log_reg.ipynb

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    "<a href=\"https://colab.research.google.com/github/MLRG-CEFET-RJ/ml-class/blob/master/ppcic_ml_logreg.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ],
   "metadata": {
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   "cell_type": "markdown",
   "metadata": {
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    "id": "jh3MKB2R3FVB"
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   "source": [
    "# Logistic Regression\n",
    "\n",
    "The predictive model that the logistic regression algorithm learns corresponds to a vector of coefficients $\\Theta \\in \\Re^{n + 1}$, that is:\n",
    "\n",
    "$$\n",
    "\\Theta =  [\\theta_0, \\theta_1, \\theta_2, \\cdots, \\theta_n]\n",
    "$$\n",
    "\n",
    "Consider a binary classification task (i.e., the target can only assume two values, 0 or 1). A logistic regression model for this task would predict the most likely class for an instance $\\mathbf{x} = [x_0, x_1, x_2, \\cdots, x_n]$ by doing the following:\n",
    "\n",
    "1. Compute $z = \\Theta^T \\cdot \\mathbf{x}$, i.e., $z \\in \\Re$ is the dot product between the vectors $\\Theta$ and $\\mathbf{x}$. Notice that $z$ is just a weighted sum: $\\theta_0 + \\theta_1 \\times x_1 + \\theta_2 \\times x_2 + \\cdots  + \\theta_n \\times x_n$.\n",
    "2. Compute $\\sigma(z)$, the logistic function.\n",
    "3. If $\\sigma(z) < 0.5$, then predict class($\\mathbf{x}$) = 0; otherwise predict class($\\mathbf{x}$) = 1.\n",
    "\n",
    "## Probabilistic classifiers\n",
    "Logistic regression builds a probabilistic classifier, i.e., it is a classification algorithm that produces probabilistic models. This means that this algorithm produces a distribution of probabilities on the possible values ​​of the target feature. In the case of binary classification, the result of the function $\\sigma(\\Theta^T \\cdot \\mathbf{x})$ is interpreted as the probability that the example $\\mathbf{x}$ belongs to the positive class, which, by convention, corresponds to 1.\n",
    "\n",
    "$\\sigma$ is known as the *sigmoid function* (aka *logistic function*). Its mathematical expression is as follows:\n",
    "\n",
    "$$\n",
    "\\sigma(z) = \\frac{1}{e^{-z} + 1}\n",
    "$$\n",
    "\n",
    "The code cell below shows a part of the graph of the logistic function.\n"
   ]
  },
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   "execution_count": null,
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    "colab_type": "code",
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    "outputId": "d5e68ab0-8aa6-481c-c3ce-0717b2040f58"
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   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "sigmoid = lambda x: 1/(1+np.exp(-x))\n",
    "\n",
    "def plot_sigmoid():\n",
    "  plt.grid()\n",
    "  plt.xlim([-10.0, 10.0])\n",
    "  plt.ylim([-0.1, 1.1])\n",
    "  xs = np.arange(-10, 10, 0.001)\n",
    "  plt.xlabel('$z$', size=10)\n",
    "  plt.ylabel('$\\sigma(z)$', size=10)\n",
    "  plt.title('Sigmoid function', size=10)\n",
    "  plt.plot(xs, sigmoid(xs), label=r'$\\sigma(z)= \\frac{1}{1+e^{-z}}$')\n",
    "  plt.legend(loc='lower right', fontsize=15)\n",
    "\n",
    "plot_sigmoid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "gwvtL7xC5Vmv"
   },
   "source": [
    "Notice that\n",
    "\n",
    "- the range of values ​​that $\\sigma(z)$ produces is the open range $ (0,1) $;\n",
    "- $\\sigma(0.0)$ is equal to 0.5;\n",
    "- for ever-increasing $z$ values ​​(in magnitude), $\\sigma(z)$ returns values ​​ever closer to $0$ or $1$.\n",
    "- $\\sigma(z) \\geq 0.5$ when $z \\geq 0$\n",
    "- $\\sigma(z) < 0.5$ when $z < 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 102
    },
    "colab_type": "code",
    "id": "1hw6vD565_Kd",
    "outputId": "f2cf6452-edf4-476c-a155-46e98a1c62af"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sigma(0.0) = 0.500\n",
      "sigma(0.5) = 0.622\n",
      "sigma(-0.5) = 0.378\n",
      "sigma(10.0) = 1.000\n",
      "sigma(-10.0) = 0.000\n"
     ]
    }
   ],
   "source": [
    "print('sigma(0.0) = %.3f' % sigmoid(0.0))\n",
    "print('sigma(0.5) = %.3f' % sigmoid(0.5))\n",
    "print('sigma(-0.5) = %.3f' % sigmoid(-0.5))\n",
    "print('sigma(10.0) = %.3f' %  sigmoid(10.0))\n",
    "print('sigma(-10.0) = %.3f' % sigmoid(-10.0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "vXLmXnqw6GI_"
   },
   "source": [
