FeatureSelection.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Machine Learning with scikit-learn\n",
    "\n",
    "Sometimes the features you have available in your initial data have little predictive strength when used in the most straightforward way.  This might be true almost regardless of choice of model class and hyperparameters.  And yet it might also be true that there are synthetic features latent in the data that are highly predictive, but that have to be *engineered* (mechanically, rather than sample-wise modification) to produce powerful features.\n",
    "\n",
    "At the same time, a highly dimension model—whether of high dimension because of the initial data collection or because of creation of extra synthetic features—may lend itself less well to modeling techniques.  In these cases, it can be more computationally tractable, as well as more predictive, to work with a subset of all available features.\n",
    "\n",
    "This is the last of three lessons that can be thought of broadly as \"Feature Engineering.\" This lesson focuses on selecting the features of most relevance.  Within this lesson, we group in *scaling* which does not discard dimensions, but does help in providing them with relevant numeric properties for best use in models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Intel(R) Extension for Scikit-learn* enabled (https://github.com/intel/scikit-learn-intelex)\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from src.setup import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling\n",
    "\n",
    "We have seen at several places the passing use of scaling to make data better regularized to allow models to perform best.  Scikit-learn provides several scaler classes that follow a similar API as models and other feature transformations.  Using these is mostly a simple drop-in step.\n",
    "\n",
    "To make examples simple, we generate a small amount of random data with values of \"features\" in somewhat different ranges and distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.54055853  0.70551593  1.7         5.67575731]\n",
      " [ 2.24520714 -0.15243041 -3.7         6.65845147]\n",
      " [ 1.84028059  0.47312565  1.8         5.55237769]\n",
      " [ 1.54104279  0.22949671 -1.8         7.55437359]\n",
      " [ 3.46701001  0.24435315 -4.5         5.37560338]]\n"
     ]
    }
   ],
   "source": [
    "rows = 100\n",
    "test_data = np.empty((rows,4))\n",
    "test_data[:,0] = np.random.random(rows) * 2 + 1.5 \n",
    "test_data[:,1] = np.random.randn(rows)\n",
    "test_data[:,2] = np.random.randint(-50, 25, rows)/10\n",
    "test_data[:,3] = np.exp(np.random.random(rows)+1.5)\n",
    "print(test_data[:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.00000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>2.586523</td>\n",
       "      <td>-0.023601</td>\n",
       "      <td>-1.64100</td>\n",
       "      <td>8.088960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.572939</td>\n",
       "      <td>0.952164</td>\n",
       "      <td>2.05648</td>\n",
       "      <td>2.165688</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "                0           1          2           3\n",
       "count  100.000000  100.000000  100.00000  100.000000\n",
       "mean     2.586523   -0.023601   -1.64100    8.088960\n",
       "std      0.572939    0.952164    2.05648    2.165688"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(test_data).describe().head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame(test_data).plot(kind='kde');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame(test_data).plot(kind='hist', bins=300);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### StandardScaler\n",
    "\n",
    "The most commonly used scaler—as the name indicates—is `StandardScaler`. \n",
    "\n",
    "This standardizes features by removing the mean and scaling to unit variance.  It loosely assumes that the underlying data is Gaussian to start with, but mostly it is fairly robust against moderate violations of that distribution.  Calculating the mean and standard deviation is per-column (as for all scalers)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.83480819,  0.76960477,  1.63280523, -1.11990248],\n",
       "       [-0.59872839, -0.13598348, -1.00626937, -0.66386054],\n",
       "       [-1.30904205,  0.52430982,  1.68167698, -1.17715965],\n",
       "       [-1.83395872,  0.26715212, -0.07770609, -0.24808716],\n",
       "       [ 1.54453257,  0.28283354, -1.39724338, -1.25919585]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "scaled1 = StandardScaler().fit_transform(test_data)\n",
    "scaled1[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1.000000e+02</td>\n",
       "      <td>1.000000e+02</td>\n",
       "      <td>1.000000e+02</td>\n",
       "      <td>1.000000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.123546e-15</td>\n",
       "      <td>2.886580e-17</td>\n",
       "      <td>1.265654e-16</td>\n",
       "      <td>3.130829e-16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.005038e+00</td>\n",
       "      <td>1.005038e+00</td>\n",
       "      <td>1.005038e+00</td>\n",
       "      <td>1.005038e+00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  0             1             2             3\n",
