Feature Selection in ML using Python. Part 1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Feature Selection using Filtering Method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Univariate (we select features without considering other features)(Using Variance, Fisher Score, Mutual Information Gain etc) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using Variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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       "<p>5 rows × 371 columns</p>\n",
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      "text/plain": [
       "   ID  var3  var15  imp_ent_var16_ult1  imp_op_var39_comer_ult1  \\\n",
       "0   1     2     23                 0.0                      0.0   \n",
       "1   3     2     34                 0.0                      0.0   \n",
       "2   4     2     23                 0.0                      0.0   \n",
       "3   8     2     37                 0.0                    195.0   \n",
       "4  10     2     39                 0.0                      0.0   \n",
       "\n",
       "   imp_op_var39_comer_ult3  imp_op_var40_comer_ult1  imp_op_var40_comer_ult3  \\\n",
       "0                      0.0                      0.0                      0.0   \n",
       "1                      0.0                      0.0                      0.0   \n",
       "2                      0.0                      0.0                      0.0   \n",
       "3                    195.0                      0.0                      0.0   \n",
       "4                      0.0                      0.0                      0.0   \n",
       "\n",
       "   imp_op_var40_efect_ult1  imp_op_var40_efect_ult3  ...  \\\n",
       "0                      0.0                      0.0  ...   \n",
       "1                      0.0                      0.0  ...   \n",
       "2                      0.0                      0.0  ...   \n",
       "3                      0.0                      0.0  ...   \n",
       "4                      0.0                      0.0  ...   \n",
       "\n",
       "   saldo_medio_var33_hace2  saldo_medio_var33_hace3  saldo_medio_var33_ult1  \\\n",
       "0                      0.0                      0.0                     0.0   \n",
       "1                      0.0                      0.0                     0.0   \n",
       "2                      0.0                      0.0                     0.0   \n",
       "3                      0.0                      0.0                     0.0   \n",
       "4                      0.0                      0.0                     0.0   \n",
       "\n",
       "   saldo_medio_var33_ult3  saldo_medio_var44_hace2  saldo_medio_var44_hace3  \\\n",
       "0                     0.0                      0.0                      0.0   \n",
       "1                     0.0                      0.0                      0.0   \n",
       "2                     0.0                      0.0                      0.0   \n",
       "3                     0.0                      0.0                      0.0   \n",
       "4                     0.0                      0.0                      0.0   \n",
       "\n",
       "   saldo_medio_var44_ult1  saldo_medio_var44_ult3          var38  TARGET  \n",
       "0                     0.0                     0.0   39205.170000       0  \n",
       "1                     0.0                     0.0   49278.030000       0  \n",
       "2                     0.0                     0.0   67333.770000       0  \n",
       "3                     0.0                     0.0   64007.970000       0  \n",
       "4                     0.0                     0.0  117310.979016       0  \n",
       "\n",
       "[5 rows x 371 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('santander-train.csv')\n",
    "data.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.feature_selection import VarianceThreshold\n",
    "from sklearn.metrics import accuracy_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data.drop(labels='TARGET', axis=1)\n",
    "y = data['TARGET']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constant fearture Removal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "VarianceThreshold(threshold=0.0)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "constant_filter = VarianceThreshold(threshold=0.0)\n",
    "constant_filter.fit(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "370\n"
     ]
    }
   ],
   "source": [
    "print(X.shape[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "336"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "###Number of retained features\n",
    "constant_filter.get_support().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Filtered train and Test Set\n",
    "X_train_filter = constant_filter.transform(X_train)\n",
    "X_test_filter = constant_filter.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "336"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train_filter.shape[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "370\n",
      "336\n"
     ]
    }
   ],
   "source": [
    "print(X_test.shape[1])\n",
    "print(X_test_filter.shape[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quasi Conatant Features Removal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "VarianceThreshold(threshold=0.01)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quasi_constant_filter = VarianceThreshold(threshold=0.01) #Removing features having >=99% Similarity\n",
    "quasi_constant_filter.fit(X_train_filter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "272"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "###Number of retained features\n",
    "quasi_constant_filter.get_support().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Filtered train and Test Set\n",
    "X_train_quasi_filter = quasi_constant_filter.transform(X_train_filter)\n",
    "X_test_quasi_filter = quasi_constant_filter.transform(X_test_filter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "272\n",
      "272\n"
     ]
    }
   ],
   "source": [
    "print(X_train_quasi_filter.shape[1])\n",
    "print(X_test_quasi_filter.shape[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Duplicate Features Removal (Removal of features having exactly same values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "### We dont have any method to remove Dublicates from columns but we have method to remove dublicates from Rows.\n",
    "### So we will take transform and Remove from rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train_T = X_train_quasi_filter.T\n",
    "X_test_T = X_test_quasi_filter.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(272, 57015)\n",
      "(272, 19005)\n"
     ]
    }
   ],
   "source": [
    "print(X_train_T.shape)\n",
    "print(X_test_T.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(X_train_T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "### We need to convert this numpy array to Pandas DataFrame "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train_T = pd.DataFrame(X_train_T)\n",
    "X_test_T = pd.DataFrame(X_test_T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### Number of Dublicate Features\n",
    "X_train_T.duplicated().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Removing these Dublicated Features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Getting Dublicated Features boolean\n",
    "duplicated_features = X_train_T.duplicated()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Selecting Non Duplicated rows\n",
    "features_to_keep = [not item for item in duplicated_features]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train_unique = X_train_T[features_to_keep].T\n",
    "X_test_unique = X_test_T[features_to_keep].T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(57015, 255)\n",
      "(19005, 255)\n"
     ]
    }
   ],
   "source": [
    "print(X_train_unique.shape)\n",
    "print(X_test_unique.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "### Building the Model and Performance Checking"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9607997895290713\n",
      "Wall time: 4.37 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "model = RandomForestClassifier(n_estimators=100, max_depth=4)\n",
    "model.fit(X_train, y_train)\n",
    "y_pred = model.predict(X_test)\n",
    "print(accuracy_score(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9607997895290713\n",
      "Wall time: 3.54 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "model = RandomForestClassifier(n_estimators=100, max_depth=4)\n",
    "model.fit(X_train_unique, y_train)\n",
    "y_pred = model.predict(X_test_unique)\n",
    "print(accuracy_score(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multivariate (we select features considering other features)(Using Pearsons Correlation) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using Correlations "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
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       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>...</th>\n",
       "      <th>262</th>\n",
       "      <th>263</th>\n",
       "      <th>264</th>\n",
       "      <th>265</th>\n",
       "      <th>266</th>\n",
       "      <th>267</th>\n",
       "      <th>268</th>\n",
       "      <th>269</th>\n",
       "      <th>270</th>\n",
       "      <th>271</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.001194</td>\n",
