Module6_Lab2_FMML20210660.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Module6_Lab2_FMML20210611.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/SreenadhSingamaneni/IIITH-FMML20210660/blob/main/Module6_Lab2_FMML20210660.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q_TjX0v1Upyt"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "plt.style.use('ggplot')\n",
        "\n",
        "# interactive visualization"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H-Cp5UaReiof"
      },
      "source": [
        "#Regression Lab 2: Loss Functions\n",
        "\n",
        "![image.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "```\n",
        "Module Coordinator : Pranav Tadimeti\n",
        "```\n"
      ],
      "metadata": {
        "id": "TSBLUen_aWef"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rbxg8WQcetL2"
      },
      "source": [
        "## Motivation\n",
        "\n",
        "The main goal of machine learning tasks is to \"learn\" something about data we feed to our models. But how does the model actually learn anything? To understand this, we need to first understand what objective functions are.\n",
        "\n",
        "Mathematically, objective functions are a function whose values we desire to minimize/maximize. In the context of machine learning, the objective is commonly referred to as a **loss function**. Loss functions indicate how well the model is doing on the dataset. \n",
        "\n",
        "The value of the objective function is simply called **loss**. Our goal is to eventually find the best model parameters that has the least average loss on the data after training.\n",
        "\n",
        "\n",
        "We are familiar with the idea of **error** from the linear regression lab. RMSE is a common loss function used in machine learning. However, there are many other loss functions employed, depending on what the task is (classification, regression etc.). In this lab, we will take a look at some common loss functions, and understand why they are used where they are.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o9lGgMhd9hAX"
      },
      "source": [
        "# 1. Regression\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "f9qiER5ef8Sh",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "13f75a19-a1b2-462b-efef-dff40161442a"
      },
      "source": [
        "# initializing random data\n",
        "\n",
        "np.random.seed(0)\n",
        "x = np.linspace(0,100,100)\n",
        "y_actual = np.copy(x)\n",
        "y_pred = x + np.random.randint(-10,10,100)\n",
        "\n",
        "plt.plot(x,y_actual,color=\"red\")\n",
        "plt.scatter(x,y_pred,color=\"blue\")\n",
        "plt.show()"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JAOKu9cGhf7t"
      },
      "source": [
        "### Mean Squared Error\n",
        "\n",
        "As we have seen before, the formula for MSE is \n",
        "\n",
        "$MSE = \\frac{1}{m} \\sum_{i=1}^n (y-y_p)^2$\n",
        "\n",
        "The image below depicts a visualization of what the squared error is. \n",
        "\n",
        "<img src=\"https://drive.google.com/uc?export=view&id=12jmqRrrqknIWKhwRpgRIJAErBjkEcyx9\" width=\"350\" height=\"350\" align=\"middle\"/>\n",
        "\n",
        "MSE is also referred to as L2 loss.\n",
        "\n",
        "Typically, we would want the units of error to be the same as the data, so we use Root Mean Squared Error instead.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "y0KIs1xP2AbG",
        "outputId": "91ba0229-0a8e-4d64-8877-3a247be9c9b9"
      },
      "source": [
        "mse = np.mean((y_actual-y_pred)**2)\n",
        "print(\"MSE is: {}\".format(mse))\n",
        "print(\"RMSE is: {}\".format(np.sqrt(mse)))"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MSE is: 38.68\n",
            "RMSE is: 6.219324722186485\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "05Gx5pbfhk3P"
      },
      "source": [
        "### Mean Absolute Error\n",
        "\n",
        "$MAE = \\frac{1}{m} \\sum_{i=1}^n |y-y_p|$\n",
        "\n",
        "MAE is also commonly referred to as L1 loss."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PfqvIN2ThjWO",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9ba78eb1-96dc-416a-9c9d-d55e914549a0"
      },
      "source": [
        "mae = np.mean(np.abs(y_actual-y_pred))\n",
        "print(\"MAE is: {}\".format(mae))"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MAE is: 5.5\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4j7VlwmH4WVU"
      },
      "source": [
        "MSE penalizes the model for making large errors by squaring the difference. However, this also means that MSE cannot handle outliers well, since they would throw the model off.\n",
        "\n",
        "On the other hand, MAE is robust to outliers. But, MAE is non-differentiable, making it difficult to perform mathematical operations on it.\n",
        "\n",
        "Hence, RMSE is most commonly used as a metric for evaluation."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "buXwWqWjhT_9"
      },
      "source": [
        "# 2. Classification\n",
        "\n",
