09_up_and_running_with_tensorflow.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "**Chapter 9 – Up and running with TensorFlow**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "_This notebook contains all the sample code and solutions to the exercices in chapter 9._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "First, let's make sure this notebook works well in both python 2 and 3, import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# To support both python 2 and python 3\n",
    "from __future__ import division, print_function, unicode_literals\n",
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "# to make this notebook's output stable across runs\n",
    "def reset_graph(seed=42):\n",
    "    tf.reset_default_graph()\n",
    "    tf.set_random_seed(seed)\n",
    "    np.random.seed(seed)\n",
    "\n",
    "# To plot pretty figures\n",
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['axes.labelsize'] = 14\n",
    "plt.rcParams['xtick.labelsize'] = 12\n",
    "plt.rcParams['ytick.labelsize'] = 12\n",
    "\n",
    "# Where to save the figures\n",
    "PROJECT_ROOT_DIR = \".\"\n",
    "CHAPTER_ID = \"tensorflow\"\n",
    "\n",
    "def save_fig(fig_id, tight_layout=True):\n",
    "    path = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID, fig_id + \".png\")\n",
    "    print(\"Saving figure\", fig_id)\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format='png', dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Creating and running a graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "\n",
    "reset_graph()\n",
    "\n",
    "x = tf.Variable(3, name=\"x\")\n",
    "y = tf.Variable(4, name=\"y\")\n",
    "f = x*x*y + y + 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor 'add_1:0' shape=() dtype=int32>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "42\n"
     ]
    }
   ],
   "source": [
    "sess = tf.Session()\n",
    "sess.run(x.initializer)\n",
    "sess.run(y.initializer)\n",
    "result = sess.run(f)\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "sess.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "with tf.Session() as sess:\n",
    "    x.initializer.run()\n",
    "    y.initializer.run()\n",
    "    result = f.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "init = tf.global_variables_initializer()\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    result = f.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "42\n"
     ]
    }
   ],
   "source": [
    "sess = tf.InteractiveSession()\n",
    "init.run()\n",
    "result = f.eval()\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "sess.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Managing graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reset_graph()\n",
    "\n",
    "x1 = tf.Variable(1)\n",
    "x1.graph is tf.get_default_graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph = tf.Graph()\n",
    "with graph.as_default():\n",
    "    x2 = tf.Variable(2)\n",
    "\n",
    "x2.graph is graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2.graph is tf.get_default_graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "15\n"
     ]
    }
   ],
   "source": [
    "w = tf.constant(3)\n",
    "x = w + 2\n",
    "y = x + 5\n",
    "z = x * 3\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    print(y.eval())  # 10\n",
    "    print(z.eval())  # 15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "15\n"
     ]
    }
   ],
   "source": [
    "with tf.Session() as sess:\n",
    "    y_val, z_val = sess.run([y, z])\n",
    "    print(y_val)  # 10\n",
    "    print(z_val)  # 15"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Using the Normal Equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.datasets import fetch_california_housing\n",
    "\n",
    "reset_graph()\n",
    "\n",
    "housing = fetch_california_housing()\n",
    "m, n = housing.data.shape\n",
    "housing_data_plus_bias = np.c_[np.ones((m, 1)), housing.data]\n",
    "\n",
    "X = tf.constant(housing_data_plus_bias, dtype=tf.float32, name=\"X\")\n",
    "y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name=\"y\")\n",
    "XT = tf.transpose(X)\n",
    "theta = tf.matmul(tf.matmul(tf.matrix_inverse(tf.matmul(XT, X)), XT), y)\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    theta_value = theta.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -3.74651413e+01],\n",
       "       [  4.35734153e-01],\n",
       "       [  9.33829229e-03],\n",
       "       [ -1.06622010e-01],\n",
       "       [  6.44106984e-01],\n",
       "       [ -4.25131839e-06],\n",
       "       [ -3.77322501e-03],\n",
       "       [ -4.26648885e-01],\n",
       "       [ -4.40514028e-01]], dtype=float32)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Compare with pure NumPy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ -3.69419202e+01]\n",
      " [  4.36693293e-01]\n",
      " [  9.43577803e-03]\n",
      " [ -1.07322041e-01]\n",
      " [  6.45065694e-01]\n",
      " [ -3.97638942e-06]\n",
      " [ -3.78654265e-03]\n",
      " [ -4.21314378e-01]\n",
      " [ -4.34513755e-01]]\n"
     ]
    }
   ],
   "source": [
    "X = housing_data_plus_bias\n",
    "y = housing.target.reshape(-1, 1)\n",
    "theta_numpy = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)\n",
    "\n",
    "print(theta_numpy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Compare with Scikit-Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ -3.69419202e+01]\n",
      " [  4.36693293e-01]\n",
      " [  9.43577803e-03]\n",
      " [ -1.07322041e-01]\n",
      " [  6.45065694e-01]\n",
      " [ -3.97638942e-06]\n",
      " [ -3.78654265e-03]\n",
      " [ -4.21314378e-01]\n",
      " [ -4.34513755e-01]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(housing.data, housing.target.reshape(-1, 1))\n",
    "\n",
    "print(np.r_[lin_reg.intercept_.reshape(-1, 1), lin_reg.coef_.T])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Using Batch Gradient Descent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Gradient Descent requires scaling the feature vectors first. We could do this using TF, but let's just use Scikit-Learn for now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "scaled_housing_data = scaler.fit_transform(housing.data)\n",
    "scaled_housing_data_plus_bias = np.c_[np.ones((m, 1)), scaled_housing_data]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  1.00000000e+00   6.60969987e-17   5.50808322e-18   6.60969987e-17\n",
      "  -1.06030602e-16  -1.10161664e-17   3.44255201e-18  -1.07958431e-15\n",
      "  -8.52651283e-15]\n",
      "[ 0.38915536  0.36424355  0.5116157  ..., -0.06612179 -0.06360587\n",
      "  0.01359031]\n",
      "0.111111111111\n",
      "(20640, 9)\n"
     ]
    }
   ],
   "source": [
    "print(scaled_housing_data_plus_bias.mean(axis=0))\n",
    "print(scaled_housing_data_plus_bias.mean(axis=1))\n",
    "print(scaled_housing_data_plus_bias.mean())\n",
    "print(scaled_housing_data_plus_bias.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Manually computing the gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0 MSE = 9.16154\n",
      "Epoch 100 MSE = 0.714501\n",
      "Epoch 200 MSE = 0.566705\n",
      "Epoch 300 MSE = 0.555572\n",
      "Epoch 400 MSE = 0.548812\n",
      "Epoch 500 MSE = 0.543636\n",
      "Epoch 600 MSE = 0.539629\n",
      "Epoch 700 MSE = 0.536509\n",
      "Epoch 800 MSE = 0.534068\n",
      "Epoch 900 MSE = 0.532147\n"
     ]
    }
   ],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_epochs = 1000\n",
    "learning_rate = 0.01\n",
    "\n",
    "X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name=\"X\")\n",
    "y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name=\"y\")\n",
    "theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
    "error = y_pred - y\n",
    "mse = tf.reduce_mean(tf.square(error), name=\"mse\")\n",
    "gradients = 2/m * tf.matmul(tf.transpose(X), error)\n",
    "training_op = tf.assign(theta, theta - learning_rate * gradients)\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "\n",
    "    for epoch in range(n_epochs):\n",
    "        if epoch % 100 == 0:\n",
    "            print(\"Epoch\", epoch, \"MSE =\", mse.eval())\n",
    "        sess.run(training_op)\n",
    "    \n",
    "    best_theta = theta.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.06855249],\n",
       "       [ 0.88740271],\n",
       "       [ 0.14401658],\n",
       "       [-0.34770882],\n",
       "       [ 0.36178368],\n",
       "       [ 0.00393812],\n",
       "       [-0.04269557],\n",
       "       [-0.66145277],\n",
       "       [-0.63752776]], dtype=float32)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Using autodiff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Same as above except for the `gradients = ...` line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_epochs = 1000\n",
    "learning_rate = 0.01\n",
    "\n",
    "X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name=\"X\")\n",
    "y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name=\"y\")\n",
    "theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
    "error = y_pred - y\n",
    "mse = tf.reduce_mean(tf.square(error), name=\"mse\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "gradients = tf.gradients(mse, [theta])[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0 MSE = 9.16154\n",
      "Epoch 100 MSE = 0.714501\n",
      "Epoch 200 MSE = 0.566705\n",
      "Epoch 300 MSE = 0.555572\n",
      "Epoch 400 MSE = 0.548812\n",
      "Epoch 500 MSE = 0.543636\n",
      "Epoch 600 MSE = 0.539629\n",
      "Epoch 700 MSE = 0.536509\n",
      "Epoch 800 MSE = 0.534068\n",
      "Epoch 900 MSE = 0.532147\n",
      "Best theta:\n",
      "[[ 2.06855249]\n",
      " [ 0.88740271]\n",
      " [ 0.14401658]\n",
      " [-0.34770882]\n",
      " [ 0.36178368]\n",
      " [ 0.00393811]\n",
      " [-0.04269556]\n",
      " [-0.66145277]\n",
      " [-0.6375277 ]]\n"
     ]
    }
   ],
   "source": [
    "training_op = tf.assign(theta, theta - learning_rate * gradients)\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "\n",
    "    for epoch in range(n_epochs):\n",
    "        if epoch % 100 == 0:\n",
    "            print(\"Epoch\", epoch, \"MSE =\", mse.eval())\n",
    "        sess.run(training_op)\n",
    "    \n",
    "    best_theta = theta.eval()\n",
    "\n",
    "print(\"Best theta:\")\n",
    "print(best_theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "How could you find the partial derivatives of the following function with regards to `a` and `b`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def my_func(a, b):\n",
    "    z = 0\n",
    "    for i in range(100):\n",
    "        z = a * np.cos(z + i) + z * np.sin(b - i)\n",
    "    return z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.21253923284754914"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_func(0.2, 0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "a = tf.Variable(0.2, name=\"a\")\n",
    "b = tf.Variable(0.3, name=\"b\")\n",
    "z = tf.constant(0.0, name=\"z0\")\n",
    "for i in range(100):\n",