    "To give you a more concrete view of what a logistic regression model does, consider a binary classification problem over a training set with 2 predictors, $x_1$ and $x_2$. Also, consider that the logistic regression algorithm produced a model represented by the vector $\\Theta = [-3, 1, 1]^T$. The code cell below is a toy implementation of a logistic regression classifier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "LF1WfLhA6Rhm"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def sigmoid(x):\n",
    "    # Sigmoid function\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "def dot_product(theta, x):\n",
    "    # Compute the weighted sum.\n",
    "    return np.dot(x, theta)\n",
    "\n",
    "def predict(theta, x):\n",
    "  y_prob = proba(theta,x)\n",
    "  return np.round(y_prob).astype(np.int)\n",
    "\n",
    "def proba(theta, x):\n",
    "    # Returns the probability that x belongs to the positive class\n",
    "    return sigmoid(dot_product(theta, x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "XFc9c9YHLcxu"
   },
   "source": [
    "Further, consider that we want to determine (predict) the class for the examples $[3,3]$ and $[0.4,1.3]$. The following code produces the probability value that $\\mathbf{x}$ belongs to the positive class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 104
    },
    "colab_type": "code",
    "id": "dS50v_iU6XAW",
    "outputId": "04c010b3-5e25-43e7-8108-5444c3879b6c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Example(s):\n",
      " [[3.  3. ]\n",
      " [0.4 1.3]]\n",
      "Predicted class(es) for each example: [0 0]\n",
      "Probability of each example belonging to the positive class: [0.00012339 0.0090133 ]\n"
     ]
    }
   ],
   "source": [
    "theta = np.asarray([-3, -1, -1]).T\n",
    "\n",
    "X = np.asarray([[3, 3],[0.4, 1.3]])\n",
    "\n",
    "print('Example(s):\\n', X)\n",
    "\n",
    "col = np.ones((2,1))\n",
    "X = np.append(col, X, axis=1)\n",
    "\n",
    "print('Predicted class(es) for each example:', predict(theta, X))\n",
    "print('Probability of each example belonging to the positive class:', proba(theta, X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ShKvWs_BF3nN"
   },
   "source": [
    "In the example above:\n",
    "\n",
    "1. How do you interpret the output when $\\Theta = [-3, 1, 1]^T$? \n",
    "2. What happens if you change $\\Theta$ to $[-3, -1, -1]^T$?\n",
    "3. What happens if you keep $\\Theta = [-3, 1, 1]^T$ and try to classify the example $\\mathbf{x}=[0.4,1.3]$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "SM3linNFpTfy"
   },
   "source": [
    "## Decision boundaries\n",
    "\n",
    "We can have a graphical intuition of the example above. Again, suppose $\\Theta = [-3, 1, 1]^T$. Then to classify an example $\\mathbf{x} = (x_1, x_2)$:\n",
    "\n",
    "$$\n",
    "\\Theta^T \\cdot \\mathbf{x} = [-3, 1, 1]^T \\cdot [1,x_1,x_2] = -3 + x_1 + x_2\n",
    "$$\n",
    "\n",
    "Recall that, if $(\\Theta^T \\cdot \\mathbf{x}) \\geq 0$, then $\\mathbf{x}$ is classified as positive. That is:\n",
    "\n",
    "$$\n",
    "-3 + x_1 + x_2 \\geq 0 \\rightarrow x_1 + x_2 \\geq 3\n",
    "$$\n",
    "\n",
    "The equation $x_1 + x_2 = 3$ actually defines what we call a *decision boundary*. According to the Wikipedia, the definition of a decision boundary is the following:\n",
    "\n",
    "> In a classification problem with two classes, a decision boundary or decision surface is a hypersurface that partitions the underlying vector space into two sets, one for each class. The classifier will classify all the points on one side of the decision boundary as belonging to one class and all those on the other side as belonging to the other class.\n",
    "\n",
    "In the case of a 2-dimensional dataset, as the space of predictors is bidimentional, the decision boundary is a simple line in the cartesian plane. This line splits the space of features in two subregions, positive and negative. See the plot below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 440
    },
    "colab_type": "code",
    "id": "QC7KqyHSuYZ-",
    "outputId": "4ececaa1-cb3f-49ef-c772-af21b5bb7012"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "point1 = [0, 3]\n",
    "point2 = [3, 0]\n",
    "\n",
    "x_values = [point1[0], point2[0]]\n",
    "y_values = [point1[1], point2[1]]\n",
    "\n",
    "plt.plot(x_values, y_values, c='black')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "7OnWmGJbOh_7"
