3_regularization.ipynb

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   "source": [
    "Deep Learning\n",
    "=============\n",
    "\n",
    "Assignment 3\n",
    "------------\n",
    "\n",
    "Previously in `2_fullyconnected.ipynb`, you trained a logistic regression and a neural network model.\n",
    "\n",
    "The goal of this assignment is to explore regularization techniques."
   ]
  },
  {
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   "source": [
    "# These are all the modules we'll be using later. Make sure you can import them\n",
    "# before proceeding further.\n",
    "from __future__ import print_function\n",
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "from six.moves import cPickle as pickle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "1HrCK6e17WzV"
   },
   "source": [
    "First reload the data we generated in _notmist.ipynb_."
   ]
  },
  {
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     "text": [
      "Training set (200000, 28, 28) (200000,)\n",
      "Validation set (10000, 28, 28) (10000,)\n",
      "Test set (10000, 28, 28) (10000,)\n"
     ]
    }
   ],
   "source": [
    "pickle_file = 'notMNIST.pickle'\n",
    "\n",
    "with open(pickle_file, 'rb') as f:\n",
    "  save = pickle.load(f)\n",
    "  train_dataset = save['train_dataset']\n",
    "  train_labels = save['train_labels']\n",
    "  valid_dataset = save['valid_dataset']\n",
    "  valid_labels = save['valid_labels']\n",
    "  test_dataset = save['test_dataset']\n",
    "  test_labels = save['test_labels']\n",
    "  del save  # hint to help gc free up memory\n",
    "  print('Training set', train_dataset.shape, train_labels.shape)\n",
    "  print('Validation set', valid_dataset.shape, valid_labels.shape)\n",
    "  print('Test set', test_dataset.shape, test_labels.shape)"
   ]
  },
  {
   "cell_type": "markdown",
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    "id": "L7aHrm6nGDMB"
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   "source": [
    "Reformat into a shape that's more adapted to the models we're going to train:\n",
    "- data as a flat matrix,\n",
    "- labels as float 1-hot encodings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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     "text": [
      "Training set (200000, 784) (200000, 10)\n",
      "Validation set (10000, 784) (10000, 10)\n",
      "Test set (10000, 784) (10000, 10)\n"
     ]
    }
   ],
   "source": [
    "image_size = 28\n",
    "num_labels = 10\n",
    "\n",
    "def reformat(dataset, labels):\n",
    "  dataset = dataset.reshape((-1, image_size * image_size)).astype(np.float32)\n",
    "  # Map 2 to [0.0, 1.0, 0.0 ...], 3 to [0.0, 0.0, 1.0 ...]\n",
    "  labels = (np.arange(num_labels) == labels[:,None]).astype(np.float32)\n",
    "  return dataset, labels\n",
    "train_dataset, train_labels = reformat(train_dataset, train_labels)\n",
    "valid_dataset, valid_labels = reformat(valid_dataset, valid_labels)\n",
    "test_dataset, test_labels = reformat(test_dataset, test_labels)\n",
    "print('Training set', train_dataset.shape, train_labels.shape)\n",
    "print('Validation set', valid_dataset.shape, valid_labels.shape)\n",
    "print('Test set', test_dataset.shape, test_labels.shape)"
   ]
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  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "cellView": "both",
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     "autoexec": {
      "startup": false,
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    "colab_type": "code",
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    "id": "RajPLaL_ZW6w"
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   "outputs": [],
   "source": [
    "def accuracy(predictions, labels):\n",
