{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Custom methods in `DropCorrelatedFeatures`\n",
    "\n",
    "In this tutorial we show how to pass a custom method to `DropCorrelatedFeatures` using the association measure [Distance Correlation](https://m-clark.github.io/docs/CorrelationComparison.pdf) from the python package [dcor](https://dcor.readthedocs.io/en/latest/index.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import dcor\n",
    "import warnings\n",
    "\n",
    "from sklearn.datasets import make_classification\n",
    "from feature_engine.selection import DropCorrelatedFeatures\n",
    "\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>var_0</th>\n",
       "      <th>var_1</th>\n",
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       "      <th>var_8</th>\n",
       "      <th>var_9</th>\n",
       "      <th>var_10</th>\n",
       "      <th>var_11</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.718421</td>\n",
       "      <td>-0.306430</td>\n",
       "      <td>0.477337</td>\n",
       "      <td>1.662651</td>\n",
       "      <td>1.621889</td>\n",
       "      <td>-0.226039</td>\n",
       "      <td>2.089741</td>\n",
       "      <td>-2.145033</td>\n",
       "      <td>2.616778</td>\n",
       "      <td>0.074477</td>\n",
       "      <td>1.402662</td>\n",
       "      <td>1.599289</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.584286</td>\n",
       "      <td>-0.871870</td>\n",
       "      <td>1.490290</td>\n",
       "      <td>3.644921</td>\n",
       "      <td>3.584239</td>\n",
       "      <td>-0.750463</td>\n",
       "      <td>-0.024631</td>\n",
       "      <td>-4.525042</td>\n",
       "      <td>5.518534</td>\n",
       "      <td>1.788593</td>\n",
       "      <td>3.077793</td>\n",
       "      <td>3.188758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.644619</td>\n",
       "      <td>-0.391961</td>\n",
       "      <td>0.891121</td>\n",
       "      <td>2.232705</td>\n",
       "      <td>2.175168</td>\n",
       "      <td>-0.278656</td>\n",
       "      <td>-1.145170</td>\n",
       "      <td>-2.897788</td>\n",
       "      <td>3.535246</td>\n",
       "      <td>-0.796662</td>\n",
       "      <td>1.883299</td>\n",
       "      <td>2.178584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.795776</td>\n",
       "      <td>-2.645368</td>\n",
       "      <td>1.568321</td>\n",
       "      <td>1.449491</td>\n",
       "      <td>1.754788</td>\n",
       "      <td>-3.226923</td>\n",
       "      <td>0.626374</td>\n",
       "      <td>0.238043</td>\n",
       "      <td>-0.310298</td>\n",
       "      <td>1.247212</td>\n",
       "      <td>1.256478</td>\n",
       "      <td>-2.376344</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.683522</td>\n",
       "      <td>-1.420178</td>\n",
       "      <td>-0.120177</td>\n",
       "      <td>1.019803</td>\n",
       "      <td>1.171396</td>\n",
       "      <td>-1.708503</td>\n",
       "      <td>-0.114110</td>\n",
       "      <td>-0.223424</td>\n",
       "      <td>0.262247</td>\n",
       "      <td>0.322612</td>\n",
       "      <td>0.877768</td>\n",
       "      <td>-0.972715</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>0.379855</td>\n",
       "      <td>-0.529128</td>\n",
       "      <td>-0.093361</td>\n",
       "      <td>2.668557</td>\n",
       "      <td>2.608481</td>\n",
       "      <td>-0.410322</td>\n",
       "      <td>-1.343059</td>\n",
       "      <td>-3.409712</td>\n",
       "      <td>4.159278</td>\n",
       "      <td>-1.287548</td>\n",
       "      <td>2.251801</td>\n",
       "      <td>2.507712</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>0.410435</td>\n",
       "      <td>-1.590386</td>\n",
       "      <td>0.301589</td>\n",
       "      <td>0.962002</td>\n",
       "      <td>1.140932</td>\n",
       "      <td>-1.931062</td>\n",
       "      <td>0.010015</td>\n",
       "      <td>0.011464</td>\n",
       "      <td>-0.025811</td>\n",
       "      <td>-1.124970</td>\n",
       "      <td>0.831563</td>\n",
       "      <td>-1.315063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>0.562542</td>\n",
       "      <td>-0.173591</td>\n",
       "      <td>-0.551323</td>\n",
       "      <td>1.456996</td>\n",
       "      <td>1.407670</td>\n",
       "      <td>-0.077131</td>\n",
       "      <td>-1.215225</td>\n",