       "      <td>-0.001853</td>\n",
       "      <td>-0.003938</td>\n",
       "      <td>0.000109</td>\n",
       "      <td>-0.003770</td>\n",
       "      <td>-0.009275</td>\n",
       "      <td>-0.010554</td>\n",
       "      <td>-0.007310</td>\n",
       "      <td>-0.007864</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.008809</td>\n",
       "      <td>-0.000128</td>\n",
       "      <td>0.001181</td>\n",
       "      <td>-0.002806</td>\n",
       "      <td>-0.002573</td>\n",
       "      <td>-0.003620</td>\n",
       "      <td>-0.006234</td>\n",
       "      <td>-0.001831</td>\n",
       "      <td>-0.000059</td>\n",
       "      <td>-0.008112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.001194</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.001827</td>\n",
       "      <td>0.001988</td>\n",
       "      <td>0.007314</td>\n",
       "      <td>0.007741</td>\n",
       "      <td>0.001417</td>\n",
       "      <td>0.001574</td>\n",
       "      <td>0.000544</td>\n",
       "      <td>0.000618</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000252</td>\n",
       "      <td>0.000687</td>\n",
       "      <td>0.000464</td>\n",
       "      <td>0.000585</td>\n",
       "      <td>0.000618</td>\n",
       "      <td>0.000582</td>\n",
       "      <td>0.000474</td>\n",
       "      <td>0.000725</td>\n",
       "      <td>0.000765</td>\n",
       "      <td>-0.000041</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.001853</td>\n",
       "      <td>-0.001827</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.040057</td>\n",
       "      <td>0.095506</td>\n",
       "      <td>0.101138</td>\n",
       "      <td>0.041632</td>\n",
       "      <td>0.048417</td>\n",
       "      <td>0.009907</td>\n",
       "      <td>0.010963</td>\n",
       "      <td>...</td>\n",
       "      <td>0.013472</td>\n",
       "      <td>0.028406</td>\n",
       "      <td>0.016710</td>\n",
       "      <td>0.027005</td>\n",
       "      <td>0.027922</td>\n",
       "      <td>0.030106</td>\n",
       "      <td>0.023319</td>\n",
       "      <td>0.035177</td>\n",
       "      <td>0.035580</td>\n",
       "      <td>0.007449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.003938</td>\n",
       "      <td>0.001988</td>\n",
       "      <td>0.040057</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.038944</td>\n",
       "      <td>0.033910</td>\n",
       "      <td>0.011242</td>\n",
       "      <td>0.010576</td>\n",
       "      <td>0.000743</td>\n",
       "      <td>0.002513</td>\n",
       "      <td>...</td>\n",
       "      <td>0.008937</td>\n",
       "      <td>-0.000840</td>\n",
       "      <td>-0.000624</td>\n",
       "      <td>-0.000586</td>\n",
       "      <td>-0.000651</td>\n",
       "      <td>0.003535</td>\n",
       "      <td>-0.000551</td>\n",
       "      <td>0.007161</td>\n",
       "      <td>0.009017</td>\n",
       "      <td>0.000423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.000109</td>\n",
       "      <td>0.007314</td>\n",
       "      <td>0.095506</td>\n",
       "      <td>0.038944</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.888244</td>\n",
       "      <td>0.350951</td>\n",
       "      <td>0.309539</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>0.057051</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001278</td>\n",
       "      <td>0.018452</td>\n",
       "      <td>0.015337</td>\n",
       "      <td>0.014867</td>\n",
       "      <td>0.016131</td>\n",
       "      <td>0.011756</td>\n",
       "      <td>0.009377</td>\n",
       "      <td>0.015979</td>\n",
       "      <td>0.014475</td>\n",
       "      <td>0.009990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-0.003770</td>\n",
       "      <td>0.007741</td>\n",
       "      <td>0.101138</td>\n",
       "      <td>0.033910</td>\n",
       "      <td>0.888244</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.316705</td>\n",
       "      <td>0.359242</td>\n",
       "      <td>0.029647</td>\n",
       "      <td>0.049465</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000221</td>\n",
       "      <td>0.031368</td>\n",
       "      <td>0.028060</td>\n",
       "      <td>0.021555</td>\n",
       "      <td>0.023983</td>\n",
       "      <td>0.010169</td>\n",
       "      <td>0.007747</td>\n",
       "      <td>0.014444</td>\n",
       "      <td>0.012988</td>\n",
       "      <td>0.011707</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-0.009275</td>\n",
       "      <td>0.001417</td>\n",
       "      <td>0.041632</td>\n",
       "      <td>0.011242</td>\n",
       "      <td>0.350951</td>\n",
       "      <td>0.316705</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.858154</td>\n",
       "      <td>0.058951</td>\n",
       "      <td>0.120411</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000253</td>\n",
       "      <td>0.004228</td>\n",
       "      <td>0.008442</td>\n",
       "      <td>0.002438</td>\n",
       "      <td>0.003520</td>\n",
       "      <td>-0.000391</td>\n",
       "      <td>-0.000455</td>\n",
       "      <td>-0.000140</td>\n",
       "      <td>-0.000289</td>\n",
       "      <td>0.002612</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-0.010554</td>\n",
       "      <td>0.001574</td>\n",
       "      <td>0.048417</td>\n",
       "      <td>0.010576</td>\n",
       "      <td>0.309539</td>\n",
       "      <td>0.359242</td>\n",
       "      <td>0.858154</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.053506</td>\n",
       "      <td>0.098173</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000278</td>\n",
       "      <td>0.008017</td>\n",
       "      <td>0.014056</td>\n",
       "      <td>0.004587</td>\n",
       "      <td>0.006548</td>\n",
       "      <td>-0.000517</td>\n",
       "      <td>-0.000499</td>\n",
       "      <td>-0.000427</td>\n",
       "      <td>-0.000540</td>\n",
       "      <td>0.005096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-0.007310</td>\n",
       "      <td>0.000544</td>\n",
       "      <td>0.009907</td>\n",
       "      <td>0.000743</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>0.029647</td>\n",
       "      <td>0.058951</td>\n",
       "      <td>0.053506</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.950170</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000098</td>\n",
       "      <td>-0.000253</td>\n",
       "      <td>-0.000172</td>\n",
       "      <td>-0.000217</td>\n",
       "      <td>-0.000229</td>\n",
       "      <td>-0.000225</td>\n",
       "      <td>-0.000176</td>\n",
       "      <td>-0.000282</td>\n",
       "      <td>-0.000297</td>\n",
       "      <td>-0.000817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-0.007864</td>\n",
       "      <td>0.000618</td>\n",
       "      <td>0.010963</td>\n",
       "      <td>0.002513</td>\n",
       "      <td>0.057051</td>\n",
       "      <td>0.049465</td>\n",
       "      <td>0.120411</td>\n",
       "      <td>0.098173</td>\n",
       "      <td>0.950170</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000111</td>\n",
       "      <td>-0.000286</td>\n",
       "      <td>-0.000195</td>\n",
       "      <td>-0.000246</td>\n",
       "      <td>-0.000260</td>\n",
       "      <td>-0.000255</td>\n",
       "      <td>-0.000200</td>\n",
       "      <td>-0.000319</td>\n",
       "      <td>-0.000337</td>\n",
       "      <td>0.000350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-0.011209</td>\n",
       "      <td>0.001240</td>\n",
       "      <td>0.034034</td>\n",
       "      <td>0.014923</td>\n",
       "      <td>0.264996</td>\n",
       "      <td>0.254774</td>\n",
       "      <td>0.720901</td>\n",
       "      <td>0.660534</td>\n",
       "      <td>0.310980</td>\n",
       "      <td>0.327589</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000222</td>\n",
       "      <td>-0.000571</td>\n",
       "      <td>-0.000390</td>\n",
       "      <td>-0.000418</td>\n",
       "      <td>-0.000414</td>\n",
       "      <td>-0.000355</td>\n",
       "      <td>-0.000399</td>\n",
       "      <td>-0.000161</td>\n",
       "      <td>-0.000285</td>\n",
       "      <td>-0.000187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.002885</td>\n",
       "      <td>0.007365</td>\n",
       "      <td>0.089275</td>\n",
       "      <td>0.038115</td>\n",
       "      <td>0.960128</td>\n",
       "      <td>0.851342</td>\n",
       "      <td>0.075178</td>\n",
       "      <td>0.073426</td>\n",
       "      <td>0.017179</td>\n",
       "      <td>0.024805</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001436</td>\n",
       "      <td>0.018388</td>\n",
       "      <td>0.013812</td>\n",
       "      <td>0.015105</td>\n",
       "      <td>0.016128</td>\n",
       "      <td>0.012635</td>\n",
       "      <td>0.010121</td>\n",
       "      <td>0.017058</td>\n",
       "      <td>0.015501</td>\n",
       "      <td>0.009859</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>-0.000915</td>\n",
       "      <td>0.007798</td>\n",
       "      <td>0.093682</td>\n",
       "      <td>0.033077</td>\n",
       "      <td>0.856835</td>\n",
       "      <td>0.961471</td>\n",
       "      <td>0.085229</td>\n",
       "      <td>0.088846</td>\n",
       "      <td>0.015881</td>\n",