        "Classification tasks involve some data, along with labels assigned to that data. For example, we may have pictures of cats and dogs, and the corresponding labels assigned to those images. We then want to train a model that can predict a label for some input image belonging to either label class (cat or dog)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qiJUcm4vhthC"
      },
      "source": [
        "## The concept of maximum likelihood\n",
        "\n",
        "Ideally, we would want to obtain a model $\\hat{\\theta}$ which maximizes the probability of correctly predicting data. Mathematically, the likelihood is:\n",
        "\n",
        "$ \\prod_{i=1}^{N}  \\: \\hat{\\theta_i}^{\\theta_i}$\n",
        "\n",
        "This is because our actual data ($\\theta_i$) is either 0 or 1 depending on the label of the data, and our predicted data ($\\hat{\\theta_i}$) is a probability. \n",
        "\n",
        "We usually consider the negative log of the likelihood, since log is monotonic and easier to deal with as an optimization problem.\n",
        "\n",
        "Hence, we have\n",
        "\n",
        "$MLE = $ arg min $\\: - \\sum_{i=1}^{N} \\theta_i \\: log \\: \\hat{\\theta_i}$\n",
        "\n",
        "\\\n",
        "\n",
        "\n",
        "## Entropy and Cross-Entropy\n",
        "\n",
        "For some event $x$, we can obtain **information** based on its probability distribution. For example, for some event that occurs with $p=1$, we gain no information. Now, if we flip a coin and see that we obtained heads, we say that we got 1 bit of information. \n",
        "\n",
        "Thus, the information $I$ of some event $x$ is:\n",
        "\n",
        "$I = -log_2 \\: p(x)$\n",
        "\n",
        "We say that events with a low probability of occuring give high information, and those with a low probability give low information.\n",
        "\n",
        "Now, if we have some random variable $X$, its **entropy** is the expected value of the information obtained.\n",
        "\n",
        "$H(x) = - \\sum_{k} p_k \\: log \\: p_k$\n",
        "\n",
        "Now, suppose we are trying to correctly predict labels of some data. Let P be the true distribution of the labels, and Q be the predicted distribution of labels. \n",
        "\n",
        "Cross-Entropy is then defined as:\n",
        "\n",
        "$H(P,Q) = - \\sum_{x} P(x)\\: log \\: Q(x)$\n",
        "\n",
        "which is basically the entropy between two probability distributions over the same events.\n",
        "\n",
        "\\\n",
        "\n",
        "\n",
        "## MLE and Cross-Entropy\n",
        "\n",
        "So, in the case of classification, the equation for minimization of the cross-entropy between the actual data and the predicted data would be:\n",
        "\n",
        "arg min $\\: -\\sum_{i=1}^{N} P(x) \\: log \\: Q(x)$\n",
        "\n",
        "$= $ arg min $\\: -\\sum_{i=1}^{N} \\theta_i \\: log \\: \\hat{\\theta_i}$\n",
        "\n",
        "\n",
        "which is exactly the same as what we had obtained for minimizing the negative log likelihood. Hence, the two problems are equivalent."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mLKuJyHth5-4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "d98d1295-b44f-454b-a9d9-2c5e434e03b8"
      },
      "source": [
        "def sigmoid(z):\n",
        "  return 1/(1 + np.exp(-z))\n",
        "\n",
        "def cross_entropy_loss(y_,y):\n",
        "  if y==1:\n",
        "    return -np.log(y_)\n",
        "  \n",
        "  return -np.log(1-y_)\n",
        "\n",
        "z = np.arange(-10, 10, 0.1)\n",
        "h_z = sigmoid(z)\n",
        "\n",
        "cost_1 = cross_entropy_loss(h_z, 1)\n",
        "cost_0 = cross_entropy_loss(h_z, 0)\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(8,6))\n",
        "plt.plot(h_z, cost_1, label='y=1')\n",
        "plt.plot(h_z, cost_0, label='y=0')\n",
        "plt.xlabel('predicted probability')\n",
        "plt.ylabel('loss')\n",
        "plt.legend(loc='best')\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## KNN-regression\n",
        "\n",
        "Till now, we have studied KNN as a classification algorithm, which uses feature similarity and voting to decide the class labels of unseen data. \n",
        "\n",
        "For regression, we use the same idea: We take the y-values of the k nearest neighbours, and compute their average, which is our predicted y-value. We do this for every x whose value we want to predict.\n",
        "\n",
        "In the visualization below, we have k=3, and the red dots are the new x-values whose output we want to predict.\n",
        "\n",
        "![image.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "f42L9ZmuWVIQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn import neighbors\n",
        "from sklearn.metrics import mean_squared_error \n",
        "from math import sqrt\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.preprocessing import MinMaxScaler\n",
        "import numpy as np"
      ],
      "metadata": {
        "id": "cQIX2HoAbqqD"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "train_path = \"https://raw.githubusercontent.com/PranavTadimeti/Regression-lab2/main/BigMart-train.csv\"\n",
        "\n",
        "train = pd.read_csv(train_path)"
