08_grid_search.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Efficiently searching for optimal tuning parameters ([video #8](https://www.youtube.com/watch?v=Gol_qOgRqfA&list=PL5-da3qGB5ICeMbQuqbbCOQWcS6OYBr5A&index=8))\n",
    "\n",
    "Created by [Data School](https://www.dataschool.io). Watch all 10 videos on [YouTube](https://www.youtube.com/playlist?list=PL5-da3qGB5ICeMbQuqbbCOQWcS6OYBr5A). Download the notebooks from [GitHub](https://github.com/justmarkham/scikit-learn-videos).\n",
    "\n",
    "**Note:** This notebook uses Python 3.9.1 and scikit-learn 0.23.2. The original notebook (shown in the video) used Python 2.7 and scikit-learn 0.16."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Agenda\n",
    "\n",
    "- How can K-fold cross-validation be used to search for an **optimal tuning parameter**?\n",
    "- How can this process be made **more efficient**?\n",
    "- How do you search for **multiple tuning parameters** at once?\n",
    "- What do you do with those tuning parameters before making **real predictions**?\n",
    "- How can the **computational expense** of this process be reduced?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Review of K-fold cross-validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Steps for cross-validation:\n",
    "\n",
    "- Dataset is split into K \"folds\" of **equal size**\n",
    "- Each fold acts as the **testing set** 1 time, and acts as the **training set** K-1 times\n",
    "- **Average testing performance** is used as the estimate of out-of-sample performance\n",
    "\n",
    "Benefits of cross-validation:\n",
    "\n",
    "- More **reliable** estimate of out-of-sample performance than train/test split\n",
    "- Can be used for selecting **tuning parameters**, choosing between **models**, and selecting **features**\n",
    "\n",
    "Drawbacks of cross-validation:\n",
    "\n",
    "- Can be computationally **expensive**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Review of parameter tuning using `cross_val_score`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Goal:** Select the best tuning parameters (aka \"hyperparameters\") for KNN on the iris dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# added empty cell so that the cell numbering matches the video"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn.model_selection import cross_val_score\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# read in the iris data\n",
    "iris = load_iris()\n",
    "\n",
    "# create X (features) and y (response)\n",
    "X = iris.data\n",
    "y = iris.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.         0.93333333 1.         1.         0.86666667 0.93333333\n",
      " 0.93333333 1.         1.         1.        ]\n"
     ]
    }
   ],
   "source": [
    "# 10-fold cross-validation with K=5 for KNN (the n_neighbors parameter)\n",
    "knn = KNeighborsClassifier(n_neighbors=5)\n",
    "scores = cross_val_score(knn, X, y, cv=10, scoring='accuracy')\n",
    "print(scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9666666666666668\n"
     ]
    }
   ],
   "source": [
    "# use average accuracy as an estimate of out-of-sample accuracy\n",
    "print(scores.mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.96, 0.9533333333333334, 0.9666666666666666, 0.9666666666666666, 0.9666666666666668, 0.9666666666666668, 0.9666666666666668, 0.9666666666666668, 0.9733333333333334, 0.9666666666666668, 0.9666666666666668, 0.9733333333333334, 0.9800000000000001, 0.9733333333333334, 0.9733333333333334, 0.9733333333333334, 0.9733333333333334, 0.9800000000000001, 0.9733333333333334, 0.9800000000000001, 0.9666666666666666, 0.9666666666666666, 0.9733333333333334, 0.96, 0.9666666666666666, 0.96, 0.9666666666666666, 0.9533333333333334, 0.9533333333333334, 0.9533333333333334]\n"
     ]
    }
   ],
   "source": [
    "# search for an optimal value of K for KNN\n",
    "k_range = list(range(1, 31))\n",
    "k_scores = []\n",
    "for k in k_range:\n",
    "    knn = KNeighborsClassifier(n_neighbors=k)\n",
    "    scores = cross_val_score(knn, X, y, cv=10, scoring='accuracy')\n",
    "    k_scores.append(scores.mean())\n",
    "print(k_scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Cross-Validated Accuracy')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the value of K for KNN (x-axis) versus the cross-validated accuracy (y-axis)\n",
    "plt.plot(k_range, k_scores)\n",
    "plt.xlabel('Value of K for KNN')\n",
    "plt.ylabel('Cross-Validated Accuracy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## More efficient parameter tuning using `GridSearchCV`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Allows you to define a **grid of parameters** that will be **searched** using K-fold cross-validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import GridSearchCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]\n"
