"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n"
],
"text/plain": [
""
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# code for loading the format for the notebook\n",
"import os\n",
"\n",
"# path : store the current path to convert back to it later\n",
"path = os.getcwd()\n",
"os.chdir(os.path.join('..', 'notebook_format'))\n",
"\n",
"from formats import load_style\n",
"load_style(plot_style = False)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Ethen 2018-09-15 15:40:09 \n",
"\n",
"CPython 3.6.4\n",
"IPython 6.4.0\n",
"\n",
"numpy 1.14.1\n",
"pandas 0.23.0\n",
"matplotlib 2.2.2\n",
"tensorflow 1.7.0\n"
]
}
],
"source": [
"os.chdir(path)\n",
"\n",
"# 1. magic for inline plot\n",
"# 2. magic to print version\n",
"# 3. magic so that the notebook will reload external python modules\n",
"# 4. magic to enable retina (high resolution) plots\n",
"# https://gist.github.com/minrk/3301035\n",
"%matplotlib inline\n",
"%load_ext watermark\n",
"%load_ext autoreload\n",
"%autoreload 2\n",
"%config InlineBackend.figure_format = 'retina'\n",
"\n",
"\n",
"import numpy as np\n",
"import pandas as pd\n",
"import tensorflow as tf\n",
"import matplotlib.pyplot as plt\n",
"\n",
"%watermark -a 'Ethen' -d -t -v -p numpy,pandas,matplotlib,tensorflow"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Deep Learning (Almost) from scratch"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Neural Network Introduction"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The basic computational unit of the brain is a **neuron**. Approximately 86 billion neurons can be found in the human nervous system and they are connected with approximately 10^14 - 10^15 **synapses**. The diagram below shows a cartoon drawing of the mathematical model. Each neuron receives input signals from its **dendrites** and produces output signals along its (single) **axon**. The axon eventually branches out and connects via synapses to dendrites of other neurons. \n",
"\n",
"\n",
"\n",
"In the computational model of a neuron, the signals that travel along the axons (e.g. \\\\(x_0\\\\)) interact multiplicatively (e.g. \\\\(w_0 x_0\\\\)) with the dendrites of the other neuron based on the synaptic strength at that synapse (e.g. \\\\(w_0\\\\)). The idea is that the synaptic strengths (the weights \\\\(w\\\\)) are learnable and control the strength of influence (and its direction: excitory (positive weight) or inhibitory (negative weight)) of one neuron on another. In the basic model, the dendrites carry the signal to the cell body where they all get summed (e.g. $\\sum_iw_ix_i + b$, there will always be an extra bias term $b$). If the final sum is above a certain threshold, the neuron can *fire*, sending a spike along its axon. In the computational model, we assume that the precise timings of the spikes do not matter, and that only the frequency of the firing communicates information. Based on this interpretation, we model the *firing rate* of the neuron with an **activation function** \\\\(f\\\\). Historically, a common choice of activation function is the **sigmoid function** \\\\(\\sigma(x) = 1/(1+e^{-x})\\\\), since it takes a real-valued input (the signal strength after the sum) and squashes it to range between 0 and 1. We will see details of these activation functions later."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Neural Network Architectures"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Neural Networks are modeled as collections of neurons that are connected in an acyclic graph. In other words, the outputs of some neurons can become inputs to other neurons. Cycles are not allowed since that would imply an infinite loop in the forward pass of a network. Instead of an amorphous blobs of connected neurons, Neural Network models are often organized into distinct layers of neurons. For regular neural networks, the most common layer type is the **fully-connected layer** in which neurons between two adjacent layers are fully pairwise connected, but neurons within a single layer share no connections. Below is an example Neural Network of a 3-layer neural network with an inputs layer of size 3, two hidden layers each having size 4 and an output layer with size 1. Notice that in both cases there are connections (synapses) between neurons across layers, but not within a layer (Yes, they look like a bunch of softmax stacked together).\n",
"\n",
"\n",
"\n",