       "count  1.000000e+02  1.000000e+02  1.000000e+02  1.000000e+02\n",
       "mean   1.123546e-15  2.886580e-17  1.265654e-16  3.130829e-16\n",
       "std    1.005038e+00  1.005038e+00  1.005038e+00  1.005038e+00"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(scaled1).describe().head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame(scaled1).plot(kind='kde');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame(scaled1).plot(kind='hist', bins=300);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RobustScaler\n",
    "\n",
    "This scales features using statistics that are robust to outliers. It removes the median and scales the data according to the quantile range (defaults to IQR: Interquartile Range). The IQR is the range between the 1st quartile (25th quantile) and the 3rd quartile (75th quantile)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.20549825,  0.63859628,  0.9929078 , -0.48415493],\n",
       "       [-0.42776754, -0.08914712, -0.53900709, -0.23001103],\n",
       "       [-0.87469075,  0.44147382,  1.0212766 , -0.51606331],\n",
       "       [-1.20496377,  0.2348183 ,  0.        ,  0.00169193],\n",
       "       [ 0.92075368,  0.2474201 , -0.76595745, -0.5617806 ]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import RobustScaler\n",
    "scaled2 = RobustScaler().fit_transform(test_data)\n",
    "scaled2[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>-0.051053</td>\n",
       "      <td>0.020131</td>\n",
       "      <td>0.045106</td>\n",
       "      <td>0.139946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.632361</td>\n",
       "      <td>0.807662</td>\n",
       "      <td>0.583399</td>\n",
       "      <td>0.560089</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                0           1           2           3\n",
       "count  100.000000  100.000000  100.000000  100.000000\n",
       "mean    -0.051053    0.020131    0.045106    0.139946\n",
       "std      0.632361    0.807662    0.583399    0.560089"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(scaled2).describe().head(3)"
   ]
  },
  {
   "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": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame(scaled2).plot(kind='kde');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame(scaled2).plot(kind='hist', bins=300);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MinMaxScaler\n",
    "\n",
    "Transforms features by scaling each feature to a given range. This estimator scales and translates each feature individually such that it is in the given range on the training set, by default between zero and one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.00329958, 0.55435255, 0.94366197, 0.14232507],\n",
       "       [0.36328745, 0.38306952, 0.18309859, 0.27235909],\n",
       "       [0.1564203 , 0.50795744, 0.95774648, 0.12599899],\n",
       "       [0.00354697, 0.45931862, 0.45070423, 0.39091109],\n",
       "       [0.98747689, 0.4622846 , 0.07042254, 0.10260751]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import MinMaxScaler\n",
    "scaled3 = MinMaxScaler().fit_transform(test_data)\n",
    "scaled3[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.537657</td>\n",
       "      <td>0.408789</td>\n",
       "      <td>0.473099</td>\n",
       "      <td>0.461650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.292701</td>\n",
       "      <td>0.190093</td>\n",
       "      <td>0.289645</td>\n",
       "      <td>0.286573</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.311064</td>\n",
       "      <td>0.270191</td>\n",
       "      <td>0.221831</td>\n",
       "      <td>0.210625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.561288</td>\n",
       "      <td>0.404051</td>\n",
       "      <td>0.450704</td>\n",
       "      <td>0.390045</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.773934</td>\n",
       "      <td>0.505552</td>\n",
       "      <td>0.718310</td>\n",
       "      <td>0.722280</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                0           1           2           3\n",
       "count  100.000000  100.000000  100.000000  100.000000\n",
       "mean     0.537657    0.408789    0.473099    0.461650\n",
       "std      0.292701    0.190093    0.289645    0.286573\n",
       "min      0.000000    0.000000    0.000000    0.000000\n",
       "25%      0.311064    0.270191    0.221831    0.210625\n",
       "50%      0.561288    0.404051    0.450704    0.390045\n",
       "75%      0.773934    0.505552    0.718310    0.722280\n",
       "max      1.000000    1.000000    1.000000    1.000000"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(scaled3).describe()"
   ]
  },
  {
   "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": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame(scaled3).plot(kind='kde');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame(scaled3).plot(kind='hist', bins=300);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MaxAbsScaler\n",
    "\n",
    "Scales each feature by its maximum absolute value.  This estimator scales and translates each feature individually such that the maximal absolute value of each feature in the training set will be 1.0. It does not shift/center the data, and thus does not destroy any sparsity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.44122823,  0.24015626,  0.34      ,  0.46685674],\n",