       "      <td>0.023875</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000318</td>\n",
       "      <td>0.031117</td>\n",
       "      <td>0.025807</td>\n",
       "      <td>0.021655</td>\n",
       "      <td>0.023668</td>\n",
       "      <td>0.011005</td>\n",
       "      <td>0.008415</td>\n",
       "      <td>0.015542</td>\n",
       "      <td>0.014021</td>\n",
       "      <td>0.010994</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>-0.001956</td>\n",
       "      <td>0.000333</td>\n",
       "      <td>0.086469</td>\n",
       "      <td>0.018321</td>\n",
       "      <td>0.288963</td>\n",
       "      <td>0.267425</td>\n",
       "      <td>0.087097</td>\n",
       "      <td>0.063574</td>\n",
       "      <td>0.091121</td>\n",
       "      <td>0.094393</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000839</td>\n",
       "      <td>0.007507</td>\n",
       "      <td>0.001985</td>\n",
       "      <td>0.009333</td>\n",
       "      <td>0.009312</td>\n",
       "      <td>0.048972</td>\n",
       "      <td>0.026171</td>\n",
       "      <td>0.047412</td>\n",
       "      <td>0.034033</td>\n",
       "      <td>0.002997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>-0.002429</td>\n",
       "      <td>0.001437</td>\n",
       "      <td>0.073743</td>\n",
       "      <td>0.014696</td>\n",
       "      <td>0.257614</td>\n",
       "      <td>0.278681</td>\n",
       "      <td>0.070499</td>\n",
       "      <td>0.058034</td>\n",
       "      <td>0.062798</td>\n",
       "      <td>0.069333</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000764</td>\n",
       "      <td>0.013049</td>\n",
       "      <td>0.009210</td>\n",
       "      <td>0.010521</td>\n",
       "      <td>0.010923</td>\n",
       "      <td>0.039657</td>\n",
       "      <td>0.020873</td>\n",
       "      <td>0.038490</td>\n",
       "      <td>0.027449</td>\n",
       "      <td>0.002187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.000759</td>\n",
       "      <td>0.003455</td>\n",
       "      <td>0.105260</td>\n",
       "      <td>0.031436</td>\n",
       "      <td>0.626025</td>\n",
       "      <td>0.547829</td>\n",
       "      <td>0.096415</td>\n",
       "      <td>0.073083</td>\n",
       "      <td>0.081736</td>\n",
       "      <td>0.090238</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000034</td>\n",
       "      <td>0.002501</td>\n",
       "      <td>-0.001319</td>\n",
       "      <td>0.007034</td>\n",
       "      <td>0.006417</td>\n",
       "      <td>0.043618</td>\n",
       "      <td>0.024495</td>\n",
       "      <td>0.044368</td>\n",
       "      <td>0.033259</td>\n",
       "      <td>0.006190</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>-0.002379</td>\n",
       "      <td>0.000363</td>\n",
       "      <td>0.086437</td>\n",
       "      <td>0.018233</td>\n",
       "      <td>0.288828</td>\n",
       "      <td>0.267266</td>\n",
       "      <td>0.089997</td>\n",
       "      <td>0.066318</td>\n",
       "      <td>0.150339</td>\n",
       "      <td>0.150604</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000839</td>\n",
       "      <td>0.007438</td>\n",
       "      <td>0.001961</td>\n",
       "      <td>0.009253</td>\n",
       "      <td>0.009231</td>\n",
       "      <td>0.048605</td>\n",
       "      <td>0.025971</td>\n",
       "      <td>0.047053</td>\n",
       "      <td>0.033769</td>\n",
       "      <td>0.002926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>-0.002709</td>\n",
       "      <td>0.001455</td>\n",
       "      <td>0.073908</td>\n",
       "      <td>0.014741</td>\n",
       "      <td>0.258878</td>\n",
       "      <td>0.279600</td>\n",
       "      <td>0.074687</td>\n",
       "      <td>0.061447</td>\n",
       "      <td>0.097427</td>\n",
       "      <td>0.105768</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000766</td>\n",
       "      <td>0.012996</td>\n",
       "      <td>0.009173</td>\n",
       "      <td>0.010479</td>\n",
       "      <td>0.010878</td>\n",
       "      <td>0.039520</td>\n",
       "      <td>0.020799</td>\n",
       "      <td>0.038355</td>\n",
       "      <td>0.027348</td>\n",
       "      <td>0.002193</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>-0.000660</td>\n",
       "      <td>0.003542</td>\n",
       "      <td>0.107445</td>\n",
       "      <td>0.032684</td>\n",
       "      <td>0.646861</td>\n",
       "      <td>0.568928</td>\n",
       "      <td>0.184804</td>\n",
       "      <td>0.154371</td>\n",
       "      <td>0.119073</td>\n",
       "      <td>0.129487</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000061</td>\n",
       "      <td>0.002380</td>\n",
       "      <td>-0.001342</td>\n",
       "      <td>0.006843</td>\n",
       "      <td>0.006239</td>\n",
       "      <td>0.042713</td>\n",
       "      <td>0.023962</td>\n",
       "      <td>0.043473</td>\n",
       "      <td>0.032567</td>\n",
       "      <td>0.006044</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>-0.003303</td>\n",
       "      <td>0.000536</td>\n",
       "      <td>0.015611</td>\n",
       "      <td>0.000196</td>\n",
       "      <td>0.009554</td>\n",
       "      <td>0.010130</td>\n",
       "      <td>0.012111</td>\n",
       "      <td>0.010131</td>\n",
       "      <td>-0.000209</td>\n",
       "      <td>0.001556</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000097</td>\n",
       "      <td>-0.000250</td>\n",
       "      <td>-0.000171</td>\n",
       "      <td>-0.000215</td>\n",
       "      <td>-0.000227</td>\n",
       "      <td>-0.000073</td>\n",
       "      <td>-0.000175</td>\n",
       "      <td>-0.000266</td>\n",
       "      <td>-0.000229</td>\n",
       "      <td>0.005908</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>-0.000177</td>\n",
       "      <td>-0.000333</td>\n",
       "      <td>0.108362</td>\n",
       "      <td>0.019151</td>\n",
       "      <td>0.231237</td>\n",
       "      <td>0.235623</td>\n",
       "      <td>0.297645</td>\n",
       "      <td>0.279684</td>\n",
       "      <td>0.129796</td>\n",
       "      <td>0.146295</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000733</td>\n",
       "      <td>0.004910</td>\n",
       "      <td>0.005283</td>\n",
       "      <td>0.002952</td>\n",
       "      <td>0.003252</td>\n",
       "      <td>0.010825</td>\n",
       "      <td>0.012335</td>\n",
       "      <td>0.007643</td>\n",
       "      <td>0.008214</td>\n",
       "      <td>0.010866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.002981</td>\n",
       "      <td>-0.007953</td>\n",
       "      <td>-0.112103</td>\n",
       "      <td>-0.003191</td>\n",
       "      <td>-0.225212</td>\n",
       "      <td>-0.231946</td>\n",
       "      <td>-0.091596</td>\n",
       "      <td>-0.108781</td>\n",
       "      <td>-0.027407</td>\n",
       "      <td>-0.037565</td>\n",
       "      <td>...</td>\n",
       "      <td>0.001434</td>\n",
       "      <td>-0.061340</td>\n",
       "      <td>-0.031477</td>\n",
       "      <td>-0.050861</td>\n",
       "      <td>-0.054465</td>\n",
       "      <td>-0.006689</td>\n",
       "      <td>-0.021918</td>\n",
       "      <td>-0.016628</td>\n",
       "      <td>-0.022228</td>\n",
       "      <td>-0.004619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.005065</td>\n",
       "      <td>0.038243</td>\n",
       "      <td>-0.097325</td>\n",
       "      <td>0.017214</td>\n",
       "      <td>0.031854</td>\n",
       "      <td>0.029959</td>\n",
       "      <td>-0.016478</td>\n",
       "      <td>-0.021715</td>\n",
       "      <td>-0.004643</td>\n",
       "      <td>-0.007621</td>\n",
       "      <td>...</td>\n",
       "      <td>0.004822</td>\n",
       "      <td>-0.015515</td>\n",
       "      <td>-0.006131</td>\n",
       "      <td>-0.012546</td>\n",
       "      <td>-0.013573</td>\n",
       "      <td>0.006758</td>\n",
       "      <td>-0.001856</td>\n",
       "      <td>0.004923</td>\n",
       "      <td>0.003175</td>\n",
       "      <td>-0.033673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>-0.003937</td>\n",
       "      <td>0.006976</td>\n",
       "      <td>0.111137</td>\n",
       "      <td>0.005038</td>\n",
       "      <td>0.223314</td>\n",
       "      <td>0.204796</td>\n",
       "      <td>0.045954</td>\n",
       "      <td>0.035723</td>\n",
       "      <td>0.028660</td>\n",
       "      <td>0.032299</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.001266</td>\n",
       "      <td>0.002134</td>\n",
       "      <td>-0.002222</td>\n",
       "      <td>0.005820</td>\n",
       "      <td>0.005618</td>\n",
       "      <td>0.001796</td>\n",
       "      <td>0.003057</td>\n",
       "      <td>0.007784</td>\n",
       "      <td>0.010947</td>\n",
       "      <td>-0.001131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>-0.004784</td>\n",
       "      <td>0.006479</td>\n",
       "      <td>0.099849</td>\n",
       "      <td>0.006821</td>\n",
       "      <td>0.244720</td>\n",
       "      <td>0.224385</td>\n",
       "      <td>0.050260</td>\n",
       "      <td>0.039392</td>\n",
       "      <td>0.031108</td>\n",
       "      <td>0.035061</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.001175</td>\n",
       "      <td>0.002754</td>\n",
       "      <td>-0.002063</td>\n",
