DecisionTreesForTitanicDataset.ipynb

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   },
   "source": [
    "# Tatanic Dataset Assignment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "4941339c-affb-404a-8bc9-49c0c3c0ea94"
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    {
     "data": {
      "text/plain": [
       "891"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "require 'csv'\n",
    "require 'open-uri'\n",
    "\n",
    "csv = open(\"https://gist.githubusercontent.com/akhilstanislavose/46023ee10af448b9bb6a9656624cd03c/raw/ce0be9103e55f401f895b153ae6fc293cb91c241/titanic.csv\").read\n",
    "dataset = CSV.parse(csv, :headers => true)\n",
    "\n",
    "dataset.count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "59b5d37d-f935-4930-bf6f-afefe72d77b2"
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   "outputs": [
    {
     "data": {
      "text/plain": [
       ":purity"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def entropy(probablities)\n",
    "  -1 * probablities.reduce(0.0) { |sum,p| sum += p > 0 ? p * Math.log2(p) : 0 }\n",
    "end\n",
    "\n",
    "def gini(probablities)\n",
    "  probablities.reduce(0.0) { |sum,p| sum += p * (1 - p) }\n",
    "end\n",
    "\n",
    "def purity(mixtures, &block)\n",
    "  purity = mixtures.reduce(0.0) do |sum,m|\n",
    "    size = m.reduce(:+).to_f\n",
    "    sum += size > 0 ? size * yield(m.collect { |n| n/size }) : 0\n",
    "  end\n",
    "  purity / mixtures.flatten.reduce(:+)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "bb14d4f6-d34e-4adb-b16d-5787f97757cf"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Entropy of dataset = 0.9607079018756469\n",
      "Gini of dataset    = 0.4730129578614427\n"
     ]
    }
   ],
   "source": [
    "died     = dataset.select { |e| e['survived'] == '0' }.count\n",
    "survived = dataset.select { |e| e['survived'] == '1' }.count\n",
    "\n",
    "dataset_entropy = purity([[died,survived]]) { |ps| entropy(ps) }\n",
    "dataset_gini    = purity([[died,survived]]) { |ps| gini(ps) }\n",
    "\n",
    "puts \"Entropy of dataset = #{dataset_entropy}\"\n",
    "puts \"Gini of dataset    = #{dataset_gini}\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "991dce32-a1e6-4965-b0c1-5c75ea66f289"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Information Gain after gender split using Entropy = 0.2176601066606143\n",
      "Information Gain after gender split using Gini    = 0.13964795747285225\n"
     ]
    }
   ],
   "source": [
    "survived_female = dataset.select { |e| e['survived'] == '1' && e['sex'] == 'female' }.count\n",
    "survived_male   = dataset.select { |e| e['survived'] == '1' && e['sex'] == 'male'   }.count\n",
    "\n",
    "died_female     = dataset.select { |e| e['survived'] == '0' && e['sex'] == 'female' }.count\n",
    "died_male       = dataset.select { |e| e['survived'] == '0' && e['sex'] == 'male'   }.count\n",
    "\n",
    "gender_split = [[survived_female, died_female],[survived_male, died_male]]\n",
    "\n",
    "gender_split_entropy = purity(gender_split) { |ps| entropy(ps) }\n",
    "gender_split_gini    = purity(gender_split) { |ps| gini(ps)    }\n",
    "\n",
    "puts \"Information Gain after gender split using Entropy = #{dataset_entropy - gender_split_entropy}\"\n",
    "puts \"Information Gain after gender split using Gini    = #{dataset_gini - gender_split_gini}\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Information Gain after pclass split using Entropy = 0.08383104529601149\n",
      "Information Gain after pclass split using Gini    = 0.05462157677138346\n"
     ]
    }
   ],
   "source": [
    "survived_pclass_1 = dataset.select { |e| e['survived'] == '1' && e['pclass'] == '1' }.count\n",