       "      <td>-1.963863</td>\n",
       "      <td>2.396559</td>\n",
       "      <td>1.678760</td>\n",
       "      <td>1.227821</td>\n",
       "      <td>1.551989</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>0.187248</td>\n",
       "      <td>-0.355866</td>\n",
       "      <td>-1.385539</td>\n",
       "      <td>1.304138</td>\n",
       "      <td>1.288720</td>\n",
       "      <td>-0.324460</td>\n",
       "      <td>0.260543</td>\n",
       "      <td>-1.580115</td>\n",
       "      <td>1.926655</td>\n",
       "      <td>-1.330030</td>\n",
       "      <td>1.101843</td>\n",
       "      <td>1.071300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>0.105134</td>\n",
       "      <td>-2.982815</td>\n",
       "      <td>0.309657</td>\n",
       "      <td>2.085668</td>\n",
       "      <td>2.406926</td>\n",
       "      <td>-3.593946</td>\n",
       "      <td>-0.339890</td>\n",
       "      <td>-0.387522</td>\n",
       "      <td>0.451001</td>\n",
       "      <td>-0.221839</td>\n",
       "      <td>1.796291</td>\n",
       "      <td>-2.113529</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 12 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        var_0     var_1     var_2     var_3     var_4     var_5     var_6  \\\n",
       "0   -0.718421 -0.306430  0.477337  1.662651  1.621889 -0.226039  2.089741   \n",
       "1    0.584286 -0.871870  1.490290  3.644921  3.584239 -0.750463 -0.024631   \n",
       "2   -1.644619 -0.391961  0.891121  2.232705  2.175168 -0.278656 -1.145170   \n",
       "3    1.795776 -2.645368  1.568321  1.449491  1.754788 -3.226923  0.626374   \n",
       "4   -0.683522 -1.420178 -0.120177  1.019803  1.171396 -1.708503 -0.114110   \n",
       "..        ...       ...       ...       ...       ...       ...       ...   \n",
       "995  0.379855 -0.529128 -0.093361  2.668557  2.608481 -0.410322 -1.343059   \n",
       "996  0.410435 -1.590386  0.301589  0.962002  1.140932 -1.931062  0.010015   \n",
       "997  0.562542 -0.173591 -0.551323  1.456996  1.407670 -0.077131 -1.215225   \n",
       "998  0.187248 -0.355866 -1.385539  1.304138  1.288720 -0.324460  0.260543   \n",
       "999  0.105134 -2.982815  0.309657  2.085668  2.406926 -3.593946 -0.339890   \n",
       "\n",
       "        var_7     var_8     var_9    var_10    var_11  \n",
       "0   -2.145033  2.616778  0.074477  1.402662  1.599289  \n",
       "1   -4.525042  5.518534  1.788593  3.077793  3.188758  \n",
       "2   -2.897788  3.535246 -0.796662  1.883299  2.178584  \n",
       "3    0.238043 -0.310298  1.247212  1.256478 -2.376344  \n",
       "4   -0.223424  0.262247  0.322612  0.877768 -0.972715  \n",
       "..        ...       ...       ...       ...       ...  \n",
       "995 -3.409712  4.159278 -1.287548  2.251801  2.507712  \n",
       "996  0.011464 -0.025811 -1.124970  0.831563 -1.315063  \n",
       "997 -1.963863  2.396559  1.678760  1.227821  1.551989  \n",
       "998 -1.580115  1.926655 -1.330030  1.101843  1.071300  \n",
       "999 -0.387522  0.451001 -0.221839  1.796291 -2.113529  \n",
       "\n",
       "[1000 rows x 12 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X, _ = make_classification(\n",
    "    n_samples=1000,\n",
    "    n_features=12,\n",
    "    n_redundant=6,\n",
    "    n_clusters_per_class=1,\n",
    "    weights=[0.50],\n",
    "    class_sep=2,\n",
    "    random_state=1,\n",
    ")\n",
    "\n",
    "colnames = [\"var_\" + str(i) for i in range(12)]\n",
    "X = pd.DataFrame(X, columns=colnames)\n",
    "\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>var_0</th>\n",
       "      <th>var_1</th>\n",
       "      <th>var_2</th>\n",
       "      <th>var_3</th>\n",
       "      <th>var_6</th>\n",
       "      <th>var_7</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.718421</td>\n",
       "      <td>-0.306430</td>\n",
       "      <td>0.477337</td>\n",
       "      <td>1.662651</td>\n",
       "      <td>2.089741</td>\n",
       "      <td>-2.145033</td>\n",
       "      <td>0.074477</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.584286</td>\n",
       "      <td>-0.871870</td>\n",
       "      <td>1.490290</td>\n",
       "      <td>3.644921</td>\n",
       "      <td>-0.024631</td>\n",
       "      <td>-4.525042</td>\n",
       "      <td>1.788593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.644619</td>\n",