   },
   "source": [
    "In particular, all the examples that fall above this line are classified as being positive, while the examples predicted as negative are located below this line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 457
    },
    "colab_type": "code",
    "id": "DEoPYF7H4rnl",
    "outputId": "6c4f2d2a-93da-4dc2-c656-bb86b7717840"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "data = np.array([\n",
    "    [0.4, 1.3],\n",
    "    [3, 3]\n",
    "])\n",
    "\n",
    "col = np.ones((2,1))\n",
    "x = np.append(col, data, axis=1)\n",
    "\n",
    "y_pred = predict(theta, x)\n",
    "print(y_pred)\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.scatter(data[:,0], data[:, 1], c=np.array([0,1]), s=50,\n",
    "           cmap=\"RdBu\", vmin=-.2, vmax=1.2,\n",
    "           edgecolor=\"white\", linewidth=1)\n",
    "\n",
    "plt.plot(x_values, y_values, c='black')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zUaevC9HoMkK"
   },
   "source": [
    "Let us draw the decision boundary defined by the vector $\\Theta = [-3, 1, 1]^T$ along with the examples in the toy dataset presented above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 497
    },
    "colab_type": "code",
    "id": "Y0OARtsvKvyK",
    "outputId": "f58fc22b-a548-47d4-ecc9-70aba18c4da2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa566272828>]"
      ]
     },
     "execution_count": 36,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('classic')\n",
    "np.set_printoptions(precision=3, suppress=True)\n",
    "\n",
    "colormap = np.array(['r', 'b'])\n",
    "\n",
    "def plot_scatter(X, y, colormap):\n",
    "  plt.grid()\n",
    "  plt.xlim([-5.0, 5.0])\n",
    "  plt.ylim([-5.0, 5.0])\n",
    "  plt.xlabel('$x_1$', size=20)\n",
    "  plt.ylabel('$x_2$', size=20)\n",
    "  plt.title('Input 2D points', size=18)\n",
    "  plt.scatter(X[:,0], X[:, 1], s=50, c=colormap[y])\n",
    "\n",
    "plot_scatter(X, y, colormap)\n",
    "\n",
    "point1 = [-5, 8]\n",
    "point2 = [5, -2]\n",
    "\n",
    "x_values = [point1[0], point2[0]]\n",
    "y_values = [point1[1], point2[1]]\n",
    "\n",
    "plt.plot(x_values, y_values, c='black')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "V20itV5QlayV"
   },
   "source": [
    "By analysing the image above, it should be clear that the decision boundary defined by the vector $\\Theta = [-3, 1, 1]^T$ is **not** the best one, in the sense that it does not correctly classify many of the examples in the training dataset. In particular, the *prediction error* of the corresponding classifier is $8/17 \\approx 47\\%$, which is worst than tossing a coin to determine the class of an new example!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "f81qGdXd6Pz2"
   },
   "source": [
    "## Optimization problems\n",
    "\n",
    "By now, you should understand that the goal in logistic regression is to find the components of the vector $\\Theta$, taking as input a data matrix $X$ and a response vector $y$. You should also understand that, from the infinitely many vectors $\\Theta$, we want to find the one that minimizes the prediction error of the corresponding model.\n",
    "\n",
    "To determine the most appropriate parameter vector $\\Theta$, logistic regression must solve an optimization problem. An optimization problem is one in which, given a function, we want to find the point that corresponds to the optimal value (minimum or maximum) of the function.\n",
    "\n",
    "As an illustration, the following code computes the minimum value of the function $f(x) = x^3 - 3x^2 + 7$ within the range $[3,500]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "colab_type": "code",
    "id": "mQI8O4sW68HX",
    "outputId": "7c9ecfde-7b7d-40a8-b507-b75896c785f8"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "f1 = lambda x: (x ** 3)-(3 *(x ** 2))+7\n",
    "\n",
    "# Get 1000 evenly spaced num bers between -1 and 3 (arbitratil chosen to ensure steep curve)\n",
    "x = np.linspace(-0.5,3,500)\n",
    "\n",
    "# Plot the curve\n",
    "plt.plot(x, f1(x))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "iTHIXan16_Ye",
    "outputId": "26379c18-998f-4abd-b358-c6aba436fa37"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "Minimum of function occurs at x = 2.00\n"
     ]
    }
   ],
   "source": [
    "from scipy import optimize\n",
    "\n",
    "result = optimize.minimize_scalar(f1)\n",
    "print(result.success) # check if solver was successful\n",