     ]
    }
   ],
   "source": [
    "# define the parameter values that should be searched\n",
    "k_range = list(range(1, 31))\n",
    "print(k_range)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'n_neighbors': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]}\n"
     ]
    }
   ],
   "source": [
    "# create a parameter grid: map the parameter names to the values that should be searched\n",
    "param_grid = dict(n_neighbors=k_range)\n",
    "print(param_grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# instantiate the grid\n",
    "grid = GridSearchCV(knn, param_grid, cv=10, scoring='accuracy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- You can set **`n_jobs = -1`** to run computations in parallel (if supported by your computer and OS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv=10, estimator=KNeighborsClassifier(n_neighbors=30),\n",
       "             param_grid={'n_neighbors': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,\n",
       "                                         13, 14, 15, 16, 17, 18, 19, 20, 21, 22,\n",
       "                                         23, 24, 25, 26, 27, 28, 29, 30]},\n",
       "             scoring='accuracy')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fit the grid with data\n",
    "grid.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean_test_score</th>\n",
       "      <th>std_test_score</th>\n",
       "      <th>params</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.960000</td>\n",
       "      <td>0.053333</td>\n",
       "      <td>{'n_neighbors': 1}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.953333</td>\n",
       "      <td>0.052068</td>\n",
       "      <td>{'n_neighbors': 2}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 3}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 4}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 5}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 6}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 7}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 8}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 9}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 10}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 11}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 12}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.980000</td>\n",
       "      <td>0.030551</td>\n",
       "      <td>{'n_neighbors': 13}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.044222</td>\n",
       "      <td>{'n_neighbors': 14}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 15}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 16}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 17}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.980000</td>\n",
       "      <td>0.030551</td>\n",
       "      <td>{'n_neighbors': 18}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 19}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.980000</td>\n",
       "      <td>0.030551</td>\n",
       "      <td>{'n_neighbors': 20}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.033333</td>\n",
       "      <td>{'n_neighbors': 21}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.033333</td>\n",
       "      <td>{'n_neighbors': 22}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 23}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.960000</td>\n",
       "      <td>0.044222</td>\n",
       "      <td>{'n_neighbors': 24}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.033333</td>\n",
       "      <td>{'n_neighbors': 25}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.960000</td>\n",
       "      <td>0.044222</td>\n",
       "      <td>{'n_neighbors': 26}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 27}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.953333</td>\n",
       "      <td>0.042687</td>\n",
       "      <td>{'n_neighbors': 28}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.953333</td>\n",
       "      <td>0.042687</td>\n",
       "      <td>{'n_neighbors': 29}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.953333</td>\n",
       "      <td>0.042687</td>\n",
       "      <td>{'n_neighbors': 30}</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mean_test_score  std_test_score               params\n",
       "0          0.960000        0.053333   {'n_neighbors': 1}\n",
       "1          0.953333        0.052068   {'n_neighbors': 2}\n",
       "2          0.966667        0.044721   {'n_neighbors': 3}\n",
       "3          0.966667        0.044721   {'n_neighbors': 4}\n",
       "4          0.966667        0.044721   {'n_neighbors': 5}\n",
       "5          0.966667        0.044721   {'n_neighbors': 6}\n",