    "    z = a * tf.cos(z + i) + z * tf.sin(b - i)\n",
    "\n",
    "grads = tf.gradients(z, [a, b])\n",
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's compute the function at $a=0.2$ and $b=0.3$, and the partial derivatives at that point with regards to $a$ and with regards to $b$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.212537\n",
      "[-1.1388494, 0.19671395]\n"
     ]
    }
   ],
   "source": [
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    print(z.eval())\n",
    "    print(sess.run(grads))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Using a `GradientDescentOptimizer`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_epochs = 1000\n",
    "learning_rate = 0.01\n",
    "\n",
    "X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name=\"X\")\n",
    "y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name=\"y\")\n",
    "theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
    "error = y_pred - y\n",
    "mse = tf.reduce_mean(tf.square(error), name=\"mse\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
    "training_op = optimizer.minimize(mse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0 MSE = 9.16154\n",
      "Epoch 100 MSE = 0.714501\n",
      "Epoch 200 MSE = 0.566705\n",
      "Epoch 300 MSE = 0.555572\n",
      "Epoch 400 MSE = 0.548812\n",
      "Epoch 500 MSE = 0.543636\n",
      "Epoch 600 MSE = 0.539629\n",
      "Epoch 700 MSE = 0.536509\n",
      "Epoch 800 MSE = 0.534068\n",
      "Epoch 900 MSE = 0.532147\n",
      "Best theta:\n",
      "[[ 2.06855249]\n",
      " [ 0.88740271]\n",
      " [ 0.14401658]\n",
      " [-0.34770882]\n",
      " [ 0.36178368]\n",
      " [ 0.00393811]\n",
      " [-0.04269556]\n",
      " [-0.66145277]\n",
      " [-0.6375277 ]]\n"
     ]
    }
   ],
   "source": [
    "init = tf.global_variables_initializer()\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "\n",
    "    for epoch in range(n_epochs):\n",
    "        if epoch % 100 == 0:\n",
    "            print(\"Epoch\", epoch, \"MSE =\", mse.eval())\n",
    "        sess.run(training_op)\n",
    "    \n",
    "    best_theta = theta.eval()\n",
    "\n",
    "print(\"Best theta:\")\n",
    "print(best_theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Using a momentum optimizer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_epochs = 1000\n",
    "learning_rate = 0.01\n",
    "\n",
    "X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name=\"X\")\n",
    "y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name=\"y\")\n",
    "theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
    "error = y_pred - y\n",
    "mse = tf.reduce_mean(tf.square(error), name=\"mse\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "optimizer = tf.train.MomentumOptimizer(learning_rate=learning_rate,\n",
    "                                       momentum=0.9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "training_op = optimizer.minimize(mse)\n",
    "\n",
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best theta:\n",
      "[[ 2.06855798]\n",
      " [ 0.82962859]\n",
      " [ 0.11875337]\n",
      " [-0.26554456]\n",
      " [ 0.30571091]\n",
      " [-0.00450251]\n",
      " [-0.03932662]\n",
      " [-0.89986444]\n",
      " [-0.87052065]]\n"
     ]
    }
   ],
   "source": [
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "\n",
    "    for epoch in range(n_epochs):\n",
    "        sess.run(training_op)\n",
    "    \n",
    "    best_theta = theta.eval()\n",
    "\n",
    "print(\"Best theta:\")\n",
    "print(best_theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Feeding data to the training algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Placeholder nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 6.  7.  8.]]\n"
     ]
    }
   ],
   "source": [
    "reset_graph()\n",
    "\n",
    "A = tf.placeholder(tf.float32, shape=(None, 3))\n",
    "B = A + 5\n",
    "with tf.Session() as sess:\n",
    "    B_val_1 = B.eval(feed_dict={A: [[1, 2, 3]]})\n",
    "    B_val_2 = B.eval(feed_dict={A: [[4, 5, 6], [7, 8, 9]]})\n",
    "\n",
    "print(B_val_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  9.  10.  11.]\n",
      " [ 12.  13.  14.]]\n"
     ]
    }
   ],
   "source": [
    "print(B_val_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Mini-batch Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "n_epochs = 1000\n",
    "learning_rate = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n + 1), name=\"X\")\n",
    "y = tf.placeholder(tf.float32, shape=(None, 1), name=\"y\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
    "error = y_pred - y\n",
    "mse = tf.reduce_mean(tf.square(error), name=\"mse\")\n",
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
    "training_op = optimizer.minimize(mse)\n",
    "\n",
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "n_epochs = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "batch_size = 100\n",
    "n_batches = int(np.ceil(m / batch_size))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def fetch_batch(epoch, batch_index, batch_size):\n",
    "    np.random.seed(epoch * n_batches + batch_index)  # not shown in the book\n",
    "    indices = np.random.randint(m, size=batch_size)  # not shown\n",
    "    X_batch = scaled_housing_data_plus_bias[indices] # not shown\n",
    "    y_batch = housing.target.reshape(-1, 1)[indices] # not shown\n",
    "    return X_batch, y_batch\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "\n",
    "    for epoch in range(n_epochs):\n",
    "        for batch_index in range(n_batches):\n",
    "            X_batch, y_batch = fetch_batch(epoch, batch_index, batch_size)\n",
    "            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
    "\n",
    "    best_theta = theta.eval()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.07033372],\n",
       "       [ 0.86371452],\n",
       "       [ 0.12255151],\n",
       "       [-0.31211874],\n",
       "       [ 0.38510373],\n",
       "       [ 0.00434168],\n",
       "       [-0.01232954],\n",
       "       [-0.83376896],\n",
       "       [-0.80304712]], dtype=float32)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Saving and restoring a model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0 MSE = 9.16154\n",
      "Epoch 100 MSE = 0.714501\n",
      "Epoch 200 MSE = 0.566705\n",
      "Epoch 300 MSE = 0.555572\n",
      "Epoch 400 MSE = 0.548812\n",
      "Epoch 500 MSE = 0.543636\n",
      "Epoch 600 MSE = 0.539629\n",
      "Epoch 700 MSE = 0.536509\n",
      "Epoch 800 MSE = 0.534068\n",
      "Epoch 900 MSE = 0.532147\n"
     ]
    }
   ],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_epochs = 1000                                                                       # not shown in the book\n",
    "learning_rate = 0.01                                                                  # not shown\n",
    "\n",
    "X = tf.constant(scaled_housing_data_plus_bias, dtype=tf.float32, name=\"X\")            # not shown\n",
    "y = tf.constant(housing.target.reshape(-1, 1), dtype=tf.float32, name=\"y\")            # not shown\n",
    "theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "y_pred = tf.matmul(X, theta, name=\"predictions\")                                      # not shown\n",
    "error = y_pred - y                                                                    # not shown\n",
    "mse = tf.reduce_mean(tf.square(error), name=\"mse\")                                    # not shown\n",
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)            # not shown\n",
    "training_op = optimizer.minimize(mse)                                                 # not shown\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "saver = tf.train.Saver()\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "\n",
    "    for epoch in range(n_epochs):\n",
    "        if epoch % 100 == 0:\n",
    "            print(\"Epoch\", epoch, \"MSE =\", mse.eval())                                # not shown\n",
    "            save_path = saver.save(sess, \"/tmp/my_model.ckpt\")\n",
    "        sess.run(training_op)\n",
    "    \n",
    "    best_theta = theta.eval()\n",
    "    save_path = saver.save(sess, \"/tmp/my_model_final.ckpt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.06855249],\n",
       "       [ 0.88740271],\n",
       "       [ 0.14401658],\n",
       "       [-0.34770882],\n",
       "       [ 0.36178368],\n",
       "       [ 0.00393811],\n",
       "       [-0.04269556],\n",
       "       [-0.66145277],\n",
       "       [-0.6375277 ]], dtype=float32)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from /tmp/my_model_final.ckpt\n"
     ]
    }
   ],
   "source": [
    "with tf.Session() as sess:\n",
    "    saver.restore(sess, \"/tmp/my_model_final.ckpt\")\n",
    "    best_theta_restored = theta.eval() # not shown in the book"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(best_theta, best_theta_restored)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "If you want to have a saver that loads and restores `theta` with a different name, such as `\"weights\"`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "saver = tf.train.Saver({\"weights\": theta})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "By default the saver also saves the graph structure itself in a second file with the extension `.meta`. You can use the function `tf.train.import_meta_graph()` to restore the graph structure. This function loads the graph into the default graph and returns a `Saver` that can then be used to restore the graph state (i.e., the variable values):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "INFO:tensorflow:Restoring parameters from /tmp/my_model_final.ckpt\n"
     ]
    }
   ],
   "source": [
    "reset_graph()\n",
    "# notice that we start with an empty graph.\n",
    "\n",
    "saver = tf.train.import_meta_graph(\"/tmp/my_model_final.ckpt.meta\")  # this loads the graph structure\n",
    "theta = tf.get_default_graph().get_tensor_by_name(\"theta:0\") # not shown in the book\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    saver.restore(sess, \"/tmp/my_model_final.ckpt\")  # this restores the graph's state\n",
    "    best_theta_restored = theta.eval() # not shown in the book"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
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    {
     "data": {
      "text/plain": [
       "True"
      ]
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     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "np.allclose(best_theta, best_theta_restored)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This means that you can import a pretrained model without having to have the corresponding Python code to build the graph. This is very handy when you keep tweaking and saving your model: you can load a previously saved model without having to search for the version of the code that built it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Visualizing the graph\n",
    "## inside Jupyter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true,
