5. Statistics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Satistics - Introduction\n",
    "\n",
    "https://numpy.org/doc/stable/reference/routines.statistics.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Simple Statistical Exploration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[7.16622070e-01, 8.67937006e-01, 8.56064808e-01, 8.57568350e-01,\n",
       "        3.67796230e-01, 2.14346363e-01, 6.31599734e-01, 3.57119296e-01,\n",
       "        4.35844862e-01, 2.35483572e-01],\n",
       "       [7.22209004e-01, 9.63310994e-01, 8.16973750e-01, 8.06853501e-01,\n",
       "        6.89970795e-01, 5.83418094e-01, 2.65411361e-02, 7.51624520e-01,\n",
       "        9.59391711e-02, 4.15581862e-01],\n",
       "       [8.57467652e-01, 9.63049501e-01, 7.90326873e-01, 7.95018533e-01,\n",
       "        7.18152201e-01, 4.38823904e-01, 6.45775017e-01, 7.60717860e-01,\n",
       "        9.24224445e-01, 3.13183949e-01],\n",
       "       [3.83836565e-01, 8.56498268e-01, 5.93058237e-01, 2.46908006e-01,\n",
       "        3.10960918e-01, 6.21511447e-01, 2.91997569e-01, 8.13963097e-01,\n",
       "        2.01951380e-01, 5.79517413e-01],\n",
       "       [8.41978469e-02, 3.81861596e-01, 1.24320969e-01, 1.92482070e-01,\n",
       "        4.70194470e-01, 9.69335675e-01, 2.07682914e-01, 8.99462218e-01,\n",
       "        3.56681685e-01, 2.10451446e-01],\n",
       "       [2.50727875e-01, 4.45871405e-01, 4.75621851e-01, 1.76392569e-01,\n",
       "        4.44494388e-01, 1.97214743e-01, 2.23416686e-01, 9.79333246e-01,\n",
       "        2.13115739e-01, 3.26530393e-01],\n",
       "       [6.18496895e-01, 8.46193255e-01, 9.20304738e-01, 4.49655661e-01,\n",
       "        6.66495695e-01, 7.23878345e-01, 4.71483753e-01, 3.35079701e-01,\n",
       "        2.80457713e-01, 4.17035078e-01],\n",
       "       [3.74931699e-01, 1.64469071e-02, 8.24518210e-01, 4.40508140e-01,\n",
       "        3.04546586e-01, 9.61964988e-01, 9.13281778e-01, 1.08067818e-01,\n",
       "        3.52596222e-01, 9.71936660e-01],\n",
       "       [6.24254898e-01, 6.83181203e-01, 7.55043126e-01, 5.46638933e-01,\n",
       "        1.40146074e-01, 8.45252325e-02, 2.54143985e-01, 4.85118512e-04,\n",
       "        8.08711713e-01, 9.33249065e-01],\n",
       "       [4.10573251e-01, 6.30441143e-01, 6.04971277e-01, 4.07647377e-01,\n",
       "        8.25351233e-01, 5.19909474e-01, 9.76184695e-02, 8.11742544e-01,\n",
       "        6.04160360e-01, 4.48347194e-01]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.random.rand(10,10)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 10)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9793332463866128"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00048511851159238617"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.523381592476641"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.47355280212201306"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2772531462004282"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.06873698,  0.03278827,  0.03668793, -0.00331421, -0.05083651,\n",
       "        -0.00850994,  0.02390898, -0.02626347,  0.03131505, -0.01397033],\n",
       "       [ 0.03278827,  0.09816338,  0.01792033,  0.04059124,  0.01004886,\n",
       "         0.02993195,  0.03987967, -0.05153719, -0.00568755,  0.03430207],\n",
       "       [ 0.03668793,  0.01792033,  0.04244191, -0.00450095, -0.0155604 ,\n",
       "         0.00718968,  0.00519803, -0.05720041,  0.00948249,  0.01091863],\n",
       "       [-0.00331421,  0.04059124, -0.00450095,  0.05553323,  0.03406878,\n",
       "         0.03667575,  0.01972246, -0.01604353, -0.00940025,  0.02010751],\n",
       "       [-0.05083651,  0.01004886, -0.0155604 ,  0.03406878,  0.09681987,\n",