       "6          0.966667        0.044721   {'n_neighbors': 7}\n",
       "7          0.966667        0.044721   {'n_neighbors': 8}\n",
       "8          0.973333        0.032660   {'n_neighbors': 9}\n",
       "9          0.966667        0.044721  {'n_neighbors': 10}\n",
       "10         0.966667        0.044721  {'n_neighbors': 11}\n",
       "11         0.973333        0.032660  {'n_neighbors': 12}\n",
       "12         0.980000        0.030551  {'n_neighbors': 13}\n",
       "13         0.973333        0.044222  {'n_neighbors': 14}\n",
       "14         0.973333        0.032660  {'n_neighbors': 15}\n",
       "15         0.973333        0.032660  {'n_neighbors': 16}\n",
       "16         0.973333        0.032660  {'n_neighbors': 17}\n",
       "17         0.980000        0.030551  {'n_neighbors': 18}\n",
       "18         0.973333        0.032660  {'n_neighbors': 19}\n",
       "19         0.980000        0.030551  {'n_neighbors': 20}\n",
       "20         0.966667        0.033333  {'n_neighbors': 21}\n",
       "21         0.966667        0.033333  {'n_neighbors': 22}\n",
       "22         0.973333        0.032660  {'n_neighbors': 23}\n",
       "23         0.960000        0.044222  {'n_neighbors': 24}\n",
       "24         0.966667        0.033333  {'n_neighbors': 25}\n",
       "25         0.960000        0.044222  {'n_neighbors': 26}\n",
       "26         0.966667        0.044721  {'n_neighbors': 27}\n",
       "27         0.953333        0.042687  {'n_neighbors': 28}\n",
       "28         0.953333        0.042687  {'n_neighbors': 29}\n",
       "29         0.953333        0.042687  {'n_neighbors': 30}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# view the results as a pandas DataFrame\n",
    "import pandas as pd\n",
    "pd.DataFrame(grid.cv_results_)[['mean_test_score', 'std_test_score', 'params']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'n_neighbors': 1}\n",
      "0.96\n"
     ]
    }
   ],
   "source": [
    "# examine the first result\n",
    "print(grid.cv_results_['params'][0])\n",
    "print(grid.cv_results_['mean_test_score'][0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.96       0.95333333 0.96666667 0.96666667 0.96666667 0.96666667\n",
      " 0.96666667 0.96666667 0.97333333 0.96666667 0.96666667 0.97333333\n",
      " 0.98       0.97333333 0.97333333 0.97333333 0.97333333 0.98\n",
      " 0.97333333 0.98       0.96666667 0.96666667 0.97333333 0.96\n",
      " 0.96666667 0.96       0.96666667 0.95333333 0.95333333 0.95333333]\n"
     ]
    }
   ],
   "source": [
    "# print the array of mean scores only\n",
    "grid_mean_scores = grid.cv_results_['mean_test_score']\n",
    "print(grid_mean_scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Cross-Validated Accuracy')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the results\n",
    "plt.plot(k_range, grid_mean_scores)\n",
    "plt.xlabel('Value of K for KNN')\n",
    "plt.ylabel('Cross-Validated Accuracy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9800000000000001\n",
      "{'n_neighbors': 13}\n",
      "KNeighborsClassifier(n_neighbors=13)\n"
     ]
    }
   ],
   "source": [
    "# examine the best model\n",
    "print(grid.best_score_)\n",
    "print(grid.best_params_)\n",
    "print(grid.best_estimator_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Searching multiple parameters simultaneously"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- **Example:** tuning `max_depth` and `min_samples_leaf` for a `DecisionTreeClassifier`\n",
    "- Could tune parameters **independently**: change `max_depth` while leaving `min_samples_leaf` at its default value, and vice versa\n",
    "- But, best performance might be achieved when **neither parameter** is at its default value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define the parameter values that should be searched\n",
    "k_range = list(range(1, 31))\n",
    "weight_options = ['uniform', 'distance']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'n_neighbors': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], 'weights': ['uniform', 'distance']}\n"
     ]
    }
   ],
   "source": [
    "# create a parameter grid: map the parameter names to the values that should be searched\n",
    "param_grid = dict(n_neighbors=k_range, weights=weight_options)\n",
    "print(param_grid)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv=10, estimator=KNeighborsClassifier(n_neighbors=30),\n",
       "             param_grid={'n_neighbors': [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,\n",
       "                                         13, 14, 15, 16, 17, 18, 19, 20, 21, 22,\n",
       "                                         23, 24, 25, 26, 27, 28, 29, 30],\n",
       "                         'weights': ['uniform', 'distance']},\n",