    "\n",
    "print('Minimum of function occurs at x = %.2f' % result.x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "aGNrwqEV7Dtp"
   },
   "source": [
    "The concept of optimization is also applicable to functions of more than one variable.\n",
    "\n",
    "In the following example, a function of two variables (a paraboloid in this case) is used to illustrate the optimization procedure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 248
    },
    "colab_type": "code",
    "id": "idBS3YI97S89",
    "outputId": "80948e8a-31e5-409f-fb61-e21c308d129b"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits import mplot3d\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def f_paraboloide(x, y):\n",
    "    return x ** 2 + y ** 2\n",
    "\n",
    "x = np.linspace(-6, 6, 30)\n",
    "y = np.linspace(-6, 6, 30)\n",
    "\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z = f_paraboloide(X, Y)\n",
    "fig = plt.figure()\n",
    "ax = plt.axes(projection='3d')\n",
    "ax.contour3D(X, Y, Z, 50, cmap='binary')\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('z');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 248
    },
    "colab_type": "code",
    "id": "K6vuwnT17WdY",
    "outputId": "31b6cb77-df69-4bb6-f418-db255be81da2"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.axes(projection='3d')\n",
    "ax.plot_surface(X, Y, Z, rstride=1, cstride=1,\n",
    "                cmap='viridis', edgecolor='none')\n",
    "ax.set_title('surface');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 170
    },
    "colab_type": "code",
    "id": "HXM1BZDR7Z93",
    "outputId": "ac181564-5ef3-48e4-ea47-3c6727b31ac7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "     fun: 5.8281095370852615e-15\n",
       "     jac: array([-1.2166366e-07,  8.3183572e-08])\n",
       " message: 'Optimization terminated successfully.'\n",
       "    nfev: 12\n",
       "     nit: 1\n",
       "    njev: 3\n",
       "  status: 0\n",
       " success: True\n",
       "       x: array([-6.82824108e-08,  3.41412054e-08])"
      ]
     },
     "execution_count": 10,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import optimize\n",
    "\n",
    "def f2(x):\n",
    "    return (x[0]**2 + x[1]**2)\n",
    "\n",
    "optimize.minimize(f2, [2, -1], method=\"CG\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "RwBUOrUh7g_K"
   },
   "source": [
    "In general, optimization problems are difficult, because the function in question can be complex, as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 248
    },
    "colab_type": "code",
    "id": "a84n2clz7kvr",
    "outputId": "16984f04-3d2a-43cf-a494-1a398ca96231"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits import mplot3d\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def f(x, y):\n",
    "    return np.sin(np.sqrt(x ** 2 + y ** 2))\n",
    "\n",
    "x = np.linspace(-6, 6, 30)\n",
    "y = np.linspace(-6, 6, 30)\n",
    "\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z = f(X, Y)\n",
    "fig = plt.figure()\n",
    "ax = plt.axes(projection='3d')\n",
    "ax.contour3D(X, Y, Z, 50, cmap='binary')\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.set_zlabel('z');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "wyJLEgfQ8MN8"
   },
   "source": [
    "Logistic regression has to solve an optimization problem to find the best vector of parameters given the training dataset. In particular, the type of optimization problem to be solved in the logistic regression is minimization: given a function $J(\\Theta)$ that measures the error of the classification model on the training data, the objective is to find the combination of components of $\\Theta$ such that it produces the minimum value for $J(\\Theta)$.\n",
    "\n",
    "Consider a binary classification problem in which there are $m$ examples in the training set. Also, consider that $y^{(i)} \\in \\{0.1\\}$ is the class associated with the $i$-th training example, and that $\\sigma(z_i)$ is the value of the sigmoid function corresponding to the $i$-th training example, $z_i = \\Theta^T \\cdot \\mathbf{x}^{(i)}$. The cost function that logistic regression must minimize is called *cross entropy loss* or *logistic loss*. Its definition is as follows:\n",
    "\n",
    "$$\n",
    "J(\\Theta) = -\\frac{1}{m} \\sum_{i = 1}^{m} [ y^{(i)} \\log (\\sigma(z_i)) + (1-y^{(i)}) \\log (1 - \\sigma(z_i))]\n",
    "$$\n",
    "\n",