       "      <td>0.006639</td>\n",
       "      <td>0.006444</td>\n",
       "      <td>0.002340</td>\n",
       "      <td>0.003602</td>\n",
       "      <td>0.008863</td>\n",
       "      <td>0.012282</td>\n",
       "      <td>-0.005225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>-0.001350</td>\n",
       "      <td>0.010038</td>\n",
       "      <td>0.265369</td>\n",
       "      <td>0.037083</td>\n",
       "      <td>0.018713</td>\n",
       "      <td>0.017347</td>\n",
       "      <td>0.026768</td>\n",
       "      <td>0.018109</td>\n",
       "      <td>-0.001578</td>\n",
       "      <td>-0.002316</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.001822</td>\n",
       "      <td>-0.000782</td>\n",
       "      <td>-0.003198</td>\n",
       "      <td>0.002195</td>\n",
       "      <td>0.001942</td>\n",
       "      <td>0.004872</td>\n",
       "      <td>0.002020</td>\n",
       "      <td>0.007931</td>\n",
       "      <td>0.009128</td>\n",
       "      <td>0.013046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>-0.004962</td>\n",
       "      <td>0.008150</td>\n",
       "      <td>0.221017</td>\n",
       "      <td>0.045699</td>\n",
       "      <td>0.025734</td>\n",
       "      <td>0.025472</td>\n",
       "      <td>0.025483</td>\n",
       "      <td>0.019351</td>\n",
       "      <td>-0.002532</td>\n",
       "      <td>-0.003016</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.001479</td>\n",
       "      <td>0.000895</td>\n",
       "      <td>-0.002596</td>\n",
       "      <td>0.004220</td>\n",
       "      <td>0.004003</td>\n",
       "      <td>-0.000267</td>\n",
       "      <td>-0.002269</td>\n",
       "      <td>0.006119</td>\n",
       "      <td>0.007664</td>\n",
       "      <td>0.010743</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>-0.003578</td>\n",
       "      <td>0.008753</td>\n",
       "      <td>0.300709</td>\n",
       "      <td>0.032633</td>\n",
       "      <td>-0.019486</td>\n",
       "      <td>-0.020961</td>\n",
       "      <td>0.006721</td>\n",
       "      <td>0.011318</td>\n",
       "      <td>-0.003139</td>\n",
       "      <td>-0.003619</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.001587</td>\n",
       "      <td>-0.001007</td>\n",
       "      <td>0.004456</td>\n",
       "      <td>-0.001386</td>\n",
       "      <td>-0.001116</td>\n",
       "      <td>0.006982</td>\n",
       "      <td>0.002763</td>\n",
       "      <td>0.004441</td>\n",
       "      <td>0.005266</td>\n",
       "      <td>0.016192</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>-0.004356</td>\n",
       "      <td>0.007885</td>\n",
       "      <td>0.244545</td>\n",
       "      <td>0.025602</td>\n",
       "      <td>-0.018936</td>\n",
       "      <td>-0.022367</td>\n",
       "      <td>0.002173</td>\n",
       "      <td>0.001413</td>\n",
       "      <td>-0.002778</td>\n",
       "      <td>-0.003217</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.001432</td>\n",
       "      <td>-0.003683</td>\n",
       "      <td>-0.002513</td>\n",
       "      <td>-0.002915</td>\n",
       "      <td>-0.002987</td>\n",
       "      <td>0.008197</td>\n",
       "      <td>0.003591</td>\n",
       "      <td>0.005484</td>\n",
       "      <td>0.006458</td>\n",
       "      <td>0.012430</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>-0.004770</td>\n",
       "      <td>0.007743</td>\n",
       "      <td>0.241895</td>\n",
       "      <td>0.025676</td>\n",
       "      <td>-0.019386</td>\n",
       "      <td>-0.022292</td>\n",
       "      <td>0.002487</td>\n",
       "      <td>0.001741</td>\n",
       "      <td>-0.002718</td>\n",
       "      <td>-0.003149</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.001406</td>\n",
       "      <td>-0.003617</td>\n",
       "      <td>-0.002468</td>\n",
       "      <td>-0.002854</td>\n",
       "      <td>-0.002920</td>\n",
       "      <td>0.002332</td>\n",
       "      <td>0.002312</td>\n",
       "      <td>0.001707</td>\n",
       "      <td>0.002191</td>\n",
       "      <td>0.012166</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>241</th>\n",
       "      <td>-0.005764</td>\n",
       "      <td>0.002447</td>\n",
       "      <td>0.113958</td>\n",
       "      <td>0.001485</td>\n",
       "      <td>-0.005107</td>\n",
       "      <td>-0.004993</td>\n",
       "      <td>0.003789</td>\n",
       "      <td>0.004768</td>\n",
       "      <td>-0.000793</td>\n",
       "      <td>-0.000934</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000442</td>\n",
       "      <td>0.002479</td>\n",
       "      <td>-0.000776</td>\n",
       "      <td>0.004043</td>\n",
       "      <td>0.004044</td>\n",
       "      <td>-0.000666</td>\n",
       "      <td>-0.000738</td>\n",
       "      <td>-0.000712</td>\n",
       "      <td>-0.000836</td>\n",
       "      <td>0.005372</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>242</th>\n",
       "      <td>-0.008832</td>\n",
       "      <td>0.004587</td>\n",
       "      <td>0.186981</td>\n",
       "      <td>0.012294</td>\n",
       "      <td>-0.005741</td>\n",
       "      <td>-0.007929</td>\n",
       "      <td>0.016765</td>\n",
       "      <td>0.011420</td>\n",
       "      <td>-0.001674</td>\n",
       "      <td>-0.001923</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000831</td>\n",
       "      <td>0.000188</td>\n",
       "      <td>-0.001459</td>\n",
       "      <td>0.001695</td>\n",
       "      <td>0.001545</td>\n",
       "      <td>-0.000578</td>\n",
       "      <td>-0.001223</td>\n",
       "      <td>0.000539</td>\n",
       "      <td>0.000239</td>\n",
       "      <td>0.009293</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>243</th>\n",
       "      <td>-0.007737</td>\n",
       "      <td>0.004621</td>\n",
       "      <td>0.188530</td>\n",
       "      <td>0.010547</td>\n",
       "      <td>-0.005057</td>\n",
       "      <td>-0.007410</td>\n",
       "      <td>0.019207</td>\n",
       "      <td>0.013484</td>\n",
       "      <td>-0.001688</td>\n",
       "      <td>-0.001939</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000837</td>\n",
       "      <td>0.000137</td>\n",
       "      <td>-0.001470</td>\n",
       "      <td>0.001575</td>\n",
       "      <td>0.001442</td>\n",
       "      <td>-0.000839</td>\n",
       "      <td>-0.001307</td>\n",
       "      <td>0.000320</td>\n",
       "      <td>0.000205</td>\n",
       "      <td>0.009141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>244</th>\n",
       "      <td>-0.004465</td>\n",
       "      <td>0.005136</td>\n",
       "      <td>0.190970</td>\n",
       "      <td>0.000212</td>\n",
       "      <td>-0.014646</td>\n",
       "      <td>-0.015349</td>\n",
       "      <td>0.014596</td>\n",
       "      <td>0.010674</td>\n",
       "      <td>-0.001974</td>\n",
       "      <td>-0.002245</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000932</td>\n",
       "      <td>-0.002398</td>\n",
       "      <td>-0.001636</td>\n",
       "      <td>-0.002058</td>\n",
       "      <td>-0.002173</td>\n",
       "      <td>0.005269</td>\n",
       "      <td>0.001692</td>\n",
       "      <td>0.003824</td>\n",
       "      <td>0.004624</td>\n",
       "      <td>0.015507</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>245</th>\n",
       "      <td>-0.002826</td>\n",
       "      <td>0.002924</td>\n",
       "      <td>0.109579</td>\n",
       "      <td>0.000027</td>\n",
       "      <td>0.001376</td>\n",
       "      <td>-0.000567</td>\n",
       "      <td>0.043268</td>\n",
       "      <td>0.030460</td>\n",
       "      <td>-0.001140</td>\n",
       "      <td>-0.001292</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000531</td>\n",
       "      <td>-0.001365</td>\n",
       "      <td>-0.000932</td>\n",
       "      <td>-0.001172</td>\n",
       "      <td>-0.001238</td>\n",
       "      <td>0.005606</td>\n",
       "      <td>0.001874</td>\n",
       "      <td>0.004309</td>\n",
       "      <td>0.004521</td>\n",
       "      <td>0.010277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>246</th>\n",
       "      <td>-0.004877</td>\n",
       "      <td>0.005661</td>\n",
       "      <td>0.211582</td>\n",
       "      <td>0.013550</td>\n",
       "      <td>-0.017858</td>\n",
       "      <td>-0.018976</td>\n",
       "      <td>0.010919</td>\n",
       "      <td>0.007473</td>\n",
       "      <td>-0.002179</td>\n",
       "      <td>-0.002477</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.001028</td>\n",
       "      <td>-0.002644</td>\n",
       "      <td>-0.001804</td>\n",
       "      <td>-0.002241</td>\n",
       "      <td>-0.002356</td>\n",
       "      <td>0.003270</td>\n",
       "      <td>0.000900</td>\n",
       "      <td>0.002486</td>\n",
       "      <td>0.003306</td>\n",
       "      <td>0.017709</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>247</th>\n",
       "      <td>-0.004422</td>\n",
       "      <td>0.005627</td>\n",
       "      <td>0.209938</td>\n",
       "      <td>0.016862</td>\n",
       "      <td>-0.017376</td>\n",
       "      <td>-0.018666</td>\n",
       "      <td>0.012633</td>\n",
       "      <td>0.008488</td>\n",
       "      <td>-0.002162</td>\n",