       "             scoring='accuracy')"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# instantiate and fit the grid\n",
    "grid = GridSearchCV(knn, param_grid, cv=10, scoring='accuracy')\n",
    "grid.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean_test_score</th>\n",
       "      <th>std_test_score</th>\n",
       "      <th>params</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.960000</td>\n",
       "      <td>0.053333</td>\n",
       "      <td>{'n_neighbors': 1, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.960000</td>\n",
       "      <td>0.053333</td>\n",
       "      <td>{'n_neighbors': 1, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.953333</td>\n",
       "      <td>0.052068</td>\n",
       "      <td>{'n_neighbors': 2, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.960000</td>\n",
       "      <td>0.053333</td>\n",
       "      <td>{'n_neighbors': 2, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 3, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 3, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 4, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 4, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 5, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 5, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 6, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 6, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 7, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 7, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 8, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 8, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 9, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 9, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 10, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 10, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 11, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 11, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 12, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.044222</td>\n",
       "      <td>{'n_neighbors': 12, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.980000</td>\n",
       "      <td>0.030551</td>\n",
       "      <td>{'n_neighbors': 13, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 13, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.044222</td>\n",
       "      <td>{'n_neighbors': 14, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 14, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 15, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.980000</td>\n",
       "      <td>0.030551</td>\n",
       "      <td>{'n_neighbors': 15, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 16, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 16, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 17, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>0.980000</td>\n",
       "      <td>0.030551</td>\n",
       "      <td>{'n_neighbors': 17, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>0.980000</td>\n",
       "      <td>0.030551</td>\n",
       "      <td>{'n_neighbors': 18, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 18, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 19, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>0.980000</td>\n",
       "      <td>0.030551</td>\n",
       "      <td>{'n_neighbors': 19, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>0.980000</td>\n",
       "      <td>0.030551</td>\n",
       "      <td>{'n_neighbors': 20, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 20, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.033333</td>\n",
       "      <td>{'n_neighbors': 21, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 21, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.033333</td>\n",
       "      <td>{'n_neighbors': 22, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 22, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 23, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 23, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>0.960000</td>\n",
       "      <td>0.044222</td>\n",
       "      <td>{'n_neighbors': 24, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 24, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.033333</td>\n",
       "      <td>{'n_neighbors': 25, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 25, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>0.960000</td>\n",
       "      <td>0.044222</td>\n",
       "      <td>{'n_neighbors': 26, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 26, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'n_neighbors': 27, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>0.980000</td>\n",
       "      <td>0.030551</td>\n",
