Assignment1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Assignment 1: Face-Classification Three-Ways\n",
    "\n",
    "In this assignment you will implement a face classifier and train it using three different approaches:\n",
    "* Logistic Regression using Stochastic Gradient Descent\n",
    "* Logistic Regression using Newton's Method\n",
    "* Gaussian Discriminant Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup\n",
    "\n",
    "First import the required packages and do some setup:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "\n",
    "import time\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.io import loadmat\n",
    "from sklearn.model_selection import train_test_split\n",
    "from assignment1 import sigmoid, cost_function, gradient_function, logistic_SGD, logistic_Newton, gda, predict_function\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "# Set default parameters for plots\n",
    "plt.rcParams['figure.figsize'] = (12.0, 6.0)\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "plt.rcParams['image.cmap'] = 'gray'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now load the data set. It consists of 19'832 grayscale images of size 24 x 24. Each image has a corresponding label which we set to 0 for non-face and 1 for face."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Load the dataset\n",
    "data = loadmat('faces.mat')\n",
    "labels = np.squeeze(data['Labels'])\n",
    "labels[labels == -1] = 0    # Want labels in {0, 1}\n",
    "data = data['Data']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We divide the dataset into two subsets: One for training and one for testing. This approach is called cross-validation and is standard practice in Machine Learning.\n",
    "The classifier will be learnt only on the data in the training set! The test set then gives you an estimate of how well the classifier will perform on new unseen data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training data shape:  (13882, 576)\n",
      "Training labels shape:  (13882,)\n",
      "Test data shape:  (5950, 576)\n",
      "Test labels shape:  (5950,)\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(data, labels, test_size=0.3)\n",
    "num_train = X_train.shape[0]\n",
    "num_test = X_test.shape[0]\n",
    "\n",
    "# As a sanity check, we print out the size of the training and test data.\n",
    "print('Training data shape: ', X_train.shape)\n",
    "print('Training labels shape: ', y_train.shape)\n",
    "print('Test data shape: ', X_test.shape)\n",
    "print('Test labels shape: ', y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the images are stored as vectors now. Let's visualize some examples to check that the data is fine. We of course have to reshape the images first:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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YaNjlz+WIy4DLm6CLeczhVXADv8dEWKUo80An3CSQo7cbZmDM1C53ggDZHUyS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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x258e8b8f518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize some examples from the dataset.\n",
    "samples_per_class = 10\n",
    "classes = [0, 1]\n",
    "train_imgs = np.reshape(X_train, [-1, 24, 24], order='F')\n",
    "\n",
    "for y, cls in enumerate(classes):\n",