       "      <td>-0.002458</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.001021</td>\n",
       "      <td>-0.002628</td>\n",
       "      <td>-0.001793</td>\n",
       "      <td>-0.002238</td>\n",
       "      <td>-0.002356</td>\n",
       "      <td>0.003210</td>\n",
       "      <td>0.000726</td>\n",
       "      <td>0.002554</td>\n",
       "      <td>0.003314</td>\n",
       "      <td>0.017081</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>248</th>\n",
       "      <td>0.004757</td>\n",
       "      <td>0.002221</td>\n",
       "      <td>0.124535</td>\n",
       "      <td>0.008924</td>\n",
       "      <td>-0.003063</td>\n",
       "      <td>-0.000326</td>\n",
       "      <td>0.006189</td>\n",
       "      <td>0.013538</td>\n",
       "      <td>-0.000860</td>\n",
       "      <td>-0.000974</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000400</td>\n",
       "      <td>-0.001029</td>\n",
       "      <td>-0.000702</td>\n",
       "      <td>-0.000884</td>\n",
       "      <td>-0.000933</td>\n",
       "      <td>-0.000898</td>\n",
       "      <td>-0.000718</td>\n",
       "      <td>-0.001123</td>\n",
       "      <td>-0.001186</td>\n",
       "      <td>0.013665</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>249</th>\n",
       "      <td>0.001328</td>\n",
       "      <td>0.001383</td>\n",
       "      <td>0.077214</td>\n",
       "      <td>-0.001088</td>\n",
       "      <td>-0.000356</td>\n",
       "      <td>-0.000065</td>\n",
       "      <td>0.001468</td>\n",
       "      <td>0.005037</td>\n",
       "      <td>-0.000529</td>\n",
       "      <td>-0.000600</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000246</td>\n",
       "      <td>-0.000634</td>\n",
       "      <td>-0.000432</td>\n",
       "      <td>-0.000544</td>\n",
       "      <td>-0.000575</td>\n",
       "      <td>-0.000539</td>\n",
       "      <td>-0.000442</td>\n",
       "      <td>-0.000674</td>\n",
       "      <td>-0.000713</td>\n",
       "      <td>0.006903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>250</th>\n",
       "      <td>0.005404</td>\n",
       "      <td>0.002355</td>\n",
       "      <td>0.128441</td>\n",
       "      <td>0.016592</td>\n",
       "      <td>-0.004918</td>\n",
       "      <td>-0.002584</td>\n",
       "      <td>0.004983</td>\n",
       "      <td>0.011339</td>\n",
       "      <td>-0.000913</td>\n",
       "      <td>-0.001035</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000425</td>\n",
       "      <td>-0.001093</td>\n",
       "      <td>-0.000746</td>\n",
       "      <td>-0.000938</td>\n",
       "      <td>-0.000991</td>\n",
       "      <td>-0.000972</td>\n",
       "      <td>-0.000763</td>\n",
       "      <td>-0.001217</td>\n",
       "      <td>-0.001284</td>\n",
       "      <td>0.014631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>251</th>\n",
       "      <td>0.006132</td>\n",
       "      <td>0.002355</td>\n",
       "      <td>0.127667</td>\n",
       "      <td>0.018842</td>\n",
       "      <td>-0.005191</td>\n",
       "      <td>-0.003179</td>\n",
       "      <td>0.004225</td>\n",
       "      <td>0.010106</td>\n",
       "      <td>-0.000912</td>\n",
       "      <td>-0.001034</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000425</td>\n",
       "      <td>-0.001092</td>\n",
       "      <td>-0.000745</td>\n",
       "      <td>-0.000938</td>\n",
       "      <td>-0.000990</td>\n",
       "      <td>-0.000971</td>\n",
       "      <td>-0.000762</td>\n",
       "      <td>-0.001216</td>\n",
       "      <td>-0.001283</td>\n",
       "      <td>0.014372</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>252</th>\n",
       "      <td>0.005222</td>\n",
       "      <td>0.000156</td>\n",
       "      <td>0.003506</td>\n",
       "      <td>-0.000224</td>\n",
       "      <td>-0.000889</td>\n",
       "      <td>-0.000909</td>\n",
       "      <td>-0.000157</td>\n",
       "      <td>-0.000172</td>\n",
       "      <td>-0.000061</td>\n",
       "      <td>-0.000069</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000028</td>\n",
       "      <td>-0.000073</td>\n",
       "      <td>-0.000050</td>\n",
       "      <td>-0.000063</td>\n",
       "      <td>-0.000066</td>\n",
       "      <td>-0.000065</td>\n",
       "      <td>-0.000051</td>\n",
       "      <td>-0.000081</td>\n",
       "      <td>-0.000086</td>\n",
       "      <td>-0.000953</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>254</th>\n",
       "      <td>0.005222</td>\n",
       "      <td>0.000156</td>\n",
       "      <td>0.003506</td>\n",
       "      <td>-0.000224</td>\n",
       "      <td>-0.000889</td>\n",
       "      <td>-0.000909</td>\n",
       "      <td>-0.000157</td>\n",
       "      <td>-0.000172</td>\n",
       "      <td>-0.000061</td>\n",
       "      <td>-0.000069</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000028</td>\n",
       "      <td>-0.000073</td>\n",
       "      <td>-0.000050</td>\n",
       "      <td>-0.000063</td>\n",
       "      <td>-0.000066</td>\n",
       "      <td>-0.000065</td>\n",
       "      <td>-0.000051</td>\n",
       "      <td>-0.000081</td>\n",
       "      <td>-0.000086</td>\n",
       "      <td>-0.000953</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>255</th>\n",
       "      <td>-0.003811</td>\n",
       "      <td>0.000210</td>\n",
       "      <td>0.015363</td>\n",
       "      <td>-0.000297</td>\n",
       "      <td>0.000075</td>\n",
       "      <td>0.000119</td>\n",
       "      <td>-0.000131</td>\n",
       "      <td>0.000537</td>\n",
       "      <td>-0.000082</td>\n",
       "      <td>-0.000092</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000038</td>\n",
       "      <td>0.000659</td>\n",
       "      <td>-0.000067</td>\n",
       "      <td>0.001757</td>\n",
       "      <td>0.001536</td>\n",
       "      <td>0.003734</td>\n",
       "      <td>0.001838</td>\n",
       "      <td>0.003642</td>\n",
       "      <td>0.002637</td>\n",
       "      <td>0.006087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>256</th>\n",
       "      <td>-0.004175</td>\n",
       "      <td>0.000175</td>\n",
       "      <td>0.013234</td>\n",
       "      <td>-0.000250</td>\n",
       "      <td>-0.000935</td>\n",
       "      <td>-0.000892</td>\n",
       "      <td>-0.000140</td>\n",
       "      <td>0.000123</td>\n",
       "      <td>-0.000068</td>\n",
       "      <td>-0.000077</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000032</td>\n",
       "      <td>-0.000081</td>\n",
       "      <td>-0.000055</td>\n",
       "      <td>-0.000070</td>\n",
       "      <td>-0.000074</td>\n",
       "      <td>-0.000072</td>\n",
       "      <td>-0.000057</td>\n",
       "      <td>-0.000091</td>\n",
       "      <td>-0.000096</td>\n",
       "      <td>0.005926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>257</th>\n",
       "      <td>-0.003134</td>\n",
       "      <td>0.000301</td>\n",
       "      <td>0.018995</td>\n",
       "      <td>-0.000344</td>\n",
       "      <td>0.000163</td>\n",
       "      <td>0.000121</td>\n",
       "      <td>0.000720</td>\n",
       "      <td>0.001150</td>\n",
       "      <td>-0.000116</td>\n",
       "      <td>-0.000132</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000054</td>\n",
       "      <td>0.001836</td>\n",
       "      <td>-0.000095</td>\n",
       "      <td>0.004689</td>\n",
       "      <td>0.004118</td>\n",
       "      <td>0.004483</td>\n",
       "      <td>0.002107</td>\n",
       "      <td>0.004346</td>\n",
       "      <td>0.003203</td>\n",
       "      <td>0.006390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>258</th>\n",
       "      <td>-0.003449</td>\n",
       "      <td>0.000290</td>\n",
       "      <td>0.019038</td>\n",
       "      <td>-0.000361</td>\n",
       "      <td>0.000305</td>\n",
       "      <td>0.000227</td>\n",
       "      <td>0.000848</td>\n",
       "      <td>0.001095</td>\n",
       "      <td>-0.000112</td>\n",
       "      <td>-0.000127</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000052</td>\n",
       "      <td>0.001442</td>\n",
       "      <td>-0.000091</td>\n",
       "      <td>0.003725</td>\n",
       "      <td>0.003268</td>\n",
       "      <td>0.004767</td>\n",
       "      <td>0.002291</td>\n",
       "      <td>0.004635</td>\n",
       "      <td>0.003389</td>\n",
       "      <td>0.006392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>259</th>\n",
       "      <td>0.000807</td>\n",
       "      <td>0.000219</td>\n",
       "      <td>0.009150</td>\n",
       "      <td>-0.000314</td>\n",
       "      <td>-0.001249</td>\n",
       "      <td>-0.001131</td>\n",
       "      <td>-0.000220</td>\n",
       "      <td>-0.000242</td>\n",
       "      <td>-0.000085</td>\n",
       "      <td>-0.000097</td>\n",
       "      <td>...</td>\n",
       "      <td>0.229483</td>\n",
       "      <td>-0.000102</td>\n",
       "      <td>-0.000070</td>\n",
       "      <td>-0.000088</td>\n",
       "      <td>-0.000093</td>\n",
       "      <td>0.004084</td>\n",
       "      <td>-0.000071</td>\n",
       "      <td>0.013095</td>\n",
       "      <td>0.010577</td>\n",
       "      <td>-0.000791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>260</th>\n",
       "      <td>0.000163</td>\n",
       "      <td>0.000157</td>\n",