    "To get an insight into the cost function above, let's consider the cost corresponding to the $i$-th training example:\n",
    "\n",
    "$$\n",
    "\\text{cost}_i = y^{(i)} \\log(\\sigma(z_i)) + (1-y^{(i)}) \\log(1 - \\sigma(z_i))\n",
    "$$\n",
    "\n",
    "In the above expression, note that the cost tends to zero when the the value values produced by the hypothesis $\\sigma(z_i)$ tends to the value of $y^{(i)}$ (ground thruth):\n",
    "\n",
    "- $\\left[(\\sigma(z_i) \\rightarrow 0) \\text{ and } (y^{(i)} = 0)\\right] \\Rightarrow (\\text{cost}_i \\rightarrow 0)$\n",
    "- $\\left[(\\sigma(z_i) \\rightarrow  1) \\text{ and } (y^{(i)} = 1)\\right] \\Rightarrow (\\text{cost}_i \\rightarrow 0)$\n",
    "\n",
    "However, if the hypothesis predicts a different value compared to $y^{(i)}$, we have one of the following two cases:\n",
    "\n",
    "- $\\left[(\\sigma(z_i) \\rightarrow 0) \\text{ and } (y^{(i)} = 1)\\right] \\Rightarrow (\\text{cost}_i \\rightarrow \\infty)$ \n",
    "- $\\left[(\\sigma(z_i) \\rightarrow 1) \\text{ and } (y^{(i)} = 0)\\right] \\Rightarrow (\\text{cost}_i \\rightarrow \\infty)$\n",
    "\n",
    "The above analysis considers only the extreme values ​​that $\\sigma(z_i)$ can take. In any case, the general conclusion we should draw is that the minimization algorithm is penalized when it selects a $\\Theta$ vector that produces the wrong prediction for the $i$-th example.\n",
    "\n",
    "The above explanation was given in the context of a single example. What the function $J(\\Theta)$ does is to compute the *average error* over all $m$ training examples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "TLUdfI95-XSR"
   },
   "source": [
    "### Gradient Descent (and its variants)\n",
    "\n",
    "One of the most used methods to numerically perform the minimization that the logistic regression needs is [gradient descent](en.wikipedia.org/wiki/Gradient_descent). Using this method, the process of minimizing the cost function occurs in an iterative way. At each iteration, a small change is made to the components of the $\\Theta$ parameter vector:\n",
    "\n",
    "Repeat until convergence: \n",
    "$$\n",
    "\\theta_j := \\theta_j - \\alpha \\sum_{i = 1}^{m}(\\sigma(\\Theta^T \\cdot \\mathbf{x}^{(i)}) - y^{(i)}) \\, x_j^{(i)}\n",
    "$$\n",
    "\n",
    "In the update expression presented above, $\\alpha$ is a numerical value called *learning rate*. This constant controls the amount of update on the components of $\\Theta$.\n",
    "\n",
    "There are numerous gradient-based optimization methods. The study of these methods is outside the scope of this course. In any case, the following animation ([source]((https://www.datasciencecentral.com/profiles/blogs/an-overview-of-gradient-descent-optimization-algorithms))) illustrates the behavior of some of these methods while minimizing a given function. notice how some of these methods manage to scape the local minima, while some others remain stuck in it.\n",
    "\n",
    "![alt text](http://storage.ning.com/topology/rest/1.0/file/get/2808327843?profile=original)\n",
    "\n",
    "The learning rate is a hyperparameter of logistic regression. The following animation (source: [Machine Learning Refined](https://github.com/jermwatt/machine_learning_refined)\n",
    ") illustrates the effect of different learning rate values ​​on the optimization process. When $\\alpha$ is defined as too large and the evaluation sequence starts to get out of control, the sequence of steps is said to diverge. On the other hand, if the value of $\\alpha$ is very small, the convergence of the process can take significantly.\n",
    "\n",
    "![alt text](https://github.com/jermwatt/machine_learning_refined/blob/gh-pages/html/gifs/steplength_1D.gif?raw=true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "p70uCAmG_74A"
   },
   "source": [
    "## Logistic Regression in Scikit-Learn\n",
    "\n",
    "The cells below * illustrate the use of the [LogisticRegression](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html) class.\n",
    "\n",
    "One of the parameters for instantiating the `LogisticRegression` class is called *solver*, which defines the optimization method to be used during training.\n",
    "\n",
    "*example adapted from the book [Hands-on Machine Learning with Scikit-Learn and Tensoflow](https://www.amazon.com/Hands-Machine-Learning-Scikit-Learn-TensorFlow/dp/1491962291)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "mlQ1Gg8UA1sD"
   },