       "         0.03356765, -0.00601017, -0.01500941, -0.0759788 ,  0.0324855 ],\n",
       "       [-0.00850994,  0.02993195,  0.00718968,  0.03667575,  0.03356765,\n",
       "         0.0581328 , -0.00229493, -0.04089154, -0.03034172,  0.03377649],\n",
       "       [ 0.02390898,  0.03987967,  0.00519803,  0.01972246, -0.00601017,\n",
       "        -0.00229493,  0.04676247,  0.00605692,  0.00312176,  0.00634826],\n",
       "       [-0.02626347, -0.05153719, -0.05720041, -0.01604353, -0.01500941,\n",
       "        -0.04089154,  0.00605692,  0.13017446,  0.01244017, -0.04495907],\n",
       "       [ 0.03131505, -0.00568755,  0.00948249, -0.00940025, -0.0759788 ,\n",
       "        -0.03034172,  0.00312176,  0.01244017,  0.11204687, -0.01455545],\n",
       "       [-0.01397033,  0.03430207,  0.01091863,  0.02010751,  0.0324855 ,\n",
       "         0.03377649,  0.00634826, -0.04495907, -0.01455545,  0.04560073]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cov(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Mean and std of row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.50433178, 0.66547913, 0.67612038, 0.49196731, 0.49381086,\n",
       "       0.53149283, 0.3763541 , 0.58175954, 0.42736833, 0.48513166])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(A,axis =0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.22924647, 0.28962689, 0.22578381, 0.24259586, 0.21017855,\n",
       "       0.2908006 , 0.26627669, 0.33170298, 0.25736132, 0.25495454])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(A,axis =0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Mean and std of col"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.55403823, 0.58724228, 0.72067399, 0.49002029, 0.38966709,\n",
       "       0.37327189, 0.57290808, 0.5268799 , 0.48303793, 0.53607623])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(A,axis =1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.2487233 , 0.29723231, 0.19544236, 0.22356186, 0.29519126,\n",
       "       0.2287346 , 0.20514927, 0.34228207, 0.31755658, 0.20258494])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(A,axis = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Feature Scaling:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 1. Mini-max scalar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[59, 39, 55, 69, 55, 10, 89, 79, 71, 77],\n",
       "       [36, 72, 69, 36, 38, 43, 21, 53, 65, 18],\n",
       "       [29, 78, 85, 77, 11, 85, 73, 83, 47, 82],\n",
       "       [17, 70, 94, 48, 10, 68, 92, 96, 12, 56],\n",
       "       [ 5, 54, 30, 57, 86, 49, 10, 22, 17, 73],\n",
       "       [46, 36, 63, 60, 64, 95, 76, 64, 13, 93],\n",
       "       [79, 98, 56, 67, 38, 21, 16, 67, 15, 13],\n",
       "       [45, 11, 90, 26, 64, 25, 10, 33, 97, 36],\n",
       "       [86, 88, 68, 24, 40, 20, 17, 59, 83, 74],\n",
       "       [67, 76, 64, 47, 73, 82, 77, 67, 15, 49]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = (100*np.random.rand(10,10)).astype(int)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "A_mm = (A - A.min())/(A.max()-A.min())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.58064516, 0.3655914 , 0.53763441, 0.68817204, 0.53763441,\n",
       "        0.05376344, 0.90322581, 0.79569892, 0.70967742, 0.77419355],\n",
       "       [0.33333333, 0.72043011, 0.68817204, 0.33333333, 0.35483871,\n",
       "        0.40860215, 0.17204301, 0.51612903, 0.64516129, 0.13978495],\n",
       "       [0.25806452, 0.78494624, 0.86021505, 0.77419355, 0.06451613,\n",
       "        0.86021505, 0.7311828 , 0.83870968, 0.4516129 , 0.82795699],\n",
       "       [0.12903226, 0.69892473, 0.95698925, 0.46236559, 0.05376344,\n",
       "        0.67741935, 0.93548387, 0.97849462, 0.07526882, 0.5483871 ],\n",
       "       [0.        , 0.52688172, 0.2688172 , 0.55913978, 0.87096774,\n",
