https://en.wikipedia.org/wiki/Naive_Bayes_classifier

Naive_bayes_classifier_korean_unit.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Naive Bayes Classifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic Knowledge"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random.choice([1, 2, 3, 4, 5, 6])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ex1. Rolling Dice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = []\n",
    "\n",
    "for i in range(10000):\n",
    "    choice = random.choice([1, 2, 3, 4, 5, 6])\n",
    "    result.append(choice)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jVfW7Q4v2ANva9DbgtqH6u9vdQBcAzw4NFUmSVtjqMda9EHgX8GCSz7Xah4CPArckuRz4EvDOtmwv8BZgDvgm8J4x9i1JGtPIAVBV/wjkKIs3H6F9AVeMuj9J0vLySWBJ6pQBIEmdMgAkqVMGgCR1ygCQpE4ZAJLUKQNAkjplAEhSpwwASeqUASBJnTIAJKlTBoAkdcoAkKROGQCS1CkDQJI6teIBkGRLki8kmUty1UrvX5I0sKIBkGQV8HHgYuBc4LIk565kHyRJAyt9BnA+MFdVj1fVc8DNwNYV7oMkiZUPgHXAgaH5+VaTJK2wDF7Vu0I7S94BbKmqX2rz7wJeX1XvHWqzHdjeZl8DfAFYC3x1xTp66vI4HOaxGPA4DHgcDlsLnFFVU0s1HPml8CM6CGwYml/fav9PVe0AdgzXksxW1czJ796pzeNwmMdiwOMw4HE4rB2L6eNpu9JDQPcCm5JsTHIacCmwZ4X7IElihc8Aqur5JO8FbgdWAbuqav9K9kGSNLDSQ0BU1V5g7wmutmPpJl3wOBzmsRjwOAx4HA477mOxoheBJUmnDv8UhCR16pQOgCS7khxK8tCk+zJJSTYkuTPJw0n2J3n/pPs0CUm+N8lnk3y+HYf/Oek+TVKSVUn+OclfTLovk5TkiSQPJvlcktlJ92dSkqxJcmuSR5M8kuSnl1znVB4CSvIG4BvADVX12kn3Z1KSnAOcU1X3J/kPwH3AJVX18IS7tqKShMH9zd9I8jLgH4H3V9XdE+7aRCS5EpgBfqCq3jbp/kxKkieAmarq+jmAJLuBf6iq69tdli+vqq8da51T+gygqu4Cnp50Pyatqp6sqvvb9L8Cj9DhE9Q18I02+7L2c+r+BnMSJVkPvBW4ftJ90eQleQXwBmAnQFU9t9Q//nCKB4BeLMk08Drgnsn2ZDLasMfngEPAvqrq8jgAvwd8APjOpDtyCijgb5Lc1/6SQI82AgvAH7dhweuTnLHUSgbAS0iS7wc+CfxaVX190v2ZhKr6dlX9JIOnyM9P0t3QYJK3AYeq6r5J9+UU8Z+q6jwGf2X4ijZ03JvVwHnAdVX1OuDfgCX/3L4B8BLRxrw/CdxYVZ+adH8mrZ3e3glsmXRfJuBC4O1t7Ptm4E1J/mSyXZqcqjrYPg8Bn2bwV4d7Mw/MD50R38ogEI7JAHgJaBc/dwKPVNXvTro/k5JkKsmaNv19wM8Bj062Vyuvqq6uqvXt771cCnymqn5xwt2aiCRntBsjaEMeFwHd3TVYVU8BB5K8ppU2A0veJLLiTwKfiCQ3AW8E1iaZB66pqp2T7dVEXAi8C3iwjX8DfKg9Vd2Tc4Dd7cVC3wPcUlVd3wIpzgY+PfgdidXAn1bVX0+2SxPzPuDGdgfQ48B7llrhlL4NVJJ08jgEJEmdMgAkqVMGgCR1ygCQpE4ZAJLUKQNAkjplAEhSpwwASerU/wXvOA8oId7+hAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(result, bins=6, rwidth=0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ex2. Fliping a coin"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = []\n",
    "for _ in range(10):\n",
    "    choice = random.choice([0, 1])\n",
    "    result.append(choice)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 0, 1, 0, 0, 1, 0, 0, 0]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Several times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def coin_flip():\n",
    "    result = []\n",
    "    for _ in range(10):\n",
    "        choice = random.choice([0, 1])\n",
    "        result.append(choice)\n",
    "    return sum(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coin_flip()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = []\n",
    "for _ in range(100):\n",
    "    result.append(coin_flip())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(result);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = []\n",
    "for _ in range(10000):\n",
    "    result.append(coin_flip())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(result);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = []\n",
    "for _ in range(100000):\n",
    "    result.append(coin_flip())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(result);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.00496"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean = np.mean(result)\n",
    "mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.576983005108172"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "std = np.std(result)\n",
    "std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Probability Density Function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$${\\frac  1{\\sigma {\\sqrt  {2\\pi }}}}\\;\\exp \\left(-{\\frac  {\\left(x-\\mu \\right)^{2}}{2\\sigma ^{2}}}\\right)\\!$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normal_dist(x, mu, sigma):\n",
    "    value = 1/(sigma*np.sqrt(2*np.pi)) * np.exp(-((x-mu)**2)/(2*sigma**2))\n",
    "    return value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[7, 7, 3, 5, 6]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2529769222819525"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normal_dist(5, mean, std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.20731455506830634"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normal_dist(6, mean, std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.01005864270443588"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normal_dist(1, mean, std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0016767927425059594"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normal_dist(10, mean, std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "dist_data = []\n",
    "for i in result:\n",