    "survived_pclass_2 = dataset.select { |e| e['survived'] == '1' && e['pclass'] == '2' }.count\n",
    "survived_pclass_3 = dataset.select { |e| e['survived'] == '1' && e['pclass'] == '3' }.count\n",
    "\n",
    "died_pclass_1     = dataset.select { |e| e['survived'] == '0' && e['pclass'] == '1' }.count\n",
    "died_pclass_2     = dataset.select { |e| e['survived'] == '0' && e['pclass'] == '2' }.count\n",
    "died_pclass_3     = dataset.select { |e| e['survived'] == '0' && e['pclass'] == '3' }.count\n",
    "\n",
    "pclass_split = [\n",
    "  [survived_pclass_1,died_pclass_1],\n",
    "  [survived_pclass_2,died_pclass_2],\n",
    "  [survived_pclass_3,died_pclass_3]\n",
    "]\n",
    "\n",
    "pclass_split_entropy = purity(pclass_split) { |ps| entropy(ps) }\n",
    "pclass_split_gini    = purity(pclass_split) { |ps| gini(ps)    }\n",
    "\n",
    "puts \"Information Gain after pclass split using Entropy = #{dataset_entropy - pclass_split_entropy}\"\n",
    "puts \"Information Gain after pclass split using Gini    = #{dataset_gini - pclass_split_gini}\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Embarked types = [\"S\", \"C\", \"Q\", \"NA\"]\n",
      "Information Gain after embarked split using Entropy = 0.024047090707960517\n",
      "Information Gain after embarked split using Gini    = 0.015751498294317823\n"
     ]
    }
   ],
   "source": [
    "embarked_types = dataset.collect { |e| e['embarked'] }.uniq\n",
    "puts \"Embarked types = #{embarked_types}\"\n",
    "\n",
    "survived_embarked_S  = dataset.select { |e| e['survived'] == '1' && e['embarked'] == 'S' }.count\n",
    "survived_embarked_C  = dataset.select { |e| e['survived'] == '1' && e['embarked'] == 'C' }.count\n",
    "survived_embarked_Q  = dataset.select { |e| e['survived'] == '1' && e['embarked'] == 'Q' }.count\n",
    "survived_embarked_NA = dataset.select { |e| e['survived'] == '1' && e['embarked'] == 'NA' }.count\n",
    "\n",
    "died_embarked_S      = dataset.select { |e| e['survived'] == '0' && e['embarked'] == 'S' }.count\n",
    "died_embarked_C      = dataset.select { |e| e['survived'] == '0' && e['embarked'] == 'C' }.count\n",
    "died_embarked_Q      = dataset.select { |e| e['survived'] == '0' && e['embarked'] == 'Q' }.count\n",
    "died_embarked_NA     = dataset.select { |e| e['survived'] == '0' && e['embarked'] == 'NA' }.count\n",
    "\n",
    "embarked_split = [\n",
    "  [survived_embarked_S, died_embarked_S],\n",
    "  [survived_embarked_C, died_embarked_C],\n",
    "  [survived_embarked_Q, died_embarked_Q],\n",
    "  [survived_embarked_NA, died_embarked_NA]\n",
    "]\n",
    "\n",
    "embarked_split_entropy = purity(embarked_split) { |ps| entropy(ps) }\n",
    "embarked_split_gini    = purity(embarked_split) { |ps| gini(ps)    }\n",
    "\n",
    "puts \"Information Gain after embarked split using Entropy = #{dataset_entropy - embarked_split_entropy}\"\n",
    "puts \"Information Gain after embarked split using Gini    = #{dataset_gini - embarked_split_gini}\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpresent": {
     "id": "eb9152cb-1134-42d1-93e0-aa1bbc423097"
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   },
   "source": [
    "**IG(gender_split) > IG(pclass_split) > IG(embarked_split)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "40583111-b20f-4929-a49e-8b2c475e7d3f"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Information Gain after male-embarked split using Entropy = 0.05942132128706379\n",
      "Information Gain after male-embarked split using Gini    = 0.033595808771653746\n"
     ]
    }
   ],
   "source": [
    "survived_male_embarked_S  = dataset.select { |e| e['survived'] == '1' && e['sex'] == 'male' && e['embarked'] == 'S' }.count\n",