    "    idxs = np.flatnonzero(np.equal(y_train, cls))\n",
    "    idxs = np.random.choice(idxs, samples_per_class, replace=False)\n",
    "    for i, idx in enumerate(idxs):\n",
    "        plt_idx = y * samples_per_class + i + 1\n",
    "        plt.subplot(len(classes), samples_per_class, plt_idx)\n",
    "        plt.imshow(train_imgs[idx])\n",
    "        plt.axis('off')\n",
    "        plt.title(cls)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we add the intercept term by concatenating a vector of ones to the train and test data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Add intercept to X and normalize to range [0, 1]\n",
    "X_train = np.concatenate((np.ones((num_train, 1)), X_train/255.), axis=1)\n",
    "X_test = np.concatenate((np.ones((num_test, 1)), X_test/255.), axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 1: Sigmoid [5 Points]\n",
    "\n",
    "**TODO**: Implement the sigmoid function in ***assignment1/sigmoid.py*** according to the specifications. \n",
    "\n",
    "**NOTE**: The function should work with inputs of arbitrary shape!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JQsVERmjG9QVKiOG2DwDwEj+FAcADPr/THXOWaltFrWZPm6SctHivIwFA2KMY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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x258e8b5a5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Test your sigmoid\n",
    "z_test = np.arange(-5, 5, 0.01)\n",
    "g_test = sigmoid(z_test)\n",
    "plt.plot(z_test, g_test)\n",
    "plt.title('Sigmoid')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 2: Log-Likelihood [10 Points]\n",
    "\n",
    "**TODO**: Implement the log-likelihood for Logistic Regression in ***assignment1/cost_function.py*** according to specs.\n",
    "\n",
    "What value of the cost do you expect with a parameter vector *theta* of all zeros? Check your implementation for this!\n",
    "\n",
    "**Hint**: No for-loops are required! Use np.sum and np.dot instead..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Log-likelihood with initial theta:  399.945923183\n"
     ]
    }
   ],
   "source": [
    "# Test your cost-function\n",
    "theta_0 = np.zeros(X_train.shape[1])\n",
    "l_0 = cost_function(theta_0, X_train, y_train)\n",
    "print('Log-likelihood with initial theta: ', l_0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 3: The Gradient [10 Points]\n",
    "\n",
    "**TODO**: Implement the gradient of the log-likelihood for Logistic Regression in ***assignment1/gradient_function.py*** according to specs. \n",
    "\n",
    "**NOTE**: Your implementation should work with a single example x (i.e., a vector) or multiple examples X (i.e., a matrix).\n",
    "\n",
    "Consider again what value you would expect with *theta* equal to zero and test your implementation:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.  1.  1.  1.  1.  1.  1.  1.  1.  1.]\n"
     ]
    }
   ],
   "source": [
    "# Test your implementation\n",
    "x_test = np.ones([2, 10])\n",
    "theta_0 = np.zeros(10)\n",
    "grad_0 = gradient_function(theta_0, x_test, 1.0)\n",
    "print(grad_0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exersice 4: The Learning Algorithmms\n",
    "\n",
    "This is the main part of the assignment. Correctness of the implementation is required to get the points (work on speed later). \n",
