KNN_Tuning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a445c04b",
   "metadata": {},
   "source": [
    "## Selecting $k$ for $k$-NN regression\n",
    "\n",
    "**(A crash course in hyperparameter tuning)**\n",
    "\n",
    "In this notebook we will show you a method for selecting the number of neighbors, $k$, to be used in the $k$-NN regression problem. This is an introduction to the broader topic of **hyperparameter tuning** in machine learning algorithms. \n",
    "\n",
    "$k$ is, as we say, a ***hyperparameter*** of the algorithm. A hyperparameter is a parameter (sorry, it is a confusing name) of the model/algorithm that cannot be learned from the data during training, and has to be externally set by us (or chatGPT). This, as we are going to see, does not mean that we do not have ways to set the best hyperparameters, just that they are not automatically being learned during the training of an ML model. \n",
    "\n",
    "This is in contrast to the **parameters** (usually weights) that are being learned during training. In fact, $k$-NN **does not** have any trainable parameters. As we say, it is a *lazy learner*. It also has only one hyperparameter, $k$.\n",
    "\n",
    "To make the distinction between **hyperparameters** and **parameters** more clear, consider a polynomial regression of the form:\n",
    "\n",
    "\\begin{equation}\n",
    "y = \\beta_0 + \\beta_1 x + \\beta_2 x^2 + \\dots + \\beta_n x^n\n",
    "\\end{equation}\n",
    "\n",
    "In this case the **hyperparameter** is the order of the polynomial to be used, $n$, (which we set before learning) while the model **parameters** are the coefficients $\\beta$, that are being learned during training.\n",
    "\n",
    "More complex ML algorithms that you are going to meet in the future have more than one hyperparameters, and finding the best value to use may be quite challenging/computationally expensive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b87f3644",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load python packages\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba0cc37a",
   "metadata": {},
   "source": [
    "Load the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8b8485b4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>TV</th>\n",
       "      <th>radio</th>\n",
       "      <th>newspaper</th>\n",
       "      <th>sales</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>230.1</td>\n",
       "      <td>37.8</td>\n",
       "      <td>69.2</td>\n",
       "      <td>22.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>44.5</td>\n",
       "      <td>39.3</td>\n",
       "      <td>45.1</td>\n",
       "      <td>10.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>17.2</td>\n",
       "      <td>45.9</td>\n",
       "      <td>69.3</td>\n",
       "      <td>9.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>151.5</td>\n",
       "      <td>41.3</td>\n",
       "      <td>58.5</td>\n",
       "      <td>18.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>180.8</td>\n",
       "      <td>10.8</td>\n",
       "      <td>58.4</td>\n",
       "      <td>12.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0     TV  radio  newspaper  sales\n",
       "0           1  230.1   37.8       69.2   22.1\n",
       "1           2   44.5   39.3       45.1   10.4\n",
       "2           3   17.2   45.9       69.3    9.3\n",
       "3           4  151.5   41.3       58.5   18.5\n",
       "4           5  180.8   10.8       58.4   12.9"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(\"Advertising.csv\")\n",
    "\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1d1ce9a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 468x468 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Dependent variable: sales\n",
    "# Independent variable: TV units\n",
    "x = data['TV'].values\n",
    "y = data['sales'].values\n",
    "\n",
    "\n",
    "# Make plot\n",
    "plt.figure(figsize=(6.5, 6.5))\n",
    "\n",
    "plt.scatter(x,y,s=15,color='mediumblue')\n",
    "plt.xlabel('TV kUnits',fontsize=20)\n",
    "plt.ylabel('Sales (k$)',fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "250710e0",
   "metadata": {},
   "source": [
    "#### Split into training-validation-test sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "35d053a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train = x[:100];y_train = y[:100] #Training set\n",
    "x_val = x[100:160];y_val = y[100:160] #Validation set\n",