       "      <td>-0.003298</td>\n",
       "      <td>-0.000224</td>\n",
       "      <td>-0.000889</td>\n",
       "      <td>0.026991</td>\n",
       "      <td>-0.000157</td>\n",
       "      <td>-0.000172</td>\n",
       "      <td>-0.000061</td>\n",
       "      <td>-0.000069</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000028</td>\n",
       "      <td>-0.000073</td>\n",
       "      <td>-0.000050</td>\n",
       "      <td>-0.000063</td>\n",
       "      <td>-0.000066</td>\n",
       "      <td>-0.000065</td>\n",
       "      <td>-0.000051</td>\n",
       "      <td>-0.000081</td>\n",
       "      <td>-0.000086</td>\n",
       "      <td>-0.001298</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>261</th>\n",
       "      <td>-0.006924</td>\n",
       "      <td>0.000210</td>\n",
       "      <td>0.012375</td>\n",
       "      <td>0.005391</td>\n",
       "      <td>0.000466</td>\n",
       "      <td>-0.000188</td>\n",
       "      <td>-0.000211</td>\n",
       "      <td>-0.000232</td>\n",
       "      <td>-0.000082</td>\n",
       "      <td>-0.000093</td>\n",
       "      <td>...</td>\n",
       "      <td>0.950235</td>\n",
       "      <td>-0.000098</td>\n",
       "      <td>-0.000067</td>\n",
       "      <td>-0.000084</td>\n",
       "      <td>-0.000089</td>\n",
       "      <td>0.001398</td>\n",
       "      <td>-0.000068</td>\n",
       "      <td>0.004588</td>\n",
       "      <td>0.003689</td>\n",
       "      <td>-0.001562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>262</th>\n",
       "      <td>-0.008809</td>\n",
       "      <td>0.000252</td>\n",
       "      <td>0.013472</td>\n",
       "      <td>0.008937</td>\n",
       "      <td>0.001278</td>\n",
       "      <td>0.000221</td>\n",
       "      <td>-0.000253</td>\n",
       "      <td>-0.000278</td>\n",
       "      <td>-0.000098</td>\n",
       "      <td>-0.000111</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.000118</td>\n",
       "      <td>-0.000080</td>\n",
       "      <td>-0.000101</td>\n",
       "      <td>-0.000107</td>\n",
       "      <td>0.003847</td>\n",
       "      <td>-0.000082</td>\n",
       "      <td>0.012370</td>\n",
       "      <td>0.009986</td>\n",
       "      <td>-0.001545</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>263</th>\n",
       "      <td>-0.000128</td>\n",
       "      <td>0.000687</td>\n",
       "      <td>0.028406</td>\n",
       "      <td>-0.000840</td>\n",
       "      <td>0.018452</td>\n",
       "      <td>0.031368</td>\n",
       "      <td>0.004228</td>\n",
       "      <td>0.008017</td>\n",
       "      <td>-0.000253</td>\n",
       "      <td>-0.000286</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000118</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.682823</td>\n",
       "      <td>0.858582</td>\n",
       "      <td>0.897964</td>\n",
       "      <td>0.001429</td>\n",
       "      <td>-0.000211</td>\n",
       "      <td>0.001121</td>\n",
       "      <td>0.001287</td>\n",
       "      <td>0.003312</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>264</th>\n",
       "      <td>0.001181</td>\n",
       "      <td>0.000464</td>\n",
       "      <td>0.016710</td>\n",
       "      <td>-0.000624</td>\n",
       "      <td>0.015337</td>\n",
       "      <td>0.028060</td>\n",
       "      <td>0.008442</td>\n",
       "      <td>0.014056</td>\n",
       "      <td>-0.000172</td>\n",
       "      <td>-0.000195</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000080</td>\n",
       "      <td>0.682823</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.404886</td>\n",
       "      <td>0.452079</td>\n",
       "      <td>-0.000184</td>\n",
       "      <td>-0.000144</td>\n",
       "      <td>-0.000230</td>\n",
       "      <td>-0.000243</td>\n",
       "      <td>0.001151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>265</th>\n",
       "      <td>-0.002806</td>\n",
       "      <td>0.000585</td>\n",
       "      <td>0.027005</td>\n",
       "      <td>-0.000586</td>\n",
       "      <td>0.014867</td>\n",
       "      <td>0.021555</td>\n",
       "      <td>0.002438</td>\n",
       "      <td>0.004587</td>\n",
       "      <td>-0.000217</td>\n",
       "      <td>-0.000246</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000101</td>\n",
       "      <td>0.858582</td>\n",
       "      <td>0.404886</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.992950</td>\n",
       "      <td>0.003898</td>\n",
       "      <td>-0.000181</td>\n",
       "      <td>0.003254</td>\n",
       "      <td>0.003687</td>\n",
       "      <td>0.003273</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>266</th>\n",
       "      <td>-0.002573</td>\n",
       "      <td>0.000618</td>\n",
       "      <td>0.027922</td>\n",
       "      <td>-0.000651</td>\n",
       "      <td>0.016131</td>\n",
       "      <td>0.023983</td>\n",
       "      <td>0.003520</td>\n",
       "      <td>0.006548</td>\n",
       "      <td>-0.000229</td>\n",
       "      <td>-0.000260</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000107</td>\n",
       "      <td>0.897964</td>\n",
       "      <td>0.452079</td>\n",
       "      <td>0.992950</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.003401</td>\n",
       "      <td>-0.000191</td>\n",
       "      <td>0.002823</td>\n",
       "      <td>0.003203</td>\n",
       "      <td>0.003331</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>267</th>\n",
       "      <td>-0.003620</td>\n",
       "      <td>0.000582</td>\n",
       "      <td>0.030106</td>\n",
       "      <td>0.003535</td>\n",
       "      <td>0.011756</td>\n",
       "      <td>0.010169</td>\n",
       "      <td>-0.000391</td>\n",
       "      <td>-0.000517</td>\n",
       "      <td>-0.000225</td>\n",
       "      <td>-0.000255</td>\n",
       "      <td>...</td>\n",
       "      <td>0.003847</td>\n",
       "      <td>0.001429</td>\n",
       "      <td>-0.000184</td>\n",
       "      <td>0.003898</td>\n",
       "      <td>0.003401</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.442404</td>\n",
       "      <td>0.822951</td>\n",
       "      <td>0.690004</td>\n",
       "      <td>0.001904</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>268</th>\n",
       "      <td>-0.006234</td>\n",
       "      <td>0.000474</td>\n",
       "      <td>0.023319</td>\n",
       "      <td>-0.000551</td>\n",
       "      <td>0.009377</td>\n",
       "      <td>0.007747</td>\n",
       "      <td>-0.000455</td>\n",
       "      <td>-0.000499</td>\n",
       "      <td>-0.000176</td>\n",
       "      <td>-0.000200</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.000082</td>\n",
       "      <td>-0.000211</td>\n",
       "      <td>-0.000144</td>\n",
       "      <td>-0.000181</td>\n",
       "      <td>-0.000191</td>\n",
       "      <td>0.442404</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.292239</td>\n",
       "      <td>0.258733</td>\n",
       "      <td>0.006617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>269</th>\n",
       "      <td>-0.001831</td>\n",
       "      <td>0.000725</td>\n",
       "      <td>0.035177</td>\n",
       "      <td>0.007161</td>\n",
       "      <td>0.015979</td>\n",
       "      <td>0.014444</td>\n",
       "      <td>-0.000140</td>\n",
       "      <td>-0.000427</td>\n",
       "      <td>-0.000282</td>\n",
       "      <td>-0.000319</td>\n",
       "      <td>...</td>\n",
       "      <td>0.012370</td>\n",
       "      <td>0.001121</td>\n",
       "      <td>-0.000230</td>\n",
       "      <td>0.003254</td>\n",
       "      <td>0.002823</td>\n",
       "      <td>0.822951</td>\n",
       "      <td>0.292239</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.962876</td>\n",
       "      <td>0.001935</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>270</th>\n",
       "      <td>-0.000059</td>\n",
       "      <td>0.000765</td>\n",
       "      <td>0.035580</td>\n",
       "      <td>0.009017</td>\n",
       "      <td>0.014475</td>\n",
       "      <td>0.012988</td>\n",
       "      <td>-0.000289</td>\n",
       "      <td>-0.000540</td>\n",
       "      <td>-0.000297</td>\n",
       "      <td>-0.000337</td>\n",
       "      <td>...</td>\n",
       "      <td>0.009986</td>\n",
       "      <td>0.001287</td>\n",
       "      <td>-0.000243</td>\n",
       "      <td>0.003687</td>\n",
       "      <td>0.003203</td>\n",
       "      <td>0.690004</td>\n",
       "      <td>0.258733</td>\n",
       "      <td>0.962876</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.001643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>271</th>\n",
       "      <td>-0.008112</td>\n",
       "      <td>-0.000041</td>\n",
       "      <td>0.007449</td>\n",
       "      <td>0.000423</td>\n",
       "      <td>0.009990</td>\n",
       "      <td>0.011707</td>\n",
       "      <td>0.002612</td>\n",
       "      <td>0.005096</td>\n",
       "      <td>-0.000817</td>\n",
       "      <td>0.000350</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.001545</td>\n",
       "      <td>0.003312</td>\n",
       "      <td>0.001151</td>\n",
       "      <td>0.003273</td>\n",
       "      <td>0.003331</td>\n",
       "      <td>0.001904</td>\n",
       "      <td>0.006617</td>\n",
       "      <td>0.001935</td>\n",