       "      <td>-0.391961</td>\n",
       "      <td>0.891121</td>\n",
       "      <td>2.232705</td>\n",
       "      <td>-1.145170</td>\n",
       "      <td>-2.897788</td>\n",
       "      <td>-0.796662</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.795776</td>\n",
       "      <td>-2.645368</td>\n",
       "      <td>1.568321</td>\n",
       "      <td>1.449491</td>\n",
       "      <td>0.626374</td>\n",
       "      <td>0.238043</td>\n",
       "      <td>1.247212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.683522</td>\n",
       "      <td>-1.420178</td>\n",
       "      <td>-0.120177</td>\n",
       "      <td>1.019803</td>\n",
       "      <td>-0.114110</td>\n",
       "      <td>-0.223424</td>\n",
       "      <td>0.322612</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>0.379855</td>\n",
       "      <td>-0.529128</td>\n",
       "      <td>-0.093361</td>\n",
       "      <td>2.668557</td>\n",
       "      <td>-1.343059</td>\n",
       "      <td>-3.409712</td>\n",
       "      <td>-1.287548</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>0.410435</td>\n",
       "      <td>-1.590386</td>\n",
       "      <td>0.301589</td>\n",
       "      <td>0.962002</td>\n",
       "      <td>0.010015</td>\n",
       "      <td>0.011464</td>\n",
       "      <td>-1.124970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>0.562542</td>\n",
       "      <td>-0.173591</td>\n",
       "      <td>-0.551323</td>\n",
       "      <td>1.456996</td>\n",
       "      <td>-1.215225</td>\n",
       "      <td>-1.963863</td>\n",
       "      <td>1.678760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>0.187248</td>\n",
       "      <td>-0.355866</td>\n",
       "      <td>-1.385539</td>\n",
       "      <td>1.304138</td>\n",
       "      <td>0.260543</td>\n",
       "      <td>-1.580115</td>\n",
       "      <td>-1.330030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>0.105134</td>\n",
       "      <td>-2.982815</td>\n",
       "      <td>0.309657</td>\n",
       "      <td>2.085668</td>\n",
       "      <td>-0.339890</td>\n",
       "      <td>-0.387522</td>\n",
       "      <td>-0.221839</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        var_0     var_1     var_2     var_3     var_6     var_7     var_9\n",
       "0   -0.718421 -0.306430  0.477337  1.662651  2.089741 -2.145033  0.074477\n",
       "1    0.584286 -0.871870  1.490290  3.644921 -0.024631 -4.525042  1.788593\n",
       "2   -1.644619 -0.391961  0.891121  2.232705 -1.145170 -2.897788 -0.796662\n",
       "3    1.795776 -2.645368  1.568321  1.449491  0.626374  0.238043  1.247212\n",
       "4   -0.683522 -1.420178 -0.120177  1.019803 -0.114110 -0.223424  0.322612\n",
       "..        ...       ...       ...       ...       ...       ...       ...\n",
       "995  0.379855 -0.529128 -0.093361  2.668557 -1.343059 -3.409712 -1.287548\n",
       "996  0.410435 -1.590386  0.301589  0.962002  0.010015  0.011464 -1.124970\n",
       "997  0.562542 -0.173591 -0.551323  1.456996 -1.215225 -1.963863  1.678760\n",
       "998  0.187248 -0.355866 -1.385539  1.304138  0.260543 -1.580115 -1.330030\n",
       "999  0.105134 -2.982815  0.309657  2.085668 -0.339890 -0.387522 -0.221839\n",
       "\n",
       "[1000 rows x 7 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dcor_tr = DropCorrelatedFeatures(\n",
    "    variables=None, method=dcor.distance_correlation, threshold=0.8\n",
    ")\n",
    "\n",
    "X_dcor = dcor_tr.fit_transform(X)\n",
    "\n",
    "X_dcor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the next example, we use the function [sklearn.feature_selection.mutual_info_regression](https://scikit-learn.org/stable/modules/generated/sklearn.feature_selection.mutual_info_regression.html#sklearn.feature_selection.mutual_info_regression) to calculate the Mutual Information between two numerical variables, dropping any features with a score below 0.8.\n",
    "\n",
    "Remember that the callable should take as input two 1d ndarrays and output a float value, we define a custom function calling the sklearn method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.feature_selection import mutual_info_regression\n",
    "\n",
    "def custom_mi(x, y):\n",
    "    x = x.reshape(-1, 1)\n",
    "    y = y.reshape(-1, 1)\n",
    "    return mutual_info_regression(x, y)[0] # should return a float value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>var_0</th>\n",
