf.Variable(
    tf.truncated_normal([image_size * image_size, num_labels]))
  biases = tf.Variable(tf.zeros([num_labels]))

  # Training computation.
  logits = tf.matmul(tf_train_dataset, weights) + biases
  loss = tf.reduce_mean(
    tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits))

  # Optimizer.
  optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)

  # Predictions for the training, validation, and test data.
  train_prediction = tf.nn.softmax(logits)
  valid_prediction = tf.nn.softmax(
    tf.matmul(tf_valid_dataset, weights) + biases)
  test_prediction = tf.nn.softmax(tf.matmul(tf_test_dataset, weights) + biases)

然后运行下列程序：

num_steps = 3001

with tf.Session(graph=graph) as session:
  tf.global_variables_initializer().run()
  print("Initialized")
  for step in range(num_steps):
    # Pick an offset within the training data, which has been randomized.
    # Note: we could use better randomization across epochs.
    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)
    # Generate a minibatch.
    batch_data = train_dataset[offset:(offset + batch_size), :]
    batch_labels = train_labels[offset:(offset + batch_size), :]
    # Prepare a dictionary telling the session where to feed the minibatch.
    # The key of the dictionary is the placeholder node of the graph to be fed,
    # and the value is the numpy array to feed to it.
    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}
    _, l, predictions = session.run(
      [optimizer, loss, train_prediction], feed_dict=feed_dict)
    if (step % 500 == 0):
      print("Minibatch loss at step %d: %f" % (step, l))
      print("Minibatch accuracy: %.1f%%" % accuracy(predictions, batch_labels))
      print("Validation accuracy: %.1f%%" % accuracy(
        valid_prediction.eval(), valid_labels))
  print("Test accuracy: %.1f%%" % accuracy(test_prediction.eval(), test_labels))

结果如下：

Initialized
Minibatch loss at step 0: 17.488043
Minibatch accuracy: 11.7%
Validation accuracy: 12.7%
Minibatch loss at step 500: 1.099625
Minibatch accuracy: 79.7%
Validation accuracy: 75.5%
Minibatch loss at step 1000: 1.522583
Minibatch accuracy: 76.6%
Validation accuracy: 76.4%
Minibatch loss at step 1500: 0.659283
Minibatch accuracy: 84.4%
Validation accuracy: 76.4%
Minibatch loss at step 2000: 0.849694
Minibatch accuracy: 84.4%
Validation accuracy: 77.2%
Minibatch loss at step 2500: 1.101751
Minibatch accuracy: 75.0%
Validation accuracy: 78.0%
Minibatch loss at step 3000: 1.034247
Minibatch accuracy: 78.1%
Validation accuracy: 78.4%
Test accuracy: 86.8%

这里可以很明显的发现：训练随机梯度下降（SGD）完成的很快，所花费的时间明显少于之前的简单的梯度下降（GD）.

6.简单的多层神经网络

将具有SGD的逻辑回归示例，通过修正线性单元（Relu） nn.relu()和1024个隐藏节点，将其转换为含有一个隐藏层的多层神经网络。

该模型会提高验证/测试准确性。

在这之前，可以先看如下小例子：

# Solution is available in the other "solution.py" tab

import tensorflow as tf

​

output = None

hidden_layer_weights = [

    [0.1, 0.2, 0.4],

    [0.4, 0.6, 0.6],

    [0.5, 0.9, 0.1],

    [0.8, 0.2, 0.8]]

out_weights = [

    [0.1, 0.6],

    [0.2, 0.1],

    [0.7, 0.9]]

​

# Weights and biases

weights = [

    tf.Variable(hidden_layer_weights),

    tf.Variable(out_weights)]

biases = [

    tf.Variable(tf.zeros(3)),

    tf.Variable(tf.zeros(2))]

​

# Input

features = tf.Variable([[1.0, 2.0, 3.0, 4.0], [-1.0, -2.0, -3.0, -4.0], [11.0, 12.0, 13.0, 14.0]])

​

# TODO: Create Model

hidden_layer = tf.add(tf.matmul(features, weights[0]), biases[0])

hidden_layer = tf.nn.relu(hidden_layer)

​

logits = tf.add(tf.matmul(hidden_layer, weights[1]), biases[1])