    "  return (100.0 * np.sum(np.argmax(predictions, 1) == np.argmax(labels, 1))\n",
    "          / predictions.shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sgLbUAQ1CW-1"
   },
   "source": [
    "---\n",
    "Problem 1\n",
    "---------\n",
    "\n",
    "Introduce and tune L2 regularization for both logistic and neural network models. Remember that L2 amounts to adding a penalty on the norm of the weights to the loss. In TensorFlow, you can compute the L2 loss for a tensor `t` using `nn.l2_loss(t)`. The right amount of regularization should improve your validation / test accuracy.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Answer__: By introducing L2 Regularization with beta taking values from [0.01,0.001] a higher accuracy was achieved. The improvement was in the range of +2-3%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tensor(\"Shape:0\", shape=TensorShape([Dimension(0)]), dtype=int32) Tensor(\"Shape_1:0\", shape=TensorShape([Dimension(0)]), dtype=int32)\n"
     ]
    }
   ],
   "source": [
    "batch_size = 128\n",
    "beta = 0.001\n",
    "graph = tf.Graph()\n",
    "with graph.as_default():\n",
    "\n",
    "  # Input data. For the training data, we use a placeholder that will be fed\n",
    "  # at run time with a training minibatch.\n",
    "  tf_train_dataset = tf.placeholder(tf.float32,\n",
    "                                    shape=(batch_size, image_size * image_size))\n",
    "  tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))\n",
    "  tf_valid_dataset = tf.constant(valid_dataset)\n",
    "  tf_test_dataset = tf.constant(test_dataset)\n",
    "  \n",
    "  # Variables.\n",
    "  weights = tf.Variable(\n",
    "    tf.truncated_normal([image_size * image_size, 1024]))\n",
    "  biases = tf.Variable(tf.zeros([1024]))\n",
    "  \n",
    "  weights1 = tf.Variable(\n",
    "    tf.truncated_normal([ 1024,num_labels]))\n",
    "  biases1 = tf.Variable(tf.zeros([num_labels]))\n",
    "\n",
    "  # Training computation.\n",
    "  logits = tf.matmul(tf_train_dataset, weights) + biases\n",
    "  hidden = tf.nn.relu(logits)\n",
    "    \n",
    "  logits1 = tf.matmul(hidden, weights1) + biases1\n",
    "  loss = tf.reduce_mean(\n",
    "    tf.nn.softmax_cross_entropy_with_logits(logits1, tf_train_labels))\n",
    "    \n",
    "  n_loss = loss + beta*(tf.nn.l2_loss(weights)+tf.nn.l2_loss(weights1)+tf.nn.l2_loss(biases)+tf.nn.l2_loss(biases1))\n",
    "  print(tf.shape(loss),tf.shape(n_loss))\n",
    "  # Optimizer.\n",
    "  optimizer = tf.train.GradientDescentOptimizer(0.5).minimize(loss)\n",
    "  \n",
    "  # Predictions for the training, validation, and test data.\n",
    "  train_prediction = tf.nn.relu(logits1)\n",
    "  valid_prediction = tf.nn.relu(tf.matmul(tf.nn.relu(tf.matmul(tf_valid_dataset, weights) + biases), weights1) + biases1)\n",
    "  test_prediction = tf.nn.relu(tf.matmul(tf.nn.relu(tf.matmul(tf_test_dataset, weights) + biases), weights1) + biases1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 347.753174\n",
      "Minibatch accuracy: 19.5%\n",
      "Validation accuracy: 35.8%\n",
      "Minibatch loss at step 500: 17.004389\n",
      "Minibatch accuracy: 77.3%\n",
      "Validation accuracy: 80.4%\n",
      "Minibatch loss at step 1000: 1.510549\n",
      "Minibatch accuracy: 92.2%\n",
      "Validation accuracy: 82.3%\n",
      "Minibatch loss at step 1500: 5.253856\n",
      "Minibatch accuracy: 74.2%\n",
      "Validation accuracy: 81.9%\n",
      "Minibatch loss at step 2000: 11.585231\n",
      "Minibatch accuracy: 82.8%\n",
      "Validation accuracy: 81.7%\n",
      "Minibatch loss at step 2500: 9.322313\n",
      "Minibatch accuracy: 80.5%\n",
      "Validation accuracy: 82.4%\n",