       "       [ 0.6430452 , -0.05188702, -0.74      ,  0.54768779],\n",
       "       [ 0.52707101,  0.16105106,  0.36      ,  0.45670821],\n",
       "       [ 0.44136692,  0.07812024, -0.36      ,  0.62138144],\n",
       "       [ 0.99297927,  0.08317734, -0.9       ,  0.44216772]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import MaxAbsScaler\n",
    "scaled4 = MaxAbsScaler().fit_transform(test_data)\n",
    "scaled4[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.740801</td>\n",
       "      <td>-0.008034</td>\n",
       "      <td>-0.328200</td>\n",
       "      <td>0.665354</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.164094</td>\n",
       "      <td>0.324115</td>\n",
       "      <td>0.411296</td>\n",
       "      <td>0.178138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.439378</td>\n",
       "      <td>-0.705033</td>\n",
       "      <td>-1.000000</td>\n",
       "      <td>0.378385</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.613768</td>\n",
       "      <td>-0.244349</td>\n",
       "      <td>-0.685000</td>\n",
       "      <td>0.509313</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.754049</td>\n",
       "      <td>-0.016112</td>\n",
       "      <td>-0.360000</td>\n",
       "      <td>0.620843</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.873263</td>\n",
       "      <td>0.156950</td>\n",
       "      <td>0.020000</td>\n",
       "      <td>0.827365</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.420000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                0           1           2           3\n",
       "count  100.000000  100.000000  100.000000  100.000000\n",
       "mean     0.740801   -0.008034   -0.328200    0.665354\n",
       "std      0.164094    0.324115    0.411296    0.178138\n",
       "min      0.439378   -0.705033   -1.000000    0.378385\n",
       "25%      0.613768   -0.244349   -0.685000    0.509313\n",
       "50%      0.754049   -0.016112   -0.360000    0.620843\n",
       "75%      0.873263    0.156950    0.020000    0.827365\n",
       "max      1.000000    1.000000    0.420000    1.000000"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(scaled4).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame(scaled4).plot(kind='kde');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame(scaled4).plot(kind='hist', bins=300);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ...and others\n",
    "\n",
    "A number of other scalers exists for special purposes.  An interesting one is `QuantileTransformer` that normalizes feature values by quantile (default `n_quantiles=1000`).  In effect this treats values in an ordinal way, eliminating any effect of outliers.  Output distributions other than the default `'uniform'` can be selected as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature Selection\n",
    "\n",
    "One way to reduce features in a dataset is to throw some of them away.  In principle, features thrown away can be engineered features such as those resulting from decompositions or those discussed below that are combined or synthesized from raw features.  Scikit-learn gives you several ways to choose features to discard; or euqivalently, features to keep.\n",
    "\n",
    "There are several univariate feature selectors in scikit-learn.  `SelectKBest` is essentially the same as `SelectPercentile`, merely different in whether you indicate a number of percentage of features to keep.  Obviously, it is easy to derive one from the other based on number of features in the raw data. Just slightly different are false positive rate (`SelectFpr`), false discovery rate (`SelectFdr`), or family wise error (`SelectFwe`).  \n",
    "\n",
    "All of these let you specify a scoring function the judges the quality of the estimate using just one feature.  For regression, there are `f_regression`, `mutual_info_regression`; for classification: `chi2`, `f_classif`, `mutual_info_classif`.  You can also, in principle, use a custom function to evaluate strength of a single feature for prediction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "cancer = load_breast_cancer()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Univariate\n",
    "\n",
    "Let us look at the Wisconsin cancer dataset from perspective of simply identifying the most important features (in the raw dataset).  Notice that we use the entire dataset for this purpose, not only a training portion of it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((569, 30), (569, 5))"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.feature_selection import SelectKBest\n",
    "from sklearn.feature_selection import chi2\n",
    "\n",
    "selector = SelectKBest(chi2, k=5)\n",
    "X_new = selector.fit_transform(cancer.data, cancer.target)\n",
    "cancer.data.shape, X_new.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "worst area         112598.431564\n",
       "mean area           53991.655924\n",
       "area error           8758.504705\n",
       "worst perimeter      3665.035416\n",
       "mean perimeter       2011.102864\n",
       "worst radius          491.689157\n",
       "mean radius           266.104917\n",
