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_functionimport numpy as npimport tensorflow as tffrom six.moves import cPickle as picklefrom 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 = 28num_labels = 10def 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, labelstrain_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 = 10000graph = 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 = 801def 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 = 128graph = 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 = 3001with 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" tabimport tensorflow as tf​output = Nonehidden_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 biasesweights = [    tf.Variable(hidden_layer_weights),    tf.Variable(out_weights)]biases = [    tf.Variable(tf.zeros(3)),    tf.Variable(tf.zeros(2))]​# Inputfeatures = 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 Modelhidden_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 resultswith 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 = 128hiden_layer_node_num = 1024graph = 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 = 3001with 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%