wine_quality_ridge_regression.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "jPb--pL1TSxv"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "import seaborn as sns"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "00F1hVpyWYYq"
      },
      "outputs": [],
      "source": [
        "df_wine_quality = pd.read_csv('winequality-red.csv')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "a4dUon4-Z0Nr",
        "outputId": "322c8b1a-b362-4aa7-e4c3-33a4fe34b362"
      },
      "outputs": [
        {
          "data": {
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>fixed acidity</th>\n",
              "      <th>volatile acidity</th>\n",
              "      <th>citric acid</th>\n",
              "      <th>residual sugar</th>\n",
              "      <th>chlorides</th>\n",
              "      <th>free sulfur dioxide</th>\n",
              "      <th>total sulfur dioxide</th>\n",
              "      <th>density</th>\n",
              "      <th>pH</th>\n",
              "      <th>sulphates</th>\n",
              "      <th>alcohol</th>\n",
              "      <th>quality</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>7.4</td>\n",
              "      <td>0.70</td>\n",
              "      <td>0.00</td>\n",
              "      <td>1.9</td>\n",
              "      <td>0.076</td>\n",
              "      <td>11.0</td>\n",
              "      <td>34.0</td>\n",
              "      <td>0.9978</td>\n",
              "      <td>3.51</td>\n",
              "      <td>0.56</td>\n",
              "      <td>9.4</td>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>7.8</td>\n",
              "      <td>0.88</td>\n",
              "      <td>0.00</td>\n",
              "      <td>2.6</td>\n",
              "      <td>0.098</td>\n",
              "      <td>25.0</td>\n",
              "      <td>67.0</td>\n",
              "      <td>0.9968</td>\n",
              "      <td>3.20</td>\n",
              "      <td>0.68</td>\n",
              "      <td>9.8</td>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>7.8</td>\n",
              "      <td>0.76</td>\n",
              "      <td>0.04</td>\n",
              "      <td>2.3</td>\n",
              "      <td>0.092</td>\n",
              "      <td>15.0</td>\n",
              "      <td>54.0</td>\n",
              "      <td>0.9970</td>\n",
              "      <td>3.26</td>\n",
              "      <td>0.65</td>\n",
              "      <td>9.8</td>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>11.2</td>\n",
              "      <td>0.28</td>\n",
              "      <td>0.56</td>\n",
              "      <td>1.9</td>\n",
              "      <td>0.075</td>\n",
              "      <td>17.0</td>\n",
              "      <td>60.0</td>\n",
              "      <td>0.9980</td>\n",
              "      <td>3.16</td>\n",
              "      <td>0.58</td>\n",
              "      <td>9.8</td>\n",
              "      <td>6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>7.4</td>\n",
              "      <td>0.70</td>\n",
              "      <td>0.00</td>\n",
              "      <td>1.9</td>\n",
              "      <td>0.076</td>\n",
              "      <td>11.0</td>\n",
              "      <td>34.0</td>\n",
              "      <td>0.9978</td>\n",
              "      <td>3.51</td>\n",
              "      <td>0.56</td>\n",
              "      <td>9.4</td>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   fixed acidity  volatile acidity  citric acid  residual sugar  chlorides  \\\n",
              "0            7.4              0.70         0.00             1.9      0.076   \n",
              "1            7.8              0.88         0.00             2.6      0.098   \n",
              "2            7.8              0.76         0.04             2.3      0.092   \n",
              "3           11.2              0.28         0.56             1.9      0.075   \n",
              "4            7.4              0.70         0.00             1.9      0.076   \n",
              "\n",
              "   free sulfur dioxide  total sulfur dioxide  density    pH  sulphates  \\\n",
              "0                 11.0                  34.0   0.9978  3.51       0.56   \n",
              "1                 25.0                  67.0   0.9968  3.20       0.68   \n",
              "2                 15.0                  54.0   0.9970  3.26       0.65   \n",
              "3                 17.0                  60.0   0.9980  3.16       0.58   \n",
              "4                 11.0                  34.0   0.9978  3.51       0.56   \n",
              "\n",
              "   alcohol  quality  \n",
              "0      9.4        5  \n",
              "1      9.8        5  \n",
              "2      9.8        5  \n",
              "3      9.8        6  \n",
              "4      9.4        5  "
            ]
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df_wine_quality.head()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "252hDDKeZ23g"
      },
      "outputs": [],
      "source": [