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   "source": [
    "from IPython.display import clear_output, Image, display, HTML\n",
    "\n",
    "def strip_consts(graph_def, max_const_size=32):\n",
    "    \"\"\"Strip large constant values from graph_def.\"\"\"\n",
    "    strip_def = tf.GraphDef()\n",
    "    for n0 in graph_def.node:\n",
    "        n = strip_def.node.add() \n",
    "        n.MergeFrom(n0)\n",
    "        if n.op == 'Const':\n",
    "            tensor = n.attr['value'].tensor\n",
    "            size = len(tensor.tensor_content)\n",
    "            if size > max_const_size:\n",
    "                tensor.tensor_content = b\"<stripped %d bytes>\"%size\n",
    "    return strip_def\n",
    "\n",
    "def show_graph(graph_def, max_const_size=32):\n",
    "    \"\"\"Visualize TensorFlow graph.\"\"\"\n",
    "    if hasattr(graph_def, 'as_graph_def'):\n",
    "        graph_def = graph_def.as_graph_def()\n",
    "    strip_def = strip_consts(graph_def, max_const_size=max_const_size)\n",
    "    code = \"\"\"\n",
    "        <script>\n",
    "          function load() {{\n",
    "            document.getElementById(\"{id}\").pbtxt = {data};\n",
    "          }}\n",
    "        </script>\n",
    "        <link rel=\"import\" href=\"https://tensorboard.appspot.com/tf-graph-basic.build.html\" onload=load()>\n",
    "        <div style=\"height:600px\">\n",
    "          <tf-graph-basic id=\"{id}\"></tf-graph-basic>\n",
    "        </div>\n",
    "    \"\"\".format(data=repr(str(strip_def)), id='graph'+str(np.random.rand()))\n",
    "\n",
    "    iframe = \"\"\"\n",
    "        <iframe seamless style=\"width:1200px;height:620px;border:0\" srcdoc=\"{}\"></iframe>\n",
    "    \"\"\".format(code.replace('\"', '&quot;'))\n",
    "    display(HTML(iframe))"
   ]
  },
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   "execution_count": 58,
   "metadata": {
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    "editable": true,
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&quot;T&quot;\\n    value {\\n      type: DT_FLOAT\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;gradients/sub_grad/Reshape_1&quot;\\n  op: &quot;Reshape&quot;\\n  input: &quot;gradients/sub_grad/Neg&quot;\\n  input: &quot;gradients/sub_grad/Shape_1&quot;\\n  attr {\\n    key: &quot;T&quot;\\n    value {\\n      type: DT_FLOAT\\n    }\\n  }\\n  attr {\\n    key: &quot;Tshape&quot;\\n    value {\\n      type: DT_INT32\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;gradients/sub_grad/tuple/group_deps&quot;\\n  op: &quot;NoOp&quot;\\n  input: &quot;^gradients/sub_grad/Reshape&quot;\\n  input: &quot;^gradients/sub_grad/Reshape_1&quot;\\n}\\nnode {\\n  name: &quot;gradients/sub_grad/tuple/control_dependency&quot;\\n  op: &quot;Identity&quot;\\n  input: &quot;gradients/sub_grad/Reshape&quot;\\n  input: &quot;^gradients/sub_grad/tuple/group_deps&quot;\\n  attr {\\n    key: &quot;T&quot;\\n    value {\\n      type: DT_FLOAT\\n    }\\n  }\\n  attr {\\n    key: &quot;_class&quot;\\n    value {\\n      list {\\n        s: &quot;loc:@gradients/sub_grad/Reshape&quot;\\n      }\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;gradients/sub_grad/tuple/control_dependency_1&quot;\\n  op: &quot;Identity&quot;\\n  input: &quot;gradients/sub_grad/Reshape_1&quot;\\n  input: &quot;^gradients/sub_grad/tuple/group_deps&quot;\\n  attr {\\n    key: &quot;T&quot;\\n    value {\\n      type: DT_FLOAT\\n    }\\n  }\\n  attr {\\n    key: &quot;_class&quot;\\n    value {\\n      list {\\n        s: &quot;loc:@gradients/sub_grad/Reshape_1&quot;\\n      }\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;gradients/predictions_grad/MatMul&quot;\\n  op: &quot;MatMul&quot;\\n  input: &quot;gradients/sub_grad/tuple/control_dependency&quot;\\n  input: &quot;theta/read&quot;\\n  attr {\\n    key: &quot;T&quot;\\n    value {\\n      type: DT_FLOAT\\n    }\\n  }\\n  attr {\\n    key: &quot;transpose_a&quot;\\n    value {\\n      b: false\\n    }\\n  }\\n  attr {\\n    key: &quot;transpose_b&quot;\\n    value {\\n      b: true\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;gradients/predictions_grad/MatMul_1&quot;\\n  op: &quot;MatMul&quot;\\n  input: &quot;X&quot;\\n  input: &quot;gradients/sub_grad/tuple/control_dependency&quot;\\n  attr {\\n    key: &quot;T&quot;\\n    value {\\n      type: DT_FLOAT\\n    }\\n  }\\n  attr {\\n    key: &quot;transpose_a&quot;\\n    value {\\n      b: true\\n    }\\n  }\\n  attr {\\n    key: &quot;transpose_b&quot;\\n    value {\\n      b: false\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;gradients/predictions_grad/tuple/group_deps&quot;\\n  op: &quot;NoOp&quot;\\n  input: &quot;^gradients/predictions_grad/MatMul&quot;\\n  input: &quot;^gradients/predictions_grad/MatMul_1&quot;\\n}\\nnode {\\n  name: &quot;gradients/predictions_grad/tuple/control_dependency&quot;\\n  op: &quot;Identity&quot;\\n  input: &quot;gradients/predictions_grad/MatMul&quot;\\n  input: &quot;^gradients/predictions_grad/tuple/group_deps&quot;\\n  attr {\\n    key: &quot;T&quot;\\n    value {\\n      type: DT_FLOAT\\n    }\\n  }\\n  attr {\\n    key: &quot;_class&quot;\\n    value {\\n      list {\\n        s: &quot;loc:@gradients/predictions_grad/MatMul&quot;\\n      }\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;gradients/predictions_grad/tuple/control_dependency_1&quot;\\n  op: &quot;Identity&quot;\\n  input: &quot;gradients/predictions_grad/MatMul_1&quot;\\n  input: &quot;^gradients/predictions_grad/tuple/group_deps&quot;\\n  attr {\\n    key: &quot;T&quot;\\n    value {\\n      type: DT_FLOAT\\n    }\\n  }\\n  attr {\\n    key: &quot;_class&quot;\\n    value {\\n      list {\\n        s: &quot;loc:@gradients/predictions_grad/MatMul_1&quot;\\n      }\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;GradientDescent/learning_rate&quot;\\n  op: &quot;Const&quot;\\n  attr {\\n    key: &quot;dtype&quot;\\n    value {\\n      type: DT_FLOAT\\n    }\\n  }\\n  attr {\\n    key: &quot;value&quot;\\n    value {\\n      tensor {\\n        dtype: DT_FLOAT\\n        tensor_shape {\\n        }\\n        float_val: 0.009999999776482582\\n      }\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;GradientDescent/update_theta/ApplyGradientDescent&quot;\\n  op: &quot;ApplyGradientDescent&quot;\\n  input: &quot;theta&quot;\\n  input: &quot;GradientDescent/learning_rate&quot;\\n  input: &quot;gradients/predictions_grad/tuple/control_dependency_1&quot;\\n  attr {\\n    key: &quot;T&quot;\\n    value {\\n      type: DT_FLOAT\\n    }\\n  }\\n  attr {\\n    key: &quot;_class&quot;\\n    value {\\n      list {\\n        s: &quot;loc:@theta&quot;\\n      }\\n    }\\n  }\\n  attr {\\n    key: &quot;use_locking&quot;\\n    value {\\n      b: false\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;GradientDescent&quot;\\n  op: &quot;NoOp&quot;\\n  input: &quot;^GradientDescent/update_theta/ApplyGradientDescent&quot;\\n}\\nnode {\\n  name: &quot;init&quot;\\n  op: &quot;NoOp&quot;\\n  input: &quot;^theta/Assign&quot;\\n}\\nnode {\\n  name: &quot;save/Const&quot;\\n  op: &quot;Const&quot;\\n  attr {\\n    key: &quot;dtype&quot;\\n    value {\\n      type: DT_STRING\\n    }\\n  }\\n  attr {\\n    key: &quot;value&quot;\\n    value {\\n      tensor {\\n        dtype: DT_STRING\\n        tensor_shape {\\n        }\\n        string_val: &quot;model&quot;\\n      }\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;save/SaveV2/tensor_names&quot;\\n  op: &quot;Const&quot;\\n  attr {\\n    key: &quot;dtype&quot;\\n    value {\\n      type: DT_STRING\\n    }\\n  }\\n  attr {\\n    key: &quot;value&quot;\\n    value {\\n      tensor {\\n        dtype: DT_STRING\\n        tensor_shape {\\n          dim {\\n            size: 1\\n          }\\n        }\\n        string_val: &quot;theta&quot;\\n      }\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;save/SaveV2/shape_and_slices&quot;\\n  op: &quot;Const&quot;\\n  attr {\\n    key: &quot;dtype&quot;\\n    value {\\n      type: DT_STRING\\n    }\\n  }\\n  attr {\\n    key: &quot;value&quot;\\n    value {\\n      tensor {\\n        dtype: DT_STRING\\n        tensor_shape {\\n          dim {\\n            size: 1\\n          }\\n        }\\n        string_val: &quot;&quot;\\n      }\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;save/SaveV2&quot;\\n  op: &quot;SaveV2&quot;\\n  input: &quot;save/Const&quot;\\n  input: &quot;save/SaveV2/tensor_names&quot;\\n  input: &quot;save/SaveV2/shape_and_slices&quot;\\n  input: &quot;theta&quot;\\n  attr {\\n    key: &quot;dtypes&quot;\\n    value {\\n      list {\\n        type: DT_FLOAT\\n      }\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;save/control_dependency&quot;\\n  op: &quot;Identity&quot;\\n  input: &quot;save/Const&quot;\\n  input: &quot;^save/SaveV2&quot;\\n  attr {\\n    key: &quot;T&quot;\\n    value {\\n      type: DT_STRING\\n    }\\n  }\\n  attr {\\n    key: &quot;_class&quot;\\n    value {\\n      list {\\n        s: &quot;loc:@save/Const&quot;\\n      }\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;save/RestoreV2/tensor_names&quot;\\n  op: &quot;Const&quot;\\n  attr {\\n    key: &quot;dtype&quot;\\n    value {\\n      type: DT_STRING\\n    }\\n  }\\n  attr {\\n    key: &quot;value&quot;\\n    value {\\n      tensor {\\n        dtype: DT_STRING\\n        tensor_shape {\\n          dim {\\n            size: 1\\n          }\\n        }\\n        string_val: &quot;theta&quot;\\n      }\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;save/RestoreV2/shape_and_slices&quot;\\n  op: &quot;Const&quot;\\n  attr {\\n    key: &quot;dtype&quot;\\n    value {\\n      type: DT_STRING\\n    }\\n  }\\n  attr {\\n    key: &quot;value&quot;\\n    value {\\n      tensor {\\n        dtype: DT_STRING\\n        tensor_shape {\\n          dim {\\n            size: 1\\n          }\\n        }\\n        string_val: &quot;&quot;\\n      }\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;save/RestoreV2&quot;\\n  op: &quot;RestoreV2&quot;\\n  input: &quot;save/Const&quot;\\n  input: &quot;save/RestoreV2/tensor_names&quot;\\n  input: &quot;save/RestoreV2/shape_and_slices&quot;\\n  attr {\\n    key: &quot;dtypes&quot;\\n    value {\\n      list {\\n        type: DT_FLOAT\\n      }\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;save/Assign&quot;\\n  op: &quot;Assign&quot;\\n  input: &quot;theta&quot;\\n  input: &quot;save/RestoreV2&quot;\\n  attr {\\n    key: &quot;T&quot;\\n    value {\\n      type: DT_FLOAT\\n    }\\n  }\\n  attr {\\n    key: &quot;_class&quot;\\n    value {\\n      list {\\n        s: &quot;loc:@theta&quot;\\n      }\\n    }\\n  }\\n  attr {\\n    key: &quot;use_locking&quot;\\n    value {\\n      b: true\\n    }\\n  }\\n  attr {\\n    key: &quot;validate_shape&quot;\\n    value {\\n      b: true\\n    }\\n  }\\n}\\nnode {\\n  name: &quot;save/restore_all&quot;\\n  op: &quot;NoOp&quot;\\n  input: &quot;^save/Assign&quot;\\n}\\n';\n",
       "          }\n",
       "        </script>\n",
       "        <link rel=&quot;import&quot; href=&quot;https://tensorboard.appspot.com/tf-graph-basic.build.html&quot; onload=load()>\n",
       "        <div style=&quot;height:600px&quot;>\n",