       "        0.47311828, 0.05376344, 0.1827957 , 0.12903226, 0.7311828 ],\n",
       "       [0.44086022, 0.33333333, 0.62365591, 0.59139785, 0.6344086 ,\n",
       "        0.96774194, 0.76344086, 0.6344086 , 0.08602151, 0.94623656],\n",
       "       [0.79569892, 1.        , 0.5483871 , 0.66666667, 0.35483871,\n",
       "        0.17204301, 0.11827957, 0.66666667, 0.10752688, 0.08602151],\n",
       "       [0.43010753, 0.06451613, 0.91397849, 0.22580645, 0.6344086 ,\n",
       "        0.21505376, 0.05376344, 0.30107527, 0.98924731, 0.33333333],\n",
       "       [0.87096774, 0.89247312, 0.67741935, 0.20430108, 0.37634409,\n",
       "        0.16129032, 0.12903226, 0.58064516, 0.83870968, 0.74193548],\n",
       "       [0.66666667, 0.76344086, 0.6344086 , 0.4516129 , 0.7311828 ,\n",
       "        0.82795699, 0.77419355, 0.66666667, 0.10752688, 0.47311828]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_mm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:595: DataConversionWarning: Data with input dtype int32 was converted to float64 by MinMaxScaler.\n",
      "  warnings.warn(msg, DataConversionWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0.66666667, 0.32183908, 0.390625  , 0.8490566 , 0.59210526,\n",
       "        0.        , 0.96341463, 0.77027027, 0.69411765, 0.8       ],\n",
       "       [0.38271605, 0.70114943, 0.609375  , 0.22641509, 0.36842105,\n",
       "        0.38823529, 0.13414634, 0.41891892, 0.62352941, 0.0625    ],\n",
       "       [0.2962963 , 0.77011494, 0.859375  , 1.        , 0.01315789,\n",
       "        0.88235294, 0.76829268, 0.82432432, 0.41176471, 0.8625    ],\n",
       "       [0.14814815, 0.67816092, 1.        , 0.45283019, 0.        ,\n",
       "        0.68235294, 1.        , 1.        , 0.        , 0.5375    ],\n",
       "       [0.        , 0.49425287, 0.        , 0.62264151, 1.        ,\n",
       "        0.45882353, 0.        , 0.        , 0.05882353, 0.75      ],\n",
       "       [0.50617284, 0.28735632, 0.515625  , 0.67924528, 0.71052632,\n",
       "        1.        , 0.80487805, 0.56756757, 0.01176471, 1.        ],\n",
       "       [0.91358025, 1.        , 0.40625   , 0.81132075, 0.36842105,\n",
       "        0.12941176, 0.07317073, 0.60810811, 0.03529412, 0.        ],\n",
       "       [0.49382716, 0.        , 0.9375    , 0.03773585, 0.71052632,\n",
       "        0.17647059, 0.        , 0.14864865, 1.        , 0.2875    ],\n",
       "       [1.        , 0.88505747, 0.59375   , 0.        , 0.39473684,\n",
       "        0.11764706, 0.08536585, 0.5       , 0.83529412, 0.7625    ],\n",
       "       [0.7654321 , 0.74712644, 0.53125   , 0.43396226, 0.82894737,\n",
       "        0.84705882, 0.81707317, 0.60810811, 0.03529412, 0.45      ]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import preprocessing\n",
    "\n",
    "A_scaled = preprocessing.MinMaxScaler().fit(A).transform(A)\n",
    "A_scaled"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 2. Standard Scalar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[17, 26, 40, 45, 98, 42, 77, 67,  1, 98],\n",
       "       [ 8, 52, 68,  2,  6, 89, 76, 44,  2,  4],\n",
       "       [30, 57,  9, 48, 57, 26, 71, 42, 49,  0],\n",
       "       [13, 18, 65, 81, 36,  2, 25,  7, 80, 18],\n",
       "       [17, 88, 95, 57, 67, 38, 12, 78, 21, 64],\n",
       "       [75, 41,  8, 72, 47, 77, 13, 98, 56, 71],\n",
       "       [96, 14, 50, 87, 24,  9, 48, 25, 11, 25],\n",
       "       [68, 16, 94, 30, 23, 41, 22, 96, 93, 33],\n",
       "       [10, 72, 84, 29, 59, 40, 86, 31, 82, 97],\n",
       "       [72, 33, 16, 78, 12,  6, 63, 25, 28, 24]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = (100*np.random.rand(10,10)).astype(int)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "A_ss = A - A.mean()/A.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[15.48180308, 24.48180308, 38.48180308, 43.48180308, 96.48180308,\n",
