nonMNIST_tensorflow_logistic_regression_regularization.py

# coding: utf-8

# In[1]:


from __future__ import print_function
import numpy as np
import tensorflow as tf
from six.moves import cPickle as pickle


# 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)


# In[3]:


image_size = 28
num_labels = 10

def reformat(dataset, labels):
  dataset = dataset.reshape((-1, image_size * image_size)).astype(np.float32)
  # Map 1 to [0.0, 1.0, 0.0 ...], 2 to [0.0, 0.0, 1.0 ...]
  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)


# In[4]:


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


# logistic model

# In[5]:


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)
    beta_regul = tf.placeholder(tf.float32)
    
    # 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)) + beta_regul * tf.nn.l2_loss(weights)

    # 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)


# In[6]:


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, beta_regul : 1e-3}
        _, 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))


# In[7]:


test_labels


# In[8]:


num_steps = 3001
regul_val = [pow(10, i) for i in np.arange(-4, -2, 0.1)]
accuracy_val = []

for regul in regul_val:
  with tf.Session(graph=graph) as session:
    tf.initialize_all_variables().run()
    
    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, beta_regul : regul}
      _, l, predictions = session.run([optimizer, loss, train_prediction], feed_dict=feed_dict)
    accuracy_val.append(accuracy(test_prediction.eval(), test_labels))


# In[9]:


import matplotlib.pyplot as plt
get_ipython().run_line_magic('matplotlib', 'inline')
plt.semilogx(regul_val, accuracy_val)
plt.grid(True)
plt.title('Test accuracy by regularization (logistic)')
plt.show()


# 1-layer neural network:

# In[10]:


batch_size = 128
num_hidden_nodes = 1024

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)
    beta_regul = tf.placeholder(tf.float32)
    # Variables.
    weights1 = tf.Variable(tf.truncated_normal([image_size * image_size, num_hidden_nodes]))
    biases1 = tf.Variable(tf.zeros([num_hidden_nodes]))
    
    weights2 = tf.Variable(tf.truncated_normal([num_hidden_nodes, num_labels]))
    biases2 = tf.Variable(tf.zeros([num_labels]))
    
    # Training computation
    lay1_train_inp = tf.matmul(tf_train_dataset, weights1) + biases1
    lay1_train = tf.nn.relu(lay1_train_inp)
    
    logits = tf.matmul(lay1_train, weights2) + biases2
    
    loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits)) + beta_regul * (tf.nn.l2_loss(weights1) + tf.nn.l2_loss(weights2))

    # Optimizer.
    optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)
  
    # Predictions for the training, validation, and test data.
    train_prediction = tf.nn.softmax(logits)
    
    lay1_valid = tf.nn.relu(tf.matmul(tf_valid_dataset, weights1) + biases1)
    valid_prediction = tf.nn.softmax(tf.matmul(lay1_valid, weights2) + biases2)
    
    lay1_test = tf.nn.relu(tf.matmul(tf_test_dataset, weights1) + biases1)
    test_prediction = tf.nn.softmax(tf.matmul(lay1_test, weights2) + biases2)


# In[11]:


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, beta_regul : 1e-3}
        
        _, 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))


# In[12]:


num_steps = 3001
regul_val = [pow(10, i) for i in np.arange(-4, -2, 0.1)]
accuracy_val = []

for regul in regul_val:    
  with tf.Session(graph=graph) as session:
    tf.initialize_all_variables().run()
    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, beta_regul : regul}
      _, l, predictions = session.run(
        [optimizer, loss, train_prediction], feed_dict=feed_dict)
    accuracy_val.append(accuracy(test_prediction.eval(), test_labels))


# In[13]:


plt.semilogx(regul_val, accuracy_val)
plt.grid(True)
plt.title('Test accuracy by regularization (1-layer net)')
plt.show()


# overfitting, restricting your case to just a few batches causes overfitting

# In[14]:


batch_size = 128
num_hidden_nodes = 1024


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)
  beta_regul = tf.placeholder(tf.float32)
  
  # Variables.
  weights1 = tf.Variable(tf.truncated_normal([image_size * image_size, num_hidden_nodes]))
  biases1 = tf.Variable(tf.zeros([num_hidden_nodes]))
  weights2 = tf.Variable(tf.truncated_normal([num_hidden_nodes, num_labels]))
  biases2 = tf.Variable(tf.zeros([num_labels]))
  