       "          <tf-graph-basic id=&quot;graph0.3745401188473625&quot;></tf-graph-basic>\n",
       "        </div>\n",
       "    \"></iframe>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_graph(tf.get_default_graph())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Using TensorBoard"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "from datetime import datetime\n",
    "\n",
    "now = datetime.utcnow().strftime(\"%Y%m%d%H%M%S\")\n",
    "root_logdir = \"tf_logs\"\n",
    "logdir = \"{}/run-{}/\".format(root_logdir, now)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "n_epochs = 1000\n",
    "learning_rate = 0.01\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n + 1), name=\"X\")\n",
    "y = tf.placeholder(tf.float32, shape=(None, 1), name=\"y\")\n",
    "theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "y_pred = tf.matmul(X, theta, name=\"predictions\")\n",
    "error = y_pred - y\n",
    "mse = tf.reduce_mean(tf.square(error), name=\"mse\")\n",
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
    "training_op = optimizer.minimize(mse)\n",
    "\n",
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "mse_summary = tf.summary.scalar('MSE', mse)\n",
    "file_writer = tf.summary.FileWriter(logdir, tf.get_default_graph())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "n_epochs = 10\n",
    "batch_size = 100\n",
    "n_batches = int(np.ceil(m / batch_size))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "with tf.Session() as sess:                                                        # not shown in the book\n",
    "    sess.run(init)                                                                # not shown\n",
    "\n",
    "    for epoch in range(n_epochs):                                                 # not shown\n",
    "        for batch_index in range(n_batches):\n",
    "            X_batch, y_batch = fetch_batch(epoch, batch_index, batch_size)\n",
    "            if batch_index % 10 == 0:\n",
    "                summary_str = mse_summary.eval(feed_dict={X: X_batch, y: y_batch})\n",
    "                step = epoch * n_batches + batch_index\n",
    "                file_writer.add_summary(summary_str, step)\n",
    "            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
    "\n",
    "    best_theta = theta.eval()                                                     # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "file_writer.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.07033372],\n",
       "       [ 0.86371452],\n",
       "       [ 0.12255151],\n",
       "       [-0.31211874],\n",
       "       [ 0.38510373],\n",
       "       [ 0.00434168],\n",
       "       [-0.01232954],\n",
       "       [-0.83376896],\n",
       "       [-0.80304712]], dtype=float32)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Name scopes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "now = datetime.utcnow().strftime(\"%Y%m%d%H%M%S\")\n",
    "root_logdir = \"tf_logs\"\n",
    "logdir = \"{}/run-{}/\".format(root_logdir, now)\n",
    "\n",
    "n_epochs = 1000\n",
    "learning_rate = 0.01\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n + 1), name=\"X\")\n",
    "y = tf.placeholder(tf.float32, shape=(None, 1), name=\"y\")\n",
    "theta = tf.Variable(tf.random_uniform([n + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "y_pred = tf.matmul(X, theta, name=\"predictions\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "with tf.name_scope(\"loss\") as scope:\n",
    "    error = y_pred - y\n",
    "    mse = tf.reduce_mean(tf.square(error), name=\"mse\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
    "training_op = optimizer.minimize(mse)\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "\n",
    "mse_summary = tf.summary.scalar('MSE', mse)\n",
    "file_writer = tf.summary.FileWriter(logdir, tf.get_default_graph())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best theta:\n",
      "[[ 2.07033372]\n",
      " [ 0.86371452]\n",
      " [ 0.12255151]\n",
      " [-0.31211874]\n",
      " [ 0.38510373]\n",
      " [ 0.00434168]\n",
      " [-0.01232954]\n",
      " [-0.83376896]\n",
      " [-0.80304712]]\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 10\n",
    "batch_size = 100\n",
    "n_batches = int(np.ceil(m / batch_size))\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "\n",
    "    for epoch in range(n_epochs):\n",
    "        for batch_index in range(n_batches):\n",
    "            X_batch, y_batch = fetch_batch(epoch, batch_index, batch_size)\n",
    "            if batch_index % 10 == 0:\n",
    "                summary_str = mse_summary.eval(feed_dict={X: X_batch, y: y_batch})\n",
    "                step = epoch * n_batches + batch_index\n",
    "                file_writer.add_summary(summary_str, step)\n",
    "            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
    "\n",
    "    best_theta = theta.eval()\n",
    "\n",
    "file_writer.flush()\n",
    "file_writer.close()\n",
    "print(\"Best theta:\")\n",
    "print(best_theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss/sub\n"
     ]
    }
   ],
   "source": [
    "print(error.op.name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "loss/mse\n"
     ]
    }
   ],
   "source": [
    "print(mse.op.name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a\n",
      "a_1\n",
      "param/a\n",
      "param_1/a\n"
     ]
    }
   ],
   "source": [
    "reset_graph()\n",
    "\n",
    "a1 = tf.Variable(0, name=\"a\")      # name == \"a\"\n",
    "a2 = tf.Variable(0, name=\"a\")      # name == \"a_1\"\n",
    "\n",
    "with tf.name_scope(\"param\"):       # name == \"param\"\n",
    "    a3 = tf.Variable(0, name=\"a\")  # name == \"param/a\"\n",
    "\n",
    "with tf.name_scope(\"param\"):       # name == \"param_1\"\n",
    "    a4 = tf.Variable(0, name=\"a\")  # name == \"param_1/a\"\n",
    "\n",
    "for node in (a1, a2, a3, a4):\n",
    "    print(node.op.name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Modularity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "An ugly flat code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "n_features = 3\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
    "\n",
    "w1 = tf.Variable(tf.random_normal((n_features, 1)), name=\"weights1\")\n",
    "w2 = tf.Variable(tf.random_normal((n_features, 1)), name=\"weights2\")\n",
    "b1 = tf.Variable(0.0, name=\"bias1\")\n",
    "b2 = tf.Variable(0.0, name=\"bias2\")\n",
    "\n",
    "z1 = tf.add(tf.matmul(X, w1), b1, name=\"z1\")\n",
    "z2 = tf.add(tf.matmul(X, w2), b2, name=\"z2\")\n",
    "\n",
    "relu1 = tf.maximum(z1, 0., name=\"relu1\")\n",
    "relu2 = tf.maximum(z1, 0., name=\"relu2\")  # Oops, cut&paste error! Did you spot it?\n",
    "\n",
    "output = tf.add(relu1, relu2, name=\"output\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Much better, using a function to build the ReLUs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "def relu(X):\n",
    "    w_shape = (int(X.get_shape()[1]), 1)\n",
    "    w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")\n",
    "    b = tf.Variable(0.0, name=\"bias\")\n",
    "    z = tf.add(tf.matmul(X, w), b, name=\"z\")\n",
    "    return tf.maximum(z, 0., name=\"relu\")\n",
    "\n",
    "n_features = 3\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
    "relus = [relu(X) for i in range(5)]\n",
    "output = tf.add_n(relus, name=\"output\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "file_writer = tf.summary.FileWriter(\"logs/relu1\", tf.get_default_graph())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Even better using name scopes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "def relu(X):\n",
    "    with tf.name_scope(\"relu\"):\n",
    "        w_shape = (int(X.get_shape()[1]), 1)                          # not shown in the book\n",
    "        w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")    # not shown\n",
    "        b = tf.Variable(0.0, name=\"bias\")                             # not shown\n",
    "        z = tf.add(tf.matmul(X, w), b, name=\"z\")                      # not shown\n",
    "        return tf.maximum(z, 0., name=\"max\")                          # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "n_features = 3\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
    "relus = [relu(X) for i in range(5)]\n",
    "output = tf.add_n(relus, name=\"output\")\n",
    "\n",
    "file_writer = tf.summary.FileWriter(\"logs/relu2\", tf.get_default_graph())\n",
    "file_writer.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Sharing Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Sharing a `threshold` variable the classic way, by defining it outside of the `relu()` function then passing it as a parameter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "def relu(X, threshold):\n",
    "    with tf.name_scope(\"relu\"):\n",
    "        w_shape = (int(X.get_shape()[1]), 1)                        # not shown in the book\n",
    "        w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")  # not shown\n",
    "        b = tf.Variable(0.0, name=\"bias\")                           # not shown\n",
    "        z = tf.add(tf.matmul(X, w), b, name=\"z\")                    # not shown\n",
    "        return tf.maximum(z, threshold, name=\"max\")\n",
    "\n",
    "threshold = tf.Variable(0.0, name=\"threshold\")\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
    "relus = [relu(X, threshold) for i in range(5)]\n",
    "output = tf.add_n(relus, name=\"output\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "def relu(X):\n",
    "    with tf.name_scope(\"relu\"):\n",
    "        if not hasattr(relu, \"threshold\"):\n",
    "            relu.threshold = tf.Variable(0.0, name=\"threshold\")\n",
    "        w_shape = int(X.get_shape()[1]), 1                          # not shown in the book\n",
    "        w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")  # not shown\n",
    "        b = tf.Variable(0.0, name=\"bias\")                           # not shown\n",
    "        z = tf.add(tf.matmul(X, w), b, name=\"z\")                    # not shown\n",
    "        return tf.maximum(z, relu.threshold, name=\"max\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
    "relus = [relu(X) for i in range(5)]\n",
    "output = tf.add_n(relus, name=\"output\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "with tf.variable_scope(\"relu\"):\n",
    "    threshold = tf.get_variable(\"threshold\", shape=(),\n",
    "                                initializer=tf.constant_initializer(0.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "with tf.variable_scope(\"relu\", reuse=True):\n",
    "    threshold = tf.get_variable(\"threshold\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "with tf.variable_scope(\"relu\") as scope:\n",
    "    scope.reuse_variables()\n",
    "    threshold = tf.get_variable(\"threshold\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "def relu(X):\n",
    "    with tf.variable_scope(\"relu\", reuse=True):\n",
    "        threshold = tf.get_variable(\"threshold\")\n",
