MLXtend_featureExtractor.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "! pip install mlxtend"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SequentialFeatureSelector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Why SequentialFeatureSelector is better than ScikitLearn Recursive Feature Elimination (RFE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "sklearn.feature_selection.RFE? RFE is computationally less complex using the feature weight coefficients (e.g., linear models) or feature importance (tree-based algorithms) to eliminate features recursively, \n",
    "whereas SFSs eliminate (or add) features based on a user-defined classifier/regression performance metric."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "import mlxtend\n",
    "from mlxtend.feature_selection import SequentialFeatureSelector as SFS\n",
    "from mlxtend.feature_selection import SequentialFeatureSelector\n",
    "from mlxtend.plotting import plot_sequential_feature_selection as plot_sfs\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sequential Backward Selection (SBS): \n",
    "#### 1- start with all the features in the dataset, and then we evaluate the performance of the algorithm\n",
    "####  2- Least significant feature is removed one byone\n",
    "#### 3- until a certain criterion is satisfied.\n",
    "\n",
    "### Sequential Forward Selection (SBS) \n",
    "\n",
    "#### 1- nitialize the algorithm with an empty set\n",
    "#### 2- Features are added by one by one (best one comes first)\n",
    "#### 3- 3- until a certain criterion is satisfied."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "SequentialFeatureSelector(estimator, k_features=1, forward=True, \n",
    "                          floating=False, verbose=0, scoring=None, cv=5, n_jobs=1, pre_dispatch='2n_jobs', \n",
    "                          clone_estimator=True, fixed_features=None)*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn.datasets import load_iris\n",
    "\n",
    "iris = load_iris()\n",
    "X = iris.data\n",
    "y = iris.target\n",
    "knn = KNeighborsClassifier(n_neighbors=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "array([[5.1, 3.5, 1.4, 0.2],\n",
       "       [4.9, 3. , 1.4, 0.2],\n",
       "       [4.7, 3.2, 1.3, 0.2],\n",
       "       [4.6, 3.1, 1.5, 0.2],\n",
       "       [5. , 3.6, 1.4, 0.2],\n",
       "       [5.4, 3.9, 1.7, 0.4],\n",
       "       [4.6, 3.4, 1.4, 0.3],\n",
       "       [5. , 3.4, 1.5, 0.2],\n",
       "       [4.4, 2.9, 1.4, 0.2],\n",
       "       [4.9, 3.1, 1.5, 0.1],\n",
       "       [5.4, 3.7, 1.5, 0.2],\n",
       "       [4.8, 3.4, 1.6, 0.2],\n",
       "       [4.8, 3. , 1.4, 0.1],\n",
       "       [4.3, 3. , 1.1, 0.1],\n",
       "       [5.8, 4. , 1.2, 0.2],\n",
       "       [5.7, 4.4, 1.5, 0.4],\n",
       "       [5.4, 3.9, 1.3, 0.4],\n",
       "       [5.1, 3.5, 1.4, 0.3],\n",
       "       [5.7, 3.8, 1.7, 0.3],\n",
       "       [5.1, 3.8, 1.5, 0.3],\n",
       "       [5.4, 3.4, 1.7, 0.2],\n",
       "       [5.1, 3.7, 1.5, 0.4],\n",
       "       [4.6, 3.6, 1. , 0.2],\n",
       "       [5.1, 3.3, 1.7, 0.5],\n",
       "       [4.8, 3.4, 1.9, 0.2],\n",
       "       [5. , 3. , 1.6, 0.2],\n",
       "       [5. , 3.4, 1.6, 0.4],\n",
       "       [5.2, 3.5, 1.5, 0.2],\n",
       "       [5.2, 3.4, 1.4, 0.2],\n",
       "       [4.7, 3.2, 1.6, 0.2],\n",
       "       [4.8, 3.1, 1.6, 0.2],\n",
       "       [5.4, 3.4, 1.5, 0.4],\n",
       "       [5.2, 4.1, 1.5, 0.1],\n",
       "       [5.5, 4.2, 1.4, 0.2],\n",
       "       [4.9, 3.1, 1.5, 0.2],\n",
       "       [5. , 3.2, 1.2, 0.2],\n",
       "       [5.5, 3.5, 1.3, 0.2],\n",
       "       [4.9, 3.6, 1.4, 0.1],\n",
       "       [4.4, 3. , 1.3, 0.2],\n",
       "       [5.1, 3.4, 1.5, 0.2],\n",
       "       [5. , 3.5, 1.3, 0.3],\n",
       "       [4.5, 2.3, 1.3, 0.3],\n",
       "       [4.4, 3.2, 1.3, 0.2],\n",
       "       [5. , 3.5, 1.6, 0.6],\n",
       "       [5.1, 3.8, 1.9, 0.4],\n",
       "       [4.8, 3. , 1.4, 0.3],\n",
       "       [5.1, 3.8, 1.6, 0.2],\n",
       "       [4.6, 3.2, 1.4, 0.2],\n",
       "       [5.3, 3.7, 1.5, 0.2],\n",
       "       [5. , 3.3, 1.4, 0.2],\n",
       "       [7. , 3.2, 4.7, 1.4],\n",
       "       [6.4, 3.2, 4.5, 1.5],\n",
       "       [6.9, 3.1, 4.9, 1.5],\n",
       "       [5.5, 2.3, 4. , 1.3],\n",
       "       [6.5, 2.8, 4.6, 1.5],\n",
       "       [5.7, 2.8, 4.5, 1.3],\n",
       "       [6.3, 3.3, 4.7, 1.6],\n",
       "       [4.9, 2.4, 3.3, 1. ],\n",
       "       [6.6, 2.9, 4.6, 1.3],\n",
       "       [5.2, 2.7, 3.9, 1.4],\n",
       "       [5. , 2. , 3.5, 1. ],\n",
       "       [5.9, 3. , 4.2, 1.5],\n",
       "       [6. , 2.2, 4. , 1. ],\n",
       "       [6.1, 2.9, 4.7, 1.4],\n",
       "       [5.6, 2.9, 3.6, 1.3],\n",
       "       [6.7, 3.1, 4.4, 1.4],\n",
       "       [5.6, 3. , 4.5, 1.5],\n",
       "       [5.8, 2.7, 4.1, 1. ],\n",
       "       [6.2, 2.2, 4.5, 1.5],\n",
       "       [5.6, 2.5, 3.9, 1.1],\n",
       "       [5.9, 3.2, 4.8, 1.8],\n",
       "       [6.1, 2.8, 4. , 1.3],\n",
       "       [6.3, 2.5, 4.9, 1.5],\n",
       "       [6.1, 2.8, 4.7, 1.2],\n",
       "       [6.4, 2.9, 4.3, 1.3],\n",
       "       [6.6, 3. , 4.4, 1.4],\n",
       "       [6.8, 2.8, 4.8, 1.4],\n",
       "       [6.7, 3. , 5. , 1.7],\n",
       "       [6. , 2.9, 4.5, 1.5],\n",
       "       [5.7, 2.6, 3.5, 1. ],\n",
       "       [5.5, 2.4, 3.8, 1.1],\n",
       "       [5.5, 2.4, 3.7, 1. ],\n",
       "       [5.8, 2.7, 3.9, 1.2],\n",
       "       [6. , 2.7, 5.1, 1.6],\n",
       "       [5.4, 3. , 4.5, 1.5],\n",
       "       [6. , 3.4, 4.5, 1.6],\n",
       "       [6.7, 3.1, 4.7, 1.5],\n",
       "       [6.3, 2.3, 4.4, 1.3],\n",
       "       [5.6, 3. , 4.1, 1.3],\n",
       "       [5.5, 2.5, 4. , 1.3],\n",
       "       [5.5, 2.6, 4.4, 1.2],\n",
       "       [6.1, 3. , 4.6, 1.4],\n",
       "       [5.8, 2.6, 4. , 1.2],\n",
       "       [5. , 2.3, 3.3, 1. ],\n",
       "       [5.6, 2.7, 4.2, 1.3],\n",
       "       [5.7, 3. , 4.2, 1.2],\n",
       "       [5.7, 2.9, 4.2, 1.3],\n",
       "       [6.2, 2.9, 4.3, 1.3],\n",
       "       [5.1, 2.5, 3. , 1.1],\n",
       "       [5.7, 2.8, 4.1, 1.3],\n",
       "       [6.3, 3.3, 6. , 2.5],\n",