       "      <td>0.001643</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>255 rows × 255 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2         3         4         5         6    \\\n",
       "0    1.000000  0.001194 -0.001853 -0.003938  0.000109 -0.003770 -0.009275   \n",
       "1    0.001194  1.000000 -0.001827  0.001988  0.007314  0.007741  0.001417   \n",
       "2   -0.001853 -0.001827  1.000000  0.040057  0.095506  0.101138  0.041632   \n",
       "3   -0.003938  0.001988  0.040057  1.000000  0.038944  0.033910  0.011242   \n",
       "4    0.000109  0.007314  0.095506  0.038944  1.000000  0.888244  0.350951   \n",
       "5   -0.003770  0.007741  0.101138  0.033910  0.888244  1.000000  0.316705   \n",
       "6   -0.009275  0.001417  0.041632  0.011242  0.350951  0.316705  1.000000   \n",
       "7   -0.010554  0.001574  0.048417  0.010576  0.309539  0.359242  0.858154   \n",
       "8   -0.007310  0.000544  0.009907  0.000743  0.032660  0.029647  0.058951   \n",
       "9   -0.007864  0.000618  0.010963  0.002513  0.057051  0.049465  0.120411   \n",
       "10  -0.011209  0.001240  0.034034  0.014923  0.264996  0.254774  0.720901   \n",
       "11   0.002885  0.007365  0.089275  0.038115  0.960128  0.851342  0.075178   \n",
       "12  -0.000915  0.007798  0.093682  0.033077  0.856835  0.961471  0.085229   \n",
       "13  -0.001956  0.000333  0.086469  0.018321  0.288963  0.267425  0.087097   \n",
       "14  -0.002429  0.001437  0.073743  0.014696  0.257614  0.278681  0.070499   \n",
       "15   0.000759  0.003455  0.105260  0.031436  0.626025  0.547829  0.096415   \n",
       "16  -0.002379  0.000363  0.086437  0.018233  0.288828  0.267266  0.089997   \n",
       "17  -0.002709  0.001455  0.073908  0.014741  0.258878  0.279600  0.074687   \n",
       "18  -0.000660  0.003542  0.107445  0.032684  0.646861  0.568928  0.184804   \n",
       "19  -0.003303  0.000536  0.015611  0.000196  0.009554  0.010130  0.012111   \n",
       "20  -0.000177 -0.000333  0.108362  0.019151  0.231237  0.235623  0.297645   \n",
       "21   0.002981 -0.007953 -0.112103 -0.003191 -0.225212 -0.231946 -0.091596   \n",
       "22   0.005065  0.038243 -0.097325  0.017214  0.031854  0.029959 -0.016478   \n",
       "23  -0.003937  0.006976  0.111137  0.005038  0.223314  0.204796  0.045954   \n",
       "24  -0.004784  0.006479  0.099849  0.006821  0.244720  0.224385  0.050260   \n",
       "25  -0.001350  0.010038  0.265369  0.037083  0.018713  0.017347  0.026768   \n",
       "26  -0.004962  0.008150  0.221017  0.045699  0.025734  0.025472  0.025483   \n",
       "27  -0.003578  0.008753  0.300709  0.032633 -0.019486 -0.020961  0.006721   \n",
       "28  -0.004356  0.007885  0.244545  0.025602 -0.018936 -0.022367  0.002173   \n",
       "29  -0.004770  0.007743  0.241895  0.025676 -0.019386 -0.022292  0.002487   \n",
       "..        ...       ...       ...       ...       ...       ...       ...   \n",
       "241 -0.005764  0.002447  0.113958  0.001485 -0.005107 -0.004993  0.003789   \n",
       "242 -0.008832  0.004587  0.186981  0.012294 -0.005741 -0.007929  0.016765   \n",
       "243 -0.007737  0.004621  0.188530  0.010547 -0.005057 -0.007410  0.019207   \n",
       "244 -0.004465  0.005136  0.190970  0.000212 -0.014646 -0.015349  0.014596   \n",
       "245 -0.002826  0.002924  0.109579  0.000027  0.001376 -0.000567  0.043268   \n",
       "246 -0.004877  0.005661  0.211582  0.013550 -0.017858 -0.018976  0.010919   \n",
       "247 -0.004422  0.005627  0.209938  0.016862 -0.017376 -0.018666  0.012633   \n",
       "248  0.004757  0.002221  0.124535  0.008924 -0.003063 -0.000326  0.006189   \n",
       "249  0.001328  0.001383  0.077214 -0.001088 -0.000356 -0.000065  0.001468   \n",
       "250  0.005404  0.002355  0.128441  0.016592 -0.004918 -0.002584  0.004983   \n",
       "251  0.006132  0.002355  0.127667  0.018842 -0.005191 -0.003179  0.004225   \n",
       "252  0.005222  0.000156  0.003506 -0.000224 -0.000889 -0.000909 -0.000157   \n",
       "254  0.005222  0.000156  0.003506 -0.000224 -0.000889 -0.000909 -0.000157   \n",
       "255 -0.003811  0.000210  0.015363 -0.000297  0.000075  0.000119 -0.000131   \n",
       "256 -0.004175  0.000175  0.013234 -0.000250 -0.000935 -0.000892 -0.000140   \n",
       "257 -0.003134  0.000301  0.018995 -0.000344  0.000163  0.000121  0.000720   \n",
       "258 -0.003449  0.000290  0.019038 -0.000361  0.000305  0.000227  0.000848   \n",
       "259  0.000807  0.000219  0.009150 -0.000314 -0.001249 -0.001131 -0.000220   \n",
       "260  0.000163  0.000157 -0.003298 -0.000224 -0.000889  0.026991 -0.000157   \n",
       "261 -0.006924  0.000210  0.012375  0.005391  0.000466 -0.000188 -0.000211   \n",
       "262 -0.008809  0.000252  0.013472  0.008937  0.001278  0.000221 -0.000253   \n",
       "263 -0.000128  0.000687  0.028406 -0.000840  0.018452  0.031368  0.004228   \n",
       "264  0.001181  0.000464  0.016710 -0.000624  0.015337  0.028060  0.008442   \n",
       "265 -0.002806  0.000585  0.027005 -0.000586  0.014867  0.021555  0.002438   \n",
       "266 -0.002573  0.000618  0.027922 -0.000651  0.016131  0.023983  0.003520   \n",
       "267 -0.003620  0.000582  0.030106  0.003535  0.011756  0.010169 -0.000391   \n",
       "268 -0.006234  0.000474  0.023319 -0.000551  0.009377  0.007747 -0.000455   \n",
       "269 -0.001831  0.000725  0.035177  0.007161  0.015979  0.014444 -0.000140   \n",
       "270 -0.000059  0.000765  0.035580  0.009017  0.014475  0.012988 -0.000289   \n",
       "271 -0.008112 -0.000041  0.007449  0.000423  0.009990  0.011707  0.002612   \n",
       "\n",
       "          7         8         9    ...       262       263       264  \\\n",
       "0   -0.010554 -0.007310 -0.007864  ... -0.008809 -0.000128  0.001181   \n",
       "1    0.001574  0.000544  0.000618  ...  0.000252  0.000687  0.000464   \n",
       "2    0.048417  0.009907  0.010963  ...  0.013472  0.028406  0.016710   \n",
       "3    0.010576  0.000743  0.002513  ...  0.008937 -0.000840 -0.000624   \n",
       "4    0.309539  0.032660  0.057051  ...  0.001278  0.018452  0.015337   \n",
       "5    0.359242  0.029647  0.049465  ...  0.000221  0.031368  0.028060   \n",
       "6    0.858154  0.058951  0.120411  ... -0.000253  0.004228  0.008442   \n",
       "7    1.000000  0.053506  0.098173  ... -0.000278  0.008017  0.014056   \n",
       "8    0.053506  1.000000  0.950170  ... -0.000098 -0.000253 -0.000172   \n",
       "9    0.098173  0.950170  1.000000  ... -0.000111 -0.000286 -0.000195   \n",
       "10   0.660534  0.310980  0.327589  ... -0.000222 -0.000571 -0.000390   \n",
       "11   0.073426  0.017179  0.024805  ...  0.001436  0.018388  0.013812   \n",
       "12   0.088846  0.015881  0.023875  ...  0.000318  0.031117  0.025807   \n",
       "13   0.063574  0.091121  0.094393  ... -0.000839  0.007507  0.001985   \n",
       "14   0.058034  0.062798  0.069333  ... -0.000764  0.013049  0.009210   \n",
       "15   0.073083  0.081736  0.090238  ... -0.000034  0.002501 -0.001319   \n",
       "16   0.066318  0.150339  0.150604  ... -0.000839  0.007438  0.001961   \n",
       "17   0.061447  0.097427  0.105768  ... -0.000766  0.012996  0.009173   \n",
       "18   0.154371  0.119073  0.129487  ... -0.000061  0.002380 -0.001342   \n",
       "19   0.010131 -0.000209  0.001556  ... -0.000097 -0.000250 -0.000171   \n",
       "20   0.279684  0.129796  0.146295  ... -0.000733  0.004910  0.005283   \n",
       "21  -0.108781 -0.027407 -0.037565  ...  0.001434 -0.061340 -0.031477   \n",
       "22  -0.021715 -0.004643 -0.007621  ...  0.004822 -0.015515 -0.006131   \n",
       "23   0.035723  0.028660  0.032299  ... -0.001266  0.002134 -0.002222   \n",
       "24   0.039392  0.031108  0.035061  ... -0.001175  0.002754 -0.002063   \n",
       "25   0.018109 -0.001578 -0.002316  ... -0.001822 -0.000782 -0.003198   \n",
       "26   0.019351 -0.002532 -0.003016  ... -0.001479  0.000895 -0.002596   \n",
       "27   0.011318 -0.003139 -0.003619  ... -0.001587 -0.001007  0.004456   \n",
       "28   0.001413 -0.002778 -0.003217  ... -0.001432 -0.003683 -0.002513   \n",
       "29   0.001741 -0.002718 -0.003149  ... -0.001406 -0.003617 -0.002468   \n",
       "..        ...       ...       ...  ...       ...       ...       ...   \n",
       "241  0.004768 -0.000793 -0.000934  ... -0.000442  0.002479 -0.000776   \n",
       "242  0.011420 -0.001674 -0.001923  ... -0.000831  0.000188 -0.001459   \n",
       "243  0.013484 -0.001688 -0.001939  ... -0.000837  0.000137 -0.001470   \n",
       "244  0.010674 -0.001974 -0.002245  ... -0.000932 -0.002398 -0.001636   \n",
       "245  0.030460 -0.001140 -0.001292  ... -0.000531 -0.001365 -0.000932   \n",
       "246  0.007473 -0.002179 -0.002477  ... -0.001028 -0.002644 -0.001804   \n",
       "247  0.008488 -0.002162 -0.002458  ... -0.001021 -0.002628 -0.001793   \n",
       "248  0.013538 -0.000860 -0.000974  ... -0.000400 -0.001029 -0.000702   \n",
       "249  0.005037 -0.000529 -0.000600  ... -0.000246 -0.000634 -0.000432   \n",
       "250  0.011339 -0.000913 -0.001035  ... -0.000425 -0.001093 -0.000746   \n",
       "251  0.010106 -0.000912 -0.001034  ... -0.000425 -0.001092 -0.000745   \n",
       "252 -0.000172 -0.000061 -0.000069  ... -0.000028 -0.000073 -0.000050   \n",
       "254 -0.000172 -0.000061 -0.000069  ... -0.000028 -0.000073 -0.000050   \n",
       "255  0.000537 -0.000082 -0.000092  ... -0.000038  0.000659 -0.000067   \n",
