Deep Learning

Assignment 2

Previously in 1_notmnist.ipynb, we created a pickle with formatted datasets for training, development and testing on the notMNIST dataset.

The goal of this assignment is to progressively train deeper and more accurate models using TensorFlow.



In [1]:

    
# These are all the modules we'll be using later. Make sure you can import them
# before proceeding further.
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









    



e:\python36\lib\site-packages\h5py\__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.
  from ._conv import register_converters as _register_converters

First reload the data we generated in 1_notmnist.ipynb.



In [2]:

    
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)









    



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

Reformat into a shape that's more adapted to the models we're going to train:

data as a flat matrix,
labels as float 1-hot encodings.



In [3]:

    
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)









    



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

We're first going to train a multinomial logistic regression using simple gradient descent.

TensorFlow works like this:

First you describe the computation that you want to see performed: what the inputs, the variables, and the operations look like. These get created as nodes over a computation graph. This description is all contained within the block below:
```
with graph.as_default():
    ...
```
Then you can run the operations on this graph as many times as you want by calling session.run(), providing it outputs to fetch from the graph that get returned. This runtime operation is all contained in the block below:
```
with tf.Session(graph=graph) as session:
    ...
```

Let's load all the data into TensorFlow and build the computation graph corresponding to our training:



In [12]:

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

Let's run this computation and iterate:



In [13]:

    
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))









    



Initialized
Loss at step 0: 19.265543
Training accuracy: 10.7%
Validation accuracy: 13.6%
Loss at step 100: 2.309912
Training accuracy: 71.9%
Validation accuracy: 70.3%
Loss at step 200: 1.867300
Training accuracy: 74.9%
Validation accuracy: 72.7%
Loss at step 300: 1.623125
Training accuracy: 76.6%
Validation accuracy: 73.2%
Loss at step 400: 1.457814
Training accuracy: 77.2%
Validation accuracy: 73.9%
Loss at step 500: 1.335056
Training accuracy: 77.7%
Validation accuracy: 74.1%
Loss at step 600: 1.238734
Training accuracy: 78.0%
Validation accuracy: 74.5%
Loss at step 700: 1.160415
Training accuracy: 78.6%
Validation accuracy: 74.8%
Loss at step 800: 1.095137
Training accuracy: 79.0%
Validation accuracy: 74.9%
Test accuracy: 82.0%

results

lesson 1 sklearn LogisticRegression

50 training samples: LogisticRegression score: 0.608200
100 training samples: LogisticRegression score: 0.708200
1000 training samples: LogisticRegression score: 0.829200
5000 training samples: LogisticRegression score: 0.846200

tensor flow results above

50: 43.3%
100: 53.1%
1000: 76.8%
5000: 81.6%
10000: 82.0%

Let's now switch to stochastic gradient descent training instead, which is much faster.

The graph will be similar, except that instead of holding all the training data into a constant node, we create a Placeholder node which will be fed actual data at every call of session.run().



In [15]:

    
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)

Let's run it:



In [16]:

    
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))









    



Initialized
Minibatch loss at step 0: 18.201649
Minibatch accuracy: 9.4%
Validation accuracy: 13.1%
Minibatch loss at step 500: 1.924816
Minibatch accuracy: 71.1%
Validation accuracy: 76.3%
Minibatch loss at step 1000: 1.962840
Minibatch accuracy: 68.0%
Validation accuracy: 77.0%
Minibatch loss at step 1500: 1.046484
Minibatch accuracy: 75.8%
Validation accuracy: 77.9%
Minibatch loss at step 2000: 1.102882
Minibatch accuracy: 76.6%
Validation accuracy: 78.2%
Minibatch loss at step 2500: 1.061870
Minibatch accuracy: 75.0%
Validation accuracy: 78.6%
Minibatch loss at step 3000: 0.888769
Minibatch accuracy: 79.7%
Validation accuracy: 78.9%
Test accuracy: 85.2%

results

Test accuracy: 85.2%

Problem

Turn the logistic regression example with SGD into a 1-hidden layer neural network with rectified linear units nn.relu() and 1024 hidden nodes. This model should improve your validation / test accuracy.

results

see prob_sgd_1hl.py. results:

Initialized
Minibatch loss at step 0: 17.917774
Minibatch accuracy: 3.9%
Validation accuracy: 9.5%
Minibatch loss at step 500: 1.992693
Minibatch accuracy: 73.4%
Validation accuracy: 76.1%
Minibatch loss at step 1000: 1.837618
Minibatch accuracy: 68.8%
Validation accuracy: 76.9%
Minibatch loss at step 1500: 1.056582
Minibatch accuracy: 79.7%
Validation accuracy: 77.2%
Minibatch loss at step 2000: 1.050543
Minibatch accuracy: 74.2%
Validation accuracy: 77.9%
Minibatch loss at step 2500: 1.484630
Minibatch accuracy: 72.7%
Validation accuracy: 78.7%
Minibatch loss at step 3000: 0.878001
Minibatch accuracy: 82.0%
Validation accuracy: 79.4%
Test accuracy: 85.4%



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