      "Minibatch loss at step 3000: 3.853630\n",
      "Minibatch accuracy: 78.9%\n",
      "Validation accuracy: 81.8%\n",
      "Test accuracy: 87.6%\n"
     ]
    }
   ],
   "source": [
    "num_steps = 3001\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.initialize_all_variables().run()\n",
    "  print(\"Initialized\")\n",
    "  for step in range(num_steps):\n",
    "    # Pick an offset within the training data, which has been randomized.\n",
    "    # Note: we could use better randomization across epochs.\n",
    "    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)\n",
    "    #print(offset)\n",
    "    # Generate a minibatch.\n",
    "    batch_data = train_dataset[offset:(offset + batch_size), :]\n",
    "    batch_labels = train_labels[offset:(offset + batch_size), :]\n",
    "    # Prepare a dictionary telling the session where to feed the minibatch.\n",
    "    # The key of the dictionary is the placeholder node of the graph to be fed,\n",
    "    # and the value is the numpy array to feed to it.\n",
    "    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}\n",
    "    _, l, predictions = session.run(\n",
    "      [optimizer, loss, train_prediction], feed_dict=feed_dict)\n",
    "    if (step % 500 == 0):\n",
    "      print(\"Minibatch loss at step %d: %f\" % (step, l))\n",
    "      print(\"Minibatch accuracy: %.1f%%\" % accuracy(predictions, batch_labels))\n",
    "      print(\"Validation accuracy: %.1f%%\" % accuracy(\n",
    "        valid_prediction.eval(), valid_labels))\n",
    "  print(\"Test accuracy: %.1f%%\" % accuracy(test_prediction.eval(), test_labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "na8xX2yHZzNF"
   },
   "source": [
    "---\n",
    "Problem 2\n",
    "---------\n",
    "Let's demonstrate an extreme case of overfitting. Restrict your training data to just a few batches. What happens?\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Answer__: By restricting my data to just the first 1000 examples, minibatch accuracy reaches 100% quickly but validation accuracy is low. Exactly what overfitting looks like. Test accuracy isn't as low as one would expect. This is due to the test set containing more 'clear' images, thus more easily recognizable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 291.119019\n",
      "Minibatch accuracy: 14.8%\n",
      "Validation accuracy: 22.8%\n",
      "Minibatch loss at step 500: 0.000001\n",
      "Minibatch accuracy: 100.0%\n",
      "Validation accuracy: 73.9%\n",
      "Minibatch loss at step 1000: 0.000000\n",
      "Minibatch accuracy: 100.0%\n",
      "Validation accuracy: 73.9%\n",
      "Minibatch loss at step 1500: 0.000000\n",
      "Minibatch accuracy: 100.0%\n",
      "Validation accuracy: 73.9%\n",
      "Minibatch loss at step 2000: 0.000000\n",
      "Minibatch accuracy: 100.0%\n",
      "Validation accuracy: 73.9%\n",
      "Minibatch loss at step 2500: 0.000000\n",
      "Minibatch accuracy: 100.0%\n",
      "Validation accuracy: 73.9%\n",
      "Minibatch loss at step 3000: 0.000000\n",
      "Minibatch accuracy: 100.0%\n",
      "Validation accuracy: 73.9%\n",
      "Test accuracy: 80.3%\n"
     ]
    }
   ],
   "source": [
    "num_steps = 3001\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.initialize_all_variables().run()\n",
    "  print(\"Initialized\")\n",
    "  for step in range(num_steps):\n",
    "    # Pick an offset within the training data, which has been randomized.\n",
    "    # Note: we could use better randomization across epochs.\n",
    "    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)\n",
    "    #Restricting training data to the first 300 examples\n",
    "    offset = offset % 300\n",
    "    # Generate a minibatch.\n",
    "    batch_data = train_dataset[offset:(offset + batch_size), :]\n",