       "       [5.8, 2.7, 5.1, 1.9],\n",
       "       [7.1, 3. , 5.9, 2.1],\n",
       "       [6.3, 2.9, 5.6, 1.8],\n",
       "       [6.5, 3. , 5.8, 2.2],\n",
       "       [7.6, 3. , 6.6, 2.1],\n",
       "       [4.9, 2.5, 4.5, 1.7],\n",
       "       [7.3, 2.9, 6.3, 1.8],\n",
       "       [6.7, 2.5, 5.8, 1.8],\n",
       "       [7.2, 3.6, 6.1, 2.5],\n",
       "       [6.5, 3.2, 5.1, 2. ],\n",
       "       [6.4, 2.7, 5.3, 1.9],\n",
       "       [6.8, 3. , 5.5, 2.1],\n",
       "       [5.7, 2.5, 5. , 2. ],\n",
       "       [5.8, 2.8, 5.1, 2.4],\n",
       "       [6.4, 3.2, 5.3, 2.3],\n",
       "       [6.5, 3. , 5.5, 1.8],\n",
       "       [7.7, 3.8, 6.7, 2.2],\n",
       "       [7.7, 2.6, 6.9, 2.3],\n",
       "       [6. , 2.2, 5. , 1.5],\n",
       "       [6.9, 3.2, 5.7, 2.3],\n",
       "       [5.6, 2.8, 4.9, 2. ],\n",
       "       [7.7, 2.8, 6.7, 2. ],\n",
       "       [6.3, 2.7, 4.9, 1.8],\n",
       "       [6.7, 3.3, 5.7, 2.1],\n",
       "       [7.2, 3.2, 6. , 1.8],\n",
       "       [6.2, 2.8, 4.8, 1.8],\n",
       "       [6.1, 3. , 4.9, 1.8],\n",
       "       [6.4, 2.8, 5.6, 2.1],\n",
       "       [7.2, 3. , 5.8, 1.6],\n",
       "       [7.4, 2.8, 6.1, 1.9],\n",
       "       [7.9, 3.8, 6.4, 2. ],\n",
       "       [6.4, 2.8, 5.6, 2.2],\n",
       "       [6.3, 2.8, 5.1, 1.5],\n",
       "       [6.1, 2.6, 5.6, 1.4],\n",
       "       [7.7, 3. , 6.1, 2.3],\n",
       "       [6.3, 3.4, 5.6, 2.4],\n",
       "       [6.4, 3.1, 5.5, 1.8],\n",
       "       [6. , 3. , 4.8, 1.8],\n",
       "       [6.9, 3.1, 5.4, 2.1],\n",
       "       [6.7, 3.1, 5.6, 2.4],\n",
       "       [6.9, 3.1, 5.1, 2.3],\n",
       "       [5.8, 2.7, 5.1, 1.9],\n",
       "       [6.8, 3.2, 5.9, 2.3],\n",
       "       [6.7, 3.3, 5.7, 2.5],\n",
       "       [6.7, 3. , 5.2, 2.3],\n",
       "       [6.3, 2.5, 5. , 1.9],\n",
       "       [6.5, 3. , 5.2, 2. ],\n",
       "       [6.2, 3.4, 5.4, 2.3],\n",
       "       [5.9, 3. , 5.1, 1.8]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n",
      "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    0.0s remaining:    0.0s\n",
      "[Parallel(n_jobs=1)]: Done   4 out of   4 | elapsed:    0.0s finished\n",
      "\n",
      "[2020-03-08 04:32:55] Features: 1/3 -- score: 0.96[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n",
      "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    0.0s remaining:    0.0s\n",
      "[Parallel(n_jobs=1)]: Done   3 out of   3 | elapsed:    0.0s finished\n",
      "\n",
      "[2020-03-08 04:32:55] Features: 2/3 -- score: 0.9666666666666668[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n",
      "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    0.0s remaining:    0.0s\n",
      "[Parallel(n_jobs=1)]: Done   2 out of   2 | elapsed:    0.0s finished\n",
      "\n",
      "[2020-03-08 04:32:55] Features: 3/3 -- score: 0.9533333333333334"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{1: {'feature_idx': (3,),\n",
       "  'cv_scores': array([0.96666667, 0.96666667, 0.93333333, 0.93333333, 1.        ]),\n",
       "  'avg_score': 0.96,\n",
       "  'feature_names': ('petal width',)},\n",
       " 2: {'feature_idx': (2, 3),\n",
       "  'cv_scores': array([0.96666667, 0.96666667, 0.93333333, 0.96666667, 1.        ]),\n",
       "  'avg_score': 0.9666666666666668,\n",
       "  'feature_names': ('petal length', 'petal width')},\n",
       " 3: {'feature_idx': (0, 2, 3),\n",
       "  'cv_scores': array([0.96666667, 0.96666667, 0.93333333, 0.93333333, 0.96666667]),\n",
       "  'avg_score': 0.9533333333333334,\n",
       "  'feature_names': ('sepal length', 'petal length', 'petal width')}}"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sfs1 = SFS(knn, \n",
    "           k_features=3, \n",
    "           forward=True, ### false will be Backward\n",
    "           floating=False, \n",
    "           verbose=2,\n",
    "           scoring='accuracy',\n",
    "           cv=5)\n",
    "\n",
    "feature_names = ('sepal length', 'sepal width', 'petal length', 'petal width')### not necesary\n",
    "sfs1 = sfs1.fit(X, y, custom_feature_names=feature_names)\n",
    "sfs1.subsets_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>feature_idx</th>\n",
       "      <th>cv_scores</th>\n",
       "      <th>avg_score</th>\n",
       "      <th>feature_names</th>\n",
       "      <th>ci_bound</th>\n",
       "      <th>std_dev</th>\n",
       "      <th>std_err</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(3,)</td>\n",
       "      <td>[0.9666666666666667, 0.9666666666666667, 0.933...</td>\n",
       "      <td>0.96</td>\n",
       "      <td>(petal width,)</td>\n",
       "      <td>0.0320608</td>\n",
       "      <td>0.0249444</td>\n",
       "      <td>0.0124722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(2, 3)</td>\n",
       "      <td>[0.9666666666666667, 0.9666666666666667, 0.933...</td>\n",
       "      <td>0.966667</td>\n",
       "      <td>(petal length, petal width)</td>\n",
       "      <td>0.0270963</td>\n",
       "      <td>0.0210819</td>\n",
       "      <td>0.0105409</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(0, 2, 3)</td>\n",
       "      <td>[0.9666666666666667, 0.9666666666666667, 0.933...</td>\n",
       "      <td>0.953333</td>\n",
       "      <td>(sepal length, petal length, petal width)</td>\n",
       "      <td>0.0209887</td>\n",
       "      <td>0.0163299</td>\n",
       "      <td>0.00816497</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  feature_idx                                          cv_scores avg_score  \\\n",
       "1        (3,)  [0.9666666666666667, 0.9666666666666667, 0.933...      0.96   \n",
       "2      (2, 3)  [0.9666666666666667, 0.9666666666666667, 0.933...  0.966667   \n",
       "3   (0, 2, 3)  [0.9666666666666667, 0.9666666666666667, 0.933...  0.953333   \n",
       "\n",
       "                               feature_names   ci_bound    std_dev     std_err  \n",
       "1                             (petal width,)  0.0320608  0.0249444   0.0124722  \n",
       "2                (petal length, petal width)  0.0270963  0.0210819   0.0105409  \n",
       "3  (sepal length, petal length, petal width)  0.0209887  0.0163299  0.00816497  "