       "        40.48180308, 75.48180308, 65.48180308, -0.51819692, 96.48180308],\n",
       "       [ 6.48180308, 50.48180308, 66.48180308,  0.48180308,  4.48180308,\n",
       "        87.48180308, 74.48180308, 42.48180308,  0.48180308,  2.48180308],\n",
       "       [28.48180308, 55.48180308,  7.48180308, 46.48180308, 55.48180308,\n",
       "        24.48180308, 69.48180308, 40.48180308, 47.48180308, -1.51819692],\n",
       "       [11.48180308, 16.48180308, 63.48180308, 79.48180308, 34.48180308,\n",
       "         0.48180308, 23.48180308,  5.48180308, 78.48180308, 16.48180308],\n",
       "       [15.48180308, 86.48180308, 93.48180308, 55.48180308, 65.48180308,\n",
       "        36.48180308, 10.48180308, 76.48180308, 19.48180308, 62.48180308],\n",
       "       [73.48180308, 39.48180308,  6.48180308, 70.48180308, 45.48180308,\n",
       "        75.48180308, 11.48180308, 96.48180308, 54.48180308, 69.48180308],\n",
       "       [94.48180308, 12.48180308, 48.48180308, 85.48180308, 22.48180308,\n",
       "         7.48180308, 46.48180308, 23.48180308,  9.48180308, 23.48180308],\n",
       "       [66.48180308, 14.48180308, 92.48180308, 28.48180308, 21.48180308,\n",
       "        39.48180308, 20.48180308, 94.48180308, 91.48180308, 31.48180308],\n",
       "       [ 8.48180308, 70.48180308, 82.48180308, 27.48180308, 57.48180308,\n",
       "        38.48180308, 84.48180308, 29.48180308, 80.48180308, 95.48180308],\n",
       "       [70.48180308, 31.48180308, 14.48180308, 76.48180308, 10.48180308,\n",
       "         4.48180308, 61.48180308, 23.48180308, 26.48180308, 22.48180308]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_ss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:595: DataConversionWarning: Data with input dtype int32 was converted to float64 by StandardScaler.\n",
      "  warnings.warn(msg, DataConversionWarning)\n",
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:595: DataConversionWarning: Data with input dtype int32 was converted to float64 by StandardScaler.\n",
      "  warnings.warn(msg, DataConversionWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[-0.74717972, -0.65678879, -0.40228321, -0.30436663,  2.05218778,\n",
       "         0.18323502,  1.00930339,  0.52228691, -1.25857909,  1.57983042],\n",
       "       [-1.03212114,  0.43088692,  0.47088965, -1.96104578, -1.37433265,\n",
       "         1.90564425,  0.97286644, -0.24284678, -1.22810502, -1.14002415],\n",
       "       [-0.33559767,  0.64005532, -1.3690103 , -0.18878437,  0.5251515 ,\n",
       "        -0.40311705,  0.79068171, -0.30938014,  0.20417627, -1.25576265],\n",
       "       [-0.87382035, -0.99145824,  0.37733541,  1.08262056, -0.25698903,\n",
       "        -1.28264517, -0.88541777, -1.47371401,  1.14887244, -0.73493943],\n",
       "       [-0.74717972,  1.93689944,  1.31287775,  0.15796243,  0.89759938,\n",
       "         0.036647  , -1.35909806,  0.88822041, -0.64909769,  0.59605324],\n",
       "       [ 1.08910942, -0.02928358, -1.40019504,  0.73587376,  0.15270363,\n",
       "         1.46588019, -1.32266112,  1.55355405,  0.41749476,  0.7985956 ],\n",
       "       [ 1.75397273, -1.15879297, -0.09043576,  1.31378509, -0.70392648,\n",
       "        -1.02611613, -0.04736803, -0.87491373, -0.95383839, -0.53239707],\n",
       "       [ 0.86748832, -1.07512561,  1.28169301, -0.88227796, -0.74117127,\n",
       "         0.14658802, -0.99472861,  1.48702068,  1.54503535, -0.30092008],\n",
       "       [-0.96880082,  1.26756054,  0.96984556, -0.92080539,  0.59964108,\n",
       "         0.10994101,  1.33723589, -0.67531364,  1.20982058,  1.5508958 ],\n",