    "    dist_data.append( normal_dist(i, mean, std) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(dist_data, '.');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(result, dist_data);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example1. Gender classification (Wikipedia Example)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Problem: classify whether a given person is a male or a female based on the measured features. The features include height, weight, and foot size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# https://en.wikipedia.org/wiki/Naive_Bayes_classifier\n",
    "text = \"\"\"male\t6\t180\t12\n",
    "male\t5.92\t190\t11\n",
    "male\t5.58\t170\t12\n",
    "male\t5.92\t165\t10\n",
    "female\t5\t100\t6\n",
    "female\t5.5\t150\t8\n",
    "female\t5.42\t130\t7\n",
    "female\t5.75\t150\t9\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "rows = text.split(\"\\n\")\n",
    "samples = [row.split(\"\\t\") for row in rows]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[['male', '6', '180', '12'],\n",
       " ['male', '5.92', '190', '11'],\n",
       " ['male', '5.58', '170', '12'],\n",
       " ['male', '5.92', '165', '10'],\n",
       " ['female', '5', '100', '6'],\n",
       " ['female', '5.5', '150', '8'],\n",
       " ['female', '5.42', '130', '7'],\n",
       " ['female', '5.75', '150', '9']]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = dict()\n",
    "data['Person'] = list()\n",
    "data['height'] = list() # feet\n",
    "data['weight'] = list() # lbs\n",
    "data['foot_size'] = list() # inches"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "# for sample in samples:\n",
    "#     data['Person'].append(sample[0])\n",
    "#     data['height'].append(float(sample[1]))\n",
    "#     data['weight'].append(float(sample[2]))\n",
    "#     data['foot_size'].append(float(sample[3]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "for sample in samples:\n",
    "    data['Person'].append(sample[0])\n",
    "    data['height'].append(float(sample[1])*30.48) # cm\n",
    "    data['weight'].append(float(sample[2])*0.453592) # kg\n",
    "    data['foot_size'].append(float(sample[3])*2.54) # cm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate a dataframe of sample dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "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>Person</th>\n",
       "      <th>height</th>\n",
       "      <th>weight</th>\n",
       "      <th>foot_size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>male</td>\n",
       "      <td>182.8800</td>\n",
       "      <td>81.64656</td>\n",
       "      <td>30.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>male</td>\n",
       "      <td>180.4416</td>\n",
       "      <td>86.18248</td>\n",
       "      <td>27.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>male</td>\n",
       "      <td>170.0784</td>\n",
       "      <td>77.11064</td>\n",
       "      <td>30.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>male</td>\n",
       "      <td>180.4416</td>\n",
       "      <td>74.84268</td>\n",
       "      <td>25.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>female</td>\n",
       "      <td>152.4000</td>\n",
       "      <td>45.35920</td>\n",
       "      <td>15.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>female</td>\n",
       "      <td>167.6400</td>\n",
       "      <td>68.03880</td>\n",
       "      <td>20.32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>female</td>\n",
       "      <td>165.2016</td>\n",
       "      <td>58.96696</td>\n",
       "      <td>17.78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>female</td>\n",
       "      <td>175.2600</td>\n",
       "      <td>68.03880</td>\n",
       "      <td>22.86</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Person    height    weight  foot_size\n",
       "0    male  182.8800  81.64656      30.48\n",
       "1    male  180.4416  86.18248      27.94\n",
       "2    male  170.0784  77.11064      30.48\n",
       "3    male  180.4416  74.84268      25.40\n",
       "4  female  152.4000  45.35920      15.24\n",
       "5  female  167.6400  68.03880      20.32\n",
       "6  female  165.2016  58.96696      17.78\n",
       "7  female  175.2600  68.03880      22.86"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generates descriptive statistics that summarize the central tendency, dispersion and shape of a dataset’s distribution, excluding NaN values.\n",
    "https://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.describe.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "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>height</th>\n",
       "      <th>weight</th>\n",
       "      <th>foot_size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>8.000000</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>8.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>171.792900</td>\n",
       "      <td>70.023265</td>\n",