# TODO: Print session results

with tf.Session() as sess:

    sess.run(tf.global_variables_initializer())

    print(sess.run(logits))

结果：

[[ 5.11000013 8.44000053]
[ 0. 0. ]
[ 24.01000214 38.23999786]]

接下来，再进行初始的任务，加入一层隐藏层和1024个节点：

batch_size = 128
hiden_layer_node_num = 1024

graph = tf.Graph()
with graph.as_default():
    # input                                                                                                             -----------------------------------------1
    tf_train_dataset = tf.placeholder(tf.float32, shape=(batch_size, image_size * image_size))
    tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))

    tf_valid_dataset = tf.constant(valid_dataset)
    tf_test_dataset = tf.constant(test_dataset)

    # Variables.                                                                                                       ------------------------------------------2
    weights1 = tf.Variable(tf.truncated_normal([image_size * image_size, hiden_layer_node_num]))
    biases1 = tf.Variable(tf.zeros([hiden_layer_node_num]))

    # input layer output (batch_size, hiden_layer_node_num)
    weights2 = tf.Variable(tf.truncated_normal([hiden_layer_node_num, num_labels]))
    biases2 = tf.Variable(tf.zeros([num_labels]))


    # Training computation.                                                                                  ------------------------------------------3
    logits = tf.matmul(tf.nn.relu(tf.matmul(tf_train_dataset, weights1) + biases1), weights2) + biases2
    loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits, tf_train_labels))

  # Optimizer.                                                                                                       -------------------------------------------4
    optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)

    # Predictions for the training, validation, and test data.                            --------------------------------------------5
    train_prediction = tf.nn.softmax(logits)
    valid_prediction = tf.nn.softmax(tf.matmul(tf.nn.relu(tf.matmul(tf_valid_dataset, weights1) + biases1), weights2) + biases2)
    test_prediction = tf.nn.softmax(tf.matmul(tf.nn.relu(tf.matmul(tf_test_dataset, weights1) + biases1), weights2) + biases2)
num_steps = 3001

with tf.Session(graph=graph) as session:
    #注意initialize_all_variables()已被global_variables_initializer()代替
    #tf.initialize_all_variables().run()
    tf.global_variables_initializer().run()
    print("Initialized")
    for step in range(num_steps):
    # Pick an offset within the training data, which has been randomized.
    # Note: we could use better randomization across epochs.
        offset = (step * batch_size) % (train_labels.shape[0] - batch_size)
    # Generate a minibatch.
        batch_data = train_dataset[offset:(offset + batch_size), :]
        batch_labels = train_labels[offset:(offset + batch_size), :]
    # Prepare a dictionary telling the session where to feed the minibatch.
    # The key of the dictionary is the placeholder node of the graph to be fed,
    # and the value is the numpy array to feed to it.
        #  传递值到tf的命名空间
        feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}
        _, l, predictions = session.run([optimizer, loss, train_prediction], feed_dict=feed_dict)
        if (step % 500 == 0):
            print("Minibatch loss at step %d: %f" % (step, l))
            print("Minibatch accuracy: %.1f%%" % accuracy(predictions, batch_labels))
            print("Validation accuracy: %.1f%%" % accuracy(valid_prediction.eval(), valid_labels))
    print("Test accuracy: %.1f%%" % accuracy(test_prediction.eval(), test_labels))

结果如下：

Initialized
Minibatch loss at step 0: 336.547974
Minibatch accuracy: 6.2%
Validation accuracy: 29.0%
Minibatch loss at step 500: 17.726200
Minibatch accuracy: 84.4%
Validation accuracy: 80.2%
Minibatch loss at step 1000: 15.383211
Minibatch accuracy: 75.0%
Validation accuracy: 81.4%
Minibatch loss at step 1500: 5.096069
Minibatch accuracy: 87.5%
Validation accuracy: 80.3%
Minibatch loss at step 2000: 3.049689
Minibatch accuracy: 82.0%
Validation accuracy: 81.2%
Minibatch loss at step 2500: 3.715914
Minibatch accuracy: 79.7%
Validation accuracy: 82.4%
Minibatch loss at step 3000: 1.516045
Minibatch accuracy: 78.9%
Validation accuracy: 82.8%
Test accuracy: 89.7%