    "x_test = x[160:];y_test = y[160:] #Test set"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4e00c8c",
   "metadata": {},
   "source": [
    "Note that the dataset is quite small and thus, generally, our results may not be that robust.\n",
    "For small datasets, instead of using a separate validation set for hyperparameter tuning, we can use the **cross validation** method that you are going to see in a future lecture."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a5ead3a",
   "metadata": {},
   "source": [
    "We want to make sure that the examples(=datapoints) are **randomly distributed among the three sets**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "ffffabb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 468x468 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make plot\n",
    "plt.figure(figsize=(6.5, 6.5))\n",
    "\n",
    "plt.scatter(x_train,y_train,s=15,color='mediumblue',label='Train')\n",
    "plt.scatter(x_val,y_val,s=15,color='orange',label='Validation')\n",
    "plt.scatter(x_test,y_test,s=15,color='red',label='Test')\n",
    "\n",
    "plt.xlabel('TV kUnits',fontsize=20)\n",
    "plt.ylabel('Sales (k$)',fontsize=20)\n",
    "plt.legend(frameon=True, loc='lower right', fontsize=17)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8c277ba",
   "metadata": {},
   "source": [
    "## $k$-NN function\n",
    "\n",
    "Here we have a function that implements $k$-NN for regression from scratch.\n",
    "`scikit-learn` has a function called `sklearn.neighbors.KNeighborsRegressor` that can perform this regression, but for a simple algorithm like this, we can easily write our own function.\n",
    "\n",
    "Specifically, it accepts a training set of points (features and labels) and a set of points whose $y$ values we want to predict. It also works for different $k$ values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "7805ed30",
   "metadata": {},
   "outputs": [],
   "source": [
    "def knn_regression(X_train, y_train, X_test, k):\n",
    "    \"\"\"\n",
    "    Perform kNN regression in one dimension.\n",
    "    \n",
    "    Parameters:\n",
    "        - X_train: array-like, training data points\n",
    "        - y_train: array-like, target values for training data points\n",
    "        - X_test: array-like, test data points\n",
    "        - k: int, number of nearest neighbors to consider\n",
    "        \n",
    "    Returns:\n",
    "        - y_pred: array-like, predicted target values for test data points\n",
    "    \"\"\"\n",
    "    # calculate distances between test points and training points\n",
    "    distances = np.abs(X_train - X_test[:, np.newaxis])\n",
    "    # find k nearest neighbors for each test point\n",
    "    k_nearest_indices = np.argpartition(distances, k, axis=1)[:, :k]\n",
    "    # predict the target value for each test point as the average of the target values of its k nearest neighbors\n",
    "    y_pred = np.mean(y_train[k_nearest_indices], axis=1)\n",
    "    return y_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "159dd7ad",
   "metadata": {},
   "source": [
    "Fun fact: **The above code was actually written by ChatGPT!!**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa9f8d15",
   "metadata": {},
   "source": [
    "### Select best $k$\n",
    "\n",
    "We are going to select the best $k$ (number of neighbors) value to use based on the performance of $k$-NN trained on the training set and evaluated on the validation set, for different values of $k$.\n",
    "\n",
    "How are we going to evaluate the performance? \n",
    "\n",
    "We can estimate the *mean absolute error* (note: there are other options, too, like the mean squared error, root mean squared error etc):\n",
    "\n",
    "\\begin{equation}\n",
    "\\mbox{MAE} = \\frac{1}{n}\\sum_i^n |\\hat{y}_i - y_i|,\n",
    "\\end{equation}\n",
    "\n",
    "where $\\hat{y}$ the predicted and $y$ the true value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "d83949b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def MAE(y_pred,y_true):\n",
    "    \"\"\"Function that gets the true and predicted y values and\n",
    "    returns the Mean Absolute Error\n",
    "    \"\"\"\n",
    "    return np.mean(np.abs(y_pred-y_true))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bbc7734d",
   "metadata": {},
   "source": [
    "Note: The above function was **not** written by ChatGPT!!!\n",
    "\n",
    "\n",