       "      <td>23.81250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>10.171813</td>\n",
       "      <td>13.137259</td>\n",
       "      <td>5.75017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>152.400000</td>\n",
       "      <td>45.359200</td>\n",
       "      <td>15.24000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>167.030400</td>\n",
       "      <td>65.770840</td>\n",
       "      <td>19.68500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>172.669200</td>\n",
       "      <td>71.440740</td>\n",
       "      <td>24.13000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>180.441600</td>\n",
       "      <td>78.244620</td>\n",
       "      <td>28.57500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>182.880000</td>\n",
       "      <td>86.182480</td>\n",
       "      <td>30.48000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           height     weight  foot_size\n",
       "count    8.000000   8.000000    8.00000\n",
       "mean   171.792900  70.023265   23.81250\n",
       "std     10.171813  13.137259    5.75017\n",
       "min    152.400000  45.359200   15.24000\n",
       "25%    167.030400  65.770840   19.68500\n",
       "50%    172.669200  71.440740   24.13000\n",
       "75%    180.441600  78.244620   28.57500\n",
       "max    182.880000  86.182480   30.48000"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>Person</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>female</th>\n",
       "      <td>4.0</td>\n",
       "      <td>165.1254</td>\n",
       "      <td>9.503946</td>\n",
       "      <td>152.4000</td>\n",
       "      <td>162.0012</td>\n",
       "      <td>166.4208</td>\n",
       "      <td>169.5450</td>\n",
       "      <td>175.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>male</th>\n",
       "      <td>4.0</td>\n",
       "      <td>178.4604</td>\n",
       "      <td>5.705001</td>\n",
       "      <td>170.0784</td>\n",
       "      <td>177.8508</td>\n",
       "      <td>180.4416</td>\n",
       "      <td>181.0512</td>\n",
       "      <td>182.88</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        count      mean       std       min       25%       50%       75%  \\\n",
       "Person                                                                      \n",
       "female    4.0  165.1254  9.503946  152.4000  162.0012  166.4208  169.5450   \n",
       "male      4.0  178.4604  5.705001  170.0784  177.8508  180.4416  181.0512   \n",
       "\n",
       "           max  \n",
       "Person          \n",
       "female  175.26  \n",
       "male    182.88  "
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby(\"Person\")['height'].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Person</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>female</th>\n",
       "      <td>4.0</td>\n",
       "      <td>60.10094</td>\n",
       "      <td>10.717961</td>\n",
       "      <td>45.35920</td>\n",
       "      <td>55.56502</td>\n",
       "      <td>63.50288</td>\n",
       "      <td>68.03880</td>\n",
       "      <td>68.03880</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>male</th>\n",
       "      <td>4.0</td>\n",
       "      <td>79.94559</td>\n",
       "      <td>5.028874</td>\n",
       "      <td>74.84268</td>\n",
       "      <td>76.54365</td>\n",
       "      <td>79.37860</td>\n",
       "      <td>82.78054</td>\n",
       "      <td>86.18248</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        count      mean        std       min       25%       50%       75%  \\\n",
       "Person                                                                       \n",
       "female    4.0  60.10094  10.717961  45.35920  55.56502  63.50288  68.03880   \n",
       "male      4.0  79.94559   5.028874  74.84268  76.54365  79.37860  82.78054   \n",
       "\n",
       "             max  \n",
       "Person            \n",
       "female  68.03880  \n",
       "male    86.18248  "
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby(\"Person\")['weight'].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
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       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Person</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>female</th>\n",
       "      <td>4.0</td>\n",
       "      <td>19.050</td>\n",
       "      <td>3.279126</td>\n",
       "      <td>15.24</td>\n",
       "      <td>17.145</td>\n",
       "      <td>19.05</td>\n",
       "      <td>20.955</td>\n",
       "      <td>22.86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>male</th>\n",
       "      <td>4.0</td>\n",
       "      <td>28.575</td>\n",
       "      <td>2.431865</td>\n",
       "      <td>25.40</td>\n",
       "      <td>27.305</td>\n",
       "      <td>29.21</td>\n",
       "      <td>30.480</td>\n",
       "      <td>30.48</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        count    mean       std    min     25%    50%     75%    max\n",