    "        w_shape = int(X.get_shape()[1]), 1                          # not shown\n",
    "        w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")  # not shown\n",
    "        b = tf.Variable(0.0, name=\"bias\")                           # not shown\n",
    "        z = tf.add(tf.matmul(X, w), b, name=\"z\")                    # not shown\n",
    "        return tf.maximum(z, threshold, name=\"max\")\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
    "with tf.variable_scope(\"relu\"):\n",
    "    threshold = tf.get_variable(\"threshold\", shape=(),\n",
    "                                initializer=tf.constant_initializer(0.0))\n",
    "relus = [relu(X) for relu_index in range(5)]\n",
    "output = tf.add_n(relus, name=\"output\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "file_writer = tf.summary.FileWriter(\"logs/relu6\", tf.get_default_graph())\n",
    "file_writer.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "def relu(X):\n",
    "    with tf.variable_scope(\"relu\"):\n",
    "        threshold = tf.get_variable(\"threshold\", shape=(), initializer=tf.constant_initializer(0.0))\n",
    "        w_shape = (int(X.get_shape()[1]), 1)\n",
    "        w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")\n",
    "        b = tf.Variable(0.0, name=\"bias\")\n",
    "        z = tf.add(tf.matmul(X, w), b, name=\"z\")\n",
    "        return tf.maximum(z, threshold, name=\"max\")\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
    "with tf.variable_scope(\"\", default_name=\"\") as scope:\n",
    "    first_relu = relu(X)     # create the shared variable\n",
    "    scope.reuse_variables()  # then reuse it\n",
    "    relus = [first_relu] + [relu(X) for i in range(4)]\n",
    "output = tf.add_n(relus, name=\"output\")\n",
    "\n",
    "file_writer = tf.summary.FileWriter(\"logs/relu8\", tf.get_default_graph())\n",
    "file_writer.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()\n",
    "\n",
    "def relu(X):\n",
    "    threshold = tf.get_variable(\"threshold\", shape=(),\n",
    "                                initializer=tf.constant_initializer(0.0))\n",
    "    w_shape = (int(X.get_shape()[1]), 1)                        # not shown in the book\n",
    "    w = tf.Variable(tf.random_normal(w_shape), name=\"weights\")  # not shown\n",
    "    b = tf.Variable(0.0, name=\"bias\")                           # not shown\n",
    "    z = tf.add(tf.matmul(X, w), b, name=\"z\")                    # not shown\n",
    "    return tf.maximum(z, threshold, name=\"max\")\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_features), name=\"X\")\n",
    "relus = []\n",
    "for relu_index in range(5):\n",
    "    with tf.variable_scope(\"relu\", reuse=(relu_index >= 1)) as scope:\n",
    "        relus.append(relu(X))\n",
    "output = tf.add_n(relus, name=\"output\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "file_writer = tf.summary.FileWriter(\"logs/relu9\", tf.get_default_graph())\n",
    "file_writer.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Extra material"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x0: my_scope/x\n",
      "x1: my_scope/x_1\n",
      "x2: my_scope/x_2\n",
      "x3: my_scope/x\n",
      "x4: my_scope_1/x\n",
      "x5: my_scope/x\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "reset_graph()\n",
    "\n",
    "with tf.variable_scope(\"my_scope\"):\n",
    "    x0 = tf.get_variable(\"x\", shape=(), initializer=tf.constant_initializer(0.))\n",
    "    x1 = tf.Variable(0., name=\"x\")\n",
    "    x2 = tf.Variable(0., name=\"x\")\n",
    "\n",
    "with tf.variable_scope(\"my_scope\", reuse=True):\n",
    "    x3 = tf.get_variable(\"x\")\n",
    "    x4 = tf.Variable(0., name=\"x\")\n",
    "\n",
    "with tf.variable_scope(\"\", default_name=\"\", reuse=True):\n",
    "    x5 = tf.get_variable(\"my_scope/x\")\n",
    "\n",
    "print(\"x0:\", x0.op.name)\n",
    "print(\"x1:\", x1.op.name)\n",
    "print(\"x2:\", x2.op.name)\n",
    "print(\"x3:\", x3.op.name)\n",
    "print(\"x4:\", x4.op.name)\n",
    "print(\"x5:\", x5.op.name)\n",
    "print(x0 is x3 and x3 is x5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The first `variable_scope()` block first creates the shared variable `x0`, named `my_scope/x`. For all operations other than shared variables (including non-shared variables), the variable scope acts like a regular name scope, which is why the two variables `x1` and `x2` have a name with a prefix `my_scope/`. Note however that TensorFlow makes their names unique by adding an index: `my_scope/x_1` and `my_scope/x_2`.\n",
    "\n",
    "The second `variable_scope()` block reuses the shared variables in scope `my_scope`, which is why `x0 is x3`. Once again, for all operations other than shared variables it acts as a named scope, and since it's a separate block from the first one, the name of the scope is made unique by TensorFlow (`my_scope_1`) and thus the variable `x4` is named `my_scope_1/x`.\n",
    "\n",
    "The third block shows another way to get a handle on the shared variable `my_scope/x` by creating a `variable_scope()` at the root scope (whose name is an empty string), then calling `get_variable()` with the full name of the shared variable (i.e. `\"my_scope/x\"`)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Strings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[b'Do' b'you' b'want' b'some' b'caf\\xc3\\xa9?']\n"
     ]
    }
   ],
   "source": [
    "reset_graph()\n",
    "\n",
    "text = np.array(\"Do you want some café?\".split())\n",
    "text_tensor = tf.constant(text)\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    print(text_tensor.eval())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Implementing a Home-Made Computation Graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f(x,y) = ((x) * (x)) * (y) + y + 2\n",
      "f(3,4) = 42\n"
     ]
    }
   ],
   "source": [
    "class Const(object):\n",
    "    def __init__(self, value):\n",
    "        self.value = value\n",
    "    def evaluate(self):\n",
    "        return self.value\n",
    "    def __str__(self):\n",
    "        return str(self.value)\n",
    "\n",
    "class Var(object):\n",
    "    def __init__(self, init_value, name):\n",
    "        self.value = init_value\n",
    "        self.name = name\n",
    "    def evaluate(self):\n",
    "        return self.value\n",
    "    def __str__(self):\n",
    "        return self.name\n",
    "\n",
    "class BinaryOperator(object):\n",
    "    def __init__(self, a, b):\n",
    "        self.a = a\n",
    "        self.b = b\n",
    "\n",
    "class Add(BinaryOperator):\n",
    "    def evaluate(self):\n",
    "        return self.a.evaluate() + self.b.evaluate()\n",
    "    def __str__(self):\n",
    "        return \"{} + {}\".format(self.a, self.b)\n",
    "\n",
    "class Mul(BinaryOperator):\n",
    "    def evaluate(self):\n",
    "        return self.a.evaluate() * self.b.evaluate()\n",
    "    def __str__(self):\n",
    "        return \"({}) * ({})\".format(self.a, self.b)\n",
    "\n",
    "x = Var(3, name=\"x\")\n",
    "y = Var(4, name=\"y\")\n",
    "f = Add(Mul(Mul(x, x), y), Add(y, Const(2))) # f(x,y) = x²y + y + 2\n",
    "print(\"f(x,y) =\", f)\n",
    "print(\"f(3,4) =\", f.evaluate())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Computing gradients\n",
    "### Mathematical differentiation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "df/dx(3,4) = 24\n",
      "df/dy(3,4) = 10\n"
     ]
    }
   ],
   "source": [
    "df_dx = Mul(Const(2), Mul(x, y))  # df/dx = 2xy\n",
    "df_dy = Add(Mul(x, x), Const(1))  # df/dy = x² + 1\n",
    "print(\"df/dx(3,4) =\", df_dx.evaluate())\n",
    "print(\"df/dy(3,4) =\", df_dy.evaluate())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Numerical differentiation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "df/dx(3,4) = 24.000400000048216\n",
      "df/dy(3,4) = 10.000000000047748\n"
     ]
    }
   ],
   "source": [
    "def gradients(func, vars_list, eps=0.0001):\n",
    "    partial_derivatives = []\n",
    "    base_func_eval = func.evaluate()\n",
    "    for var in vars_list:\n",
    "        original_value = var.value\n",
    "        var.value = var.value + eps\n",
    "        tweaked_func_eval = func.evaluate()\n",
    "        var.value = original_value\n",
    "        derivative = (tweaked_func_eval - base_func_eval) / eps\n",
    "        partial_derivatives.append(derivative)\n",
    "    return partial_derivatives\n",
    "\n",
    "df_dx, df_dy = gradients(f, [x, y])\n",
    "print(\"df/dx(3,4) =\", df_dx)\n",
    "print(\"df/dy(3,4) =\", df_dy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Symbolic differentiation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "df/dx(3,4) = 24.0\n",
      "df/dy(3,4) = 10.0\n"
     ]
    }
   ],
   "source": [
    "Const.derive = lambda self, var: Const(0)\n",
    "Var.derive = lambda self, var: Const(1) if self is var else Const(0)\n",
    "Add.derive = lambda self, var: Add(self.a.derive(var), self.b.derive(var))\n",
    "Mul.derive = lambda self, var: Add(Mul(self.a, self.b.derive(var)), Mul(self.a.derive(var), self.b))\n",
    "\n",
    "x = Var(3.0, name=\"x\")\n",
    "y = Var(4.0, name=\"y\")\n",
    "f = Add(Mul(Mul(x, x), y), Add(y, Const(2))) # f(x,y) = x²y + y + 2\n",
    "\n",
    "df_dx = f.derive(x)  # 2xy\n",
    "df_dy = f.derive(y)  # x² + 1\n",
    "print(\"df/dx(3,4) =\", df_dx.evaluate())\n",
    "print(\"df/dy(3,4) =\", df_dy.evaluate())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Automatic differentiation (autodiff) – forward mode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "class DualNumber(object):\n",
    "    def __init__(self, value=0.0, eps=0.0):\n",
    "        self.value = value\n",
    "        self.eps = eps\n",
    "    def __add__(self, b):\n",
    "        return DualNumber(self.value + self.to_dual(b).value,\n",
    "                          self.eps + self.to_dual(b).eps)\n",
    "    def __radd__(self, a):\n",
    "        return self.to_dual(a).__add__(self)\n",
    "    def __mul__(self, b):\n",
    "        return DualNumber(self.value * self.to_dual(b).value,\n",
    "                          self.eps * self.to_dual(b).value + self.value * self.to_dual(b).eps)\n",
    "    def __rmul__(self, a):\n",
    "        return self.to_dual(a).__mul__(self)\n",
    "    def __str__(self):\n",
    "        if self.eps:\n",
    "            return \"{:.1f} + {:.1f}ε\".format(self.value, self.eps)\n",
    "        else:\n",
    "            return \"{:.1f}\".format(self.value)\n",
    "    def __repr__(self):\n",
    "        return str(self)\n",
    "    @classmethod\n",
    "    def to_dual(cls, n):\n",
    "        if hasattr(n, \"value\"):\n",
    "            return n\n",
    "        else:\n",