    "\n",
    "## a) Logistic Regression with SGD [15 Points]\n",
    "\n",
    "**TODO**: Implement the function in ***assignment1/logistic_SGD.py*** according to specs.\n",
    "\n",
    "## b) Logistic Regression with Newton's Method [15 Points]\n",
    "\n",
    "**TODO**: Implement the fuction in ***assignment1/logistic_Newton.py*** according to specs.\n",
    "\n",
    "## c) Gaussian Discriminant Analysis [15 Points]\n",
    "\n",
    "**TODO**: Implement the function in ***assignment1/gda.py*** according to specs.\n",
    "\n",
    "\n",
    "\n",
    "***Hint***: No additional for-loops are required!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iter 0/10000: cost = 399.9434067488332  (0.01200246810913086s)\n",
      "Iter 1000/10000: cost = 399.37231897233306  (0.016002893447875977s)\n",
      "Iter 2000/10000: cost = 399.27404731814073  (0.01200413703918457s)\n",
      "Iter 3000/10000: cost = 399.23531780746777  (0.011998176574707031s)\n",
      "Iter 4000/10000: cost = 399.2190748947181  (0.031998634338378906s)\n",
      "Iter 5000/10000: cost = 399.2137538493539  (0.011995792388916016s)\n",
      "Iter 6000/10000: cost = 399.2142239624788  (0.012000560760498047s)\n",
      "Iter 7000/10000: cost = 399.21783743016977  (0.01199793815612793s)\n",
      "Iter 8000/10000: cost = 399.22311727731017  (0.015998363494873047s)\n",
      "Iter 9000/10000: cost = 399.22920275869245  (0.011995792388916016s)\n",
      "Total exection time: 153.7262682914734s\n"
     ]
    },
    {
     "data": {
      "image/png": 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vZ+2mdvr6XSJPkiTpRBzXah4ppd1AC3BNSqktpXR1Suli4MvA09k+vSmlG7M+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\nREVJkiaqcXsCYp4M0yo3T7y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      "text/plain": [
       "<matplotlib.figure.Figure at 0x258801c8a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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BwhoAEiCsASABwhoAEmhoIyczCzXriTR/ijYgmpiYKK6JNnIaHh4O1Z08ebK45ujRo6Gx\nnnrqqVDdgQMHimtmZmZCY23btq24Jrp/RJpGSVJbW1txze7du0NjRb8+b3Z2trhmZGQkNNaRI+Vf\nLhVt5BR9rKONtNYKR9YAkABhDQAJENYAkABhDQAJENYAkABhDQAJENYAkABhDQAJENYAkABhDQAJ\nENYAkABhDQAJENYAkEDDu+5Fuo9Ful+5e3GNJE1NTRXXDA0NhcaK6ujoKK6JdiyLdhQ8fvx4cU10\nO0b2j7m5udBY7e3tobrt27cX1/T19YXGOnjwYKjuueeeK66J7h+HDx8urpmeng6NFen0KcU6JW7Z\nsqW4ZtOm5R0zc2QNAAkQ1gCQAGENAAkQ1gCQAGENAAkQ1gCQAGENAAkQ1gCQAGENAAkQ1gCQAGEN\nAAkQ1gCQAGENAAk0vOtea2trqK5UtOve/Px8cc3Y2FhorKjINpycnAyNNTs7G6qLdIyLbHsp1ikx\nqre3N1TX399fXLN5c+zpOTIyEqpbWFgorpmYmAiNNT4+Xlyz3O50p4t2Sox061vLrqIcWQNAAoQ1\nACRAWANAAoQ1ACRAWANAAoQ1ACRAWANAAoQ1ACRAWANAAoQ1ACRAWANAAoQ1ACTQ0EZOUqxZTKTB\nT6ShihRrGhVp+CJJc3NzobpI46Lh4eHQWCdPngzVRZpNdXV1hcbaunVrqC4isn9I0ujoaHFNdNt3\ndHQ0tC4ikgPRhkyRfTEq0nyLRk4AsI4Q1gCQAGENAAksGdZmdquZHTGzh+qW3WhmB83swernTWs7\nTQDY2JZzZH2bpKvOsPzT7n5J9XP36k4LAFBvybB29/skHWvAXAAAi1jJOesPmNmPqtMk2xa7kpld\nb2b7zWx/o7+rEADWi2hYf17ShZIukXRI0icXu6K73+zu+9x9X09PT3A4ANjYQmHt7ofdfd7dFyR9\nQdJlqzstAEC9UFib2Y66P98q6aHFrgsAWLklPxtpZl+SdKWkATN7VtJHJV1pZpdIcklPSnrvGs4R\nADa8JcPa3a89w+Jb1mAuAIBF8AlGAEig4V33Ih3qIt3pIp36JGnTpvJ/v6Ld86KdASNzjHZwe+KJ\nJ0J1MzMzxTUDAwOhsc4555zimkjXN0mKvv000vUw0sFNkvbs2ROq6+3tLa6Jdpycnp4urol2PHT3\nUF0ju/UtB0fWAJAAYQ0ACRDWAJAAYQ0ACRDWAJAAYQ0ACRDWAJAAYQ0ACRDWAJAAYQ0ACRDWAJAA\nYQ0ACRDWAJBAQ7vumVmoY1yk+9jU1FRxTVTkPq1Ee3t7cc3g4GBorGPHYl9sf/DgweKaSCc2SZqc\nnCyumZ2dDY114sSJUF2kM2NfX19orK1bt4bqOjs7i2ui2zHScTLyOEvxbn2RjoJrmQUcWQNAAoQ1\nACRAWANAAoQ1ACRAWANAAoQ1ACRAWANAAoQ1ACRAWANAAoQ1ACRAWANAAoQ1ACTQ0EZOkuTujR6y\nyMzMTHFNpEnPSkQa7mzbti001uWXXx6qO3z4cHFNtJHT/Px8cU20AdHAwECorqurq7imv78/NNaW\nLVtCdZFGSaOjo6GxGvmYtba2huoiWRVpGrXcGo6sASABwhoAEiCsASABwhoAEiCsASABwhoAEiCs\nASABwhoAEiCsASABwhoAEiCsASABwhoAEiCsASCBhnfdi4h0tYt294uMFenUJ8W6nEXHi3ZwO++8\n80J1ke50jey6t7CwEBor2tGuvb29uCbaZW54eDhUd/z48eKakydPhsaK2Lw5FleR/UOKPT9bWlqK\na5abVRxZA0AChDUAJEBYA0AChDUAJEBYA0AChDUAJEBYA0AChDUAJEBYA0AChDUAJEBYA0AChDUA\nJNDwRk6RRidmtgYzObNII6doA6JoM6FIY5pIIyFJmpqaCtVFGkD19PSExmptbQ3VRUS3x9jYWHHN\n+Ph4aKyjR4+G6o4dO1ZcE22SFHnMojkQbQAVEWmyttwc4MgaABIgrAEgAcIaABJYMqzNbKeZfdvM\nHjazn5jZB6vl/WZ2j5n9tPq9be2nCwAb03KOrOckfdjd90p6laT3m9leSTdIutfdL5J0b/U3AGAN\nLBnW7n7I3X9YXR6T9Iik8yVdLen26mq3S7pmrSYJABtd0TlrM9st6VJJ35M06O6HqlVDkgYXqbne\nzPab2f7I25cAAAVhbWbdkr4q6UPuPlq/zmvf+HjGb31095vdfZ+774u+jxYANrplhbWZtaoW1He4\n+9eqxYfNbEe1foekI2szRQDAct4NYpJukfSIu3+qbtVdkq6rLl8n6eurPz0AgLS8j5v/qqR3Svqx\nmT1YLfuIpI9L+oqZvUfSU5LetjZTBAAsGdbu/h1Ji30o/3WrOx0AwJnwCUYASKChXffcPdTVLtI1\nq/YGlXKRsaJd36IdyyKdvSId1aRYl8RoXfQx6+zsLK6JdmKbmJgI1Q0PDxfXDA0NhcaKduuLPDfb\n2tpCY0WeM9HHLPr8jNy3yD683G6CHFkDQAKENQAkQFgDQAKENQAkQFgDQAKENQAkQFgDQAKENQAk\nQFgDQAKENQAkQFgDQAKENQAkQFgDQAIN7brX0tKirq6u4rpIp7PldrI6XWR+UVNTU6G62dnZ4prp\n6enQWJFucVKs81tHR0dorO7u7uKaaDfB0dHRpa90BpF9uJFjRTWyu2W06140CyL3rb29vbiGrnsA\nsI4Q1gCQAGENAAkQ1gCQAGENAAkQ1gCQAGENAAkQ1gCQAGENAAkQ1gCQAGENAAkQ1gCQQEMbOUnS\npk3l/z5Emu5ExpFizVvm5+dDYy0sLITq5ubmimsizZ8k6eTJk6G6mZmZ4prI/ZJiDX6i2z4qsg83\nunFRpJFWtPFZpC76nG5rawvVRR6zyFg0cgKAdYSwBoAECGsASICwBoAECGsASICwBoAECGsASICw\nBoAECGsASICwBoAECGsASICwBoAECGsASMAiXebCg5k9J+mpRVYPSDrasMmc/dgep2J7nIrtcarM\n22OXu5+71JUaGta/iJntd/d9zZ7H2YLtcSq2x6nYHqfaCNuD0yAAkABhDQAJnE1hfXOzJ3CWYXuc\niu1xKrbHqdb99jhrzlkDABZ3Nh1ZAwAW0fSwNrOrzOwxM3vczG5o9nyazcyeNLMfm9mDZra/2fNp\nNDO71cyOmNlDdcv6zeweM/tp9XtbM+fYSItsjxvN7GC1jzxoZm9q5hwbycx2mtm3zexhM/uJmX2w\nWr7u95GmhrWZtUj6nKQ3Stor6Voz29vMOZ0lXuvul6z3tyIt4jZJV5227AZJ97r7RZLurf7eKG7T\nC7eHJH262kcucfe7GzynZpqT9GF33yvpVZLeX2XGut9Hmn1kfZmkx939gLvPSPqypKubPCc0kbvf\nJ+nYaYuvlnR7dfl2Sdc0dFJNtMj22LDc/ZC7/7C6PCbpEUnnawPsI80O6/MlPVP397PVso3MJX3T\nzH5gZtc3ezJniUF3P1RdHpI02MzJnCU+YGY/qk6TrLv/8i+Hme2WdKmk72kD7CPNDmu80BXufolq\np4beb2avbvaEziZee/vSRn8L0+clXSjpEkmHJH2yudNpPDPrlvRVSR9y99H6det1H2l2WB+UtLPu\n7xdXyzYsdz9Y/T4i6U7VThVtdIfNbIckVb+PNHk+TeXuh9193t0XJH1BG2wfMbNW1YL6Dnf/WrV4\n3e8jzQ7r70u6yMxeYmZtkt4h6a4mz6lpzKzLzHqevyzpDZIe+sVVG8Jdkq6rLl8n6etNnEvTPR9K\nlbdqA+0jZmaSbpH0iLt/qm7Vut9Hmv6hmOptR38rqUXSre5+U1Mn1ERmdqFqR9OStFnSFzfa9jCz\nL0m6UrUuaoclfVTSP0v6iqQLVOva+DZ33xAvui2yPa5U7RSIS3pS0nvrzteua2Z2haT/kPRjSQvV\n4o+odt56Xe8jTQ9rAMDSmn0aBACwDIQ1ACRAWANAAoQ1ACRAWANAAoQ1ACRAWANAAoQ1ACTwf/Rs\nQr669BjqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x258801c86a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "method = 'sgd'\n",
    "\n",
    "# We'll meausure the execution time\n",
    "start = time.time()\n",
    "\n",
    "if method is 'sgd':\n",
    "    theta, losses = logistic_SGD(X_train, y_train)\n",
    "elif method is 'newton':\n",
    "    theta, losses = logistic_Newton(X_train, y_train)\n",
    "elif method is 'gda':\n",
    "    theta, losses = gda(X_train, y_train)\n",
    "else:\n",