  # Training computation.
  lay1_train = tf.nn.relu(tf.matmul(tf_train_dataset, weights1) + biases1)
  logits = tf.matmul(lay1_train, weights2) + biases2
  loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits=logits, labels=tf_train_labels))
  
  # Optimizer.
  optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)
  
  # Predictions for the training, validation, and test data.
  train_prediction = tf.nn.softmax(logits)
  lay1_valid = tf.nn.relu(tf.matmul(tf_valid_dataset, weights1) + biases1)
  valid_prediction = tf.nn.softmax(tf.matmul(lay1_valid, weights2) + biases2)
  lay1_test = tf.nn.relu(tf.matmul(tf_test_dataset, weights1) + biases1)
  test_prediction = tf.nn.softmax(tf.matmul(lay1_test, weights2) + biases2)


# In[15]:


num_steps = 101
num_batches = 3
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 % num_batches)* 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, beta_regul : 1e-3}
        
        _, l, predictions = session.run([optimizer, loss, train_prediction], feed_dict=feed_dict)
        if (step % 2 == 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))


# Introduce Dropout on the hidden layer of the neural network. Remember: Dropout should only be introduced during training, not evaluation, otherwise your evaluation results would be stochastic as well. TensorFlow provides nn.dropout() for that, but you have to make sure it's only inserted during training.

# In[16]:


batch_size = 128
num_hidden_nodes = 1024

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.
    weights1 = tf.Variable(tf.truncated_normal([image_size * image_size, num_hidden_nodes]))
    biases1 = tf.Variable(tf.zeros([num_hidden_nodes]))
    
    weights2 = tf.Variable(tf.truncated_normal([num_hidden_nodes, num_labels]))
    biases2 = tf.Variable(tf.zeros([num_labels]))
    
    # Training computation
    lay1_train_inp = tf.matmul(tf_train_dataset, weights1) + biases1
    lay1_train = tf.nn.relu(lay1_train_inp)
    
    drop1 = tf.nn.dropout(lay1_train, 0.5)
    
    logits = tf.matmul(drop1, weights2) + biases2
    
    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)
    
    lay1_valid = tf.nn.relu(tf.matmul(tf_valid_dataset, weights1) + biases1)
    valid_prediction = tf.nn.softmax(tf.matmul(lay1_valid, weights2) + biases2)
    
    lay1_test = tf.nn.relu(tf.matmul(tf_test_dataset, weights1) + biases1)
    test_prediction = tf.nn.softmax(tf.matmul(lay1_test, weights2) + biases2)


# In[17]:


num_steps = 101
num_batches = 3
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 % num_batches)* batch_size) % (train_labels.shape[0] - batch_size)
        offset = step % num_batches
        
        # 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 % 2 == 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))


# Try to get the best performance you can using a multi-layer model! The best reported test accuracy using a deep network is 97.1%.
# One avenue you can explore is to add multiple layers.
# 
# Another one is to use learning rate decay:
#     
# global_step = tf.Variable(0)  # count the number of steps taken.
# 
# learning_rate = tf.train.exponential_decay(0.5, step, ...)
# 
# optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss, global_step=global_step)

# In[18]:


batch_size = 128
num_hidden_nodes1 = 1024
num_hidden_nodes2 = 100
beta_regul = 1e-3

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)
    global_step = tf.Variable(0)
    
    # Variables.
    weights1 = tf.Variable(tf.truncated_normal(shape = [image_size * image_size, num_hidden_nodes1], stddev=np.sqrt(2.0 / (image_size * image_size))))
    biases1 = tf.Variable(tf.zeros([num_hidden_nodes1]))
    
    weights2 = tf.Variable(tf.truncated_normal(shape = [num_hidden_nodes1, num_hidden_nodes2], stddev=np.sqrt(2.0 / num_hidden_nodes1)))
    biases2 = tf.Variable(tf.zeros([num_hidden_nodes2]))
                           
    weights3 = tf.Variable(tf.truncated_normal(shape = [num_hidden_nodes2, num_labels], stddev=np.sqrt(2.0 / num_hidden_nodes1)))
    biases3 = tf.Variable(tf.zeros([num_labels]))
    
    # Training computation
    lay1_train_inp = tf.matmul(tf_train_dataset, weights1) + biases1
    lay1_train = tf.nn.relu(lay1_train_inp)
    
    lay2_train_inp = tf.matmul(lay1_train, weights2) + biases2
    lay2_train = tf.nn.relu(lay2_train_inp)
                           
    logits = tf.matmul(lay2_train, weights3) + biases3
    
    loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits)) + beta_regul * (tf.nn.l2_loss(weights1) + tf.nn.l2_loss(weights2) + tf.nn.l2_loss(weights3))
    