       "perimeter error       250.571896\n",
       "worst texture         174.449400\n",
       "mean texture           93.897508\n",
       "dtype: float64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kbest = pd.Series(selector.scores_, \n",
    "                  index=cancer.feature_names).sort_values(ascending=False)\n",
    "kbest.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us take a look at how models work with all 30 features versus with just the top 5 in a univariate filter.  In this example, we do not get better with this step alone (but KNN doesn't get much worse), but in some cases the score will actually improve without surplus dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "lr, knn = LinearRegression(), KNeighborsClassifier()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fit raw features:\n",
      " LR: 0.7222686011962907\n",
      "KNN: 0.9370629370629371\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    cancer.data, cancer.target, random_state=1)\n",
    "print(\"Fit raw features:\")\n",
    "print(\" LR:\", lr.fit(X_train, y_train).score(X_test, y_test))\n",
    "print(\"KNN:\", knn.fit(X_train, y_train).score(X_test, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We do *worse* with only five of the thirty features, but for KNN, not very much worse!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fit selected features:\n",
      " LR: 0.5857835011372026\n",
      "KNN: 0.9230769230769231\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    X_new, cancer.target, random_state=1)\n",
    "print(\"Fit selected features:\")\n",
    "print(\" LR:\", lr.fit(X_train, y_train).score(X_test, y_test))\n",
    "print(\"KNN:\", knn.fit(X_train, y_train).score(X_test, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model-based Feature Selection\n",
    "\n",
    "A number of selectors are based on the chosen underlying model itself rather on univariate strengths of features.  This only works with models than expose a `.coef_` or `.feature_importances_` attribute on a trained model.  Not all algorithms allow the determination of those values.\n",
    "\n",
    "We look here at recursive feature elimination which is based on a model, and arrives at the most important features by eliminating the least important, then refitting based on those that remain, and doing so repeatedly until only the number of features requested remain.  The selector `SelectFromModel` works in a similar way, but recursive selection will generally be better quality (albeit **much** slower since it involves repeated refitting)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mean area            26\n",
       "worst area           25\n",
       "mean texture         24\n",
       "area error           23\n",
       "worst perimeter      22\n",
       "texture error        21\n",
       "worst texture        20\n",
       "worst compactness    19\n",
       "mean perimeter       18\n",
       "mean radius          17\n",
       "dtype: int64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Recursive feature elimination\n",
    "from sklearn.feature_selection import RFE\n",
    "\n",
    "lr = LinearRegression()\n",
    "rfe = RFE(estimator=lr, n_features_to_select=5, step=1) \n",
    "rfe.fit(cancer.data, cancer.target)\n",
    "\n",
    "pd.Series(rfe.ranking_, index=cancer.feature_names).sort_values(ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The relative importance of features is similar, but somewhat different under recursive feature elimination than under K-best selection.  Given the nature of linear models, we mostly expect univariate elimination to behave similarly to recursive elimination based on linear regression.  Something like a decision tree (which provides `.feature_importances_`) might have a more different ranking of selected features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can go farther here and use `RFECV` to recursive eliminate features, cross-validate the model at each stage, and keep a record of the relationship between model score and number of features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.feature_selection import RFECV\n",
    "\n",
    "rf = RandomForestClassifier(max_depth=7, random_state=1)\n",
    "rfecv = RFECV(estimator=rf)\n",
    "rfecv.fit(cancer.data, cancer.target)\n",
    "\n",
    "# Plot number of features VS. cross-validation scores\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.xlabel(\"Number of features selected\")\n",
    "plt.ylabel(\"Cross validation score (nb of correct classifications)\")\n",
    "plt.plot(range(1, len(rfecv.grid_scores_) + 1), rfecv.grid_scores_)\n",
    "plt.title(\"Optimal number of features : %d\" % rfecv.n_features_)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparing Selectors\n",
    "\n",
    "In the right circumstances, it can make a **huge** difference to create synthetic features and then to select among them in the best way.  Let's go all out in trying to create a genuinely *good* model for this cancer data.  That often involves everything we have seen: polynomial expansion, scaling, and feature selection.\n",
    "\n",
    "Given relatively high initial accuracy, it is more illustrative to look at how often a model is *wrong* than its accuracy to highlight differences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "poly = PolynomialFeatures(2)\n",