       "256  0.000123 -0.000068 -0.000077  ... -0.000032 -0.000081 -0.000055   \n",
       "257  0.001150 -0.000116 -0.000132  ... -0.000054  0.001836 -0.000095   \n",
       "258  0.001095 -0.000112 -0.000127  ... -0.000052  0.001442 -0.000091   \n",
       "259 -0.000242 -0.000085 -0.000097  ...  0.229483 -0.000102 -0.000070   \n",
       "260 -0.000172 -0.000061 -0.000069  ... -0.000028 -0.000073 -0.000050   \n",
       "261 -0.000232 -0.000082 -0.000093  ...  0.950235 -0.000098 -0.000067   \n",
       "262 -0.000278 -0.000098 -0.000111  ...  1.000000 -0.000118 -0.000080   \n",
       "263  0.008017 -0.000253 -0.000286  ... -0.000118  1.000000  0.682823   \n",
       "264  0.014056 -0.000172 -0.000195  ... -0.000080  0.682823  1.000000   \n",
       "265  0.004587 -0.000217 -0.000246  ... -0.000101  0.858582  0.404886   \n",
       "266  0.006548 -0.000229 -0.000260  ... -0.000107  0.897964  0.452079   \n",
       "267 -0.000517 -0.000225 -0.000255  ...  0.003847  0.001429 -0.000184   \n",
       "268 -0.000499 -0.000176 -0.000200  ... -0.000082 -0.000211 -0.000144   \n",
       "269 -0.000427 -0.000282 -0.000319  ...  0.012370  0.001121 -0.000230   \n",
       "270 -0.000540 -0.000297 -0.000337  ...  0.009986  0.001287 -0.000243   \n",
       "271  0.005096 -0.000817  0.000350  ... -0.001545  0.003312  0.001151   \n",
       "\n",
       "          265       266       267       268       269       270       271  \n",
       "0   -0.002806 -0.002573 -0.003620 -0.006234 -0.001831 -0.000059 -0.008112  \n",
       "1    0.000585  0.000618  0.000582  0.000474  0.000725  0.000765 -0.000041  \n",
       "2    0.027005  0.027922  0.030106  0.023319  0.035177  0.035580  0.007449  \n",
       "3   -0.000586 -0.000651  0.003535 -0.000551  0.007161  0.009017  0.000423  \n",
       "4    0.014867  0.016131  0.011756  0.009377  0.015979  0.014475  0.009990  \n",
       "5    0.021555  0.023983  0.010169  0.007747  0.014444  0.012988  0.011707  \n",
       "6    0.002438  0.003520 -0.000391 -0.000455 -0.000140 -0.000289  0.002612  \n",
       "7    0.004587  0.006548 -0.000517 -0.000499 -0.000427 -0.000540  0.005096  \n",
       "8   -0.000217 -0.000229 -0.000225 -0.000176 -0.000282 -0.000297 -0.000817  \n",
       "9   -0.000246 -0.000260 -0.000255 -0.000200 -0.000319 -0.000337  0.000350  \n",
       "10  -0.000418 -0.000414 -0.000355 -0.000399 -0.000161 -0.000285 -0.000187  \n",
       "11   0.015105  0.016128  0.012635  0.010121  0.017058  0.015501  0.009859  \n",
       "12   0.021655  0.023668  0.011005  0.008415  0.015542  0.014021  0.010994  \n",
       "13   0.009333  0.009312  0.048972  0.026171  0.047412  0.034033  0.002997  \n",
       "14   0.010521  0.010923  0.039657  0.020873  0.038490  0.027449  0.002187  \n",
       "15   0.007034  0.006417  0.043618  0.024495  0.044368  0.033259  0.006190  \n",
       "16   0.009253  0.009231  0.048605  0.025971  0.047053  0.033769  0.002926  \n",
       "17   0.010479  0.010878  0.039520  0.020799  0.038355  0.027348  0.002193  \n",
       "18   0.006843  0.006239  0.042713  0.023962  0.043473  0.032567  0.006044  \n",
       "19  -0.000215 -0.000227 -0.000073 -0.000175 -0.000266 -0.000229  0.005908  \n",
       "20   0.002952  0.003252  0.010825  0.012335  0.007643  0.008214  0.010866  \n",
       "21  -0.050861 -0.054465 -0.006689 -0.021918 -0.016628 -0.022228 -0.004619  \n",
       "22  -0.012546 -0.013573  0.006758 -0.001856  0.004923  0.003175 -0.033673  \n",
       "23   0.005820  0.005618  0.001796  0.003057  0.007784  0.010947 -0.001131  \n",
       "24   0.006639  0.006444  0.002340  0.003602  0.008863  0.012282 -0.005225  \n",
       "25   0.002195  0.001942  0.004872  0.002020  0.007931  0.009128  0.013046  \n",
       "26   0.004220  0.004003 -0.000267 -0.002269  0.006119  0.007664  0.010743  \n",
       "27  -0.001386 -0.001116  0.006982  0.002763  0.004441  0.005266  0.016192  \n",
       "28  -0.002915 -0.002987  0.008197  0.003591  0.005484  0.006458  0.012430  \n",
       "29  -0.002854 -0.002920  0.002332  0.002312  0.001707  0.002191  0.012166  \n",
       "..        ...       ...       ...       ...       ...       ...       ...  \n",
       "241  0.004043  0.004044 -0.000666 -0.000738 -0.000712 -0.000836  0.005372  \n",
       "242  0.001695  0.001545 -0.000578 -0.001223  0.000539  0.000239  0.009293  \n",
       "243  0.001575  0.001442 -0.000839 -0.001307  0.000320  0.000205  0.009141  \n",
       "244 -0.002058 -0.002173  0.005269  0.001692  0.003824  0.004624  0.015507  \n",
       "245 -0.001172 -0.001238  0.005606  0.001874  0.004309  0.004521  0.010277  \n",
       "246 -0.002241 -0.002356  0.003270  0.000900  0.002486  0.003306  0.017709  \n",
       "247 -0.002238 -0.002356  0.003210  0.000726  0.002554  0.003314  0.017081  \n",
       "248 -0.000884 -0.000933 -0.000898 -0.000718 -0.001123 -0.001186  0.013665  \n",
       "249 -0.000544 -0.000575 -0.000539 -0.000442 -0.000674 -0.000713  0.006903  \n",
       "250 -0.000938 -0.000991 -0.000972 -0.000763 -0.001217 -0.001284  0.014631  \n",
       "251 -0.000938 -0.000990 -0.000971 -0.000762 -0.001216 -0.001283  0.014372  \n",
       "252 -0.000063 -0.000066 -0.000065 -0.000051 -0.000081 -0.000086 -0.000953  \n",
       "254 -0.000063 -0.000066 -0.000065 -0.000051 -0.000081 -0.000086 -0.000953  \n",
       "255  0.001757  0.001536  0.003734  0.001838  0.003642  0.002637  0.006087  \n",
       "256 -0.000070 -0.000074 -0.000072 -0.000057 -0.000091 -0.000096  0.005926  \n",
       "257  0.004689  0.004118  0.004483  0.002107  0.004346  0.003203  0.006390  \n",
       "258  0.003725  0.003268  0.004767  0.002291  0.004635  0.003389  0.006392  \n",
       "259 -0.000088 -0.000093  0.004084 -0.000071  0.013095  0.010577 -0.000791  \n",
       "260 -0.000063 -0.000066 -0.000065 -0.000051 -0.000081 -0.000086 -0.001298  \n",
       "261 -0.000084 -0.000089  0.001398 -0.000068  0.004588  0.003689 -0.001562  \n",
       "262 -0.000101 -0.000107  0.003847 -0.000082  0.012370  0.009986 -0.001545  \n",
       "263  0.858582  0.897964  0.001429 -0.000211  0.001121  0.001287  0.003312  \n",
       "264  0.404886  0.452079 -0.000184 -0.000144 -0.000230 -0.000243  0.001151  \n",
       "265  1.000000  0.992950  0.003898 -0.000181  0.003254  0.003687  0.003273  \n",
       "266  0.992950  1.000000  0.003401 -0.000191  0.002823  0.003203  0.003331  \n",
       "267  0.003898  0.003401  1.000000  0.442404  0.822951  0.690004  0.001904  \n",
       "268 -0.000181 -0.000191  0.442404  1.000000  0.292239  0.258733  0.006617  \n",
       "269  0.003254  0.002823  0.822951  0.292239  1.000000  0.962876  0.001935  \n",
       "270  0.003687  0.003203  0.690004  0.258733  0.962876  1.000000  0.001643  \n",
       "271  0.003273  0.003331  0.001904  0.006617  0.001935  0.001643  1.000000  \n",
       "\n",
       "[255 rows x 255 columns]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corrmat = X_train_unique.corr(method='pearson')\n",
    "corrmat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n"
     ]
    }
   ],
   "source": [
    "print(type(corrmat))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(255, 255)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corrmat.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Filtering out features which have correlation more than 0.85"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 5, 6, 8, 9, 10, 11, 13, 14, 15, 16, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 39, 41, 42, 43, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 65, 66, 67, 69, 70, 71, 75, 76, 78, 79, 80, 81, 82, 84, 85, 87, 88, 90, 94, 97, 104, 106, 108, 109, 110, 111, 113, 114, 116, 117, 119, 120, 124, 126, 127, 130, 131, 133, 134, 135, 136, 137, 138, 141, 144, 145, 146, 163, 170, 185, 186, 187, 197, 202, 204, 211, 212, 213, 215, 217, 219, 220, 221, 228, 230, 238, 240, 242, 244, 246, 248, 250, 252, 255, 256, 257, 261, 263, 265, 269]\n",
      "127\n"
     ]
    }
   ],
   "source": [
    "correlated_features = []\n",
    "for i in range(len(corrmat.index)):\n",
    "    for j in range(i):\n",
    "        if abs(corrmat.iloc[i, j])>0.85:\n",
    "            correlated_features.append(corrmat.columns[j])\n",
    "\n",
    "list_of_correlated_features = list(set(correlated_features))\n",
    "print(list_of_correlated_features)\n",
    "print(len(list_of_correlated_features))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(57015, 128)\n",
      "(19005, 128)\n"
     ]
    }
   ],
   "source": [
    "X_train_uncorr = X_train_unique.drop(labels=list_of_correlated_features, axis=1)\n",
    "X_test_uncorr = X_test_unique.drop(labels=list_of_correlated_features, axis=1)\n",
    "print(X_train_uncorr.shape)\n",
    "print(X_test_uncorr.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9607997895290713\n",
      "Wall time: 3.86 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "model = RandomForestClassifier(n_estimators=100, max_depth=4)\n",
    "model.fit(X_train, y_train)\n",
    "y_pred = model.predict(X_test)\n",
    "print(accuracy_score(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9607997895290713\n",
      "Wall time: 3.04 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "model = RandomForestClassifier(n_estimators=100, max_depth=4)\n",
    "model.fit(X_train_uncorr, y_train)\n",
    "y_pred = model.predict(X_test_uncorr)\n",
    "print(accuracy_score(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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