       "Person                                                              \n",
       "female    4.0  19.050  3.279126  15.24  17.145  19.05  20.955  22.86\n",
       "male      4.0  28.575  2.431865  25.40  27.305  29.21  30.480  30.48"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby(\"Person\")['foot_size'].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's say we have equiprobable classes so $P(male)= P(female) = 0.5$. This prior probability distribution might be based on our knowledge of frequencies in the larger population, or on frequency in the training set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Evidence"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The evidence (also termed normalizing constant) may be calculated:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$${\\displaystyle {\\begin{aligned}{\\text{evidence}}=P({\\text{male}})\\,p({\\text{height}}\\mid {\\text{male}})\\,p({\\text{weight}}\\mid {\\text{male}})\\,p({\\text{foot size}}\\mid {\\text{male}})\\\\+P({\\text{female}})\\,p({\\text{height}}\\mid {\\text{female}})\\,p({\\text{weight}}\\mid {\\text{female}})\\,p({\\text{foot size}}\\mid {\\text{female}})\\end{aligned}}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, given the sample, the evidence is a constant and thus scales both posteriors equally. It therefore does not affect classification and can be ignored. We now determine the probability distribution for the sex of the sample."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Posterior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$${\\displaystyle {\\text{posterior (male)}}={\\frac {P({\\text{male}})\\,p({\\text{height}}\\mid {\\text{male}})\\,p({\\text{weight}}\\mid {\\text{male}})\\,p({\\text{foot size}}\\mid {\\text{male}})}{evidence}}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$p({\\text{height}}\\mid {\\text{male}})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.023286164045900566"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_value = 170\n",
    "prob_height_male = normal_dist(test_value, 178.4604, 5.705001)\n",
    "prob_height_male"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0445845280595133e-05"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_value = 60\n",
    "prob_weight_male = normal_dist(test_value, 79.94559, 5.028874)\n",
    "prob_weight_male"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11399294791774302"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_value = 26.5\n",
    "prob_foot_size_male = normal_dist(test_value, 28.575, 2.431865)\n",
    "prob_foot_size_male"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.040861617342621e-08"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.5*prob_height_male*prob_weight_male*prob_foot_size_male"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "# prob_height_male = normal_dist(6, 5.8550, 0.187172)\n",
    "# prob_weight_male = normal_dist(130, 176.25, 11.086779)\n",
    "# prob_foot_size_male = normal_dist(8, 11.25, 0.957427)\n",
    "\n",
    "# print(prob_height_male, prob_weight_male, prob_foot_size_male)\n",
    "# print(0.5*prob_height_male*prob_weight_male*prob_foot_size_male)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.051800627867100664 1.3198510367846946e-05 0.0005162290843604684\n",
      "1.7647062145489237e-10\n"
     ]
    }
   ],
   "source": [
    "prob_height_male = normal_dist(182.88, 178.4604, 5.705001)\n",
    "prob_weight_male = normal_dist(58.96696, 79.94559, 5.028874)\n",
    "prob_foot_size_male = normal_dist(20.32, 28.575, 2.431865)\n",
    "\n",
    "print(prob_height_male, prob_weight_male, prob_foot_size_male)\n",
    "prob_male_data = 0.5*prob_height_male*prob_weight_male*prob_foot_size_male\n",
    "print(prob_male_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$${\\displaystyle {\\text{posterior (female)}}={\\frac {P({\\text{female}})\\,p({\\text{height}}\\mid {\\text{female}})\\,p({\\text{weight}}\\mid {\\text{female}})\\,p({\\text{foot size}}\\mid {\\text{female}})}{evidence}}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.007331323961664202 0.037014095469218904 0.11287035135585421\n",
      "1.531438048559744e-05\n"
     ]
    }
   ],
   "source": [
    "prob_height_female = normal_dist(182.88, 165.1254, 9.503946)\n",
    "prob_weight_female = normal_dist(58.96696, 60.10094, 10.717961)\n",
    "prob_foot_size_female = normal_dist(20.32, 19.050, 3.279126)\n",
    "\n",
    "print(prob_height_female, prob_weight_female, prob_foot_size_female)\n",
    "prob_female_data = 0.5*prob_height_female*prob_weight_female*prob_foot_size_female\n",
    "print(prob_female_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since posterior numerator is greater in the female case, we predict the sample is female."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1523196881575189e-05"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prob_male_data/prob_female_data"
   ]
  }
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