    "    raise ValueError('Method not recognised!')\n",
    "\n",
    "exec_time = time.time()-start\n",
    "print('Total exection time: {}s'.format(exec_time))\n",
    "\n",
    "if losses:\n",
    "    plt.plot(losses)\n",
    "    plt.title('Training Log-Likelihood')\n",
    "    plt.show()\n",
    "\n",
    "# We can have a look at what theta has learned to recognise as \"face\"\n",
    "plt.imshow(np.reshape(theta[1:], [24, 24], order='F'))\n",
    "plt.title('Learned theta')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 6: Testing the Classifier [10 Points]\n",
    "\n",
    "**TODO**: Implement ***assignment1/predict_function.py*** according to specs. \n",
    "\n",
    "Test your implementation with the intial all zero theta as well! Does it match your expectation?\n",
    "\n",
    "***Hint***: All the methods should score above 90% on both the test and train set!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test accuracy: 0.9141176470588235\n",
      "Training accuracy: 0.9151419103875522\n"
     ]
    }
   ],
   "source": [
    "# Test the final classifier\n",
    "pred_test, accuracy_test = predict_function(theta, X_test, y_test)\n",
    "pred_train, accuracy_train = predict_function(theta, X_train, y_train)\n",
    "print('Test accuracy: {}'.format(accuracy_test))\n",
    "print('Training accuracy: {}'.format(accuracy_train))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 7: Discussion [20 Points]\n",
    "\n",
    "Answer the following questions and justify your answers:\n",
    "\n",
    "* Based on your results, which classifier do you prefer and why?\n",
    "\n",
    "\t***Your Answer:***    \n",
    "The classifier I prefered was the Stochastic gradient descent as the cost/error got progressively smaller at each iteration. The Newton Method takes a little longer to converge to minimum as each iteration is slow due to having to compute the second derivate (Hessian), however this method takes fewer iterations to converge to the minimum. \n",
    "\n",
    "       ******\n",
    "\n",
    "* SGD vs. Newton: Give advantages and disadvantages of both approaches. How would you expect the results to change if more or less data were used during training?\n",
    "\n",
    "\t***Your Answer:***\n",
    "An Advantage of Newton compared to SGD is that it converges in less steps/iterations. I would expect the results to be largely the same given more training data, however I suspect that computing the loss would take significantly more time to compute. I would also expect Newton's method to perform better on larger, higher dimensional datasets, as it's better at achieving quadratic convergence whilst SGD is better suited to linear operations on data. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bonus: Make it fast! [15 Points]\n",
    "\n",
    "Optimise your implementations by making good use of Numpy. If your implementation of one of the methods is within a factor of two of the reference implementation you'll earn 5 additional points (a total of 15 points possible for the three methods).\n",
    "\n",
    "***Hint***: No method should be significantly slower than the others in the case of optimal implementation. On my MBP they all take less than 2 seconds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
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