    "            return cls(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "$3 + (3 + 4 \\epsilon) = 6 + 4\\epsilon$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.0 + 4.0ε"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3 + DualNumber(3, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "$(3 + 4ε)\\times(5 + 7ε) = 3 \\times 5 + 3 \\times 7ε + 4ε \\times 5 + 4ε \\times 7ε = 15 + 21ε + 20ε + 28ε^2 = 15 + 41ε + 28 \\times 0 = 15 + 41ε$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.0 + 41.0ε"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DualNumber(3, 4) * DualNumber(5, 7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42.0"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.value = DualNumber(3.0)\n",
    "y.value = DualNumber(4.0)\n",
    "\n",
    "f.evaluate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "x.value = DualNumber(3.0, 1.0)  # 3 + ε\n",
    "y.value = DualNumber(4.0)       # 4\n",
    "\n",
    "df_dx = f.evaluate().eps\n",
    "\n",
    "x.value = DualNumber(3.0)       # 3\n",
    "y.value = DualNumber(4.0, 1.0)  # 4 + ε\n",
    "\n",
    "df_dy = f.evaluate().eps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24.0"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_dx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.0"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_dy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Autodiff – Reverse mode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f(x,y) = ((x) * (x)) * (y) + y + 2\n",
      "f(3,4) = 42\n",
      "df_dx = 24.0\n",
      "df_dy = 10.0\n"
     ]
    }
   ],
   "source": [
    "class Const(object):\n",
    "    def __init__(self, value):\n",
    "        self.value = value\n",
    "    def evaluate(self):\n",
    "        return self.value\n",
    "    def backpropagate(self, gradient):\n",
    "        pass\n",
    "    def __str__(self):\n",
    "        return str(self.value)\n",
    "\n",
    "class Var(object):\n",
    "    def __init__(self, init_value, name):\n",
    "        self.value = init_value\n",
    "        self.name = name\n",
    "        self.gradient = 0\n",
    "    def evaluate(self):\n",
    "        return self.value\n",
    "    def backpropagate(self, gradient):\n",
    "        self.gradient += gradient\n",
    "    def __str__(self):\n",
    "        return self.name\n",
    "\n",
    "class BinaryOperator(object):\n",
    "    def __init__(self, a, b):\n",
    "        self.a = a\n",
    "        self.b = b\n",
    "\n",
    "class Add(BinaryOperator):\n",
    "    def evaluate(self):\n",
    "        self.value = self.a.evaluate() + self.b.evaluate()\n",
    "        return self.value\n",
    "    def backpropagate(self, gradient):\n",
    "        self.a.backpropagate(gradient)\n",
    "        self.b.backpropagate(gradient)\n",
    "    def __str__(self):\n",
    "        return \"{} + {}\".format(self.a, self.b)\n",
    "\n",
    "class Mul(BinaryOperator):\n",
    "    def evaluate(self):\n",
    "        self.value = self.a.evaluate() * self.b.evaluate()\n",
    "        return self.value\n",
    "    def backpropagate(self, gradient):\n",
    "        self.a.backpropagate(gradient * self.b.value)\n",
    "        self.b.backpropagate(gradient * self.a.value)\n",
    "    def __str__(self):\n",
    "        return \"({}) * ({})\".format(self.a, self.b)\n",
    "\n",
    "x = Var(3, name=\"x\")\n",
    "y = Var(4, name=\"y\")\n",
    "f = Add(Mul(Mul(x, x), y), Add(y, Const(2))) # f(x,y) = x²y + y + 2\n",
    "\n",
    "result = f.evaluate()\n",
    "f.backpropagate(1.0)\n",
    "\n",
    "print(\"f(x,y) =\", f)\n",
    "print(\"f(3,4) =\", result)\n",
    "print(\"df_dx =\", x.gradient)\n",
    "print(\"df_dy =\", y.gradient)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Autodiff – reverse mode (using TensorFlow)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(42.0, [24.0, 10.0])"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reset_graph()\n",
    "\n",
    "x = tf.Variable(3., name=\"x\")\n",
    "y = tf.Variable(4., name=\"y\")\n",
    "f = x*x*y + y + 2\n",
    "\n",
    "gradients = tf.gradients(f, [x, y])\n",
    "\n",
    "init = tf.global_variables_initializer()\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    init.run()\n",
    "    f_val, gradients_val = sess.run([f, gradients])\n",
    "\n",
    "f_val, gradients_val"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Exercise solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## 1. to 11."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "See appendix A."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## 12. Logistic Regression with Mini-Batch Gradient Descent using TensorFlow"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "First, let's create the moons dataset using Scikit-Learn's `make_moons()` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_moons\n",
    "\n",
    "m = 1000\n",
    "X_moons, y_moons = make_moons(m, noise=0.1, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's take a peek at the dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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i7qQkM9ZfgJHABygh0YrCmHsnarJaERDAR5pGet263F6vntsktO/4cYL27EHr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\nrQDSUMbD3M2dNI65HtK/SCf90nSbN+CQO8ijSRmGaEQoLTArzqTN1Jy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4/ADDzh+GvEBS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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f96d104cef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_moons[y_moons == 1, 0], X_moons[y_moons == 1, 1], 'go', label=\"Positive\")\n",
    "plt.plot(X_moons[y_moons == 0, 0], X_moons[y_moons == 0, 1], 'r^', label=\"Negative\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "We must not forget to add an extra bias feature ($x_0 = 1$) to every instance. For this, we just need to add a column full of 1s on the left of the input matrix $\\mathbf{X}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X_moons_with_bias = np.c_[np.ones((m, 1)), X_moons]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's check:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        , -0.05146968,  0.44419863],\n",
       "       [ 1.        ,  1.03201691, -0.41974116],\n",
       "       [ 1.        ,  0.86789186, -0.25482711],\n",
       "       [ 1.        ,  0.288851  , -0.44866862],\n",
       "       [ 1.        , -0.83343911,  0.53505665]])"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_moons_with_bias[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Looks good. Now let's reshape `y_train` to make it a column vector (i.e. a 2D array with a single column):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "y_moons_column_vector = y_moons.reshape(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now let's split the data into a training set and a test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "test_ratio = 0.2\n",
    "test_size = int(m * test_ratio)\n",
    "X_train = X_moons_with_bias[:-test_size]\n",
    "X_test = X_moons_with_bias[-test_size:]\n",
    "y_train = y_moons_column_vector[:-test_size]\n",
    "y_test = y_moons_column_vector[-test_size:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Ok, now let's create a small function to generate training batches. In this implementation we will just pick random instances from the training set for each batch. This means that a single batch may contain the same instance multiple times, and also a single epoch may not cover all the training instances (in fact it will generally cover only about two thirds of the instances). However, in practice this is not an issue and it simplifies the code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def random_batch(X_train, y_train, batch_size):\n",
    "    rnd_indices = np.random.randint(0, len(X_train), batch_size)\n",
    "    X_batch = X_train[rnd_indices]\n",
    "    y_batch = y_train[rnd_indices]\n",
    "    return X_batch, y_batch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's look at a small batch:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  1.93189866,  0.13158788],\n",
       "       [ 1.        ,  1.07172763,  0.13482039],\n",
       "       [ 1.        , -1.01148674, -0.04686381],\n",
       "       [ 1.        ,  0.02201868,  0.19079139],\n",
       "       [ 1.        , -0.98941204,  0.02473116]])"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_batch, y_batch = random_batch(X_train, y_train, 5)\n",
    "X_batch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [0],\n",
       "       [0],\n",
       "       [1],\n",
       "       [0]])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_batch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Great! Now that the data is ready to be fed to the model, we need to build that model. Let's start with a simple implementation, then we will add all the bells and whistles."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "First let's reset the default graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The _moons_ dataset has two input features, since each instance is a point on a plane (i.e., 2-Dimensional):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "n_inputs = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now let's build the Logistic Regression model. As we saw in chapter 4, this model first computes a weighted sum of the inputs (just like the Linear Regression model), and then it applies the sigmoid function to the result, which gives us the estimated probability for the positive class:\n",
    "\n",
    "$\\hat{p} = h_\\mathbf{\\theta}(\\mathbf{x}) = \\sigma(\\mathbf{\\theta}^T \\cdot \\mathbf{x})$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Recall that $\\mathbf{\\theta}$ is the parameter vector, containing the bias term $\\theta_0$ and the weights $\\theta_1, \\theta_2, \\dots, \\theta_n$. The input vector $\\mathbf{x}$ contains a constant term $x_0 = 1$, as well as all the input features $x_1, x_2, \\dots, x_n$.\n",
    "\n",
    "Since we want to be able to make predictions for multiple instances at a time, we will use an input matrix $\\mathbf{X}$ rather than a single input vector. The $i^{th}$ row will contain the transpose of the $i^{th}$ input vector $(\\mathbf{x}^{(i)})^T$. It is then possible to estimate the probability that each instance belongs to the positive class using the following equation:\n",
    "\n",
    "$ \\hat{\\mathbf{p}} = \\sigma(\\mathbf{X} \\cdot \\mathbf{\\theta})$\n",
    "\n",
    "That's all we need to build the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X = tf.placeholder(tf.float32, shape=(None, n_inputs + 1), name=\"X\")\n",
    "y = tf.placeholder(tf.float32, shape=(None, 1), name=\"y\")\n",
    "theta = tf.Variable(tf.random_uniform([n_inputs + 1, 1], -1.0, 1.0, seed=42), name=\"theta\")\n",
    "logits = tf.matmul(X, theta, name=\"logits\")\n",
    "y_proba = 1 / (1 + tf.exp(-logits))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "In fact, TensorFlow has a nice function `tf.sigmoid()` that we can use to simplify the last line of the previous code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "y_proba = tf.sigmoid(logits)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "As we saw in chapter 4, the log loss is a good cost function to use for Logistic Regression:\n",
    "\n",
    "$J(\\mathbf{\\theta}) = -\\dfrac{1}{m} \\sum\\limits_{i=1}^{m}{\\left[ y^{(i)} log\\left(\\hat{p}^{(i)}\\right) + (1 - y^{(i)}) log\\left(1 - \\hat{p}^{(i)}\\right)\\right]}$\n",