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "import numpy as np\n",
    "iris = datasets.load_iris()\n",
    "X = iris[\"data\"][:, 3:] # petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.int) # 1 if Iris-Virginica, else 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "colab_type": "code",
    "id": "TmnfaIBnMr6C",
    "outputId": "70ef85f8-2088-4f66-8796-9eedb2e45d5e"
   },
   "outputs": [
    {
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      ]
     },
     "execution_count": 52,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "_sUfIEipB44u"
   },
   "source": [
    "The next code cell fits a logistic regression model to the training set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 102
    },
    "colab_type": "code",
    "id": "o4x0KpWjB5Rw",
    "outputId": "97f92a82-b690-4d9a-f7ee-e198c38b84c2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
       "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
       "                   random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 18,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "log_reg = LogisticRegression(solver='lbfgs')\n",
    "log_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "kRxUwOD8CL6p"
   },
   "source": [
    "Once the model has been generated, it is possible to invoke the predict method, as shown in the following example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "DjZRJB7UCMVj",
    "outputId": "db50009a-dac7-41d9-c22f-dab1ae822aa3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0])"
      ]
     },
     "execution_count": 19,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg.predict([[1.7], [1.5]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fhAtNarYCeGp"
   },
   "source": [
    "The following cell produces a graph that makes it easier to interpret the generated model. In this graph, the point where the solid and dashed curves meet corresponds to the decision boundary of the generated logistic regression model.\n",
    "\n",
    "What is the decision boundary in this example?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 279
    },
    "colab_type": "code",
    "id": "9ccJ1BNbChgA",
    "outputId": "92d6472b-9041-4ffd-94f8-09cc7f184493"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", label=\"Iris-Virginica\")\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", label=\"Not Iris-Virginica\")\n",
    "\n",
    "plt.xlabel('Petal length (cm)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "jg65r9-UpFBw"
   },
   "source": [
    "The vector of coefficients of the generated logistic regression model is stored in two different attributes of the LogisticRegression class: `coef_` and `intercept_`. See the code cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "iBN9YDKCnB6O",
    "outputId": "16460b2a-aa1d-440a-d746-774faa7f602c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4.3330846]]\n",
      "[-7.1947083]\n"
     ]
    }
   ],
   "source": [
    "print(log_reg.coef_)\n",
    "print(log_reg.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AHTwJOR_Ohpr"
   },
   "source": [
    "$$\n",
    "\\Theta = [4.3, -7.19]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "LXztMJf6pbXL"
   },
   "source": [
    "By inspecting the above output, we can conclude that the decision boundary is:\n",
    "\n",
    "$$\n",
    "\\theta_0 + \\theta_1 \\times x_1 = 0\n",
    "$$\n",
    "\n",
    "If we replace the values in the above equation, we get:\n",
    "\n",
    "$$\n",
    "4.33 - 7.19 \\times x_1 = 0\n",
    "$$\n",
    "\n",
    "By a simple manipulation of the above expression, we can find that the decision boundary here is a vertical line that crosses $x_1 \\approx 1.66$, which is consistent with the plot shown above.\n",
    "\n",
    "In this example, notice that $x_1$ represents the only predictor used to generate the model, *petal length*.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "mjs5dquXoOUX",
    "outputId": "48b08052-c37c-4656-a430-4fe089ffbad8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6605080831408776"
      ]
     },
     "execution_count": 22,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "7.19/4.33"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "wygo_4LvljmC"
   },
   "source": [
    "## Case study: Toy dataset\n",
    "\n",
    "Let us go back to our toy dataset and make build a decent classifier using Scikit-Learn. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "7V76nVRml3Lk"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "X = np.array([[-0.1, 1.4],\n",