    "    batch_labels = train_labels[offset:(offset + batch_size), :]\n",
    "    # Prepare a dictionary telling the session where to feed the minibatch.\n",
    "    # The key of the dictionary is the placeholder node of the graph to be fed,\n",
    "    # and the value is the numpy array to feed to it.\n",
    "    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}\n",
    "    _, l, predictions = session.run(\n",
    "      [optimizer, loss, train_prediction], feed_dict=feed_dict)\n",
    "    if (step % 500 == 0):\n",
    "      print(\"Minibatch loss at step %d: %f\" % (step, l))\n",
    "      print(\"Minibatch accuracy: %.1f%%\" % accuracy(predictions, batch_labels))\n",
    "      print(\"Validation accuracy: %.1f%%\" % accuracy(\n",
    "        valid_prediction.eval(), valid_labels))\n",
    "  print(\"Test accuracy: %.1f%%\" % accuracy(test_prediction.eval(), test_labels))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ww3SCBUdlkRc"
   },
   "source": [
    "---\n",
    "Problem 3\n",
    "---------\n",
    "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.\n",
    "\n",
    "What happens to our extreme overfitting case?\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "-b1hTz3VWZjw"
   },
   "source": [
    "---\n",
    "Problem 4\n",
    "---------\n",
    "\n",
    "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%](http://yaroslavvb.blogspot.com/2011/09/notmnist-dataset.html?showComment=1391023266211#c8758720086795711595).\n",
    "\n",
    "One avenue you can explore is to add multiple layers.\n",
    "\n",
    "Another one is to use learning rate decay:\n",
    "\n",
    "    global_step = tf.Variable(0)  # count the number of steps taken.\n",
    "    learning_rate = tf.train.exponential_decay(0.5, step, ...)\n",
    "    optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(loss, global_step=global_step)\n",
    " \n",
    " ---\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__ANSWER__ : Combining a dropout of 20% between the two the hidden layers and L2 Regularization with beta = 0.0001 and exponential decay of learning rate I achieved __94.0%__ accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tensor(\"Shape:0\", shape=TensorShape([Dimension(0)]), dtype=int32) Tensor(\"Shape_1:0\", shape=TensorShape([Dimension(0)]), dtype=int32)\n"
     ]
    }
   ],
   "source": [
    "batch_size = 128\n",
    "beta = 0.0001\n",
    "graph = tf.Graph()\n",
    "with graph.as_default():\n",
    "\n",
    "  # Input data. For the training data, we use a placeholder that will be fed\n",
    "  # at run time with a training minibatch.\n",
    "  tf_train_dataset = tf.placeholder(tf.float32,\n",
    "                                    shape=(batch_size, image_size * image_size))\n",
    "  tf_train_labels = tf.placeholder(tf.float32, shape=(batch_size, num_labels))\n",
    "  tf_valid_dataset = tf.constant(valid_dataset)\n",
    "  tf_test_dataset = tf.constant(test_dataset)\n",
    "  \n",
    "  # Variables.\n",
    "  weights = tf.Variable(\n",
    "    tf.truncated_normal([image_size * image_size, 1024], stddev=0.05))\n",
    "  biases = tf.Variable(tf.zeros([1024]))\n",
    "  \n",
    "  weights1 = tf.Variable(\n",
    "    tf.truncated_normal([ 1024,500], stddev=0.05))\n",
    "  biases1 = tf.Variable(tf.zeros([500]))\n",
    "\n",
    "  weights2 = tf.Variable(\n",
    "    tf.truncated_normal([ 500,num_labels], stddev=0.05))\n",
    "  biases2 = tf.Variable(tf.zeros([num_labels]))\n",
    "\n",
    "  # Training computation.\n",
    "  logits = tf.matmul(tf_train_dataset, weights) + biases\n",
    "  hidden = tf.nn.relu(logits)\n",
    "    \n",
    "  logits1 = tf.nn.dropout(tf.nn.relu(tf.matmul(hidden, weights1) + biases1),keep_prob=0.8)\n",