      ],
      "metadata": {
        "id": "VLMVfcylWlWB"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Preprocess Data\n",
        "\n",
        "def preprocess(df):\n",
        "  mean_weight = df['Item_Weight'].mean()\n",
        "  df['Item_Weight'].fillna(mean_weight,inplace=True)\n",
        "\n",
        "  mode_size = df['Outlet_Size'].mode()\n",
        "  df['Outlet_Size'].fillna(mode_size,inplace=True)\n",
        "\n",
        "  df.drop(['Item_Identifier','Outlet_Identifier'],axis=1,inplace=True)\n",
        "\n",
        "  return pd.get_dummies(df)\n",
        "\n",
        "train = preprocess(train)\n",
        "\n",
        "train.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "bkMzDwYaYTlQ",
        "outputId": "fd8c807a-38d5-4c4e-f7ce-202bcd579530"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   Item_Weight  Item_Visibility  Item_MRP  Outlet_Establishment_Year  \\\n",
              "0         9.30         0.016047  249.8092                       1999   \n",
              "1         5.92         0.019278   48.2692                       2009   \n",
              "2        17.50         0.016760  141.6180                       1999   \n",
              "3        19.20         0.000000  182.0950                       1998   \n",
              "4         8.93         0.000000   53.8614                       1987   \n",
              "\n",
              "   Item_Outlet_Sales  Item_Fat_Content_LF  Item_Fat_Content_Low Fat  \\\n",
              "0          3735.1380                    0                         1   \n",
              "1           443.4228                    0                         0   \n",
              "2          2097.2700                    0                         1   \n",
              "3           732.3800                    0                         0   \n",
              "4           994.7052                    0                         1   \n",
              "\n",
              "   Item_Fat_Content_Regular  Item_Fat_Content_low fat  Item_Fat_Content_reg  \\\n",
              "0                         0                         0                     0   \n",
              "1                         1                         0                     0   \n",
              "2                         0                         0                     0   \n",
              "3                         1                         0                     0   \n",
              "4                         0                         0                     0   \n",
              "\n",
              "   ...  Outlet_Size_High  Outlet_Size_Medium  Outlet_Size_Small  \\\n",
              "0  ...                 0                   1                  0   \n",
              "1  ...                 0                   1                  0   \n",
              "2  ...                 0                   1                  0   \n",
              "3  ...                 0                   0                  0   \n",
              "4  ...                 1                   0                  0   \n",
              "\n",
              "   Outlet_Location_Type_Tier 1  Outlet_Location_Type_Tier 2  \\\n",
              "0                            1                            0   \n",
              "1                            0                            0   \n",
              "2                            1                            0   \n",
              "3                            0                            0   \n",
              "4                            0                            0   \n",
              "\n",
              "   Outlet_Location_Type_Tier 3  Outlet_Type_Grocery Store  \\\n",
              "0                            0                          0   \n",
              "1                            1                          0   \n",
              "2                            0                          0   \n",
              "3                            1                          1   \n",
              "4                            1                          0   \n",
              "\n",
              "   Outlet_Type_Supermarket Type1  Outlet_Type_Supermarket Type2  \\\n",
              "0                              1                              0   \n",
              "1                              0                              1   \n",
              "2                              1                              0   \n",
              "3                              0                              0   \n",
              "4                              1                              0   \n",
              "\n",
              "   Outlet_Type_Supermarket Type3  \n",
              "0                              0  \n",
              "1                              0  \n",
              "2                              0  \n",
              "3                              0  \n",
              "4                              0  \n",
              "\n",
              "[5 rows x 36 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-28c082b3-15ac-4988-9bd9-191efbe7bc8d\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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>Item_Weight</th>\n",
