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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The Learning Problem"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problem 1\n",
      "    What types of learning, if any, best describe the following three scenarios:\n",
      "    \n",
      "    i. A coin classifcation system is created for a vending machine. In order to do this,\n",
      "    the developers obtain exact coin specifcations from the U.S. Mint and derive\n",
      "    a statistical model of the size, weight, and denomination, which the vending\n",
      "    machine then uses to classify its coins.\n",
      "    ii. Instead of calling the U.S. Mint to obtain coin information, an algorithm is\n",
      "    presented with a large set of labeled coins. The algorithm uses this data to\n",
      "    infer decision boundaries which the vending machine then uses to classify its\n",
      "    coins.\n",
      "    iii. A computer develops a strategy for playing Tic-Tac-Toe by playing repeatedly\n",
      "    and adjusting its strategy by penalizing moves that eventually lead to losing.\n",
      "    \n",
      "    [a] (i) Supervised Learning, \n",
      "        (ii) Unsupervised Learning, \n",
      "        (iii) Reinforcement Learning\n",
      "    \n",
      "    [b] (i) Supervised Learning, \n",
      "        (ii) Not learning, \n",
      "        (iii) Unsupervised Learning\n",
      "    \n",
      "    [c] (i) Not learning, \n",
      "        (ii) Reinforcement Learning, \n",
      "        (iii) Supervised Learning\n",
      "    \n",
      "    [d] (i) Not learning, \n",
      "        (ii) Supervised Learning, \n",
      "        (iii) Reinforcement Learning\n",
      "    \n",
      "    [e] (i) Supervised Learning, \n",
      "        (ii) Reinforcement Learning, \n",
      "        (iii) Unsupervised Learning"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "    Answer: [d]"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problem 2\n",
      "    Which of the following problems are best suited for the learning approach?\n",
      "    \n",
      "    (i) Classifying numbers into primes and non-primes.\n",
      "    (ii) Detecting potential fraud in credit card charges.\n",
      "    (iii) Determining the time it would take a falling object to hit the ground.\n",
      "    (iv) Determining the optimal cycle for traffic lights in a busy intersection.\n",
      "    \n",
      "    [a] (ii) and (iv)\n",
      "    [b] (i) and (ii)\n",
      "    [c] (i), (ii), and (iii)\n",
      "    [d] (iii)\n",
      "    [e] (i) and (iii)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "    Answer: [a]"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Bins and Marbles"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problem 3\n",
      "    We have 2 opaque bags, each containing 2 balls. One bag has 2 black balls and\n",
      "    the other has a black ball and a white ball. You pick a bag at random and then pick\n",
      "    one of the balls in that bag at random. When you look at the ball, it is black. You\n",
      "    now pick the second ball from that same bag. What is the probability that this ball\n",
      "    is also black?\n",
      "    \n",
      "    [a] 1 / 4\n",
      "    [b] 1 / 3\n",
      "    [c] 1 / 2\n",
      "    [d] 2 / 3\n",
      "    [e] 3 / 4"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "    possible outcomes:\n",
      "    bag_bw -> b -> w\n",
      "    bag_bw -> w -> b\n",
      "    bag_bb -> b -> b\n",
      "    bag_bb -> b -> b\n",
      "    \n",
      "    since ball1 = b we are left with 3 possible outcomes\n",
      "    from those only 2 give us the b->b so the answer is 2/3\n",
      "    \n",
      "    Answer: [d]"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Consider a sample of 10 marbles drawn from a bin that has red and green marbles.\n",
      "The probability that any marble we draw is red is $\\mu = 0.55$ (independently, with\n",
      "replacement). We address the probability of getting no red marbles $(\\nu = 0)$ in the\n",
      "following cases:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problem 4\n",
      "    We draw only one such sample. Compute the probability that $\\nu = 0$. The\n",
      "    closest answer is (closest is the answer that makes the expression jyour answer\n",
      "    given optionj closest to 0):\n",
      "    [a] 7.331 * 10^6\n",
      "    [b] 3.405 * 10^4\n",
      "    [c] 0.289\n",
      "    [d] 0.450\n",
      "    [e] 0.550"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p_green = 1-0.55\n",
      "pow(p_green,10)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "0.0003405062891601559"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "    Answer: [b]"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problem 5\n",