    "\n",
    "One option is to implement it ourselves:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "epsilon = 1e-7  # to avoid an overflow when computing the log\n",
    "loss = -tf.reduce_mean(y * tf.log(y_proba + epsilon) + (1 - y) * tf.log(1 - y_proba + epsilon))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "But we might as well use TensorFlow's `tf.losses.log_loss()` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "loss = tf.losses.log_loss(y, y_proba)  # uses epsilon = 1e-7 by default"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The rest is pretty standard: let's create the optimizer and tell it to minimize the cost function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "learning_rate = 0.01\n",
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
    "training_op = optimizer.minimize(loss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "All we need now (in this minimal version) is the variable initializer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "init = tf.global_variables_initializer()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "And we are ready to train the model and use it for predictions!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "There's really nothing special about this code, it's virtually the same as the one we used earlier for Linear Regression:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 0 \tLoss: 0.792602\n",
      "Epoch: 100 \tLoss: 0.343463\n",
      "Epoch: 200 \tLoss: 0.30754\n",
      "Epoch: 300 \tLoss: 0.292889\n",
      "Epoch: 400 \tLoss: 0.285336\n",
      "Epoch: 500 \tLoss: 0.280478\n",
      "Epoch: 600 \tLoss: 0.278083\n",
      "Epoch: 700 \tLoss: 0.276154\n",
      "Epoch: 800 \tLoss: 0.27552\n",
      "Epoch: 900 \tLoss: 0.274912\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 1000\n",
    "batch_size = 50\n",
    "n_batches = int(np.ceil(m / batch_size))\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)\n",
    "\n",
    "    for epoch in range(n_epochs):\n",
    "        for batch_index in range(n_batches):\n",
    "            X_batch, y_batch = random_batch(X_train, y_train, batch_size)\n",
    "            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
    "        loss_val = loss.eval({X: X_test, y: y_test})\n",
    "        if epoch % 100 == 0:\n",
    "            print(\"Epoch:\", epoch, \"\\tLoss:\", loss_val)\n",
    "\n",
    "    y_proba_val = y_proba.eval(feed_dict={X: X_test, y: y_test})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Note: we don't use the epoch number when generating batches, so we could just have a single `for` loop rather than 2 nested `for` loops, but it's convenient to think of training time in terms of number of epochs (i.e., roughly the number of times the algorithm went through the training set)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "For each instance in the test set, `y_proba_val` contains the estimated probability that it belongs to the positive class, according to the model. For example, here are the first 5 estimated probabilities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.54895616],\n",
       "       [ 0.70724374],\n",
       "       [ 0.51900256],\n",
       "       [ 0.9911136 ],\n",
       "       [ 0.50859052]], dtype=float32)"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_proba_val[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "To classify each instance, we can go for maximum likelihood: classify as positive any instance whose estimated probability is greater or equal to 0.5:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True],\n",
       "       [ True],\n",
       "       [ True],\n",
       "       [ True],\n",
       "       [ True]], dtype=bool)"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = (y_proba_val >= 0.5)\n",
    "y_pred[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Depending on the use case, you may want to choose a different threshold than 0.5: make it higher if you want high precision (but lower recall), and make it lower if you want high recall (but lower precision). See chapter 3 for more details."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's compute the model's precision and recall:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.86274509803921573"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import precision_score, recall_score\n",
    "\n",
    "precision_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.88888888888888884"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recall_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's plot these predictions to see what they look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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o6W/luUSgtKyUgfcOZFH6IoqzilmUvoiB9w6ktKw02qLFHuFolki8qGczh0R+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\nykEQBEHwQpSDIAiC4MX/B4BXNRO7H//+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f96d0e11f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred_idx = y_pred.reshape(-1) # a 1D array rather than a column vector\n",
    "plt.plot(X_test[y_pred_idx, 1], X_test[y_pred_idx, 2], 'go', label=\"Positive\")\n",
    "plt.plot(X_test[~y_pred_idx, 1], X_test[~y_pred_idx, 2], 'r^', label=\"Negative\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Well, that looks pretty bad, doesn't it? But let's not forget that the Logistic Regression model has a linear decision boundary, so this is actually close to the best we can do with this model (unless we add more features, as we will show in a second)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now let's start over, but this time we will add all the bells and whistles, as listed in the exercise:\n",
    "* Define the graph within a `logistic_regression()` function that can be reused easily.\n",
    "* Save checkpoints using a `Saver` at regular intervals during training, and save the final model at the end of training.\n",
    "* Restore the last checkpoint upon startup if training was interrupted.\n",
    "* Define the graph using nice scopes so the graph looks good in TensorBoard.\n",
    "* Add summaries to visualize the learning curves in TensorBoard.\n",
    "* Try tweaking some hyperparameters such as the learning rate or the mini-batch size and look at the shape of the learning curve."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Before we start, we will add 4 more features to the inputs: ${x_1}^2$, ${x_2}^2$, ${x_1}^3$ and ${x_2}^3$. This was not part of the exercise, but it will demonstrate how adding features can improve the model. We will do this manually, but you could also add them using `sklearn.preprocessing.PolynomialFeatures`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X_train_enhanced = np.c_[X_train,\n",
    "                         np.square(X_train[:, 1]),\n",
    "                         np.square(X_train[:, 2]),\n",
    "                         X_train[:, 1] ** 3,\n",
    "                         X_train[:, 2] ** 3]\n",
    "X_test_enhanced = np.c_[X_test,\n",
    "                        np.square(X_test[:, 1]),\n",
    "                        np.square(X_test[:, 2]),\n",
    "                        X_test[:, 1] ** 3,\n",
    "                        X_test[:, 2] ** 3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "This is what the \"enhanced\" training set looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1.00000000e+00,  -5.14696757e-02,   4.44198631e-01,\n",
       "          2.64912752e-03,   1.97312424e-01,  -1.36349734e-04,\n",
       "          8.76459084e-02],\n",
       "       [  1.00000000e+00,   1.03201691e+00,  -4.19741157e-01,\n",
       "          1.06505890e+00,   1.76182639e-01,   1.09915879e+00,\n",
       "         -7.39511049e-02],\n",
       "       [  1.00000000e+00,   8.67891864e-01,  -2.54827114e-01,\n",
       "          7.53236288e-01,   6.49368582e-02,   6.53727646e-01,\n",
       "         -1.65476722e-02],\n",
       "       [  1.00000000e+00,   2.88850997e-01,  -4.48668621e-01,\n",
       "          8.34348982e-02,   2.01303531e-01,   2.41002535e-02,\n",
       "         -9.03185778e-02],\n",
       "       [  1.00000000e+00,  -8.33439108e-01,   5.35056649e-01,\n",
       "          6.94620746e-01,   2.86285618e-01,  -5.78924095e-01,\n",
       "          1.53179024e-01]])"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train_enhanced[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Ok, next let's reset the default graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "reset_graph()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now let's define the `logistic_regression()` function to create the graph. We will leave out the definition of the inputs `X` and the targets `y`. We could include them here, but leaving them out will make it easier to use this function in a wide range of use cases (e.g. perhaps we will want to add some preprocessing steps for the inputs before we feed them to the Logistic Regression model)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def logistic_regression(X, y, initializer=None, seed=42, learning_rate=0.01):\n",
    "    n_inputs_including_bias = int(X.get_shape()[1])\n",
    "    with tf.name_scope(\"logistic_regression\"):\n",
    "        with tf.name_scope(\"model\"):\n",
    "            if initializer is None:\n",
    "                initializer = tf.random_uniform([n_inputs_including_bias, 1], -1.0, 1.0, seed=seed)\n",
    "            theta = tf.Variable(initializer, name=\"theta\")\n",
    "            logits = tf.matmul(X, theta, name=\"logits\")\n",
    "            y_proba = tf.sigmoid(logits)\n",
    "        with tf.name_scope(\"train\"):\n",
    "            loss = tf.losses.log_loss(y, y_proba, scope=\"loss\")\n",
    "            optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate)\n",
    "            training_op = optimizer.minimize(loss)\n",
    "            loss_summary = tf.summary.scalar('log_loss', loss)\n",
    "        with tf.name_scope(\"init\"):\n",
    "            init = tf.global_variables_initializer()\n",
    "        with tf.name_scope(\"save\"):\n",
    "            saver = tf.train.Saver()\n",
    "    return y_proba, loss, training_op, loss_summary, init, saver"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Let's create a little function to get the name of the log directory to save the summaries for Tensorboard:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "from datetime import datetime\n",
    "\n",
    "def log_dir(prefix=\"\"):\n",
    "    now = datetime.utcnow().strftime(\"%Y%m%d%H%M%S\")\n",
    "    root_logdir = \"tf_logs\"\n",
    "    if prefix:\n",
    "        prefix += \"-\"\n",
    "    name = prefix + \"run-\" + now\n",
    "    return \"{}/{}/\".format(root_logdir, name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Next, let's create the graph, using the `logistic_regression()` function. We will also create the `FileWriter` to save the summaries to the log directory for Tensorboard:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "n_inputs = 2 + 4\n",