       "      <td>{'n_neighbors': 27, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>0.953333</td>\n",
       "      <td>0.042687</td>\n",
       "      <td>{'n_neighbors': 28, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 28, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>0.953333</td>\n",
       "      <td>0.042687</td>\n",
       "      <td>{'n_neighbors': 29, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'n_neighbors': 29, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58</th>\n",
       "      <td>0.953333</td>\n",
       "      <td>0.042687</td>\n",
       "      <td>{'n_neighbors': 30, 'weights': 'uniform'}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>59</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.033333</td>\n",
       "      <td>{'n_neighbors': 30, 'weights': 'distance'}</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mean_test_score  std_test_score  \\\n",
       "0          0.960000        0.053333   \n",
       "1          0.960000        0.053333   \n",
       "2          0.953333        0.052068   \n",
       "3          0.960000        0.053333   \n",
       "4          0.966667        0.044721   \n",
       "5          0.966667        0.044721   \n",
       "6          0.966667        0.044721   \n",
       "7          0.966667        0.044721   \n",
       "8          0.966667        0.044721   \n",
       "9          0.966667        0.044721   \n",
       "10         0.966667        0.044721   \n",
       "11         0.966667        0.044721   \n",
       "12         0.966667        0.044721   \n",
       "13         0.966667        0.044721   \n",
       "14         0.966667        0.044721   \n",
       "15         0.966667        0.044721   \n",
       "16         0.973333        0.032660   \n",
       "17         0.973333        0.032660   \n",
       "18         0.966667        0.044721   \n",
       "19         0.973333        0.032660   \n",
       "20         0.966667        0.044721   \n",
       "21         0.973333        0.032660   \n",
       "22         0.973333        0.032660   \n",
       "23         0.973333        0.044222   \n",
       "24         0.980000        0.030551   \n",
       "25         0.973333        0.032660   \n",
       "26         0.973333        0.044222   \n",
       "27         0.973333        0.032660   \n",
       "28         0.973333        0.032660   \n",
       "29         0.980000        0.030551   \n",
       "30         0.973333        0.032660   \n",
       "31         0.973333        0.032660   \n",
       "32         0.973333        0.032660   \n",
       "33         0.980000        0.030551   \n",
       "34         0.980000        0.030551   \n",
       "35         0.973333        0.032660   \n",
       "36         0.973333        0.032660   \n",
       "37         0.980000        0.030551   \n",
       "38         0.980000        0.030551   \n",
       "39         0.966667        0.044721   \n",
       "40         0.966667        0.033333   \n",
       "41         0.966667        0.044721   \n",
       "42         0.966667        0.033333   \n",
       "43         0.966667        0.044721   \n",
       "44         0.973333        0.032660   \n",
       "45         0.973333        0.032660   \n",
       "46         0.960000        0.044222   \n",
       "47         0.973333        0.032660   \n",
       "48         0.966667        0.033333   \n",
       "49         0.973333        0.032660   \n",
       "50         0.960000        0.044222   \n",
       "51         0.966667        0.044721   \n",
       "52         0.966667        0.044721   \n",
       "53         0.980000        0.030551   \n",
       "54         0.953333        0.042687   \n",
       "55         0.973333        0.032660   \n",
       "56         0.953333        0.042687   \n",
       "57         0.973333        0.032660   \n",
       "58         0.953333        0.042687   \n",
       "59         0.966667        0.033333   \n",
       "\n",
       "                                        params  \n",
       "0     {'n_neighbors': 1, 'weights': 'uniform'}  \n",
       "1    {'n_neighbors': 1, 'weights': 'distance'}  \n",
       "2     {'n_neighbors': 2, 'weights': 'uniform'}  \n",
       "3    {'n_neighbors': 2, 'weights': 'distance'}  \n",
       "4     {'n_neighbors': 3, 'weights': 'uniform'}  \n",
       "5    {'n_neighbors': 3, 'weights': 'distance'}  \n",
       "6     {'n_neighbors': 4, 'weights': 'uniform'}  \n",
       "7    {'n_neighbors': 4, 'weights': 'distance'}  \n",
       "8     {'n_neighbors': 5, 'weights': 'uniform'}  \n",
       "9    {'n_neighbors': 5, 'weights': 'distance'}  \n",
       "10    {'n_neighbors': 6, 'weights': 'uniform'}  \n",
       "11   {'n_neighbors': 6, 'weights': 'distance'}  \n",
       "12    {'n_neighbors': 7, 'weights': 'uniform'}  \n",