      "    We draw 1,000 independent samples. Compute the probability that (at least)\n",
      "    one of the samples has nu = 0. The closest answer is:\n",
      "    [a] 7.331 * 10^6\n",
      "    [b] 3.405 * 10^4\n",
      "    [c] 0.289\n",
      "    [d] 0.450\n",
      "    [e] 0.550"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "r = pow(p_green, 10) * 1000\n",
      "print r\n",
      "print 'c=', abs(r - 0.28)\n",
      "print 'd=', abs(r - 0.45)\n",
      "print 'e=', abs(r - 0.55)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.34050628916\n",
        "c= 0.0605062891602\n",
        "d= 0.10949371084\n",
        "e= 0.20949371084\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "    Answer: [c]"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Feasibility of Learning"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problem 6"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "    Answer: [e] all get same score = 3*1 + 2*3 + 1*3 + 0 * 1 = 12"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The Perceptron Learning Algorithm"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "\n",
      "import random as rnd\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "\n",
      "def generateLine():\n",
      "    points = np.random.uniform(-1, 1, (2, 2))\n",
      "    (x1,y1),(x2,y2) = points\n",
      "    k = (y2 - y1) / (x2 - x1)\n",
      "    m = y1 - k * x1\n",
      "    return k,m\n",
      "\n",
      "def generateData(line, N=10):\n",
      "    k,m = line\n",
      "    x = np.ones((N, 3))\n",
      "    x[:,1:] = np.random.uniform(-1, 1, (N, 2))\n",
      "    y = x[:,2] - (x[:,1] * k + m)\n",
      "    return x,np.sign(y)\n",
      "\n",
      "def showData(x,y, line, label):\n",
      "    pos = y > 0\n",
      "    neg = y < 0\n",
      "    plt.plot(x[:,1][pos], x[:,2][pos], 'gD')\n",
      "    plt.plot(x[:,1][neg], x[:,2][neg], 'rs')\n",
      "    k,m = line\n",
      "    v = np.array([-1.0, 1.0])\n",
      "    plt.plot(v, v * k + m, label=label)\n",
      "\n",
      "def perceptron(x, y):\n",
      "    w = np.zeros(x.shape[1], dtype=float)\n",
      "    t = 0\n",
      "    while True:\n",
      "        missed = []\n",
      "        for i, r in enumerate(x):\n",
      "            result = np.sign(np.dot(r, w))\n",
      "            u = r * (y[i] - result)\n",
      "            if result != y[i]: missed.append(u)\n",
      "        if len(missed) == 0: return w,t\n",
      "        w = w + rnd.choice(missed)\n",
      "        t += 1\n",
      "        \n",
      "def disagreement(x,y,w):\n",
      "    result = np.dot(x, w)\n",
      "    d = np.ones(y.size)[y != np.sign(result)]\n",
      "    return np.sum(d) / y.size\n",
      "        \n",
      "def runProblem(N, n=1000):\n",
      "    c = 0.0\n",
      "    d = 0.0\n",
      "    for i in xrange(n):\n",
      "        line = generateLine()\n",
      "        x,y = generateData(line, N)\n",
      "        w,t = perceptron(x,y)\n",
      "        testX, testY = generateData(line, n)\n",
      "        d += disagreement(testX, testY, w)\n",
      "        c += t\n",
      "    return {'iterations': c / n, 'disagreement': d / n}\n",
      "       \n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "line = generateLine()\n",
      "x,y = generateData(line, 10)\n",
      "w,_ = perceptron(x,y)\n",
      "\n",
      "plt.title(\"PLA training result\")\n",
      "showData(x,y, line, \"original\")\n",
      "showData(x, y, (- w[1] / w[2], - w[0] / w[2]), \"PLA\")\n",
      "plt.legend(loc='best')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 60,
       "text": [
        "<matplotlib.legend.Legend at 0x3a446d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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3B9YeHtbG9dKlun/xm74Uo2jVCnjqKWDMGBH6L74I+PiI6R2NpnmPWb07U2p6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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x2cd3bd0>"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problem 7 & 8"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "runProblem(10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 51,
       "text": [
        "{'disagreement': 0.10742300000000012, 'iterations': 10.338}"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "    Answer7: [b]\n",
      "    Answer8: [c]"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Problem 9 & 10"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "runProblem(100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 52,
       "text": [
        "{'disagreement': 0.013583999999999969, 'iterations': 92.811}"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "    Answer9:  [b]\n",
      "    Answer10: [b]"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}