"**Naming conventions.** You may also hear these networks interchangeably referred to as *\"Artificial Neural Networks\"* (ANN) or *\"Multi-Layer Perceptrons\"* (MLP) and when the network consists of more than one hidden layer, it is essentially a **deep learning** model. Notice that when we say N-layer neural network, we do not count the input layer. \n",
"\n",
"**Input layer** The number of nodes in the **input layer** is determined by the dimensionality (number of feature columns) of our data.\n",
"\n",
"**Hidden layer** The most interesting task for neural network is that we can choose the size (the number of nodes) of the hidden layer and the number of hidden layers. The more nodes we put into the hidden layer and the more hidden layers we add, the more complex functions we will be able fit. But higher dimensionality comes at a cost. First, more computation is required to make predictions and learn the network parameters. A bigger number of parameters also means we become more prone to overfitting our data. Choosing the size of the hidden layer will always depends on your specific problem (usually determined by cross validation) and it is more of an art than a science. We will play with the number of nodes in the hidden later later on and see how it affects our output.\n",
"\n",
"**Output layer** The size of (number of nodes) **output layer** is determined by the number of classes we have. Unlike all **hidden layers**, the output layer neurons most commonly do not have an activation function. This is because the last output layer is usually taken to represent the class scores (e.g. in classification), which are arbitrary real-valued numbers, or some kind of real-valued target (e.g. in regression). \n",
"\n",
"**Sizing neural networks** The two metrics that people commonly use to measure the size of neural networks are the number of neurons, or more commonly the number of parameters. Working with the example networks in the above picture: The network has 4 + 4 + 1 = 9 neurons, [3 x 4] + [4 x 4] + [4 x 1] = 12 + 16 + 4 = 32 weights (number of lines the in picture) and 4 + 4 + 1 = 9 biases (these are not shown in the picture), for a total of 41 learnable parameters.\n",
"\n",
"To give you some context, modern Convolutional Networks contain on orders of 100 million parameters and are usually made up of approximately 10-20 layers."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Feed-forward computation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"One of the primary reasons that Neural Networks are organized into layers is that this structure makes it very simple and efficient to compute using matrix vector operations (just like softmax). Working with the example three-layer neural network in the diagram above, the input would be a [3x1] vector. All connection strengths for a layer can be stored in a single matrix. For example, the first hidden layer's weights `W1` would be of size [4x3], and the biases for all units would be in the vector `b1`, of size [4x1]. Here, every single neuron has its weights in a row of `W1`, so the matrix vector multiplication `np.dot(W1,x)` evaluates the activations of all neurons in that layer. Similarly, `W2` would be a [4x4] matrix that stores the connections of the second hidden layer, and `W3` a [1x4] matrix for the last (output) layer. The full forward pass of this 3-layer neural network is then simply three matrix multiplications, interwoven with the application of the activation function:\n",
"\n",
"```python\n",
"\n",
"# forward-pass of a 3-layer neural network:\n",
"f = lambda x: 1 / ( 1 + np.exp(-x) ) # activation function (use sigmoid)\n",
"x = np.random.randn(3, 1) # random input vector of three numbers (3x1)\n",
"h1 = f(np.dot(W1, x) + b1) # calculate first hidden layer activations (4x1)\n",
"h2 = f(np.dot(W2, h1) + b2) # calculate second hidden layer activations (4x1)\n",
"out = np.dot(W3, h2) + b3 # output neuron (1x1)\n",
"\n",
"```\n",
"\n",
"In the above code, `W1,W2,W3,b1,b2,b3` are the learnable parameters of the network. Notice also that instead of having a single input column vector, the variable `x` could hold an entire batch of training data (where each input example would be a column of `x`) and then all examples would be efficiently evaluated in parallel. Notice that the final Neural Network layer usually doesn't have an activation function as it represents a (real-valued) class score in a classification setting. Thus we can apply the softmax function to convert it into our probability.\n",
"\n",