       "13   {'n_neighbors': 7, 'weights': 'distance'}  \n",
       "14    {'n_neighbors': 8, 'weights': 'uniform'}  \n",
       "15   {'n_neighbors': 8, 'weights': 'distance'}  \n",
       "16    {'n_neighbors': 9, 'weights': 'uniform'}  \n",
       "17   {'n_neighbors': 9, 'weights': 'distance'}  \n",
       "18   {'n_neighbors': 10, 'weights': 'uniform'}  \n",
       "19  {'n_neighbors': 10, 'weights': 'distance'}  \n",
       "20   {'n_neighbors': 11, 'weights': 'uniform'}  \n",
       "21  {'n_neighbors': 11, 'weights': 'distance'}  \n",
       "22   {'n_neighbors': 12, 'weights': 'uniform'}  \n",
       "23  {'n_neighbors': 12, 'weights': 'distance'}  \n",
       "24   {'n_neighbors': 13, 'weights': 'uniform'}  \n",
       "25  {'n_neighbors': 13, 'weights': 'distance'}  \n",
       "26   {'n_neighbors': 14, 'weights': 'uniform'}  \n",
       "27  {'n_neighbors': 14, 'weights': 'distance'}  \n",
       "28   {'n_neighbors': 15, 'weights': 'uniform'}  \n",
       "29  {'n_neighbors': 15, 'weights': 'distance'}  \n",
       "30   {'n_neighbors': 16, 'weights': 'uniform'}  \n",
       "31  {'n_neighbors': 16, 'weights': 'distance'}  \n",
       "32   {'n_neighbors': 17, 'weights': 'uniform'}  \n",
       "33  {'n_neighbors': 17, 'weights': 'distance'}  \n",
       "34   {'n_neighbors': 18, 'weights': 'uniform'}  \n",
       "35  {'n_neighbors': 18, 'weights': 'distance'}  \n",
       "36   {'n_neighbors': 19, 'weights': 'uniform'}  \n",
       "37  {'n_neighbors': 19, 'weights': 'distance'}  \n",
       "38   {'n_neighbors': 20, 'weights': 'uniform'}  \n",
       "39  {'n_neighbors': 20, 'weights': 'distance'}  \n",
       "40   {'n_neighbors': 21, 'weights': 'uniform'}  \n",
       "41  {'n_neighbors': 21, 'weights': 'distance'}  \n",
       "42   {'n_neighbors': 22, 'weights': 'uniform'}  \n",
       "43  {'n_neighbors': 22, 'weights': 'distance'}  \n",
       "44   {'n_neighbors': 23, 'weights': 'uniform'}  \n",
       "45  {'n_neighbors': 23, 'weights': 'distance'}  \n",
       "46   {'n_neighbors': 24, 'weights': 'uniform'}  \n",
       "47  {'n_neighbors': 24, 'weights': 'distance'}  \n",
       "48   {'n_neighbors': 25, 'weights': 'uniform'}  \n",
       "49  {'n_neighbors': 25, 'weights': 'distance'}  \n",
       "50   {'n_neighbors': 26, 'weights': 'uniform'}  \n",
       "51  {'n_neighbors': 26, 'weights': 'distance'}  \n",
       "52   {'n_neighbors': 27, 'weights': 'uniform'}  \n",
       "53  {'n_neighbors': 27, 'weights': 'distance'}  \n",
       "54   {'n_neighbors': 28, 'weights': 'uniform'}  \n",
       "55  {'n_neighbors': 28, 'weights': 'distance'}  \n",
       "56   {'n_neighbors': 29, 'weights': 'uniform'}  \n",
       "57  {'n_neighbors': 29, 'weights': 'distance'}  \n",
       "58   {'n_neighbors': 30, 'weights': 'uniform'}  \n",
       "59  {'n_neighbors': 30, 'weights': 'distance'}  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# view the results\n",
    "pd.DataFrame(grid.cv_results_)[['mean_test_score', 'std_test_score', 'params']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9800000000000001\n",
      "{'n_neighbors': 13, 'weights': 'uniform'}\n"
     ]
    }
   ],
   "source": [
    "# examine the best model\n",
    "print(grid.best_score_)\n",
    "print(grid.best_params_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using the best parameters to make predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# train your model using all data and the best known parameters\n",
    "knn = KNeighborsClassifier(n_neighbors=13, weights='uniform')\n",
    "knn.fit(X, y)\n",
    "\n",
    "# make a prediction on out-of-sample data\n",
    "knn.predict([[3, 5, 4, 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# shortcut: GridSearchCV automatically refits the best model using all of the data\n",
    "grid.predict([[3, 5, 4, 2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reducing computational expense using `RandomizedSearchCV`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Searching many different parameters at once may be computationally infeasible\n",
    "- `RandomizedSearchCV` searches a subset of the parameters, and you control the computational \"budget\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import RandomizedSearchCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# specify \"parameter distributions\" rather than a \"parameter grid\"\n",
    "param_dist = dict(n_neighbors=k_range, weights=weight_options)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- **Important:** Specify a continuous distribution (rather than a list of values) for any continous parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean_test_score</th>\n",
       "      <th>std_test_score</th>\n",