       "      <th>var_1</th>\n",
       "      <th>var_2</th>\n",
       "      <th>var_3</th>\n",
       "      <th>var_6</th>\n",
       "      <th>var_7</th>\n",
       "      <th>var_9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.718421</td>\n",
       "      <td>-0.306430</td>\n",
       "      <td>0.477337</td>\n",
       "      <td>1.662651</td>\n",
       "      <td>2.089741</td>\n",
       "      <td>-2.145033</td>\n",
       "      <td>0.074477</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.584286</td>\n",
       "      <td>-0.871870</td>\n",
       "      <td>1.490290</td>\n",
       "      <td>3.644921</td>\n",
       "      <td>-0.024631</td>\n",
       "      <td>-4.525042</td>\n",
       "      <td>1.788593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.644619</td>\n",
       "      <td>-0.391961</td>\n",
       "      <td>0.891121</td>\n",
       "      <td>2.232705</td>\n",
       "      <td>-1.145170</td>\n",
       "      <td>-2.897788</td>\n",
       "      <td>-0.796662</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.795776</td>\n",
       "      <td>-2.645368</td>\n",
       "      <td>1.568321</td>\n",
       "      <td>1.449491</td>\n",
       "      <td>0.626374</td>\n",
       "      <td>0.238043</td>\n",
       "      <td>1.247212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.683522</td>\n",
       "      <td>-1.420178</td>\n",
       "      <td>-0.120177</td>\n",
       "      <td>1.019803</td>\n",
       "      <td>-0.114110</td>\n",
       "      <td>-0.223424</td>\n",
       "      <td>0.322612</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>0.379855</td>\n",
       "      <td>-0.529128</td>\n",
       "      <td>-0.093361</td>\n",
       "      <td>2.668557</td>\n",
       "      <td>-1.343059</td>\n",
       "      <td>-3.409712</td>\n",
       "      <td>-1.287548</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>0.410435</td>\n",
       "      <td>-1.590386</td>\n",
       "      <td>0.301589</td>\n",
       "      <td>0.962002</td>\n",
       "      <td>0.010015</td>\n",
       "      <td>0.011464</td>\n",
       "      <td>-1.124970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>0.562542</td>\n",
       "      <td>-0.173591</td>\n",
       "      <td>-0.551323</td>\n",
       "      <td>1.456996</td>\n",
       "      <td>-1.215225</td>\n",
       "      <td>-1.963863</td>\n",
       "      <td>1.678760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>0.187248</td>\n",
       "      <td>-0.355866</td>\n",
       "      <td>-1.385539</td>\n",
       "      <td>1.304138</td>\n",
       "      <td>0.260543</td>\n",
       "      <td>-1.580115</td>\n",
       "      <td>-1.330030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>0.105134</td>\n",
       "      <td>-2.982815</td>\n",
       "      <td>0.309657</td>\n",
       "      <td>2.085668</td>\n",
       "      <td>-0.339890</td>\n",
       "      <td>-0.387522</td>\n",
       "      <td>-0.221839</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        var_0     var_1     var_2     var_3     var_6     var_7     var_9\n",
       "0   -0.718421 -0.306430  0.477337  1.662651  2.089741 -2.145033  0.074477\n",
       "1    0.584286 -0.871870  1.490290  3.644921 -0.024631 -4.525042  1.788593\n",
       "2   -1.644619 -0.391961  0.891121  2.232705 -1.145170 -2.897788 -0.796662\n",
       "3    1.795776 -2.645368  1.568321  1.449491  0.626374  0.238043  1.247212\n",
       "4   -0.683522 -1.420178 -0.120177  1.019803 -0.114110 -0.223424  0.322612\n",
       "..        ...       ...       ...       ...       ...       ...       ...\n",
       "995  0.379855 -0.529128 -0.093361  2.668557 -1.343059 -3.409712 -1.287548\n",
       "996  0.410435 -1.590386  0.301589  0.962002  0.010015  0.011464 -1.124970\n",
       "997  0.562542 -0.173591 -0.551323  1.456996 -1.215225 -1.963863  1.678760\n",
       "998  0.187248 -0.355866 -1.385539  1.304138  0.260543 -1.580115 -1.330030\n",
       "999  0.105134 -2.982815  0.309657  2.085668 -0.339890 -0.387522 -0.221839\n",
       "\n",
       "[1000 rows x 7 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mi_tr = DropCorrelatedFeatures(\n",
    "    variables=None, method=custom_mi, threshold=0.8\n",
    ")\n",
    "\n",
    "X_mi = mi_tr.fit_transform(X)\n",
    "X_mi"
   ]
  }
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