    "X_poly = poly.fit_transform(cancer.data)\n",
    "rfc = RandomForestClassifier(max_depth=7, random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raw features, error rate: 2.80%\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    cancer.data, cancer.target, random_state=42)\n",
    "\n",
    "acc = rfc.fit(X_train, y_train).score(X_test, y_test)\n",
    "print(f\"Raw features, error rate: {(1-acc)*100:.2f}%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scaled polynomial features, error rate: 2.80%\n"
     ]
    }
   ],
   "source": [
    "# Scale the engineered features (good practice, not directly helpful here)\n",
    "# NOTE: we use MinMaxScaler here rather than StandardScaler,\n",
    "#       because chi^2 test requires positive features\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "X_poly_scaled = MinMaxScaler().fit_transform(X_poly)\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    X_poly_scaled, cancer.target, random_state=42)\n",
    "\n",
    "acc = rfc.fit(X_train, y_train).score(X_test, y_test)\n",
    "print(f\"Scaled polynomial features, error rate: {(1-acc)*100:.2f}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Select only the best 100 features in a univariate variate way rather than swamp the model with all 496 features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Univariate best 100 poly, error rate: 3.50%\n"
     ]
    }
   ],
   "source": [
    "from sklearn.feature_selection import SelectKBest, chi2\n",
    "selector = SelectKBest(chi2, k=100)\n",
    "X_new = selector.fit_transform(X_poly_scaled, cancer.target)\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    X_new, cancer.target, random_state=42)\n",
    "\n",
    "acc = rfc.fit(X_train, y_train).score(X_test, y_test)\n",
    "print(f\"Univariate best 100 poly, error rate: {(1-acc)*100:.2f}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we spend a while longer, we can use *Recursive Features Elimination with Cross-Validation* on all 496 of our polynomial features.  This involves retraining a Random Forest composed of 7 Decision Trees 496 separate times.  So it is some computational work.  \n",
    "\n",
    "The `n_jobs=-1` parameter says to use all the CPU cores on the current machine (on the machine I usually teach on, that is 8 cores)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RFECV best 32 of 496 error rate: 2.80%\n",
      "CPU times: user 2min 20s, sys: 4.54 s, total: 2min 25s\n",
      "Wall time: 3min 24s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    X_poly_scaled, cancer.target, random_state=42)\n",
    "\n",
    "rfecv = RFECV(estimator=rfc, n_jobs=-1)\n",
    "acc = rfecv.fit(X_train, y_train).score(X_test, y_test)\n",
    "print(f\"RFECV best {rfecv.n_features_} of {X_poly_scaled.shape[1]}\", \n",
    "      f\"error rate: {(1-acc)*100:.2f}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result here is that there are 37 synthetic features—not so different in number from the original 30 dimensions—that are not only vastly better than the original features, but in facts have half the error rate of choosing 100 of the polynomial features in a univariate way.\n",
    "\n",
    "For what it is worth, I tried `k=50` and `k=100` is better, but I did not try every univariate k.  But remember that the order of selection of univariate features is fixed, so we would definitely have to go to more than 100 features to get these 37 \"Goldilocks\" features (and going too high will weaken the model because of the *curse of dimensionality*)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a passing note, I also tried using a degree-3 polynomial to create thousands of synthetic features, then after a very long run time (hours), produced something worse than the degree-2 example above.  The problem was that RFECV still selected over a thousand features in this example. Possibly other mechanisms to more aggressively winnow degree-3 features could eek out an incremental gain, but also likely is that degree-2 is best suited for this dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Next lesson\n",
    "\n",
    "**Pipelines**: In this lesson we dealt with quite a lot of what we might call *data engineering*. The need for feature selection, feature engineering, and scaling, goes beyond the base fact that \"data always comes in messy.\"  Certainly the need for data cleaning is important, and has probably not been addressed to match that importance in this course.  But even data that is spotless for an data integrity and anomaly perspective (a lofty goal) might still need to be massaged to allow models to succeed in their magic.\n",
    "\n",
    "The next lesson on pipelines will be fairly short, but very important.  We have seen a variety of ways we can manipulate data—and also ways we can tune models with hyperparameters—but we have done each of these steps one-by-one, in explicit code with extra intermediate steps lying around along the way.  Pipelines allow us to package all these steps together in one resusable API.\n",
    "\n",
    "<a href=\"Pipelines.ipynb\"><img src=\"img/open-notebook.png\" align=\"left\"/></a>"
   ]
  }
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