    "survived_male_embarked_C  = dataset.select { |e| e['survived'] == '1' && e['sex'] == 'male' && e['embarked'] == 'C' }.count\n",
    "survived_male_embarked_Q  = dataset.select { |e| e['survived'] == '1' && e['sex'] == 'male' && e['embarked'] == 'Q' }.count\n",
    "survived_male_embarked_NA = dataset.select { |e| e['survived'] == '1' && e['sex'] == 'male' && e['embarked'] == 'NA' }.count\n",
    "\n",
    "died_male_embarked_S  = dataset.select { |e| e['survived'] == '0' && e['sex'] == 'male' && e['embarked'] == 'S' }.count\n",
    "died_male_embarked_C  = dataset.select { |e| e['survived'] == '0' && e['sex'] == 'male' && e['embarked'] == 'C' }.count\n",
    "died_male_embarked_Q  = dataset.select { |e| e['survived'] == '0' && e['sex'] == 'male' && e['embarked'] == 'Q' }.count\n",
    "died_male_embarked_NA = dataset.select { |e| e['survived'] == '0' && e['sex'] == 'male' && e['embarked'] == 'NA' }.count\n",
    "\n",
    "male_embarked_split = [\n",
    "  [survived_male_embarked_S, died_male_embarked_S],\n",
    "  [survived_male_embarked_C,  died_male_embarked_C],\n",
    "  [survived_male_embarked_Q,  died_male_embarked_Q],\n",
    "  [survived_male_embarked_NA, died_male_embarked_NA]\n",
    "]\n",
    "\n",
    "male_embarked_split_entropy = purity(male_embarked_split) { |ps| entropy(ps) }\n",
    "male_embarked_split_gini    = purity(male_embarked_split) { |ps| gini(ps)    }\n",
    "\n",
    "puts \"Information Gain after male-embarked split using Entropy = #{gender_split_entropy - male_embarked_split_entropy}\"\n",
    "puts \"Information Gain after male-embarked split using Gini    = #{gender_split_gini - male_embarked_split_gini}\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
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    "nbpresent": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Information Gain after male-pclass split using Entropy = 0.08056051348939974\n",
      "Information Gain after male-pclass split using Gini    = 0.04442316613547043\n"
     ]
    }
   ],
   "source": [
    "survived_male_pclass_1  = dataset.select { |e| e['survived'] == '1' && e['sex'] == 'male' && e['pclass'] == '1' }.count\n",
    "survived_male_pclass_2  = dataset.select { |e| e['survived'] == '1' && e['sex'] == 'male' && e['pclass'] == '2' }.count\n",
    "survived_male_pclass_3  = dataset.select { |e| e['survived'] == '1' && e['sex'] == 'male' && e['pclass'] == '3' }.count\n",
    "\n",
    "died_male_pclass_1  = dataset.select { |e| e['survived'] == '0' && e['sex'] == 'male' && e['pclass'] == '1' }.count\n",
    "died_male_pclass_2  = dataset.select { |e| e['survived'] == '0' && e['sex'] == 'male' && e['pclass'] == '2' }.count\n",
    "died_male_pclass_3  = dataset.select { |e| e['survived'] == '0' && e['sex'] == 'male' && e['pclass'] == '3' }.count\n",
    "\n",
    "male_pclass_split = [\n",
    "  [survived_male_pclass_1,died_male_pclass_1],\n",
    "  [survived_male_pclass_2,died_male_pclass_2],\n",
    "  [survived_male_pclass_3,died_male_pclass_3]\n",
    "]\n",
    "\n",
    "male_pclass_split_entropy = purity(male_pclass_split) { |ps| entropy(ps) }\n",
    "male_pclass_split_gini    = purity(male_pclass_split) { |ps| gini(ps)    }\n",
    "\n",
    "puts \"Information Gain after male-pclass split using Entropy = #{gender_split_entropy - male_pclass_split_entropy}\"\n",
    "puts \"Information Gain after male-pclass split using Gini    = #{gender_split_gini - male_pclass_split_gini}\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Information Gain after female-embarked split using Entropy = -0.052903841414234765\n",
      "Information Gain after female-embarked split using Gini    = -0.0366266354137858\n"
     ]
    }
   ],
   "source": [