    "              [-0.5,-0.1],\n",
    "              [ 1.3, 0.9],\n",
    "              [-0.6, 0.4],\n",
    "              [-1.5, 0.4],\n",
    "              [ 0.2, 0.2],\n",
    "              [-0.3,-0.4],\n",
    "              [ 0.7,-0.8],\n",
    "              [ 1.1,-1.5],\n",
    "              [-1.0, 0.9],\n",
    "              [-0.5,-1.5],\n",
    "              [-1.3,-0.4],\n",
    "              [-1.4,-1.2],\n",
    "              [-0.9,-1.1],\n",
    "              [ 0.4,-1.3],\n",
    "              [-0.4, 0.6],\n",
    "              [ 0.3,-0.5]])\n",
    "\n",
    "y = np.array([0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 102
    },
    "colab_type": "code",
    "id": "mv4WnQ5ll4lx",
    "outputId": "bc29de5e-136e-45fa-fdee-dcde84062c3e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
       "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
       "                   random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 2,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "log_reg = LogisticRegression(solver='lbfgs')\n",
    "log_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "QBNnQsV-mObt",
    "outputId": "6062ba4a-acdf-4b68-b352-8b91cd4ab62b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.52160613 -1.11119985]]\n",
      "[0.38532946]\n"
     ]
    }
   ],
   "source": [
    "print(log_reg.coef_)\n",
    "print(log_reg.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 497
    },
    "colab_type": "code",
    "id": "d6LIw0EUmm6D",
    "outputId": "8eb8fa0a-85c4-413c-f88e-060483ba5605"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fab5efc8198>]"
      ]
     },
     "execution_count": 10,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('classic')\n",
    "np.set_printoptions(precision=3, suppress=True)\n",
    "\n",
    "colormap = np.array(['r', 'b'])\n",
    "\n",
    "def plot_scatter(X, y, colormap):\n",
    "  plt.grid()\n",
    "  plt.xlim([-5.0, 5.0])\n",
    "  plt.ylim([-5.0, 5.0])\n",
    "  plt.xlabel('$x_1$', size=20)\n",
    "  plt.ylabel('$x_2$', size=20)\n",
    "  plt.title('Input 2D points', size=18)\n",
    "  plt.scatter(X[:,0], X[:, 1], s=50, c=colormap[y])\n",
    "\n",
    "plot_scatter(X, y, colormap)\n",
    "\n",
    "points_x = [x/10. for x in range(-50,+50)]\n",
    "\n",
    "bias = log_reg.intercept_\n",
    "w = log_reg.coef_.T\n",
    "points_y = [-(w[0] * x + bias)/(w[1]) for x in points_x]\n",
    "plt.plot(points_x, points_y, color = 'black')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "-IsYXNt2s0an"
   },
   "source": [
    "## Case study: honor dataset\n",
    "\n",
    "Let us see a complete example of creating a logistic regression model with Scikit-Learn on the honor dataset. This is a dataset that contains 200 observations about students. The feature we will use a target is `hon` which indicates if a student is an honor class or not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 198
    },
    "colab_type": "code",
    "id": "VO_aQdwpsfn_",
    "outputId": "3bbd4dd6-b614-4428-9f96-5190ef1cb30e"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>female</th>\n",
       "      <th>read</th>\n",
       "      <th>write</th>\n",
       "      <th>math</th>\n",
       "      <th>hon</th>\n",
       "      <th>femalexmath</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>57</td>\n",
       "      <td>52</td>\n",
       "      <td>41</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>68</td>\n",
       "      <td>59</td>\n",
       "      <td>53</td>\n",
       "      <td>0</td>\n",
       "      <td>53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>44</td>\n",
       "      <td>33</td>\n",
       "      <td>54</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>63</td>\n",
       "      <td>44</td>\n",
       "      <td>47</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>47</td>\n",
       "      <td>52</td>\n",
       "      <td>57</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   female  read  write  math  hon  femalexmath\n",
       "0       0    57     52    41    0            0\n",
       "1       1    68     59    53    0           53\n",
       "2       0    44     33    54    0            0\n",
       "3       0    63     44    47    0            0\n",
       "4       0    47     52    57    0            0"
      ]
     },