       "       [ 0.99412895, -0.36395303, -1.15071708,  0.96703829, -1.15086393,\n",
       "        -1.13605715,  0.49918615, -0.87491373, -0.4357792 , -0.56133169]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import preprocessing\n",
    "\n",
    "A_scaled = preprocessing.StandardScaler().fit(A).transform(A)\n",
    "A_scaled"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Baye's Theorem: \n",
    "\n",
    "An important philosophy in Machine Learning and Statistics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src = \"https://miro.medium.com/max/1994/1*CnoTGGO7XeUpUMeXDrIfvA.png\" height=400 width=550> <img>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Important Topics:\n",
    "1. [Bayesian Classifier](https://scikit-learn.org/stable/modules/naive_bayes.html) : Example of Machine Learning in Bayesian theory\n",
    "2. [Boltzman Machine](https://en.wikipedia.org/wiki/Restricted_Boltzmann_machine): Example of Machine Learning for Physicist.\n",
    "4. [Quantum Boltzman Machine](https://arxiv.org/abs/1601.02036): Fusion of Machine Learning and Quantum Physics\n",
    "5. [Markove Random Field](https://en.wikipedia.org/wiki/Markov_random_field): Is there a Field Theory in Machine Learning?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### A simple demo illustration Baye's theorm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[38, 15, 66, 92],\n",
       "       [16, 60, 96, 18],\n",
       "       [18, 80, 14, 60],\n",
       "       [88, 41, 31, 33],\n",
       "       [88, 95, 24, 98],\n",
       "       [39, 64, 97, 76],\n",
       "       [17, 20,  1, 87],\n",
       "       [90, 34,  2, 70],\n",
       "       [81, 10, 93, 86],\n",
       "       [60, 56,  3, 63]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = (100*np.random.rand(10,4)).astype(int)\n",
    "A "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(A, columns= ['bud','green','ripen','rotten'],\\\n",
    "                  index= ['apple','guava','mango','orange','banana','pear','papaya','strwberrey','grape','melon'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": true
   },
   "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>bud</th>\n",
       "      <th>green</th>\n",
       "      <th>ripen</th>\n",
       "      <th>rotten</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>apple</th>\n",
       "      <td>38</td>\n",
       "      <td>15</td>\n",
       "      <td>66</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>guava</th>\n",
       "      <td>16</td>\n",
       "      <td>60</td>\n",
       "      <td>96</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mango</th>\n",
       "      <td>18</td>\n",
       "      <td>80</td>\n",
       "      <td>14</td>\n",
       "      <td>60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>orange</th>\n",
       "      <td>88</td>\n",
       "      <td>41</td>\n",
       "      <td>31</td>\n",
       "      <td>33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>banana</th>\n",
       "      <td>88</td>\n",
       "      <td>95</td>\n",
       "      <td>24</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pear</th>\n",
       "      <td>39</td>\n",
       "      <td>64</td>\n",
       "      <td>97</td>\n",
       "      <td>76</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>papaya</th>\n",
       "      <td>17</td>\n",
       "      <td>20</td>\n",
       "      <td>1</td>\n",
       "      <td>87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>strwberrey</th>\n",
       "      <td>90</td>\n",
       "      <td>34</td>\n",
       "      <td>2</td>\n",
       "      <td>70</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>grape</th>\n",
       "      <td>81</td>\n",
       "      <td>10</td>\n",
       "      <td>93</td>\n",