    "survived_female_embarked_S  = dataset.select { |e| e['survived'] == '1' && e['sex'] == 'female' && e['embarked'] == 'S' }.count\n",
    "survived_female_embarked_C  = dataset.select { |e| e['survived'] == '1' && e['sex'] == 'female' && e['embarked'] == 'C' }.count\n",
    "survived_female_embarked_Q  = dataset.select { |e| e['survived'] == '1' && e['sex'] == 'female' && e['embarked'] == 'Q' }.count\n",
    "survived_female_embarked_NA = dataset.select { |e| e['survived'] == '1' && e['sex'] == 'female' && e['embarked'] == 'NA' }.count\n",
    "\n",
    "died_female_embarked_S  = dataset.select { |e| e['survived'] == '0' && e['sex'] == 'female' && e['embarked'] == 'S' }.count\n",
    "died_female_embarked_C  = dataset.select { |e| e['survived'] == '0' && e['sex'] == 'female' && e['embarked'] == 'C' }.count\n",
    "died_female_embarked_Q  = dataset.select { |e| e['survived'] == '0' && e['sex'] == 'female' && e['embarked'] == 'Q' }.count\n",
    "died_female_embarked_NA = dataset.select { |e| e['survived'] == '0' && e['sex'] == 'female' && e['embarked'] == 'NA' }.count\n",
    "\n",
    "female_embarked_split = [\n",
    "  [survived_female_embarked_S, died_female_embarked_S],\n",
    "  [survived_female_embarked_C,  died_female_embarked_C],\n",
    "  [survived_female_embarked_Q,  died_female_embarked_Q],\n",
    "  [survived_female_embarked_NA, died_female_embarked_NA]\n",
    "]\n",
    "\n",
    "female_embarked_split_entropy = purity(female_embarked_split) { |ps| entropy(ps) }\n",
    "female_embarked_split_gini    = purity(female_embarked_split) { |ps| gini(ps)    }\n",
    "\n",
    "puts \"Information Gain after female-embarked split using Entropy = #{gender_split_entropy - female_embarked_split_entropy}\"\n",
    "puts \"Information Gain after female-embarked split using Gini    = #{gender_split_gini - female_embarked_split_gini}\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "nbpresent": {
     "id": "47bdbb1f-6df0-4030-b568-605093a81ad6"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Information Gain after female-pclass split using Entropy = 0.12696481072875554\n",
      "Information Gain after female-pclass split using Gini    = 0.05036773218080309\n"
     ]
    }
   ],
   "source": [
    "survived_female_pclass_1  = dataset.select { |e| e['survived'] == '1' && e['sex'] == 'female' && e['pclass'] == '1' }.count\n",
    "survived_female_pclass_2  = dataset.select { |e| e['survived'] == '1' && e['sex'] == 'female' && e['pclass'] == '2' }.count\n",
    "survived_female_pclass_3  = dataset.select { |e| e['survived'] == '1' && e['sex'] == 'female' && e['pclass'] == '3' }.count\n",
    "\n",
    "died_female_pclass_1  = dataset.select { |e| e['survived'] == '0' && e['sex'] == 'female' && e['pclass'] == '1' }.count\n",
    "died_female_pclass_2  = dataset.select { |e| e['survived'] == '0' && e['sex'] == 'female' && e['pclass'] == '2' }.count\n",
    "died_female_pclass_3  = dataset.select { |e| e['survived'] == '0' && e['sex'] == 'female' && e['pclass'] == '3' }.count\n",
    "\n",
    "female_pclass_split = [\n",
    "  [survived_female_pclass_1,died_female_pclass_1],\n",
    "  [survived_female_pclass_2,died_female_pclass_2],\n",
    "  [survived_female_pclass_3,died_female_pclass_3]\n",
    "]\n",
    "\n",
    "female_pclass_split_entropy = purity(female_pclass_split) { |ps| entropy(ps) }\n",
    "female_pclass_split_gini    = purity(female_pclass_split) { |ps| gini(ps)    }\n",
    "\n",
    "puts \"Information Gain after female-pclass split using Entropy = #{gender_split_entropy - female_pclass_split_entropy}\"\n",
    "puts \"Information Gain after female-pclass split using Gini    = #{gender_split_gini - female_pclass_split_gini}\""
   ]
  }
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