       "      <th>params</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'weights': 'distance', 'n_neighbors': 16}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.033333</td>\n",
       "      <td>{'weights': 'uniform', 'n_neighbors': 22}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.980000</td>\n",
       "      <td>0.030551</td>\n",
       "      <td>{'weights': 'uniform', 'n_neighbors': 18}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'weights': 'uniform', 'n_neighbors': 27}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.953333</td>\n",
       "      <td>0.042687</td>\n",
       "      <td>{'weights': 'uniform', 'n_neighbors': 29}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'weights': 'distance', 'n_neighbors': 10}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.966667</td>\n",
       "      <td>0.044721</td>\n",
       "      <td>{'weights': 'distance', 'n_neighbors': 22}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.044222</td>\n",
       "      <td>{'weights': 'uniform', 'n_neighbors': 14}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.044222</td>\n",
       "      <td>{'weights': 'distance', 'n_neighbors': 12}</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.973333</td>\n",
       "      <td>0.032660</td>\n",
       "      <td>{'weights': 'uniform', 'n_neighbors': 15}</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   mean_test_score  std_test_score                                      params\n",
       "0         0.973333        0.032660  {'weights': 'distance', 'n_neighbors': 16}\n",
       "1         0.966667        0.033333   {'weights': 'uniform', 'n_neighbors': 22}\n",
       "2         0.980000        0.030551   {'weights': 'uniform', 'n_neighbors': 18}\n",
       "3         0.966667        0.044721   {'weights': 'uniform', 'n_neighbors': 27}\n",
       "4         0.953333        0.042687   {'weights': 'uniform', 'n_neighbors': 29}\n",
       "5         0.973333        0.032660  {'weights': 'distance', 'n_neighbors': 10}\n",
       "6         0.966667        0.044721  {'weights': 'distance', 'n_neighbors': 22}\n",
       "7         0.973333        0.044222   {'weights': 'uniform', 'n_neighbors': 14}\n",
       "8         0.973333        0.044222  {'weights': 'distance', 'n_neighbors': 12}\n",
       "9         0.973333        0.032660   {'weights': 'uniform', 'n_neighbors': 15}"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# n_iter controls the number of searches\n",
    "rand = RandomizedSearchCV(knn, param_dist, cv=10, scoring='accuracy', n_iter=10, random_state=5)\n",
    "rand.fit(X, y)\n",
    "pd.DataFrame(rand.cv_results_)[['mean_test_score', 'std_test_score', 'params']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9800000000000001\n",
      "{'weights': 'uniform', 'n_neighbors': 18}\n"
     ]
    }
   ],
   "source": [
    "# examine the best model\n",
    "print(rand.best_score_)\n",
    "print(rand.best_params_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.98, 0.98, 0.98, 0.98, 0.973, 0.98, 0.973, 0.98, 0.98, 0.98, 0.973, 0.98, 0.98, 0.973, 0.973, 0.98, 0.98, 0.973, 0.973, 0.98]\n"
     ]
    }
   ],
   "source": [
    "# run RandomizedSearchCV 20 times (with n_iter=10) and record the best score\n",
    "best_scores = []\n",
    "for _ in range(20):\n",
    "    rand = RandomizedSearchCV(knn, param_dist, cv=10, scoring='accuracy', n_iter=10)\n",
    "    rand.fit(X, y)\n",
    "    best_scores.append(round(rand.best_score_, 3))\n",
    "print(best_scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Resources\n",
    "\n",
    "- scikit-learn documentation: [Grid search](https://scikit-learn.org/stable/modules/grid_search.html), [GridSearchCV](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html), [RandomizedSearchCV](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.RandomizedSearchCV.html)\n",
    "- Timed example: [Comparing randomized search and grid search](https://scikit-learn.org/stable/auto_examples/model_selection/plot_randomized_search.html)\n",
    "- scikit-learn workshop by Andreas Mueller: [Video segment on randomized search](https://youtu.be/0wUF_Ov8b0A?t=17m38s) (3 minutes), [related notebook](https://github.com/amueller/pydata-nyc-advanced-sklearn/blob/master/Chapter%203%20-%20Randomized%20Hyper%20Parameter%20Search.ipynb)\n",
    "- Paper by Yoshua Bengio: [Random Search for Hyper-Parameter Optimization](http://www.jmlr.org/papers/volume13/bergstra12a/bergstra12a.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comments or Questions?\n",
    "\n",
    "- Email: <kevin@dataschool.io>\n",
    "- Website: https://www.dataschool.io\n",
    "- Twitter: [@justmarkham](https://twitter.com/justmarkham)\n",
    "\n",
    "© 2021 [Data School](https://www.dataschool.io). All rights reserved."
   ]
  }
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