    "logdir = log_dir(\"logreg\")\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, n_inputs + 1), name=\"X\")\n",
    "y = tf.placeholder(tf.float32, shape=(None, 1), name=\"y\")\n",
    "\n",
    "y_proba, loss, training_op, loss_summary, init, saver = logistic_regression(X, y)\n",
    "\n",
    "file_writer = tf.summary.FileWriter(logdir, tf.get_default_graph())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "At last we can train the model! We will start by checking whether a previous training session was interrupted, and if so we will load the checkpoint and continue training from the epoch number we saved. In this example we just save the epoch number to a separate file, but in chapter 11 we will see how to store the training step directly as part of the model, using a non-trainable variable called `global_step` that we pass to the optimizer's `minimize()` method.\n",
    "\n",
    "You can try interrupting training to verify that it does indeed restore the last checkpoint when you start it again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 0 \tLoss: 0.629985\n",
      "Epoch: 500 \tLoss: 0.161224\n",
      "Epoch: 1000 \tLoss: 0.119032\n",
      "Epoch: 1500 \tLoss: 0.0973292\n",
      "Epoch: 2000 \tLoss: 0.0836979\n",
      "Epoch: 2500 \tLoss: 0.0743758\n",
      "Epoch: 3000 \tLoss: 0.0675021\n",
      "Epoch: 3500 \tLoss: 0.0622069\n",
      "Epoch: 4000 \tLoss: 0.0580268\n",
      "Epoch: 4500 \tLoss: 0.054563\n",
      "Epoch: 5000 \tLoss: 0.0517083\n",
      "Epoch: 5500 \tLoss: 0.0492377\n",
      "Epoch: 6000 \tLoss: 0.0471673\n",
      "Epoch: 6500 \tLoss: 0.0453766\n",
      "Epoch: 7000 \tLoss: 0.0438187\n",
      "Epoch: 7500 \tLoss: 0.0423742\n",
      "Epoch: 8000 \tLoss: 0.0410892\n",
      "Epoch: 8500 \tLoss: 0.0399709\n",
      "Epoch: 9000 \tLoss: 0.0389202\n",
      "Epoch: 9500 \tLoss: 0.0380107\n",
      "Epoch: 10000 \tLoss: 0.0371557\n"
     ]
    }
   ],
   "source": [
    "n_epochs = 10001\n",
    "batch_size = 50\n",
    "n_batches = int(np.ceil(m / batch_size))\n",
    "\n",
    "checkpoint_path = \"/tmp/my_logreg_model.ckpt\"\n",
    "checkpoint_epoch_path = checkpoint_path + \".epoch\"\n",
    "final_model_path = \"./my_logreg_model\"\n",
    "\n",
    "with tf.Session() as sess:\n",
    "    if os.path.isfile(checkpoint_epoch_path):\n",
    "        # if the checkpoint file exists, restore the model and load the epoch number\n",
    "        with open(checkpoint_epoch_path, \"rb\") as f:\n",
    "            start_epoch = int(f.read())\n",
    "        print(\"Training was interrupted. Continuing at epoch\", start_epoch)\n",
    "        saver.restore(sess, checkpoint_path)\n",
    "    else:\n",
    "        start_epoch = 0\n",
    "        sess.run(init)\n",
    "\n",
    "    for epoch in range(start_epoch, n_epochs):\n",
    "        for batch_index in range(n_batches):\n",
    "            X_batch, y_batch = random_batch(X_train_enhanced, y_train, batch_size)\n",
    "            sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
    "        loss_val, summary_str = sess.run([loss, loss_summary], feed_dict={X: X_test_enhanced, y: y_test})\n",
    "        file_writer.add_summary(summary_str, epoch)\n",
    "        if epoch % 500 == 0:\n",
    "            print(\"Epoch:\", epoch, \"\\tLoss:\", loss_val)\n",
    "            saver.save(sess, checkpoint_path)\n",
    "            with open(checkpoint_epoch_path, \"wb\") as f:\n",
    "                f.write(b\"%d\" % (epoch + 1))\n",
    "\n",
    "    saver.save(sess, final_model_path)\n",
    "    y_proba_val = y_proba.eval(feed_dict={X: X_test_enhanced, y: y_test})\n",
    "    os.remove(checkpoint_epoch_path)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Once again, we can make predictions by just classifying as positive all the instances whose estimated probability is greater or equal to 0.5:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "y_pred = (y_proba_val >= 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.97979797979797978"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precision_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.97979797979797978"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recall_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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yeiSL5vpNOhscnoN8OIO7zDy9SZfZZ7TKQWorJYB0r5E0dfbUesUA0BTKzy9n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\nOdVQChswFEMrkrLvkgFRDkL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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f96d29e95f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred_idx = y_pred.reshape(-1) # a 1D array rather than a column vector\n",
    "plt.plot(X_test[y_pred_idx, 1], X_test[y_pred_idx, 2], 'go', label=\"Positive\")\n",
    "plt.plot(X_test[~y_pred_idx, 1], X_test[~y_pred_idx, 2], 'r^', label=\"Negative\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now that's much, much better! Apparently the new features really helped a lot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Try starting the tensorboard server, find the latest run and look at the learning curve (i.e., how the loss evaluated on the test set evolves as a function of the epoch number):\n",
    "\n",
    "```\n",
    "$ tensorboard --logdir=tf_logs\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Now you can play around with the hyperparameters (e.g. the `batch_size` or the `learning_rate`) and run training again and again, comparing the learning curves. You can even automate this process by implementing grid search or randomized search. Below is a simple implementation of a randomized search on both the batch size and the learning rate. For the sake of simplicity, the checkpoint mechanism was removed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0\n",
      "  logdir: tf_logs/logreg-run-20170606195328/\n",
      "  batch size: 19\n",
      "  learning_rate: 0.00443037524522\n",
      "  training: .....................\n",
      "  precision: 0.979797979798\n",
      "  recall: 0.979797979798\n",
      "Iteration 1\n",
      "  logdir: tf_logs/logreg-run-20170606195605/\n",
      "  batch size: 80\n",
      "  learning_rate: 0.00178264971514\n",
      "  training: .....................\n",
      "  precision: 0.969696969697\n",
      "  recall: 0.969696969697\n",
      "Iteration 2\n",
      "  logdir: tf_logs/logreg-run-20170606195646/\n",
      "  batch size: 73\n",
      "  learning_rate: 0.00203228544324\n",
      "  training: .....................\n",
      "  precision: 0.969696969697\n",
      "  recall: 0.969696969697\n",
      "Iteration 3\n",
      "  logdir: tf_logs/logreg-run-20170606195730/\n",
      "  batch size: 6\n",
      "  learning_rate: 0.00449152382514\n",
      "  training: .....................\n",
      "  precision: 0.980198019802\n",
      "  recall: 1.0\n",
      "Iteration 4\n",
      "  logdir: tf_logs/logreg-run-20170606200523/\n",
      "  batch size: 24\n",
      "  learning_rate: 0.0796323472178\n",
      "  training: .....................\n",
      "  precision: 0.980198019802\n",
      "  recall: 1.0\n",
      "Iteration 5\n",
      "  logdir: tf_logs/logreg-run-20170606200726/\n",
      "  batch size: 75\n",
      "  learning_rate: 0.000463425058329\n",
      "  training: .....................\n",
      "  precision: 0.912621359223\n",
      "  recall: 0.949494949495\n",
      "Iteration 6\n",
      "  logdir: tf_logs/logreg-run-20170606200810/\n",
      "  batch size: 86\n",
      "  learning_rate: 0.0477068184194\n",
      "  training: .....................\n",
      "  precision: 0.98\n",
      "  recall: 0.989898989899\n",
      "Iteration 7\n",
      "  logdir: tf_logs/logreg-run-20170606200851/\n",
      "  batch size: 87\n",
      "  learning_rate: 0.000169404470952\n",
      "  training: .....................\n",
      "  precision: 0.888888888889\n",
      "  recall: 0.808080808081\n",
      "Iteration 8\n",
      "  logdir: tf_logs/logreg-run-20170606200932/\n",
      "  batch size: 61\n",
      "  learning_rate: 0.0417146119941\n",
      "  training: .....................\n",
      "  precision: 0.980198019802\n",
      "  recall: 1.0\n",
      "Iteration 9\n",
      "  logdir: tf_logs/logreg-run-20170606201026/\n",
      "  batch size: 92\n",
      "  learning_rate: 0.000107429229684\n",
      "  training: .....................\n",
      "  precision: 0.882352941176\n",
      "  recall: 0.757575757576\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import reciprocal\n",
    "\n",
    "n_search_iterations = 10\n",
    "\n",
    "for search_iteration in range(n_search_iterations):\n",
    "    batch_size = np.random.randint(1, 100)\n",
    "    learning_rate = reciprocal(0.0001, 0.1).rvs(random_state=search_iteration)\n",
    "\n",
    "    n_inputs = 2 + 4\n",
    "    logdir = log_dir(\"logreg\")\n",
    "    \n",
    "    print(\"Iteration\", search_iteration)\n",
    "    print(\"  logdir:\", logdir)\n",
    "    print(\"  batch size:\", batch_size)\n",
    "    print(\"  learning_rate:\", learning_rate)\n",
    "    print(\"  training: \", end=\"\")\n",
    "\n",
    "    reset_graph()\n",
    "\n",
    "    X = tf.placeholder(tf.float32, shape=(None, n_inputs + 1), name=\"X\")\n",
    "    y = tf.placeholder(tf.float32, shape=(None, 1), name=\"y\")\n",
    "\n",
    "    y_proba, loss, training_op, loss_summary, init, saver = logistic_regression(\n",
    "        X, y, learning_rate=learning_rate)\n",
    "\n",
    "    file_writer = tf.summary.FileWriter(logdir, tf.get_default_graph())\n",
    "\n",
    "    n_epochs = 10001\n",
    "    n_batches = int(np.ceil(m / batch_size))\n",
    "\n",
    "    final_model_path = \"./my_logreg_model_%d\" % search_iteration\n",
    "\n",
    "    with tf.Session() as sess:\n",
    "        sess.run(init)\n",
    "\n",
    "        for epoch in range(n_epochs):\n",
    "            for batch_index in range(n_batches):\n",
    "                X_batch, y_batch = random_batch(X_train_enhanced, y_train, batch_size)\n",
    "                sess.run(training_op, feed_dict={X: X_batch, y: y_batch})\n",
    "            loss_val, summary_str = sess.run([loss, loss_summary], feed_dict={X: X_test_enhanced, y: y_test})\n",
    "            file_writer.add_summary(summary_str, epoch)\n",
    "            if epoch % 500 == 0:\n",
    "                print(\".\", end=\"\")\n",
    "\n",
    "        saver.save(sess, final_model_path)\n",
    "\n",
    "        print()\n",
    "        y_proba_val = y_proba.eval(feed_dict={X: X_test_enhanced, y: y_test})\n",
    "        y_pred = (y_proba_val >= 0.5)\n",
    "        \n",
    "        print(\"  precision:\", precision_score(y_test, y_pred))\n",
    "        print(\"  recall:\", recall_score(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The `reciprocal()` function from SciPy's `stats` module returns a random distribution that is commonly used when you have no idea of the optimal scale of a hyperparameter. See the exercise solutions for chapter 2 for more details. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": []
  }
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