    "  \n",
    "  logits2 = tf.matmul(logits1,weights2)+biases2\n",
    "\n",
    "  loss = tf.reduce_mean(\n",
    "    tf.nn.softmax_cross_entropy_with_logits(logits2, tf_train_labels))\n",
    "    \n",
    "  n_loss = loss + beta*(tf.nn.l2_loss(weights)+tf.nn.l2_loss(weights1)+tf.nn.l2_loss(weights2)+tf.nn.l2_loss(biases)+tf.nn.l2_loss(biases1)+tf.nn.l2_loss(biases2))\n",
    "  print(tf.shape(loss),tf.shape(n_loss))\n",
    "  # Optimizer.\n",
    "  #global_step = tf.Variable(0)  # count the number of steps taken.\n",
    "  learning_rate = tf.train.exponential_decay(0.4, batch_size,150 ,0.9)\n",
    "  optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(n_loss)\n",
    "  \n",
    "  # Predictions for the training, validation, and test data.\n",
    "  train_prediction = tf.nn.softmax(logits2)\n",
    "  valid_prediction = tf.nn.softmax(tf.matmul(tf.nn.relu(tf.matmul(tf.nn.relu(tf.matmul(tf_train_dataset, weights) + biases), weights1) + biases1),weights2)+biases2)\n",
    "  test_prediction = tf.nn.softmax(tf.matmul(tf.nn.relu(tf.matmul(tf.nn.relu(tf.matmul(tf_test_dataset, weights) + biases), weights1) + biases1),weights2)+biases2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initialized\n",
      "Minibatch loss at step 0: 2.378294\n",
      "Minibatch accuracy: 14.8%\n",
      "Minibatch loss at step 500: 0.521816\n",
      "Minibatch accuracy: 82.0%\n",
      "Minibatch loss at step 1000: 0.203692\n",
      "Minibatch accuracy: 93.8%\n",
      "Minibatch loss at step 1500: 0.481113\n",
      "Minibatch accuracy: 85.2%\n",
      "Minibatch loss at step 2000: 0.500569\n",
      "Minibatch accuracy: 85.2%\n",
      "Minibatch loss at step 2500: 0.263198\n",
      "Minibatch accuracy: 91.4%\n",
      "Minibatch loss at step 3000: 0.348032\n",
      "Minibatch accuracy: 88.3%\n",
      "Test accuracy: 94.0%\n"
     ]
    }
   ],
   "source": [
    "num_steps = 3001\n",
    "\n",
    "with tf.Session(graph=graph) as session:\n",
    "  tf.initialize_all_variables().run()\n",
    "  print(\"Initialized\")\n",
    "  for step in range(num_steps):\n",
    "    # Pick an offset within the training data, which has been randomized.\n",
    "    # Note: we could use better randomization across epochs.\n",
    "    offset = (step * batch_size) % (train_labels.shape[0] - batch_size)\n",
    "    # Generate a minibatch.\n",
    "    batch_data = train_dataset[offset:(offset + batch_size), :]\n",
    "    batch_labels = train_labels[offset:(offset + batch_size), :]\n",
    "    # Prepare a dictionary telling the session where to feed the minibatch.\n",
    "    # The key of the dictionary is the placeholder node of the graph to be fed,\n",
    "    # and the value is the numpy array to feed to it.\n",
    "    feed_dict = {tf_train_dataset : batch_data, tf_train_labels : batch_labels}\n",
    "    _, l, predictions = session.run(\n",
    "      [optimizer, loss, train_prediction], feed_dict=feed_dict)\n",
    "    if (step % 500 == 0):\n",
    "      print(\"Minibatch loss at step %d: %f\" % (step, l))\n",
    "      print(\"Minibatch accuracy: %.1f%%\" % accuracy(predictions, batch_labels))\n",
    "     # print(\"Validation accuracy: %.1f%%\" % accuracy(\n",
    "       # valid_prediction.eval(), valid_labels))\n",
    "  print(\"Test accuracy: %.1f%%\" % accuracy(test_prediction.eval(), test_labels))"
   ]
  },
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   "execution_count": null,
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   "source": []
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  {
   "cell_type": "code",
   "execution_count": null,
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   },
   "outputs": [],
   "source": []
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