     "execution_count": 53,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df_honor_data = pd.read_csv('https://raw.githubusercontent.com/OmaymaS/Logistic-Regression-Coefficients-Interpretation/master/honordata.csv')\n",
    "df_honor_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "2ulQVfDttplz"
   },
   "outputs": [],
   "source": [
    "X = df_honor_data.drop(columns=['hon'])\n",
    "y = df_honor_data.hon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 225
    },
    "colab_type": "code",
    "id": "U1SMcciePjzD",
    "outputId": "2a93aa71-0499-4c60-a968-e16208693aeb"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      0\n",
       "1      0\n",
       "2      0\n",
       "3      0\n",
       "4      0\n",
       "      ..\n",
       "195    0\n",
       "196    0\n",
       "197    0\n",
       "198    1\n",
       "199    1\n",
       "Name: hon, Length: 200, dtype: int64"
      ]
     },
     "execution_count": 57,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 52
    },
    "colab_type": "code",
    "id": "MuCoFedmuBjG",
    "outputId": "db9099e7-6cfa-4507-a916-64799ff356d1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(200, 5)\n",
      "(200,)\n"
     ]
    }
   ],
   "source": [
    "print(X.shape)\n",
    "print(y.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sRTZ5WPx25Nm"
   },
   "source": [
    "In classification, it is very common to split the available observations in two datasets: training and test. In Scikit-Learn, we can do this by using the `train_test_split` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 104
    },
    "colab_type": "code",
    "id": "wkfWHBBmuLGS",
    "outputId": "5a657934-0bc1-4041-d386-3db654c60b5a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
       "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
       "                   random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 42,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
    "\n",
    "log_reg = LogisticRegression(solver='lbfgs')\n",
    "log_reg.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 69
    },
    "colab_type": "code",
    "id": "xpTA85LzSKEd",
    "outputId": "ecddbaa6-308b-48c7-86ba-ad257299be85"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(200, 5)\n",
      "(160, 5)\n",
      "(40, 5)\n"
     ]
    }
   ],
   "source": [
    "print(X.shape)\n",
    "print(X_train.shape)\n",
    "print(X_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "p_Wx4vawBl9n"
   },
   "source": [
    "The following image illustrates the effect of applying the function `train_test_split` on the data matrix $X$ and response vector $y$. From these, two data matrices and two response vectors are created. \n",
    "\n",
    "![alt text](https://res.cloudinary.com/dyd911kmh/image/upload/f_auto,q_auto:best/v1543836883/image_6_cfpjpr.png)\n",
    "\n",
    "Please notice that, each time `train_test_split` is called, it randomly selects which examples to put in the training and test datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Mqn_JCdDu3_d"
   },
   "outputs": [],
   "source": [
    "y_pred = log_reg.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "Pv-9bu4pvf1y",
    "outputId": "9d65f56a-8c20-4ec4-93fe-1e36cbc0f0b3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0\n",
      " 0 0 1]\n"
     ]
    }
   ],
   "source": [
    "print(y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "colab_type": "code",
    "id": "K-wxSlgCvINK",
    "outputId": "cb252eb9-2eef-4f3c-bf19-659a8d03bd44"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 44,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "accuracy_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "ACq9NUm6vdBo",
    "outputId": "fe489296-c03e-4a44-e55a-2a003efc2bf7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0\n",
      " 0 0 1]\n"
     ]
    }
   ],
   "source": [
    "print(y_test.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "7IDz3Iw2v74G",
    "outputId": "436f03f9-7757-4062-ee5c-faac924496a7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1.05519995e-02 -1.67596700e-03  2.32999559e+00 -3.62224213e-02\n",
      "  -1.02388613e-02]]\n",
      "[-138.314996]\n"
     ]
    }
   ],
   "source": [
    "print(log_reg.coef_)\n",
    "print(log_reg.intercept_)"
   ]
  }
 ],
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   "collapsed_sections": [],
   "include_colab_link": true,
   "name": "ppcic_ml_logreg.ipynb",
   "provenance": []
  },
  "kernelspec": {
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