              "      <th>Item_Visibility</th>\n",
              "      <th>Item_MRP</th>\n",
              "      <th>Outlet_Establishment_Year</th>\n",
              "      <th>Item_Outlet_Sales</th>\n",
              "      <th>Item_Fat_Content_LF</th>\n",
              "      <th>Item_Fat_Content_Low Fat</th>\n",
              "      <th>Item_Fat_Content_Regular</th>\n",
              "      <th>Item_Fat_Content_low fat</th>\n",
              "      <th>Item_Fat_Content_reg</th>\n",
              "      <th>...</th>\n",
              "      <th>Outlet_Size_High</th>\n",
              "      <th>Outlet_Size_Medium</th>\n",
              "      <th>Outlet_Size_Small</th>\n",
              "      <th>Outlet_Location_Type_Tier 1</th>\n",
              "      <th>Outlet_Location_Type_Tier 2</th>\n",
              "      <th>Outlet_Location_Type_Tier 3</th>\n",
              "      <th>Outlet_Type_Grocery Store</th>\n",
              "      <th>Outlet_Type_Supermarket Type1</th>\n",
              "      <th>Outlet_Type_Supermarket Type2</th>\n",
              "      <th>Outlet_Type_Supermarket Type3</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>9.30</td>\n",
              "      <td>0.016047</td>\n",
              "      <td>249.8092</td>\n",
              "      <td>1999</td>\n",
              "      <td>3735.1380</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>5.92</td>\n",
              "      <td>0.019278</td>\n",
              "      <td>48.2692</td>\n",
              "      <td>2009</td>\n",
              "      <td>443.4228</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>17.50</td>\n",
              "      <td>0.016760</td>\n",
              "      <td>141.6180</td>\n",
              "      <td>1999</td>\n",
              "      <td>2097.2700</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>19.20</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>182.0950</td>\n",
              "      <td>1998</td>\n",
              "      <td>732.3800</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>8.93</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>53.8614</td>\n",
              "      <td>1987</td>\n",
              "      <td>994.7052</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>5 rows × 36 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-28c082b3-15ac-4988-9bd9-191efbe7bc8d')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-28c082b3-15ac-4988-9bd9-191efbe7bc8d button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-28c082b3-15ac-4988-9bd9-191efbe7bc8d');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "train , test = train_test_split(train, test_size = 0.3)\n",
        "\n",
        "x_train = train.drop('Item_Outlet_Sales', axis=1)\n",
        "y_train = train['Item_Outlet_Sales']\n",
        "\n",
        "x_test = test.drop('Item_Outlet_Sales', axis = 1)\n",
        "y_test = test['Item_Outlet_Sales']"
      ],
      "metadata": {
        "id": "JyYJSSj-Z3mT"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "scaler = MinMaxScaler(feature_range=(0, 1))\n",
        "\n",
        "x_train_scaled = scaler.fit_transform(x_train)\n",
        "x_train = pd.DataFrame(x_train_scaled)\n",
        "\n",
        "x_test_scaled = scaler.fit_transform(x_test)\n",
        "x_test = pd.DataFrame(x_test_scaled)"
      ],
      "metadata": {
        "id": "Pp38lIDgZsyn"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def knn_regression(k,x_train,y_train,x_test,y_test):\n",
        "    model = neighbors.KNeighborsRegressor(n_neighbors = k)\n",
        "\n",
        "    model.fit(x_train, y_train)  \n",
        "    pred=model.predict(x_test) \n",
        "    error = sqrt(mean_squared_error(y_test,pred)) \n",
        "    rmse_val.append(error) "
      ],
      "metadata": {
        "id": "XM_GDnVqbVKI"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "rmse_val = [] \n",
        "\n",
        "for k in range(1,21):\n",
        "  knn_regression(k,x_train,y_train,x_test,y_test)\n",
        "\n",
        "figure = plt.figure(figsize=(10,10))\n",
        "plt.plot(np.arange(1,21),rmse_val)\n",
        "plt.xlabel(\"K\")\n",
        "plt.ylabel(\"Loss\")\n",
        "plt.show()\n",
        "\n",
        "rmse_val = np.asarray(rmse_val)\n",
        "print(\"Minimum error {} is at k = {}\".format(np.min(rmse_val),np.argmin(rmse_val)))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "P0rIZOClcKI6",
        "outputId": "1e8e7eae-0cc3-4aa8-f6ba-f3da7bc2ceb5"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Minimum error 1278.5816281094171 is at k = 6\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Exercises\n",
        "\n",
        "1. Try out these loss functions on regression tasks, and try to understand the model performance based on the loss function.\n",
        "2. Explore other loss functions and try to understand when and why they are used.\n",
        "3. Try out KNN-regression on other datasets see which values of K give the best results."
      ],
      "metadata": {
        "id": "0QNjfdMXk2AH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "_SjkEs7p2Mdh"
      },
      "execution_count": 12,
      "outputs": []
    }
  ]
}