       "      <td>86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>melon</th>\n",
       "      <td>60</td>\n",
       "      <td>56</td>\n",
       "      <td>3</td>\n",
       "      <td>63</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            bud  green  ripen  rotten\n",
       "apple        38     15     66      92\n",
       "guava        16     60     96      18\n",
       "mango        18     80     14      60\n",
       "orange       88     41     31      33\n",
       "banana       88     95     24      98\n",
       "pear         39     64     97      76\n",
       "papaya       17     20      1      87\n",
       "strwberrey   90     34      2      70\n",
       "grape        81     10     93      86\n",
       "melon        60     56      3      63"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "bud       535\n",
       "green     475\n",
       "ripen     427\n",
       "rotten    683\n",
       "dtype: int64"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2120"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(df.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "38"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.loc['apple','bud']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "bud       38\n",
       "green     15\n",
       "ripen     66\n",
       "rotten    92\n",
       "Name: apple, dtype: int32"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.loc['apple',:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "apple         66\n",
       "guava         96\n",
       "mango         14\n",
       "orange        31\n",
       "banana        24\n",
       "pear          97\n",
       "papaya         1\n",
       "strwberrey     2\n",
       "grape         93\n",
       "melon          3\n",
       "Name: ripen, dtype: int32"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.loc[:,'ripen']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- P(ripen|apple) = ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3127962085308057"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.loc['apple','ripen']/df.loc['apple',:].sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- P(apple|ripen) = ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.15456674473067916"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.loc['apple','ripen']/df.loc[:,'ripen'].sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Implementing Baye's theorem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- $P(apple|ripen) = \\frac{p(ripen|apple)*p(apple)}{p(ripen)}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.15456674473067916"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_apple = df.loc['apple',:].sum()/sum(df.sum())\n",
    "p_ripen_given_apple = df.loc['apple','ripen']/df.loc['apple',:].sum()\n",
    "p_ripen = df.loc[:,'ripen'].sum()/sum(df.sum())\n",
    "\n",
    "p_apple_given_ripen = (p_ripen_given_apple*p_apple)/p_ripen\n",
    "p_apple_given_ripen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Mini Assignment:\n",
    "1. Generate a randum array of size 10 by 10 and convert it to pandas dataframe with column name and row name of your interest\n",
    "2. Perform feature scaling (minimax scalar and standard scalar) by direct calculation of minimunm, maximum, mean, standard deviation from dataframe/array\n",
    "3. Implement Scikit-learn preprocessing pipeline to perform feature scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "language_info": {
   "codemirror_mode": {
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   "file_extension": ".py",
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   "pygments_lexer": "ipython3",
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  "widgets": {
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