S11b_Excercises_solutions.ipynb

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   "source": [
    "# Execute before using this notebook if using google colab\n",
    "kernel = str(get_ipython())\n",
    "if 'google.colab' in kernel:    \n",
    "    !wget https://raw.githubusercontent.com/fredzett/rmqa/master/utils.py -P local_modules -nc \n",
    "    !npx degit fredzett/rmqa/data data\n",
    "    import sys\n",
    "    sys.path.append('local_modules')"
   ]
  },
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   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from patsy import dmatrices\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.tree import export_graphviz\n",
    "from sklearn.datasets import make_classification\n",
    "\n",
    "from subprocess import call\n",
    "from IPython.display import Image\n",
    "\n",
    "plt.rcParams['font.size'] = 12\n",
    "plt.rcParams['figure.figsize'] = [9,7]\n",
    "plt.rcParams['figure.dpi'] = 80\n",
    "plt.rcParams[\"axes.spines.right\"] = False\n",
    "plt.rcParams[\"axes.spines.top\"] = False"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Excercise 1"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement a function to calculate __gini impurity__ in python. The function should\n",
    "\n",
    "- take as input an array of (dependent) variables assuming 2 classes (0 and 1)\n",
    "- return as an output the gini impurity \n",
    "\n",
    "Gini impurity is given by:\n",
    "\n",
    "\\begin{equation}\n",
    "G_i = 1 - \\sum_{j=1}^n p_{i,j}^2\n",
    "\\end{equation}\n",
    "\n",
    "Use the below data to test your function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.array((0,1,1,0,1,0,0,0,0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution - Exercise 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
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   "outputs": [
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     "execution_count": 14,
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   ],
   "source": [
    "# manual solution\n",
    "1 - ((6/9)**2 + (3/9)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# class wise solution\n",
    "def gini1(arr):\n",
    "    p0 = sum(arr == 0) / len(arr)\n",
    "    p1 = sum(arr == 1) / len(arr)\n",
    "    return 1 - (p0**2 + p1**2)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 21,
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     "execution_count": 21,
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   "source": [
    "gini1(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# vectorized solution using np.bincount\n",
    "def gini2(arr):\n",
    "    probabilities = np.bincount(data) / len(data)\n",
    "    return 1 - sum(probabilities**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
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     "execution_count": 29,
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   "source": [
    "gini2(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check pure node"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
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     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = np.array((0,0,0,0))\n",
    "gini1(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
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     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "gini2(data)"
   ]
  }
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