    "Now we run $k$-NN for $k$ in the range [1-10] (since our training set is equal to 100 it does not make much sense to go to a very large number of k)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "24429c0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "MAEs = np.zeros(10)\n",
    "\n",
    "# k=11 is not included\n",
    "for k in range(1,11):\n",
    "    \n",
    "    # Get predictions for current k \n",
    "    # Predictions are on the **validation** set\n",
    "    y_pred_k = knn_regression(x_train,y_train,x_val,k)\n",
    "    \n",
    "    # calculate MAE and store it\n",
    "    # Note we use k-1 as index here for MAE\n",
    "    MAEs[k-1] = MAE(y_pred_k,y_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "61526b33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x468 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define an array of k values to be used on the x axis\n",
    "ks = np.arange(1,11)\n",
    "\n",
    "\n",
    "# Make plot\n",
    "plt.figure(figsize=(8, 6.5))\n",
    "\n",
    "plt.scatter(ks,MAEs,s=40,color='mediumblue')\n",
    "plt.plot(ks,MAEs,c='mediumblue')\n",
    "plt.grid(ls='--')\n",
    "plt.title('MAE as a function of $k$',fontsize=15)\n",
    "plt.xlabel(r'$k$', fontsize=20)\n",
    "plt.ylabel('MAE', fontsize=20)\n",
    "plt.xticks(ks)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa5ea159",
   "metadata": {},
   "source": [
    "Beautiful, isn't it?? We can clearly see that the optimal $k$, that minimizes the MAE is $k=3$, that gives a MAE a little bit less than $2.6$.\n",
    "\n",
    "Ok, as we said, it does not make much sense to consider $k>10$ for a training dataset of 100 points (notice: on the other hand, if our training set was really large, probably, a much larger number of neighbors could probably make **a lot** of sense - always get a feeling of your data). But how the plot would look like if we considered up to 80 nearest neighbors? Let's check, just for fun!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "8008b20b",
   "metadata": {},
   "outputs": [],
   "source": [
    "MAEs = np.zeros(80)\n",
    "\n",
    "# k=11 is not included\n",
    "for k in range(1,81):\n",
    "    \n",
    "    # Get predictions for current k \n",
    "    # Predictions are on the **validation** set\n",
    "    y_pred_k = knn_regression(x_train,y_train,x_val,k)\n",
    "    \n",
    "    # calculate MAE and store it\n",
    "    # Note we use k-1 as index here for MAE\n",
    "    MAEs[k-1] = MAE(y_pred_k,y_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "c1919438",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x468 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define an array of k values to be used on the x axis\n",
    "ks = np.arange(1,81)\n",
    "\n",
    "\n",
    "# Make plot\n",
    "plt.figure(figsize=(8, 6.5))\n",
    "\n",
    "plt.scatter(ks,MAEs,s=40,color='mediumblue')\n",
    "plt.plot(ks,MAEs,c='mediumblue')\n",
    "plt.grid(ls='--')\n",
    "plt.title('MAE as a function of $k$',fontsize=15)\n",
    "plt.xlabel(r'$k$', fontsize=20)\n",
    "plt.ylabel('MAE', fontsize=20)\n",
    "#plt.xticks(ks)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f39e1883",
   "metadata": {},
   "source": [
    "What do we have here? A nice illustration of the **Bias-Variance trade-off**!!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a05e95f",
   "metadata": {},
   "source": [
    "### Evaluate on the test set\n",
    "\n",
    "Now that we have selected the optimal value of $k$ ($k=3$), the final step is to train the algorithm for that value of $k$ and evaluate on the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "e564c9c0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE on the test set: 3.3841666666666668\n"
     ]
    }
   ],
   "source": [
    "# predict values on the test set for k=3 \n",
    "y_preds = knn_regression(x_train,y_train,x_test,3)\n",
    "\n",
    "# Estimate MAE\n",
    "MAE_test = MAE(y_preds,y_test)\n",
    "\n",
    "# Print\n",
    "print('MAE on the test set:', MAE_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "473de70e",
   "metadata": {},
   "source": [
    "Question: Why is this value so different than what we had on the test set? Can we do anything about that? \n",
    "\n",
    "Try to split the dataset differently, use other metrics (like RMSE), other datasets... Also check the resampling methods in a future lecture...."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "73dcaac8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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