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "pd.DataFrame.from_dict(sfs1.get_metric_dict()).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n",
      "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    0.0s remaining:    0.0s\n",
      "[Parallel(n_jobs=1)]: Done   4 out of   4 | elapsed:    0.0s finished\n",
      "\n",
      "[2020-03-08 04:36:08] Features: 1/4 -- score: 0.96[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n",
      "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    0.0s remaining:    0.0s\n",
      "[Parallel(n_jobs=1)]: Done   3 out of   3 | elapsed:    0.0s finished\n",
      "\n",
      "[2020-03-08 04:36:08] Features: 2/4 -- score: 0.9666666666666668[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n",
      "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    0.0s remaining:    0.0s\n",
      "[Parallel(n_jobs=1)]: Done   2 out of   2 | elapsed:    0.0s finished\n",
      "\n",
      "[2020-03-08 04:36:08] Features: 3/4 -- score: 0.9533333333333334[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.\n",
      "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    0.0s remaining:    0.0s\n",
      "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    0.0s finished\n",
      "\n",
      "[2020-03-08 04:36:08] Features: 4/4 -- score: 0.9733333333333334"
     ]
    },
    {
     "data": {
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xqyPHKzs7u6/KUikxvinLxOYsLY2h3aTRg4mrsWIpojMXAsTO9i7aOnLdNRLJUkRzw8iftkc+B86NkHRKNDdkaE5U/xYKRleuwHNbd5GPf7QpKTTAN2UZ1xSDSTbtFxOuasV2ufauUIrY2dHFjt3JUgSkUyFAjG8a3lJENTxwOJeQSonGVAgMRQULweRPr7ST27Kru3qxpTHD+OYME5oauoOJdw92RclSxM5YzdTWkcMKoY1TqVCKyNZJKaIaoyu3zo2AlNQdGIq6e3Tt6OBP23YT+yXQmE0zocl7dI0lxd9CR1eB3Z05dnZ00ba7i/ZypYjGLKl94OLCA4dzg9Bnj65cgW07O3r06GrMppkQG+GbGjI0ZLxH12iVLxgdXXk6c/nY1bWzRykChR582UyKyaOsFFGNffeTOTcCsplQ9ZCUyxfYvquLl7a3I6AANBR7dDVnaW7I0JQNvWO8Eb4+JEsR7Z052hKliKJ9rRRRjVo/c3wh8DUgDXzHzK4uWT+H8HjYA4AtwAfNbJOkvwD+NbHp64GzzOx2SdcBbwdeiesWm9mqWn4O5/ZGsUdXS6J7cL5Q6NGjS4T2lQlNDYxvztLSmPEeXcMkXzA6c3k6umIpIrZHWMF63Ae0r5ciqlGzb0FSGrgGeCewCVghabmZPZbY7EvA9Wb2fUknAFcB55jZvcARMZ0pwHrg7sR+nzGzW2uVd+dqLZ1K0dyQ6tWjq70rx/bdnd3dMEP34AwTmhtoaQwlkwbv0TUoyVJER1cMEIlShFkI8mO1FFGNWobPo4H1ZrYBQNLNwOlAMnDMAz4V5+8Fbi+TzvuAn5vZrhrm1bkRl0qJpoYMTclgEnt0Pb9tN/lCIWwn0dyYYUJzlvGNWe/RVUa5UsTO9i7yeSuOp7NPlyKW/zjLV65q4rlnT2TGTLj6Kjj77KFLv5bf2AxgY+L1JuCYkm1WA2cSqrPeA0yQtL+ZvZzY5izgKyX7XSnpMuCXwEVm1jGkOXeuTvTXo+ul7e08n9/V3XOnuSHDxOZwr0lTQ5rGzNjo0RUCRChFtLWHButij6ZCohQxboyUIpb/OMuln2mmfXf4rJs2wpIlYd1QBY+RDrWfBr4haTFwP7AZ6G59knQg8EbgrsQ+FwPPAw3AUuCzwBWlCUtaAiwBmDZtGq2trYPKYK59N0+te2hQ+7ra6GjfxYa1K0c6G3UnOY5akSTSqTA+WUp7hsiphba2tkH/nVWqOEbcnoE8rcc4QMnx2caqf77if3QHjaJdu+DCC9uZMePBIXmPWgaOzcCsxOuZcVk3M3uWUOJA0njgvWa2LbHJXwE/MbOuxD7PxdkOSd8jBJ9ezGwpIbAwf/58W7BgwaA+xJ13/ycHHXqU1ynXkQ1rV3LwYfNHOhujQi5foDMXbkIrlkyymRQTm7KMS/ToGoruwa2trQz276xUr1JEeyftncn7IkJ36Gw6NSZKEf0pFOCpDSlWP5Jm9cNpXnih/Ei4L7zQNGTHp5aBYwVwiKS5hIBxFvCB5AaSpgJbzKxAKEksK0ljUVye3OdAM3tOoavJGcDaGuXfuVGvrx5dbR1xwMfYCJ9Ohx5dE1qytMQbF4djwMdkW8Tuzhzbd8e2iMSo0cUAMakl7T3MgC0vi9UPp7sDxaOrM2x/JXwv48YZDY3QWabyfvbsoctDzQKHmeUknU+oZkoDy8xsnaQrgJVmthxYAFwlyQhVVR8r7i/pIEKJ5b6SpG+UdAChNLoKOK9Wn8G5fVG5Hl35Yo+ul4ujBwulCD26moamR1dnLk9nLt4X0Z6jrb2L3Z257ucFpOMQHGOlLaISHe3w2No9QWL1Ixk2PRParVIp43WvL7Dw1C4OPzLH4W/O85pDCtzx055tHAAtLXDllUOXr5q2cZjZncCdJcsuS8zfCpTtVmtmTxEa2EuXnzC0uXTOpVMi3WePrp4DPrYUe3TFAR9LH+FbWorYsTvcF5Ev7Hko2J5SRIOXIqLSKqc1j6T53WNpcrnw/bz6wAKHvznPBz7UweFvznPom/K0tPRO57QzQ81+6FWl2KtKo6ZXlXNuFOuvR9eL29t5bmvPHl2duTxrn9lCe2c+lFoSpYiWxqx3Fy5RrHJa80goUaxZ1bPK6Y1H5Pnb8zo4/Mg8bzoyz7RXV/5AptPO7OK0M7v4w5oV/I+3/jmTxzUOad49cLhRY0/f9BM4cLrxqYvbu6+u3PAoN0aXmZHLh2fJpyQmtmS9FFFiMFVO6ToezswDhxsVSvumP7tZXPqZZgAPHiNMEtlM6O5bOk7XWDRUVU71zAOHG3a5HGx/RWzdIl7ZFqZt28S2rXF+6575sC7F5o3CrOdVbPtuccmFzTy8Is3sgwocNLfAnLkFZs0u0DC0JXPn+rTlZYWqpoeHvsqpXnngcIM2mACwbato29F3NUYqZUycZEzez5g02Zgy1Tj4kBybnsmW3b6jA352e0P3H2oxjekzjNkH5Tno4IIHFTdkBqpyOmSUVTkNlgcONywBYP8DQgCYPDm8nryfhfn9EvOTC0yYCKkytR0rH8zw7Obe7zd9htG6Ygdbt4hnnkrx1B9TPLUh1T3vQcUNVrLKqdiA/cRjabq69p0qp8HywLEPGQ0BYLA+dXF7r77pTc2hgRxgvynGflPyHP7mfK99Pai4SlRS5fQ3f7dvVTkNlgeOOrQvB4DBKu2bXk2vqloElTlzC8w5yIPKaFVa5bRmVZqNT4c6pbFU5TRYHjj6cOONcMkl8MwzJ3Lg9AKfurij6t47wx0AisvqOQDsjWLf9KEcq2qgoPL0H1M8/ZQHldGsUICn/5hKtEuUr3JadE7nmKtyGiwPHGXceGMYhnjXLgDx7OY0l366mT89L456S94DwBhRDCpHHOVBZTSptMrpTUfmOXyMVzkNlgeOMi65pBg09mhvF//yheZe2yYDwOT9+g4Ak6ckgoEHgFHPg0p9SFY5FRuwvcqp9jxwlPHMM32tMb77w10eAFy/hjKozJmbDwHFgwpmPW+s8yqn3vIFo6MrT2cuhxGeTVKLmzI9cJQxezY8/XTv5dNnGH++IDf8GXL7jL6Cihls2+pBJam0yunR1Wle2RZOgl7lFOQLBdo783TlC2AhSEwa18Ck5nG0NGZ4cFOGcY3l74HaGx44yrjyymQbR5Ds+uncUJPGdlDpaIfH16V7lCZKq5ze9Ze5MV/llMsXYomi0F2amDyukUktDTQ3ZmgchmeogAeOsorDD4deVTboXlXODYV9Lah4lVPlumKgyOULCMhkUkwZ38jElgaa4wO3RoIHjj6cfXaY7rz7l7zmsPn+6FhXl+ohqAw0anGyymnNqjCVVjktXhLuvh6rVU5FyUCBQWNDmv1joGhpzAzJI36HggcO5/ZR1QaV4nw1QWX1w2ku/6eeoxb/04XN/Ne9GfJ5vMppAF25Au1deQqFAgWgOZtm/wmNTGpppLlhaJ4FXwseOJwbg4YqqHQ/9zWhs0P89LYGr3IqIzwZsUC+UACgKZvmVZOamNDcUNeBopQHDudcD9UElc9c0PveppCGcf9DO4Yju3Wt+AjdfD48EbG5IcO0YqBozJBNj86+/DUNHJIWAl8D0sB3zOzqkvVzgGXAAcAW4INmtimuywOPxk2fMbPT4vK5wM3A/sBDwDlm1lnLz+GcC0qDyr9e3VR21OIDp4+9doriY3XbO/MULHz+cY1ZXj25hfHNWZobRm+gKFWzTyEpDVwDnAzMAxZJmley2ZeA683sTcAVwFWJdbvN7Ig4nZZY/kXgX83stcBW4MO1+gzOuf596uJ2mpp7Bomx0nXdLNxst31XJ9t2dvDKrk4kMX1KC6+fsR9Hzp3KvFn7MX3KOCY2N+wzQQNqW+I4GlhvZhsAJN0MnA48lthmHvCpOH8vcHt/CSp0UD4B+EBc9H3gcuBbQ5Zr51zF9mbU4tHGzOjMhV5PhYKhVChRzNh/HOMas7Q0pkmPkWEkahk4ZgAbE683AceUbLMaOJNQnfUeYIKk/c3sZaBJ0kogB1xtZrcTqqe2mVkukeaMcm8uaQmwBGDatGm0trYO6kPk2nfz1LqHBrWvq42O9l1sWLtypLPhosNeB8u+F45LY1No/d6wdoQzNUTM6K52AkinRDolUimRkmgD/jRy2RtQW1vboM99/RnpxvFPA9+QtBi4H9gMFFvj5pjZZkkHA7+S9CjwSqUJm9lSYCnA/PnzbcGCBYPK4J13/ycHHXqU38dRR4ZyWHU3dEb7cSmY0dmVp70rnIKEmNCSZXJLA+ObsjQ1ZEinRtd5oLW1lcGe+/pTy8CxGZiVeD0zLutmZs8SShxIGg+818y2xXWb4/8bJLUCRwK3AZMlZWKpo1eazjlXiUJso+joyoNBKiUmNGeZNrmFcY2ZURkohkstA8cK4JDYC2ozcBZ72iYAkDQV2GJmBeBiQg8rJO0H7DKzjrjN8cA/m5lJuhd4H6Fn1bnAT2v4GZxz+4hCwejI5ensymNASmJicwMH7tdCS2OG5oaM1yxUqGaBw8xyks4H7iJ0x11mZuskXQGsNLPlwALgKklGqKr6WNz9DcC/SSoQen5dbWbFRvXPAjdL+gLwCPDdWn0GVz/yhQL5gpHLG3kzduzuJCXFOucUqVj37FxRMVAkSxSTxjUwfb8WWhqzNDWkPVAMUk3bOMzsTuDOkmWXJeZvBW4ts99vgDf2keYGQo8tt4/IF6xnYCiEAd3Mwn0DRhgFtDmbpqUxywvpFNOnjKOzK9yFG/rO58LQ0pEI+wHdwSUdGzSLjZtu39L9LIrYRpFKi8ktIVCMa8rSmPVAMVRGunHc7eMKBSMXg0IIDIVe22TTKRqzaVqaMzRm0jRm02TTKTLpFJm0yKRTPf7gn06nePXk3mNXFCy8Rz5fIJd4v85cGIa6s6tARy5Pe0eOQgEM6xFggO4AUwwuxWDj6s+ehxaFqqdsKsWkliyT9g/PomjKpodliPGxyAOHG7SCGfl8z8BgseuiEAUzMmnRlM0wvjFNU0OGhkyKbCZNJq3u4DBUJ+aURCqmW0nec/lCDGxhPgSZMHXk8mEAus4c+YLF0ZiExTAjKVFV5kFmOAz00KJGDxTDxgOHK6vc1btZzyv0VEo0ZtLdV3dN2XQICinF0kKqbtsdUlLFA8qVq0orBpnQ2BpKNbs78hRsz5B/xe9JyQCTmPeTXP+SDy1KSWTSGpGHFrnePHCMQWbhKrsQr7TzBaNgBZKjnKYEjdkMTdkMjQ0pmrKhtFAMCNm0xsxdsuFEX12QCQEmzHflCnQWq8y68nTkCuzsyIc2nEQpBmKpKbUnuBSDzVg4QebyYYjxYnVmNpNiv/ExUIzgQ4tcbx449jFWLCkk6vgLZpBoaJbobkuY2JylsSFNYyYdgkKitOCqVwwyDRX8ZSVLMblCgXw+DJJXDDCd3VVnIcgUFUt9oz3IlD60qCG756FFHijqmweOUab0ajZf6DnAnAQNMShMyIb/i0EhmxbpGBxGy8llXxYa4hkwyJhZbJNJtCfljc586GraFdtlilfrZr3TSPYmS/YyG05dsWovlytgCs+i2H9CIxOb6+vpdm5gHjjqSM9qjkKiUTZ0TUV7uqWGIRBSNHQHhVR3icGDwr5FEmmJdAoa6f/kWixx5ooXFjHYFE/axd5l7V25nkEm8Tymnm0xg79HptxDiw6YOPoeWuR688AxTJLdUouBoahY9VDsljqxJTQ2N2bTZFJ9d0t1rpRiI3I4Jw8cZIodH/Z0gojVY7EtpjOX39OTqfgelL9Hxgx27O4MDy0CmhszvGpSExObG2jyQLFP8cAxBArF9oTuwJD8IwuNn5lUCArJbqkNmTTpGnRLda4SksimRTYNDNCeUMk9Moh98qFFrjcPHBVI9vfPx95Igh5F+8ZsmW6paXWXGOq1W6pzlajkHpnNv08zfcq4YcyVGykeOAaQViiCNzVkaMymaM5myGZCm0J6jHVLdc458MAxoMZsmsNmTxnpbDjnXN3wS2XnnHNV8cDhnHOuKh44nHPOVcUDh3POuap44HDOOVcVDxzOOeeqUtPAIWmhpCckrZd0UZn1cyT9UtIaSa2SZsblR0h6QNK6uO6vE/tcJ+mPklbF6YhafgbnnHM91SxwSEoD10oFEDwAABYOSURBVAAnA/OARZLmlWz2JeB6M3sTcAVwVVy+C/iQmR0KLAS+KmlyYr/PmNkRcVpVq8/gnHOut4oCh6QWSf9L0rXx9SGSTh1gt6OB9Wa2wcw6gZuB00u2mQf8Ks7fW1xvZr83sz/E+WeBF4ADKsmrc8652qr0zvHvAQ8Bx8XXm4EfAT/rZ58ZwMbE603AMSXbrAbOBL4GvAeYIGl/M3u5uIGko4EG4MnEfldKugz4JXCRmXWUvrmkJcASgGnTptHa2jrARyyvra1t0Pu62vBjUp/8uNSfWh2TSgPHa8zsryUtAjCzXRqahz58GviGpMXA/YSAlC+ulHQgcANwrpkVh5y9GHieEEyWAp8lVHP1YGZL43rmz59vCxYsGFQGW1tbGey+rjb8mNQnPy71p1bHpNLA0SmpmTgMv6TXAL2u8ktsBmYlXs+My7rFaqgzY5rjgfea2bb4eiJwB3CJmT2Y2Oe5ONsh6XuE4OOcc26YVNo4/jngF8AsSTcSqoj+cYB9VgCHSJorqQE4C1ie3EDSVEnFPFwMLIvLG4CfEBrOby3Z58D4v4AzgLUVfgbnnHNDoKISh5ndI+lh4FjCUyg+YWYvDbBPTtL5wF2ER5EtM7N1kq4AVprZcmABcJUkI1RVfSzu/lfA24D9YzUWwOLYg+pGSQfEfKwCzqv40zrnnNtrFQUOSe8BfmVmd8TXkyWdYWa397efmd0J3Fmy7LLE/K3ArWX2+wHwgz7SPKGSPDvnnKuNiquqzOyV4ovYDvG52mTJOedcPas0cJTbzh8C5ZxzY1ClgWOlpK9Iek2cvkK4r8M559wYU2nguADoBP49Th3sach2zjk3hlTaq2on0GuQQuecc2NPpb2qXke40e6g5D7ew8k558aeShu4fwR8G/gOiSFBnHPOjT2VBo6cmX2rpjlxzjk3KlTaOP4fkj4q6UBJU4pTTXPmnHOuLlVa4jg3/v+ZxDIDDh7a7DjnnKt3lfaqmlvrjDjnnBsdKr77W9JhhCf2NRWXmdn1tciUc865+lVpd9zPEUaynUcYtPBk4P8BHjicc26MqbRx/H3AicDzZvY3wOHApJrlyjnnXN2qNHDsjo9uzcUn871Az6f7OeecGyMqbeNYKWkycC1hcMM24IGa5co551zdqrRX1Ufj7Lcl/QKYaGZrapct55xz9aqaXlVvIjFWlaTXmtmPa5Qv55xzdaqiNg5Jy4BlwHuBd8fp1Ar2WyjpCUnrJfUaXVfSHEm/lLRGUqukmYl150r6Q5zOTSw/StKjMc2vS1Iln8E559zQqLTEcayZzasmYUlp4BrgncAmYIWk5Wb2WGKzLwHXm9n3JZ0AXAWcE4cz+Rwwn3CH+kNx363At4CPAP9N6Bq8EPh5NXlzzjk3eJX2qnpAUlWBAzgaWG9mG8ysE7gZOL1km3nAr+L8vYn17wLuMbMtMVjcAyyUdCChfeVBMzPCfSRnVJkv55xze6HSEsf1hODxPOHpfwLMzN7Uzz4zgI2J15uAY0q2WQ2cCXwNeA8wQdL+few7I06byizvRdISYAnAtGnTaG1t7SerfWtraxv0vq42/JjUJz8u9adWx6TSwPFd4BzgUaAwhO//aeAbkhYD9wObGaLnfZjZUmApwPz5823BggWDSqe1tZXB7utqw49JffLjUn9qdUwqDRwvmtnyKtPeTM+bBGfGZd3M7FlCiQNJ44H3mtk2SZsJQ5wk922N+88sWd4jTeecc7VVaRvHI5J+KGmRpDOL0wD7rAAOkTRXUgNwFtAj+EiaKqmYh4sJPbcA7gJOkrSfpP2Ak4C7zOw5YLukY2Nvqg8BP63wMzjnnBsClZY4mgltGycllhnQ530cZpaTdD4hCKSBZWa2TtIVwMpYglkAXCXJCFVVH4v7bpH0vwnBB+AKM9sS5z8KXBfz9HO8R5Vzzg2rAQNH7Fb7spl9utrEzexOQpfZ5LLLEvO3Arf2sW/x3pHS5SuBw6rNi3POuaExYFWVmeWB44chL84550aBSquqVklaDvwI2Flc6EOOOOfc2FNp4GgCXgZOSCzrt43DOefcvqnS0XH/ptYZcc45NzpUOsjhTEk/kfRCnG5LDkjonHNu7Kj0Po7vEe7BmB6n/4jLnHPOjTGVBo4DzOx7ZpaL03XAATXMl3POuTpVaeB4WdIHJaXj9EFCY7lzzrkxptLA8bfAXwHPA88B7wO8wdw558agfntVSfqimX0WONrMThumPDnnnKtjA5U4TomDCV48HJlxzjlX/wa6j+MXwFZgvKTtxAc4sedBThNrnD/nnHN1pt8Sh5l9xswmA3eY2UQzm5D8f5jy6Jxzro4M2DgeR8f1IOGccw6ofHTcgqRJw5Af55xzda7SQQ7bgEcl3UPP0XE/XpNcOeecq1uVBo4f4yPhOueco/LRcb8vqRmYbWZP1DhPzjnn6lilo+O+G1hF6J6LpCPig50G2m+hpCckrZd0UZn1syXdK+kRSWsknRKXny1pVWIqSDoirmuNaRbXvaqaD+ycc27vVDrkyOXA0cA2ADNbBRzc3w6xN9Y1wMnAPGCRpHklm10K3GJmRwJnAd+M6d9oZkeY2RHAOcAf43sWnV1cb2YvVPgZnHPODYFKA0eXmb1SsqwwwD5HA+vNbIOZdQI3A6eXbGPs6eo7CXi2TDqL4r7OOefqQKWN4+skfQBISzoE+DjwmwH2mQFsTLzeBBxTss3lwN2SLgDGAe8ok85f0zvgfE9SHrgN+IKZWelOkpYASwCmTZtGa2vrANktr62tbdD7utrwY1Kf/LjUn1odk0oDxwXAJUAH8EPgLuALQ/D+i4DrzOzLko4DbpB0mJkVACQdA+wys7WJfc42s82SJhACxznA9aUJm9lSYCnA/PnzbcGCBYPKYGtrK4Pd19WGH5P65Mel/tTqmAw0Om4TcB7wWuBR4Dgzy1WY9mZgVuL1zLgs6cPAQgAzeyC+31Sg2G5xFnBTcgcz2xz/3yHph4QqsV6BwznnXG0M1MbxfWA+IWicDHypirRXAIdImiupgRAESntiPQOcCCDpDUAT8GJ8nSI8A6S7fUNSRtLUOJ8FTgXW4pxzbtgMVFU1z8zeCCDpu8BvK03YzHKSzidUa6WBZWa2TtIVwEozWw5cCFwr6ZOEhvLFifaKtwEbzWxDItlG4K4YNNLAfwLXVpon55xze2+gwNFVnImBoKrEzexO4M6SZZcl5h8Dju9j31bg2JJlO4GjqsqEc865ITVQ4Dg8PocDwjM4mpPP5fCh1Z1zbuzpN3CYWXq4MuKcc250qPQGQOeccw7wwOGcc65KHjicc85VxQOHc865qnjgcM45VxUPHM4556rigcM551xVPHA455yrigcO55xzVfHA4ZxzrioeOJxzzlXFA4dzzrmqeOBwzjlXFQ8czjnnquKBwznnXFU8cDjnnKtKTQOHpIWSnpC0XtJFZdbPlnSvpEckrZF0Slx+kKTdklbF6duJfY6S9GhM8+uq9nm2zjnn9krNAoekNHANcDIwD1gkaV7JZpcCt5jZkcBZwDcT6540syPidF5i+beAjwCHxGlhrT6Dc8653mpZ4jgaWG9mG8ysE7gZOL1kGwOKzy2fBDzbX4KSDgQmmtmDZmbA9cAZQ5tt55xz/en3meN7aQawMfF6E3BMyTaXA3dLugAYB7wjsW6upEeA7cClZvZfMc1NJWnOKPfmkpYASwCmTZtGa2vroD5EW1vboPd1teHHpD75cak/tTomtQwclVgEXGdmX5Z0HHCDpMOA54DZZvaypKOA2yUdWk3CZrYUWAowf/58W7BgwaAy2NraymD3dbXhx6Q++XGpP7U6JrUMHJuBWYnXM+OypA8T2yjM7AFJTcBUM3sB6IjLH5L0JPC6uP/MAdJ0zjlXQ7Vs41gBHCJprqQGQuP38pJtngFOBJD0BqAJeFHSAbFxHUkHExrBN5jZc8B2ScfG3lQfAn5aw8/gnHOuRM1KHGaWk3Q+cBeQBpaZ2TpJVwArzWw5cCFwraRPEhrKF5uZSXobcIWkLqAAnGdmW2LSHwWuA5qBn8fJOefcMKlpG4eZ3QncWbLsssT8Y8DxZfa7DbitjzRXAocNbU6dc85Vyu8cd845VxUPHM4556rigcM551xVPHA455yrigcO55xzVfHA4ZxzrioeOJxzzlXFA4dzzrmqeOBwzjlXFQ8czjnnquKBwznnXFU8cDjnnKuKBw7nnHNV8cDhnHOuKh44nHPOVcUDh3POuap44HDOOVcVDxzOOeeqUtPAIWmhpCckrZd0UZn1syXdK+kRSWsknRKXv1PSQ5Iejf+fkNinNaa5Kk6vquVncM4511PNnjkuKQ1cA7wT2ASskLQ8Pme86FLgFjP7lqR5hOeTHwS8BLzbzJ6VdBhwFzAjsd/Z8dnjzjnnhlktSxxHA+vNbIOZdQI3A6eXbGPAxDg/CXgWwMweMbNn4/J1QLOkxhrm1TnnXIVqGThmABsTrzfRs9QAcDnwQUmbCKWNC8qk817gYTPrSCz7Xqym+l+SNIR5ds45N4CaVVVVaBFwnZl9WdJxwA2SDjOzAoCkQ4EvAicl9jnbzDZLmgDcBpwDXF+asKQlwBKAadOm0draOqgMtrW1DXpfVxt+TOqTH5f6U6tjUsvAsRmYlXg9My5L+jCwEMDMHpDUBEwFXpA0E/gJ8CEze7K4g5ltjv/vkPRDQpVYr8BhZkuBpQDz58+3BQsWDOpDtLa2Mth9XW34MalPflzqT62OSS2rqlYAh0iaK6kBOAtYXrLNM8CJAJLeADQBL0qaDNwBXGRmvy5uLCkjaWqczwKnAmtr+Bmcc86VqFngMLMccD6hR9TjhN5T6yRdIem0uNmFwEckrQZuAhabmcX9XgtcVtLtthG4S9IaYBWhBHNtrT6Dc8653mraxmFmdxIavZPLLkvMPwYcX2a/LwBf6CPZo4Yyj84556rjd44755yrigcO55xzVfHA4ZxzrioeOJxzzlXFA4dzzrmqeOBwzjlXFQ8czjnnquKBwznnXFU8cDjnnKuKBw7nnHNV8cDhnHOuKh44nHPOVcUDh3POuap44HDOOVcVDxzOOeeq4oHDOedcVTxwOOecq4oHDuecc1XxwOGcc64qNQ0ckhZKekLSekkXlVk/W9K9kh6RtEbSKYl1F8f9npD0rkrTdM45V1s1CxyS0sA1wMnAPGCRpHklm10K3GJmRwJnAd+M+86Lrw8FFgLflJSuME3nnHM1VMsSx9HAejPbYGadwM3A6SXbGDAxzk8Cno3zpwM3m1mHmf0RWB/TqyRN55xzNZSpYdozgI2J15uAY0q2uRy4W9IFwDjgHYl9HyzZd0acHyhNACQtAZbEl22Snqgy/0VTgZcGua+rDT8m9cmPS/3Z22Myp9zCWgaOSiwCrjOzL0s6DrhB0mFDkbCZLQWW7m06klaa2fwhyJIbIn5M6pMfl/pTq2NSy8CxGZiVeD0zLkv6MKENAzN7QFITIUL2t+9AaTrnnKuhWrZxrAAOkTRXUgOhsXt5yTbPACcCSHoD0AS8GLc7S1KjpLnAIcBvK0zTOedcDdWsxGFmOUnnA3cBaWCZma2TdAWw0syWAxcC10r6JKGhfLGZGbBO0i3AY0AO+JiZ5QHKpVmrzxDtdXWXG3J+TOqTH5f6U5NjonCeds455yrjd44755yrigcO55xzVfHA0QdJyyS9IGntSOfFBZJmxSFqHpO0TtInRjpPDiQ1SfqtpNXxuHx+pPPkgjjixiOSfjaU6Xrg6Nt1xK7Crm7kgAvNbB5wLPAxH3KmLnQAJ5jZ4cARwEJJx45wnlzwCeDxoU7UA0cfzOx+YMtI58PtYWbPmdnDcX4H4Q9iRv97uVqzoC2+zMbJe92MMEkzgb8EvjPUaXvgcKOSpIOAI4H/HtmcOOiuElkFvADcY2Z+XEbeV4F/BApDnbAHDjfqSBoP3Ab8g5ltH+n8ODCzvJkdQRjN4eihGjrIDY6kU4EXzOyhWqTvgcONKpKyhKBxo5n9eKTz43oys23AvXj74Eg7HjhN0lOEUcRPkPSDoUrcA4cbNSQJ+C7wuJl9ZaTz4wJJB0iaHOebgXcCvxvZXI1tZnaxmc00s4MIQzP9ysw+OFTpe+Dog6SbgAeAP5O0SdKHRzpPjuOBcwhXT6vidMpAO7maOxC4V9Iawnhy95jZkHb/dPXFhxxxzjlXFS9xOOecq4oHDuecc1XxwOGcc64qHjicc85VxQOHc865qnjgcKOaJJP05cTrT0u6fIjSvk7S+4YirQHe5/2SHpd0b8nygyTtTnQ9XhUfmVxt+oslTR+6HLuxzgOHG+06gDMlTR3pjCRJquaxzB8GPmJmf1Fm3ZNmdkRi6hxEdhYDVQWOKvPvxhgPHG60yxGeq/zJ0hWlJQZJbfH/BZLuk/RTSRskXS3p7PhMiUclvSaRzDskrZT0+zj+T3FAv3+RtELSGkl/l0j3vyQtBx4rk59FMf21kr4Yl10GvBX4rqR/qeQDSzpJ0gOSHpb0ozh2F5Iui3laK2mpgvcB84EbY4mlWdJTxUArab6k1jh/uaQbJP0auCHeEX5bTHOFpOPjdm9PlIAekTShkny7fYiZ+eTTqJ2ANmAi8BQwCfg0cHlcdx3wvuS28f8FwDbCHc+NwGbg83HdJ4CvJvb/BeEC6xBgE9AELAEujds0AiuBuTHdncDcMvmcDjwDHABkgF8BZ8R1rcD8MvscBOwGVsXpGmAqcD8wLm7zWeCyOD8lse8NwLvLpR+/q6lxfj7QGucvBx4CmuPrHwJvjfOzCUO9APwHcHycHw9kRvp34NPwTl4cdaOemW2XdD3wccKJthIrzOw5AElPAnfH5Y8CySqjW8ysAPxB0gbg9cBJwJsSpZlJhMDSCfzWzP5Y5v3eQjhBvxjf80bgbcDtA+TzSQujzhL3OxWYB/w6DN1FA2FoHIC/kPSPQAswBVhHOMlXY7mZFb/DdwDz4vsATIylm18DX4mf4cdmtqnK93CjnAcOt6/4KvAw8L3EshyxOlZSinCSLepIzBcSrwv0/LsoHZPHAAEXmNldyRWSFhBKHLUkwlhQi0reuwn4JqFksTF2EGjqI43u76XMNsn8p4Bjzay9ZJurJd0BnEIIYO8yMx/UcAzxNg63TzCzLcAthIbmoqeAo+L8aYQn01Xr/ZJSsd3jYOAJ4C7g7+MQ70h6naRxA6TzW+DtkqZKSgOLgPsGkZ8HgeMlvTa+9zhJr2NPAHgplgqSvcF2AMl2iKfY8728t5/3uhu4oPhC0hHx/9eY2aNm9kXCoIavH8TncKOYBw63L/kyoQ2g6FrCyXo1cByDKw08Qzjp/xw4L159f4fQ+P2wpLXAvzFA6T1Wi11EeFbFauAhM/tptZmJVV2LgZviaLQPAK+38ByMa4G1hMC2IrHbdcC3i43jwOeBr0laCeT7ebuPA/NjB4DHgPPi8n+IDfBrgC7Cd+PGEB8d1znnXFW8xOGcc64qHjicc85VxQOHc865qnjgcM45VxUPHM4556rigcM551xVPHA455yryv8HtwcUeq9G1SIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sfs = SFS(knn, \n",
    "          k_features=4, \n",
    "          forward=True, \n",
    "          floating=False, \n",
    "          scoring='accuracy',\n",
    "          verbose=2,\n",
    "          cv=5)\n",
    "\n",
    "sfs = sfs.fit(X, y)\n",
    "\n",
    "fig1 = plot_sfs(sfs.get_metric_dict(), kind='std_dev')\n",
    "\n",
    "plt.ylim([0.8, 1])\n",
    "plt.title('Sequential Forward Selection (w. StdDev)')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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666IFmXw4GCAcCgxqSK8mNV9DWkTuBn6uqjeLyLXAo6p6sx93A/A7Vf1lkesWAYsApkyZctSSJUtGrUMikaClpWXU148nGUPJcX3fc85x+32ggcDA/i6lk071EY017Z2idSCjWnIaRUa15FRChkJ/d1kRr4E81ddLNN7stc3ke04UsFsvulHKzCT7aGtrHdX1CxcuXK6q84vFVawoJyL3A/sWiVqsqr/2z1kM5IBb9jR9Vb0OuA5g/vz5umDBglHrunTpUvbm+vEkIy/n+BNOoC+dY0dvmq1dKbKOSyjo1RBCwb0feL9yxTLmHlb0my0b1ZBRLTmNIqNaciotI+e49KVzbHr+SSbvf7hXEwgGyl4LcFyXVU8vr8jvvmLGQVVPHi5eRM4DTgdO0l3Vl3XAzILTZvhhxh6S7/JZrLtnfwGm4Jx8H/7CPv+7n6/9NYJMzuWJVVtxHCUYDNAUDdISqG5joWHUM6FggLamCFsDQktsbP42atVb6fXAhcAJqtpXEHUXcKuIXIPXIH0A8LcaqDgmyeRclq/c0l+1Ba96W+g5lP6/uwIHjQFgUO23ID3BcV2aouH+boeGYTQetWohvBaIAvf5jTaPquoHVPVpEbkN+Ceeu+lD1lOpNHqSWbKOS0ssvNtgrEqwTcQMg2E0OLXqrTRvmLgrgSurqM6Yx1XlxS09BEQIjIHeHoZh1D82ZXcDsCORJpnOYYV5wzDKhRmHMY7juqzdmqA5PjYbvQzDqE/MOIxxNnclyTou4TJ0HzUMw8hjOcoYJp11eGlbL63xSK1VMQyjwTDjMIbZsKOXYMB6DhmGUX7MOIxRetNZNnUlx+wAG8Mw6hszDmMQVWXt1gSxcPHJvQzDMPYWMw5jkK6+DN19GZqiNsupYRiVwYzDGMNxlTVbEzSbO8kwjApixmGMsbU7RTrr9K9QZRiGUQnMOIwhso7Luu0JWm3Am2EYFcaMwxhi484+VCEYsNdmGEZlsVxmjJDK5NiwvY8WqzUYhlEFzDiMEV7aliAcCtisq4ZhVAUzDmOAnmSWbYm0DXgzDKNqmHGoc/JrNTRFbEyDYRjVw4xDnZNfqyFmxsEwjCpixqGOsbUaDMOoFWYc6hhbq8EwjFphuU6dYms1GIZRS8w41Cm2VoNhGLXEjEMdYms1GIZRa2piHETkahF5RkSeEpE7RaTDD58tIkkRecLfvl8L/WqJrdVgGEY9UKuaw33AYap6OPBv4JKCuBdU9Qh/+0Bt1KsdtlaDYRj1QE2Mg6req6o5//BRYEYt9Kg3bK0GwzDqBVHV2iogcjfwc1W9WURmA0/j1Sa6gc+o6kNDXLcIWAQwZcqUo5YsWTJqHRKJBC0tLaO+vlwyco6SyTmjboROp/qIxppGdW29yWkUGdWS0ygyqiWnUe5FgUyyj7a21lFdv3DhwuWqOr9YXMWMg4jcD+xbJGqxqv7aP2cxMB84W1VVRKJAi6puE5GjgF8Bh6pq93Cy5s+fr8uWLRu1rkuXLmXBggWjvr4cMrKOyz9e3EZTNDTqKblXrljG3MOKvueyUg05jSKjWnIaRUa15DTKvTiuy6qnl3PqKSeP6noRGdI4VMyxrarDaisi5wGnAyepb6FUNQ2k/f3lIvICcCAw+px/jGBrNRiGUU/UqrfS64ELgTNUta8gfLKIBP39ucABwMpa6FhNbK0GwzDqjVp1ibkWiAL3+d01H/V7Jh0PfF5EsoALfEBVt9dIx6phazUYhlFv1MQ4qOq8IcJvB26vsjo1Jb9Ww4SWWK1VMQzD6Mcc3DXE1mowDKNeMeNQQ2ytBsMw6hUzDjXC1mowDKOeMeNQI2ytBsMw6hnLmWqArdVgGEa9Y8ahBthaDYZh1DtmHKqMrdVgGMZYwIxDFbG1GgzDGCuYcagitlaDYRhjBTMOVcTWajAMY6xgxqFK5BwlnXWIhIK1VsUwDGNEzDhUgUzOIZNzaLUBb4ZhjBHMOFSBtVsTgK3VYBjG2MFyqwqzI5Fia3fKxjQYhjGmMONQQbKOy+otPTYS2jCMMYcZhwqyblsC14VwyB6zYRhjC8u1KsTO3jSbupLWCG0YxpjEjEMFyDouqzf30BIL20howzDGJGYcKsC6bQkcV21Mg2EYYxYzDmWmuy/Dpp3mTjIMY2xjxqGM5ByXlZu7aYmbO8kwjLGNGYcysm57L7mca+4kwzDGPDUzDiLyBRF5SkSeEJF7RWSaHy4i8i0Red6PP7JWOu4JPcksG3f20dpkYxoMwxj71LLmcLWqHq6qRwD3AJf64acCB/jbIuB7NdKvZBzXZdXmbpqjYQLmTjIMowGomXFQ1e6Cw2ZA/f0zgZ+ox6NAh4hMrbqCe8D6HX1ksg7RsLmTDMNoDERVRz6rUsJFrgTOBbqAhaq6RUTuAb6kqv/nn/NH4CJVXTbg2kV4NQumTJly1JIlS0atRyKRoKWlZVTXuqokMw6hEeZOSqf6iMaaRiWjVKoho1pyGkVGteQ0ioxqyWmUe1Egk+yjra11VNcvXLhwuarOLxZX0pJkItIEfBKYparvE5EDgINU9Z4Rrrsf2LdI1GJV/bWqLgYWi8glwIeBy0rRB0BVrwOuA5g/f74uWLCg1EsHsXTpUkZzveO6/HPtDkRkxFrDyhXLmHtY0XdQNqoho1pyGkVGteQ0ioxqyWmUe3Fcl1VPLx9V/jUSpa5XeSOwHDjWP14H/AKvrWBIVPXkEtO/BfgtnnFYB8wsiJvhh9UdG3f0kco6dDRHa62KYRhGWSm1zWF/Vf0KkAVQ1T5gr1pe/dpHnjOBZ/z9u4Bz/V5Lrwa6VHXD3siqBL2pLC9t76XNeicZhtGAlGocMiISx280FpH9gfReyv6SiKwQkaeAU4CP+uG/BVYCzwPXA/+7l3LKjuMqKzd30xQJWe8ko6bcdUeYBUe3currTmTB0a3cdUf5R+ZXQ4ZRf5TqVroM+D0wU0RuAY4Dztsbwar65iHCFfjQ3qRdaTZ19ZFMO3S2mDvJGJq77ghzzVUxNqw/kanTlE9ckuKMs7NlTf8zn4qTSnoFlPXrhM98Kg5QNjnVkGHUJyUZB1W9T0QeB16N5076qKpurahmdUpvOstLW3tpN3eSMQyjzVSzWejpFhI9Qk839PQIPd1CT4+Q8P/nj+++M9yffp5UUrj4Y3G+8/UoquC64LqCuuw6VlA3H5cPl/79/jiFTBoGepBTSeHKy2Icd3yOiZNq19vRqCyl9lZ6E/AnVf2Nf9whImep6q8qql2d4aqyenMPsUiQgC37OWapRInecaCvFxI9Qm+v8KXPxYpm3JddHOfRh0ODMv+E/z+VGvm7isWU1jYllSwen8vBwYc6BAIQCADi/Q/4/yUAgYB6+/k4f192O0+5/jvFa8c7tgU49vA29pvjcOTRDkceneOoox3mznOxpdIbg5LdSqp6Z/5AVXeKyGXAuDIOm7v66EvnrHfSGKZYiX7xBXHWvyTMf5VDb6+XUfcmoLdX6E14WyJB/34+vDAsmSytsNCbgD8/EKK11cvg29uV6TNcWtugtVVpaVXvf5v2n+P9x4trU8K+y3/B0a2sXzdY7rTpyje+P4Tl2EN+86tIURmTJru8+/1plj8WYun9Ie68zatJd3S6vPIo32Ack+PlhzvE4mVRxagypRqHYmWBUq9tCJKZHGu29tJm60FXlNGU6lUh0QM7dgg7dwTYuUPYsV3YuUPYuV38cGHH9gCP/TVILrt7ZpdOCdd8aegcLBbzMu3mFqW5GZpblMlTXObsv3tYS6vS3Kw0t8AXPhNj+7bBP5tp05Wlj/WM7uEM4BOXpHYzdACxuPfMysVQMi6+zHsv7yWDKqxeGeDxx4IsfyzE448FeeB+z4KFw8qhhzscOd8zFkcd7ZgraoxQaga/TESuAb7jH38Ib9zDuMBVZdWmbqKhIEFzJ1WMYqX6T38izl//EmTOXLc/8+/P+Au2XK74exFR2juUzk6lo1PJDWlnlBt/1jcgk1eamiE0imKQ41DxjDtvND1jKhVp9C5FhgjM2d9lzv4ub367F759m/DE8iDL/xZi+WNBbv5xhB/9wKtxD+WKqnQDvrFnlPrZfwT4LPBz//g+6rxHUTnZ0pUkkcpZ76QykkrCi6sDrF4VYPULQV5cFeCuO8JkMrtn8pmM8ItbveceDiudE7xMvqNTmTvPpaNT6Zzg//fDC89pa1eCBYPXh3PFHHdCrmz3V42MOy/njLOzFR2JOxoZEyYqJ56S48RTvGeaScOKp4L9tYuBrqip01yeezbYb+StV1TtKbW3Ui9wcYV1qUtSmRxrtiZssBt7XrLLZOClNQFeXBVg1cr8/yAvrgywYf3uLpdJk10ymeLpiCjLn+2mudkrpe4N1XDF5KlGxj1WiETxawtOUVfUr34RHlT7SyWFa66KmXGoEaX2VjoQuACYXXiNqp5YGbXqA1eVVVt6iJg7aciuma4LRx2TY/XKIKtX7m4I1q0N4Di7nlt7h8vsuS5HH5tjzlyX/ea4zJ7rMHuOS0vr0KX6qdOUUc6LOIhqleiN4Rnoirp9SfGBdevXCTdeF+GMs7PWVlFlSnUr/QL4PvBDwKmcOvXFlq4UPX0ZOltitVal5nz1yuJdMy88P05hP/imJmX2XJdDX+5w+llZzwDM8YxC54Thf9zVKtVbib7+mDpNixYMwmG46vI4V18R44QTc7zp/2VYcFKOiFXkK06pxiGnqnW/6E45SWUd1mztGVfuJMeBdS8JLzwXZOXzgf7/K58PsHPH0J3Xr7i6jzn7ezWByfvoqF0/VqofvwxVMLji6iSHHOZw520Rfn17mD/e20xHp8sb35Tl7LdlOOTl7l67Go3ilGoc7haR/wXupGBOJVXdXhGtaoyq8uLmHkLBAMExMKJnT9sCUklYtTJQYAQCrHzBcwulCwZhTZjoMneey+vekOV3d4fp7ireNfNt7yhv7xgr1Y8/RioYfOozKT5+cYqH/xzijp+HWXJzhJ/+KMpBBzu86W0Zzjg7y6TJ5nYqJ6Uah3f6/z9VEKbA3PKqUx9s60nR1ZcZE72Thpum4TUn5LzM//kAK58Pekbg+SDr1gqq3vkiyoxZLvsf4HLcf+aYO89h/wM8o1DoBjr61U7VGnKN8clIBYNQCE44MccJJ+bo2pnkt3dFuOO2MF/63O5up4Unm9upHJTaW2lOpRWpF9JZh9VbemiNj42ZJ6+5aui2ANfdFR6NKXPmurzilTne9FbXNwBeY3ApI1jN5WPUE+0dcM65Gc45N8PzzwW487Ywv/5lhD/dZ26nclHy8B4ROQw4BOhvnVXVn1RCqVqhqqzZ0kMwECAUrH93EsCG9cW/fNeFiy9L9huB6TN0r+e8MZePUY/MO8DlU4vTfPyiNH95yHM7/fyW4m4nG2hXOqV2Zb0MWIBnHH4LnAr8H9BQxmFbIs323gwTxoA7afMm4Qff9mbeLMa06cq73z/EwAHDaEBCITh+YY7jFxZ3Ox10sMNz/w6SzdhAu1IotSz5FuAkYKOqvgt4BdBeMa1qQCbn8OLmHtrq3J20batw1edinHRsK7feFOGYYx2isd0thLUFGOOdvNvpF/f08tsHe3j3B9I8889dhiFPfqCdMZhSjUNSVV0gJyJtwGZ2X+d5zLNmawIRqVt30o7twle/GOWkV7dy0/URTjsjyx8eSnDz7b1c+dUk06a7iCjTprtccXXSSkKG4ZN3Ow1Vy16/XoaMG8/sycR7HXjLdi4HEsAjFdOqyjiusr0nVZeD3bq74MYfRPnxD6P09cIbzszy4U+kmTvP7T/H2gIMY2SGGmiHCme+toXz3pfm9LOyROrfq1wVSiomq+r/qupOVf0+8Frgnb57acyTyTmkcw4tdTYVd6IHvvP1KAtf1cZ3vhHj+IVZ7vlTgmu+m9zNMBiGURqfuCRFLD7YBfvWc9I4Dlz88SZOOLqVb38tyrat1sVpT3orHU7B3EoiMk9V76iQXlWjN5UDhXCduJN6e+HmH0W54fsRdu4IcPLrs3zkkykOPtQMgmHsDcN1x1aFvzwU5MfXR/n212L84NooZ7wpy7nvTfOyQ8bnb6/U3ko/Ag4HngbyT0qBMW8c6oVkH9x6U4TrvhNlx/YAC07Ocv4FvaNufI0AACAASURBVBx2+Pj8MA2jEgzlghWB4453OO74PlY+H+AnN0S487YIv1wS4dWvyfGu96U54aRcXS2B6nXLjbJh/UnMmgVXXgnveEf50i+15vBqVT2kfGKNPOkU/PzmCD+4NsqWzQFec0KW8y/o44ijxs38hoZRV8yd53L5VSk+dmGa224Jc/ONUd7/zmZmz3U49z0Z3vS2DM3NtdVx4MwIL74IixZ5ceUyEKXawUdEpGzGQUS+ICJPicgTInKviEzzwxeISJcf/oSIXFoumfVGJu3VFE4+rpUrLo2z/wEut96Z4Ec/M8NgGPVAR6ey6MMZ/vhoD9d8t4+2duXzi+OcML+Nr3whxvqXqt8usWO78NijQb7wmcEzI/T1weLF5ZNVas3hJ3gGYiPexHsCqKoePkq5V6vqZwFE5HzgUuADftxDqnr6KNOtOwaOyPzohSmyGfjuN2KsXxfgyKNzXP2tPl59nBkEw6hHwmE4/awsp5+V5e/Lgvz4+gg3Xudtp5yW5V2LMmUv0CV64Llngzz3bGC3/1s2D1+eX7OmfDqUahxuAP4H+Ae72hxGjap2Fxw247VfNBzFJsW7+GNxVIVXHJnjyq8m+Y/jczb3i2GMEV453+GV85OsfynFzTdG+fktEX53d4RXHJnjvPdlOOW0LOFw6TMlJ/vghecD/PuZIM8/G+TfzwZ4/tkg69ftMgKxmDLvIIfXLMhx4EEO8w5y+cwFcTZtHGwoZs0q372KljD6Q0QeUdVjyycWRORK4FygC1ioqltEZAFwO/ASsB64QFWfHuL6RcAigClTphy1ZMmSUenhuEpvIkE03jSq64fj3P/+DzZvHjyrXXt7hiW3PVR2o5BO9RGNlf8+aiGnUWRUS06jyKiWnHLJSCaD3HffVH5950zWrWti0qQUhx62g0ce2YdMetfi5dGowzn/tYop+6Z4cXUzq1e38OKLzWzcEO+fITkcdpk5s5f99utlv9kJ9pvdy+zZCaZMSQ1qCP/TH6fwzW8cTHqAjAsueJaTT95csv4LFy5crqpFB0eVahy+C3QAd7P7eg5D9lYSkfuBfYtELVbVXxecdwkQU9XL/NHXrqomROQ04JuqesBI+s2fP1+XLVs24n0UY0cizSMPP8QBhx89quuH46Dpbf0vvhAR5dl13UWu2DuqNQiuGnIaRUa15DSKjGrJKbcM14UH/xjixuujPPp/wztkgkFlzv4uBxzkcMBBu/7Pmu0SKnlwQWFvpQCzZsmoeiuJyJDGoVRV4nhG4ZSCsGG7sqrqySWmfQveZH6XFbqbVPW3IvJdEZmkqltLTKuuGGpE5tRpDelFM4xxSyAAC1+bY+Frc0MWCkG5508JZs91y7LexBlnZ3nDWWlWPb2cU08pNbstnRGNg4gEgW2qekG5hIrIAar6nH94JvCMH74vsElVVUSOwetNta1ccqvNCSdn+dlNu4/Ft0nxDKOxGapQOG26cuDLxs64pRG7sqqqAxxXZrlfEpEVIvIUXm3ko374W4AVIvIk8C3g7VqK36sO6doJ9/4mzMz9HJsUzzDGEUNN0zHWCoWlupWeEJG7gF8AvfnA0U6foapvHiL8WuDa0aRZb3z1izF27hBuuLWXQw5zbVI8wxgnNMqqiaUahxiee+fEgjCbPmMIHn8syM9vjvKu96c55LCxU400DKM8NMJMyaWuId0QM7BWg2wWLrs4ztRpLudfMLaqkYZhGHlKmj5DRGaIyJ0istnfbheRGZVWbixy0/URnv1XkM9ekaz5/CuGYRijpdS5lW4E7gKm+dvdfphRwLqXhG9/LcZJp2Q5+fW5WqtjGIYxako1DpNV9UZVzfnbj4HJFdRrzKEKn/90HBH47BXJWqtjGIaxV5RqHLaJyH+LSNDf/psxPP6gEtz7uxAP3B/mIxekmDZjTPa+NQzD6KdU4/Bu4G3ARmAD3ngEa6T2SSTgis/GedkhDu98b6bW6hiGYew1w/ZWEpEvq+pFwDGqekaVdBpzfOvqGJs3Ctde37dHc6MYhmHUKyPVHE4TEQEuqYYyY5Gnn/KWFDzn3AyvONLWZDAMozEYqZz7e2AH0CIi3fiL/LBrsZ+2CutX1zgOfPaiOBMmKp+42MY0GIbROAxbc1DVT6lqB/AbVW1T1dbC/1XSsW659aYIK54M8enLU7S111obwzCM8jFig7Q/K+u4NwQD2bRRuOZLMY47Pssbzhpbc6YYhmGMRKmzsroiYmXjAr54WYxsFi6/KmXLfBqG0XCU2rcmAfxDRO5j91lZz6+IVnXOnx8I8bu7I3zswhT7zbGJ9QzDaDxKNQ53YDOwAt6C4JdfEmfuPIf3fjA98gWGYRhjkFJnZb1JROLALFV9tsI61TXf/WaUl9YEuPn2BJHoyOcbhmGMRUqdlfWNwBN4XVsRkSP8xX/GFc89G+CG70V509syHHOsjWkwDKNxKXX6jMuBY4CdAKr6BDC3QjrVJa4Ll14Up6VVueizNqbBMIzGplTjkFXVrgFh46ol9o6fh1n+txAXfibFhIk2sZ5hGI1NqQ3ST4vIfwFBETkAOB/4S+XUqi+2bxO+ckWM+a/K8ea325gGwzAan1JrDh8BDgXSwK1AF/CxSilVb3z5CzF6E8Lnv5y0MQ2GYYwLRpqVNQZ8AJgH/AM4VlXH1RJnf/1LkDtvi/CB81PMO3BcedIMwxjHjFRzuAmYj2cYTgW+Wm4FROSTIqIiMsk/FhH5log8LyJPiciR5ZZZKpm01wg9Y5bLB8+3MQ2GYYwfRmpzOERVXw4gIjcAfyuncBGZCZwCrCkIPhU4wN9eBXzP/191rv9ulFUvBPnhLb3Em2qhgWEYRm0YqebQ3/paIXfS14EL8aYBz3Mm8BP1eBToEJGpFZA9LC+uCvC9b0U59Y0Zjl84rjxphmEYiOrQ3TJFxGHXXEoCxIE+yrCeg4icCZyoqh8VkdXAfFXdKiL3AF9S1f/zz/sjcJGqLhtw/SJgEcCUKVOOWrJkyaj0cFylN5EgWlA1UIXFlxzBM8+0c/0NjzBx4t4v/ZlO9RGNVbb6UQ0Z1ZLTKDKqJadRZFRLTqPciwKZZB9tba2jun7hwoXLVXV+sbhh3UqqGhyVRB8RuR/Yt0jUYuDTeC6lUaGq1wHXAcyfP18XLFgwqnR2JNI88vBDzD1s1/O5584wjz/exKVXJjn6hMNHq+JurFyxbDcZlaAaMqolp1FkVEtOo8iolpxGuRfHdVn19HJGm/8NR0VXPFbVk4uFi8jLgTnAk94qpMwAHheRY4B1wMyC02f4YVWhuwu+eHmMlx+R45xz977GYBiGMRapqHEYClX9B7BP/niAW+ku4MMisgSvIbpLVTdUS7evXRVj+zbh+p8mCe5VvckwDGPsUhPjMAK/BU4Dnsdr33hXtQQ/sTzIkp9GeOd7Mxx6uI1pMAxj/FIXxkFVZxfsK/ChauuQy8FnL4ozZV/l/E/ZxHqGYYxv6sI41AM3/TDCs/8Mcu0NvbS01FobwzCM2lLq3EoNzebNUb51dYwTX5vlta+3MQ2GYRjj2jjccgscfkiEd537GlIpOPY/szaxnmEYBuPYrXTLLbBoEfT1edZAFb52VZzOCXDG2TYtt2EY45txW3NYvBj6+nYPSyWFa66K1UYhwzCMOmLcGoc1a4qHb1hvfiXDMIxxaxxmzSoePnWaLQFqGIYxbo3DlVdC04D5sGJx5ROX2BgHwzCMcWsc3vEOuO46mDFTEVGmTXe54uqkNUYbhmEwjnsrgWcgTjszwyMPP8QBhx9da3UMwzDqhnFbc6gmriqOq7jDrJ1hGIZRT5hxqAI9fRkCAWFnb5pszib0Mwyj/jHjUGGyjksgIETDQV42rYNUNkdvyto1jLHFcCtGGo3JuG5zqAa9ySxz9m1jxRpob45y6MwJrNzczY5EmvbmCAGbr8MYBY7rknOUnOOScz23ZVdvGti1ILsM2M+H7AobcCwypBEICDiq7EykEYGmaJhwyMqWjYwZhwqSzORojoWY0BLtD4uGgxw4tYP123tZv6OX1niEcNB+ZMbuOK6X8ef/59urBEFRwqEA8UiItqYwsXCIrheDHDitA8Q7R8Q3CH7ZY/cwzywUlktkt7Bd50rBSUvXhjh89kR29qbZ3JUkkcgQCgZoioYIBuwbbjTMOFQIVSWVcTh0Zueg2kEwIMyc1EJLLMQLm7oJB4M0Re1VjCdcV8kVlP5d1d1K+uFggHgkSEssTDwaJBoKEg4GCIcChIKBot9UW1Ok4npHw0GmdDSxT3ucvkyOHQnPUDiuejpHQ1YbbhAsR6oQPcks+7THaI6FhzynsyXGYdEwKzd2sbM3TXtTZLeSmjH2UFVc9TL/fC81R5WdvssnTzAgfsk/RDwS8jJ/P+MPBwMEA/X9HYgIzdEwzdEw0yY0k0hl2dadYlsihSrEwkGi4aB9z2MYMw4VwHFdFGXahOYRz42Fgxw0vZOXtiXYuKOPtqYIIXMz1Q1eZu9n8q7ulul7J+xyxSiKCP0ZfD7D3xwMsP++bYSDQcJBIRwKNJQbJiBCWzxCWzzCzEkt9CQzbO5OsrMvgwBN0RCRkC3IPtYw41ABepJZZk1qKfkHEQwI+01upTUW5oVN3UTDQeIRezWVxHFdXIVEKovrl+6Ffhc94Ll4RCDiu3Si0SAR37UTCQUJBoRgIOD/37UNLC2vDgaY0DI+ZvsNBQN0tsTobImRyTns7M2wqauPHYk0wYDQHLP2ibGC5UBlJp11iIWDTGqL7/G1E1pjxKMhXtjYTVdvmjZzM+01rqtkHZdMzsVxHfLZfzgUICAwqTXqZf5+aX73jL7+3Tv1TCQUZJ/2uNc+kc71N2Rnc1lCoQBNkRABe751ixmHMtObznLw9M5RZyrxSIiDZ3SwdmuCTV1J2psiVtIqAVe9ht1MziXnuH6xH7+0GqazJUpTJEQk7Ll7QsEAS1cHmTmptdaqjwuaoiGaoiH27WyiN5VjW0+SrT1p1FWikSAxa5+oO8w4lJFEKsvEluhe9xoJBgLM3qeNlliYVZt7zM1UgKqSc/K1AaffCIhAczTMxNYozdEw0XCQiO/+MeqHgAit8TCt8TAzJ7n0JLNs7krS1ZcBsF57dURN34SIfBL4KjBZVbeKyALg18Aq/5Q7VPXztdJvT3D9/ugzylgSndQWpyka5oWNXTV3M7mukso6ZHIOjrt775vCLpj9Yf395nfvMz9of4jzAHKOS9ZxyeZcXFdRgQBCLBKkvSlCSyxENBzyjUDASp5jjGAgQEdzlI7mKJmcQ1dfhs07k/6gPtdqzDWmZsZBRGYCpwAD12R7SFVPr4FKe0V3MsP0ic3EwuUtqTZFQxw8o5M1WxNs6UrS3lw9N1M255LM5HBcJRgQJrRG6WxuIbE2xKEzJ6Dqja51VVH1SvWq3nG+kTffu8c7Btd1cV1w1cVxGRDv/QdvEFjWcWmJhmhuDxOPhIj4tQHrR994REJBJrfFmdwWZ8PzQbp6M9Zzr8bUsubwdeBCvJrCmCabcwmHAkxp3/NG6FIIBQPM2aeV1niYVZt6aIqGiJbZCIGXqaezDulsDlUhHg0ybUITbfHIboObvOkTKvfpqCoPvhTi8P0mVkyGUb+EAsKB09p5bkM3LTGbpqNWSC0m1BKRM4ETVfWjIrIamF/gVrodeAlYD1ygqk8PkcYiYBHAlClTjlqyZMmodHFcpTeRIBpvGvnkIci5SiwcHLYROpFI0NLSMmoZefIZuCqD5KVTfURje3Yf+ZJ/3i8UDEj/CNyhCujlupfhaBQZ1ZLTKDIK5Tiu960HAkK564qj+a3UoxwFMsk+2tpG585euHDhclWdXyyuYsZBRO4H9i0StRj4NHCKqnYNMA5tgKuqCRE5Dfimqh4wkqz58+frsmXLRqXnjkR6rxb76UvniIWDHDitfVif99KlS1mwYMGoZAwk67i8uKWH7T1eO0TeSKxcsYy5hxV9z/2oKhnfXaRAJBRgYmuM9qYIzSXOkVPOe2l0GdWS0ygyBsrpSWZ5Zt0ObxR5GWvLpfxWxoIcx3VZ9fRyTj3l5FFdLyJDGoeK+QZUtai2IvJyYA7wpJ+ZzgAeF5FjVHVjwfW/FZHvisgkVd1aKT33hnwp/oCpwxuGchMOBth/ShutsSSrt/T0984ZUk9XSWZy3loSAq2xsDfoLh62LoRGXdMaD3PIzE6eXbcTV9V67VWRqj9pVf0HsE/+eEDNYV9gk6qqiByDt97EtmrrWCqJZJapnU016X4nIkzpaKI5Fub5jV1kks5u8ZmcQyrj4LpKMCh0tkTpbI7SHAvbLLDGmKI5GubgGZ6B6EvnrLtrlai3p/wW4IMikgOSwNu1TlcZyTkuIrBvZ+X9lsPREgtzyIxOXtzcw0ZX2dmbAhViQzQmG8ZYJB4J8bIZnfx7/U4SqSwtw0xoaZSHmhsHVZ1dsH8tcG3ttCmdnmSGuVPa6qIUHgkFmTe1nRefCTJ3SjstseHdTIYxFomFg7xsegf/Xt9FTzJDa7zyU5SPZ2qfs41BUpkcTdEwE1rrZzI1ESEUECa2xswwGA1LJBTkoOkdxMJBuv1R1UZlMOOwh6h6jbuz92k1V41h1IBwMMCB0zpoiYX7l0Y1yo8Zhz0kkcoyuS1uPk/DqCGhYIB5U9voaImyI5Eecu1rY/SYcdgD8gu+TJ848iI+hmFUlmAgwJx92pjcFmNnb8YMRJkx47AHdPdl9mgRH8MwKkswIOy3Tyv7tHsGwjUDUTbMOJRIJucQi4xuER/DMCpHQLyVFKdNaGJnIt0/eaOxd5hxKJFEMst+k1ttZTDDqENEhOkTmpk1uYWdvelda3wbo8aMQwkkUlkmtkZp38tFfAzDqBwiwtTOZmbv00ZXbxrHdWut0pjGjMMI5NcgnjGx8rNRGoax90zpiLP/1Ha6+jJkHTMQo8WMwwj0JDNM72wiZhN+GcaYYVJrjAOntpNIZr0JJ409xozDMGRzLqFggCkdtZ0/yTCMPaezJcZB09rpTWe99caNPcKMwzD0pLLMmtRiSxUaxhilvTnKwTM6SWZypLNmIPYEy/WGoC+do60pTGdLtNaqGIaxF7TEvCm/MzmHZCZXa3XGDGYciuAt4pNj1qQWWwjHMBqA5qg3tb2rSl/aDEQpmHEoQiKZ9RbSidr8SYbRKMQiIQ6e3klAsJHUJWDGYQD5RXym1ngRH8Mwyk807E35LSLsSKTJWVfXITHjMICeZJaZNn+SYTQskVCQWDjInCmtpLI5unptyo1iWOf9AtJZh3g0yMQ6WsTHMIzKMLktTmdzlM3dSdZt6yUgQms8bO2MPlZz8FFVelNZZk9us0V8DGOcEAoGmNbZzCtmT2Ria5QdvWl6U9laq1UXmHHwSaRyTG6P0xq3RmjDGG9EQkFm79PGy2dNpCkaYnsiRWqcd3s14wAo4Lgu0yfYIj6GMZ5pioY4cFoHB8/o7G+0Hq/Tb5hxwHMpzZzUTDRsjdCGYUBbPMKhMzuZt28bGcdhR2L8zfJaE+MgIpeLyDoRecLfTiuIu0REnheRZ0XkddXQJxgIMLnNuq4ahrELEWFCa4yXz5rIfpNb6E35PZvGyRiJWvZW+rqqfrUwQEQOAd4OHApMA+4XkQNVtWKTosQjQaLhgC3iYxhGUYIBYUpHExNaY2zc2ceGHX2EAgFaYqGG7tlUb26lM4ElqppW1VXA88AxlRQYi4Ssd5JhGCMSDgaYObGFw/ebSEdzhJ29mZpMxeG6Sjrr0JPM0N2XRahM/iVagyqSiFwOnAd0A8uAT6rqDhG5FnhUVW/2z7sB+J2q/rJIGouARQBTpkw5asmSJaPWJ5FI0NJS2cV8GkVGteQ0ioxqyWkUGdWSUw4ZriqZnIvjKkERipUx06k+orHRu6wVUPXaRfsRCIoQCAgBEfp6e2ltHd29LFy4cLmqzi8WVzG3kojcD+xbJGox8D3gC3j3/gXga8C79yR9Vb0OuA5g/vz5umDBglHrunTpUvbm+vEko1pyGkVGteQ0ioxqySmXDFWlqy/D2q0JkpkcLfEI4YIp/leuWMbcw4rmvbvhqpLNuWQdl5zjIAgKxMJBWuJhWmNhouEQ0XBg0OwNlXpeFTMOqnpyKeeJyPXAPf7hOmBmQfQMP8wwDKPuEBE6mqO0NUXY3pNi7bYEvSmlNR4Zsh3TcV0yOZdszsVVRfBqHS2xEB3NMVpiYSKhfFto7Tz/NWmQFpGpqrrBP3wTsMLfvwu4VUSuwWuQPgD4Ww1UNAzDKJmACJPa4nQ0R9nSneQlfzoOBRKpLDnHRQEBwqEAbbEwzR1h4pEQ0VCQSChQd43bteqt9BUROQLPrbQaeD+Aqj4tIrcB/wRywIcq2VPJMAyjnISCAaZ2NjOxNcaGHX1sASa2RmmOhomFg0TDwTGzsmRNjIOq/s8wcVcCV1ZRHcMwjLISCQXZb3Irq8JBZk1qrbU6o2JsmDDDMAyjqphxMAzDMAZhxsEwDMMYhBkHwzAMYxBmHAzDMIxBmHEwDMMwBmHGwTAMwxiEGQfDMAxjEDWZlbXciMgW4MW9SGISsLVM6jS6jGrJaRQZ1ZLTKDKqJcfuxWM/VZ1cLKIhjMPeIiLLhpq21mTURk6jyKiWnEaRUS05di8jY24lwzAMYxBmHAzDMIxBmHHwuM5k1J2cRpFRLTmNIqNacuxeRsDaHAzDMIxBWM3BMAzDGIQZB8MwDGMQ49Y4iMiPRGSziKwY+exRy5gpIg+IyD9F5GkR+WiF5MRE5G8i8qQv53OVkOPLCorI30XknpHPHrWM1SLyDxF5QkSWVUhGh4j8UkSeEZF/icixZU7/IF///NYtIh8rp4wCWR/33/sKEfmZiMQqIOOjfvpPl/M+iv0ORWSCiNwnIs/5/zsrIOOt/r24IrLX3UCHkHG1/309JSJ3ikhHheR8wZfxhIjcKyLT9lYOAKo6LjfgeOBIYEUFZUwFjvT3W4F/A4dUQI4ALf5+GPgr8OoK3dMngFuBeyr43FYDkyr8/m8C3uvvR4COCsoKAhvxBhyVO+3pwCog7h/fBpxXZhmH4a3z3oS3euT9wLwypT3odwh8BbjY378Y+HIFZBwMHAQsBeZX6D5OAUL+/pf39j6GkdNWsH8+8P1yvJtxW3NQ1T8D2yssY4OqPu7v9wD/wvsxl1uOqmrCPwz7W9l7GojIDOANwA/LnXY1EZF2vB/ZDQCqmlHVnRUUeRLwgqruzSj+4QgBcREJ4WXg68uc/sHAX1W1T1VzwIPA2eVIeIjf4Zl4xhv//1nllqGq/1LVZ/cm3RJk3Os/L4BHgRkVktNdcNhMmX7749Y4VBsRmQ28Eq9UX4n0gyLyBLAZuE9VKyHnG8CFgFuBtAtR4F4RWS4iiyqQ/hxgC3Cj7yL7oYg0V0BOnrcDP6tEwqq6DvgqsAbYAHSp6r1lFrMC+E8RmSgiTcBpwMwyyyhkiqpu8Pc3AlMqKKtavBv4XaUSF5ErRWQt8A7g0nKkacahCohIC3A78LEBVr5sqKqjqkfglU6OEZHDypm+iJwObFbV5eVMdwheo6pHAqcCHxKR48ucfgivav49VX0l0Ivnvig7IhIBzgB+UaH0O/FK2nOAaUCziPx3OWWo6r/w3CL3Ar8HngCccsoYRrZSgVpwNRGRxUAOuKVSMlR1sarO9GV8uBxpmnGoMCISxjMMt6jqHZWW57tHHgBeX+akjwPOEJHVwBLgRBG5ucwygP7SMKq6GbgTOKbMIl4CXiqoXf0Sz1hUglOBx1V1U4XSPxlYpapbVDUL3AH8R7mFqOoNqnqUqh4P7MBrP6sUm0RkKoD/f3MFZVUUETkPOB14h2/oKs0twJvLkZAZhwoiIoLn1/6Xql5TQTmT8z0hRCQOvBZ4ppwyVPUSVZ2hqrPx3CR/UtWyllABRKRZRFrz+3iNemXtUaaqG4G1InKQH3QS8M9yyijgHCrkUvJZA7xaRJr87+0kvLatsiIi+/j/Z+G1N9xabhkF3AW8099/J/DrCsqqGCLyejw37Bmq2ldBOQcUHJ5JuX775WjVHosb3g92A5DFK0m+pwIyXoNXJX4Kryr+BHBaBeQcDvzdl7MCuLTCz24BFeqtBMwFnvS3p4HFFZJzBLDMf2a/AjorIKMZ2Aa0V/h9fM7PEFYAPwWiFZDxEJ4BfRI4qYzpDvodAhOBPwLP4fWMmlABGW/y99PAJuAPFZDxPLC24Le/172IhpBzu//unwLuBqaX493Y9BmGYRjGIMytZBiGYQzCjINhGIYxCDMOhmEYxiDMOBiGYRiDMONgGIZhDMKMg1HXiIiKyNcKji8QkcvLlPaPReQt5UhrBDlv9Wd+fWBA+GwRSQ6YvTUyivTPK9tMnIbhY8bBqHfSwNkiMqnWihTiT3JXKu8B3qeqC4vEvaCqRxRsmVGocx7e1Bkls4f6G+MQMw5GvZPDWyP34wMjBpb8RSTh/18gIg+KyK9FZKWIfElE3iHemhf/EJH9C5I5WUSWici//fmj8pMYXi0ij/nz5L+/IN2HROQuioyoFpFz/PRXiMiX/bBL8QZD3iAiV5dywyJyiog8IiKPi8gv/Lm5EJFLfZ1WiMh14vEWYD5wi1/ziIu3HsYk/5r5IrLU379cRH4qIg8DP/VH1t/up/mYiBznn3dCQU3m7/kR68Y4oxIjNm2zrVwbkADa8NZ4aAcuAC73434MvKXwXP//AmAn3noaUWAd8Dk/7qPANwqu/z1eIekAvBGnMWAR8Bn/nCjeSOo5frq9wJwiek7Dm8piMt7Efn8CzvLjllJkzQBgNpBk1wja7wCTgD8Dzf45F+GPeKdgpDDeSOg3FkufgvUw8AzHUn//cmA5u9Z+uBVvkkOAWXjTvIA3yvY4f78Ff00C28bXZlVLo+5R1W4R+QneQibJEi97TP1pn0XkBbwZRQH+ARS6d25TVRd4TkRWAi/Dm8/p8IJaSTue9pDBZgAAAgtJREFU8cgAf1PVVUXkHY2XCW/xZd6Ct2bEr0bQ8wX1ZtPFv+504BDgYW+qJCLAI370QhG5EG/Nhgl404vcPUL6A7lLVfPP8GTgEF8OQJtfS3kYuMa/hztU9aU9lGE0AGYcjLHCN4DHgRsLwnL4rlERCeBlpHnSBftuwbHL7t/9wPljFG9lvY+o6h8KI0RkAV7NoZII3noc5wyQHQO+i1dDWOs3yg+1HGj/cylyTqH+AbwVA1MDzvmSiPwGb92Gh0Xkdapa1okcjfrH2hyMMYGqbsdbAvM9BcGrgaP8/TPwVsDbU94qIgG/HWIu8CzwB+CD/nTriMiBMvJiQH8DThCRSSISxJuN9cFR6PMocJyIzPNlN4vIgezK5Lf6pfvCXlY9eMvQ5lnNrucy3PTN9wIfyR+IyBH+//1V9R+q+mXgMbzalDHOMONgjCW+hueTz3M9Xob8JHAsoyvVr8HL2H8HfMAvRf8Qr8H5cfEWcv8BI9SyfRfWxXhraTwJLFfVPZ5q2ndLnQf8TP5/e3dsg0AMBAFw3Q0FUBQRohUypE9ogx6IPqCdJzh/dBLZSwQzoQvwyj5pb4w19aV02mpPx5Jq33ylLu3dM8ljH0inWlrvY4x3fi/luSY5z6H7J8llnt/m0HtNtX8etsGM/6WVFYDGywGARjgA0AgHABrhAEAjHABohAMAjXAAoPkCBHJfyiKiIGsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.datasets import load_boston\n",
    "\n",
    "boston = load_boston()\n",
    "X, y = boston.data, boston.target\n",
    "\n",
    "lr = LinearRegression()\n",
    "\n",
    "sfs = SFS(lr, \n",
    "          k_features=13, \n",
    "          forward=True, \n",
    "          floating=False, \n",
    "          scoring='neg_mean_squared_error',\n",
    "          cv=10)\n",
    "\n",
    "sfs = sfs.fit(X, y)\n",
    "fig = plot_sfs(sfs.get_metric_dict(), kind='std_err')\n",
    "\n",
    "plt.title('Sequential Forward Selection (w. StdErr)')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature Importance Permutation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Take a model that was fit to the training dataset\n",
    "#### Estimate the predictive performance of the model on an independent dataset (e.g., validation dataset) and record it as the baseline performance\n",
    "#### For each feature i:\n",
    " ##### randomly permute feature column i in the original dataset\n",
    " #### record the predictive performance of the model on the dataset with the permuted column\n",
    " #### compute the feature importance as the difference between the baseline performance (step 2) and the performance on the permuted dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.model_selection import train_test_split\n",
    "from mlxtend.evaluate import feature_importance_permutation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_classification\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "\n",
    "# Build a classification task using 3 informative features\n",
    "X, y = make_classification(n_samples=10000,\n",
    "                           n_features=10,\n",
    "                           n_informative=3,\n",
    "                           n_redundant=0,\n",
    "                           n_repeated=0,\n",
    "                           n_classes=2,\n",
    "                           random_state=0,\n",
    "                           shuffle=False)\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    X, y, test_size=0.3, random_state=1, stratify=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training accuracy: 100.0\n",
      "Test accuracy: 95.06666666666666\n",
      "[0.283357   0.30846795 0.24204291 0.02229767 0.02364941 0.02390578\n",
      " 0.02501543 0.0234225  0.02370816 0.0241332 ]\n"
     ]
    }
   ],
   "source": [
    "forest = RandomForestClassifier(n_estimators=250,\n",
    "                                random_state=0)\n",
    "\n",
    "forest.fit(X_train, y_train)\n",
    "\n",
    "print('Training accuracy:', np.mean(forest.predict(X_train) == y_train)*100)\n",
    "print('Test accuracy:', np.mean(forest.predict(X_test) == y_test)*100)\n",
    "\n",
    "importance_vals = forest.feature_importances_\n",
    "print(importance_vals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.26      ,  0.26511111,  0.25977778, -0.00155556, -0.00044444,\n",
       "        0.        ,  0.00144444,  0.        , -0.00088889, -0.00222222])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "imp_vals, orgin_value = feature_importance_permutation(\n",
    "    predict_method=forest.predict, \n",
    "    X=X_test,\n",
    "    y=y_test,\n",
    "    metric='accuracy',\n",
    "    num_rounds=3, ####If num_rounds > 1, the permutation is repeated multiple times (with different random seeds\n",
    "    seed=1)\n",
    "\n",
    "imp_vals ### mean values of rounds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.26833333,  0.254     ,  0.25766667],\n",
       "       [ 0.26733333,  0.274     ,  0.254     ],\n",
       "       [ 0.261     ,  0.25766667,  0.26066667],\n",
       "       [-0.002     , -0.00133333, -0.00133333],\n",
       "       [-0.00033333, -0.00133333,  0.00033333],\n",
       "       [ 0.00066667,  0.001     , -0.00166667],\n",
       "       [ 0.00233333, -0.00033333,  0.00233333],\n",
       "       [ 0.00066667,  0.00033333, -0.001     ],\n",
       "       [ 0.00066667, -0.00166667, -0.00166667],\n",
       "       [-0.00233333, -0.00233333, -0.002     ]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "orgin_value "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.25999999999999995"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(.26833333+0.254\n",
    "+0.25766667)/3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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