    # Optimizer.
    learning_rate = tf.train.exponential_decay(0.5, global_step, 1000, 0.65,staircase = True)
    optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss, global_step = global_step)
                           
    # Predictions for the training, validation, and test data.
    train_prediction = tf.nn.softmax(logits)
    
    lay1_valid = tf.nn.relu(tf.matmul(tf_valid_dataset, weights1) + biases1)    
    lay2_valid = tf.nn.relu(tf.matmul(lay1_valid, weights2) + biases2)

    valid_prediction = tf.nn.softmax(tf.matmul(lay2_valid, weights3) + biases3)
    
    lay1_test = tf.nn.relu(tf.matmul(tf_test_dataset, weights1) + biases1)
    lay2_test = tf.nn.relu(tf.matmul(lay1_test, weights2) + biases2)

    test_prediction = tf.nn.softmax(tf.matmul(lay2_test, weights3) + biases3)


# In[19]:


num_steps = 9001
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)
        # offset = step % num_batches
        
        # 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))


# try one layer deeper with dropouts.

# In[22]:


batch_size = 128
num_hidden_nodes1 = 1024
num_hidden_nodes2 = 256
num_hidden_nodes3 = 128
keep_prob = 0.5

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)
    global_step = tf.Variable(0)
    
    # Variables.
    weights1 = tf.Variable(tf.truncated_normal(shape = [image_size * image_size, num_hidden_nodes1], stddev=np.sqrt(2.0 / (image_size * image_size))))
    biases1 = tf.Variable(tf.zeros([num_hidden_nodes1]))
    
    weights2 = tf.Variable(tf.truncated_normal(shape = [num_hidden_nodes1, num_hidden_nodes2], stddev=np.sqrt(2.0 / num_hidden_nodes1)))
    biases2 = tf.Variable(tf.zeros([num_hidden_nodes2]))
                           
    weights3 = tf.Variable(tf.truncated_normal(shape = [num_hidden_nodes2, num_hidden_nodes3], stddev=np.sqrt(2.0 / num_hidden_nodes1)))
    biases3 = tf.Variable(tf.zeros([num_hidden_nodes3]))
    
    weights4 = tf.Variable(tf.truncated_normal(shape = [num_hidden_nodes3, num_labels], stddev=np.sqrt(2.0 / num_hidden_nodes1)))
    biases4 = tf.Variable(tf.zeros([num_labels]))
    
    # Training computation
    lay1_train_inp = tf.matmul(tf_train_dataset, weights1) + biases1
    lay1_train = tf.nn.relu(lay1_train_inp)
    
    lay2_train_inp = tf.matmul(lay1_train, weights2) + biases2
    lay2_train = tf.nn.relu(lay2_train_inp)
    
    lay3_train_inp = tf.matmul(lay2_train, weights3) + biases3
    lay3_train = tf.nn.relu(lay3_train_inp)
    
    logits = tf.matmul(lay3_train, weights4) + biases4
    
    loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels=tf_train_labels, logits=logits))
    
    # Optimizer.
    learning_rate = tf.train.exponential_decay(0.5, global_step, 1000, 0.65,staircase = True)
    optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss, global_step = global_step)
                           
    # Predictions for the training, validation, and test data.
    train_prediction = tf.nn.softmax(logits)
    
    lay1_valid = tf.nn.relu(tf.matmul(tf_valid_dataset, weights1) + biases1)    
    lay2_valid = tf.nn.relu(tf.matmul(lay1_valid, weights2) + biases2)
    lay3_valid = tf.nn.relu(tf.matmul(lay2_valid, weights3) + biases3)
    
    valid_prediction = tf.nn.softmax(tf.matmul(lay3_valid, weights4) + biases4)
    
    lay1_test = tf.nn.relu(tf.matmul(tf_test_dataset, weights1) + biases1)
    lay2_test = tf.nn.relu(tf.matmul(lay1_test, weights2) + biases2)
    lay3_test = tf.nn.relu(tf.matmul(lay2_test, weights3) + biases3)
    
    test_prediction = tf.nn.softmax(tf.matmul(lay3_test, weights4) + biases4)


# In[23]:


num_steps = 18001
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)
        # offset = step % num_batches
        
        # 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))


# some things are left