"> The forward pass of a fully-connected layer corresponds to one matrix multiplication followed by a bias offset and an activation function."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Tensorflow Implementation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A lot of it should look extremely familiar after going through the softmax implementation."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Extracting MNIST_data/train-images-idx3-ubyte.gz\n",
"Extracting MNIST_data/train-labels-idx1-ubyte.gz\n",
"Extracting MNIST_data/t10k-images-idx3-ubyte.gz\n",
"Extracting MNIST_data/t10k-labels-idx1-ubyte.gz\n"
]
}
],
"source": [
"# import MNIST data, and prevent warnings about dataset will be deprecated\n",
"# https://stackoverflow.com/questions/49901806/tensorflow-importing-mnist-warnings\n",
"old_v = tf.logging.get_verbosity()\n",
"tf.logging.set_verbosity(tf.logging.ERROR)\n",
"\n",
"from tensorflow.examples.tutorials.mnist import input_data\n",
"mnist = input_data.read_data_sets('MNIST_data/', one_hot = True)\n",
"\n",
"tf.logging.set_verbosity(old_v)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# extract trainig/testing data and labels\n",
"X_train, y_train = mnist.train.images, mnist.train.labels\n",
"X_test, y_test = mnist.test.images, mnist.test.labels\n",
"\n",
"# global parameters\n",
"learning_rate = 0.005\n",
"batch_size = 2048\n",
"n_epochs = 15\n",
"\n",
"# network parameters (only one hidden layer)\n",
"n_hidden_1 = 256 # 1st hidden layer's size (number of nodes)\n",
"n_input = X_train.shape[1] # MNIST data input (image's shape: 28*28)\n",
"n_class = y_train.shape[1] # MNIST total classes (0-9 digits)\n",
"\n",
"# place holder for the data and label\n",
"X = tf.placeholder(tf.float32, [None, n_input])\n",
"y = tf.placeholder(tf.float32, [None, n_class])\n",
"\n",
"# store layers' weight & bias\n",
"params = {\n",
" 'W1': tf.Variable(tf.random_normal([n_input, n_hidden_1])),\n",
" 'W2': tf.Variable(tf.random_normal([n_hidden_1, n_class])),\n",
" 'b1': tf.Variable(tf.random_normal([n_hidden_1])),\n",
" 'b2': tf.Variable(tf.random_normal([n_class]))\n",
"}\n",
"\n",
"# Hidden layer with sigmoid activation\n",
"# Output layer with softmax activation\n",
"layer1 = tf.nn.sigmoid(tf.matmul(X, params['W1']) + params['b1'])\n",
"output = tf.nn.softmax(tf.matmul(layer1, params['W2']) + params['b2'])\n",
"output = tf.clip_by_value(output, 1e-10, 1.0)\n",
"\n",
"# cross entropy cost function\n",
"cross_entropy = tf.reduce_mean(-tf.reduce_sum(y * tf.log(output), axis = 1))\n",
"\n",
"# Define loss and optimizer and initializing the variables,\n",
"# more description on adam optimizer later\n",
"train_step = tf.train.AdamOptimizer(learning_rate).minimize(cross_entropy)\n",
"init = tf.global_variables_initializer()\n",
"\n",
"# predicted accuracy\n",
"correct_prediction = tf.equal(tf.argmax(y, axis = 1), tf.argmax(output, axis = 1))\n",
"accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"> [StackOverflow](http://stackoverflow.com/questions/33712178/tensorflow-nan-bug) In some samples, certain classes could be excluded with certainty after a while, resulting in output probability = 0 for that sample. This yields a log(0) for the cross entropy calculation for that particular sample/class. Hence the cost will become NaN. The way to resolve this is to use `tf.clip_by_value` to specify a boundary for the maximum and minimum value."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"12.517099\n",
"0.9874096\n",
"0.6466728\n",
"0.37521496\n",
"0.30614406\n",
"0.24187014\n",
"0.21222906\n",
"0.13695246\n",
"0.15252227\n"
]
}
],
"source": [
"# record the training history so we can visualize them later\n",
"cost_train_history = []\n",
"acc_train_history = []\n",
"acc_test_history = []\n",
"\n",
"with tf.Session() as sess:\n",
" sess.run(init)\n",
"\n",
" # epochs is the number of times that we loop through the \n",
" # entire training data\n",
" iterations = int(n_epochs * X_train.shape[0] / batch_size)\n",
" for i in range(iterations):\n",
" X_batch, y_batch = mnist.train.next_batch(batch_size)\n",
" _, acc_train, c_train = sess.run([train_step, accuracy, cross_entropy],\n",
" feed_dict = {X: X_batch, y: y_batch})\n",
" if i % 50 == 0:\n",
" print(c_train)\n",
"\n",
" # average cost across the batch size\n",
" cost = c_train / batch_size\n",
" cost_train_history.append(cost)\n",
" acc_train_history.append(acc_train)\n",
" acc_test = sess.run(accuracy, feed_dict = {X: X_test, y: y_test})\n",
" acc_test_history.append(acc_test)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9246"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"acc_test_history[len(acc_test_history) - 1]"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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