        "dwq_norm = df_wine_quality[[\"volatile acidity\",\"citric acid\", \"alcohol\",\"sulphates\", \"quality\"]].copy()#taking the four features that have highest correlation with the target variable"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "z_nN1F9KaATP",
        "outputId": "d6a60820-3eb7-4ddb-e09e-fde976108434"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df_wine_quality['quality'].min()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "teQpr6X4aCDr"
      },
      "outputs": [],
      "source": [
        "#normalizing the dataframe\n",
        "for col in range(dwq_norm.shape[1]):\n",
        "  for row in range(dwq_norm.shape[0]):\n",
        "    dwq_norm.iloc[row,col] = (dwq_norm.iloc[row,col]-dwq_norm.iloc[:,col].min())/(dwq_norm.iloc[:,col].max()-dwq_norm.iloc[:,col].min())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        },
        "id": "sLAQDQfVaJQT",
        "outputId": "2cc918da-b146-4521-d14f-38b7a1733c92"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
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              "\n",
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              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>volatile acidity</th>\n",
              "      <th>citric acid</th>\n",
              "      <th>alcohol</th>\n",
              "      <th>sulphates</th>\n",
              "      <th>quality</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.397260</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.153846</td>\n",
              "      <td>0.137725</td>\n",
              "      <td>0.400000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.520548</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.654147</td>\n",
              "      <td>0.291190</td>\n",
              "      <td>0.605263</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.438356</td>\n",
              "      <td>0.04</td>\n",
              "      <td>0.654147</td>\n",
              "      <td>0.275080</td>\n",
              "      <td>0.605263</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.109589</td>\n",
              "      <td>0.56</td>\n",
              "      <td>0.654147</td>\n",
              "      <td>0.237492</td>\n",
              "      <td>0.736842</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.401528</td>\n",
              "      <td>0.00</td>\n",
              "      <td>0.627021</td>\n",
              "      <td>0.226752</td>\n",
              "      <td>0.605263</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1594</th>\n",
              "      <td>0.586223</td>\n",
              "      <td>0.08</td>\n",
              "      <td>0.936630</td>\n",
              "      <td>0.516663</td>\n",
              "      <td>0.823256</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1595</th>\n",
              "      <td>0.534501</td>\n",
              "      <td>0.10</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.723808</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1596</th>\n",
              "      <td>0.493123</td>\n",
              "      <td>0.13</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.712300</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1597</th>\n",
              "      <td>0.632773</td>\n",
              "      <td>0.12</td>\n",
              "      <td>0.926241</td>\n",
              "      <td>0.666268</td>\n",
              "      <td>0.823256</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1598</th>\n",
              "      <td>0.286234</td>\n",
              "      <td>0.47</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.608728</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>1599 rows × 5 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "      volatile acidity  citric acid   alcohol  sulphates   quality\n",
              "0             0.397260         0.00  0.153846   0.137725  0.400000\n",
              "1             0.520548         0.00  0.654147   0.291190  0.605263\n",
              "2             0.438356         0.04  0.654147   0.275080  0.605263\n",
              "3             0.109589         0.56  0.654147   0.237492  0.736842\n",
              "4             0.401528         0.00  0.627021   0.226752  0.605263\n",
              "...                ...          ...       ...        ...       ...\n",
              "1594          0.586223         0.08  0.936630   0.516663  0.823256\n",
              "1595          0.534501         0.10  1.000000   0.723808  1.000000\n",
              "1596          0.493123         0.13  1.000000   0.712300  1.000000\n",
              "1597          0.632773         0.12  0.926241   0.666268  0.823256\n",
              "1598          0.286234         0.47  1.000000   0.608728  1.000000\n",
              "\n",
              "[1599 rows x 5 columns]"
            ]
          },
          "execution_count": 7,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "dwq_norm"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "MaBXEDT-aMIK"
      },
      "outputs": [],
      "source": [
        "features = [\"volatile acidity\",\"citric acid\", \"alcohol\",\"sulphates\"]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "tF9FCNFhaPwN"
      },
      "outputs": [],
      "source": [
        "x_df = dwq_norm[features] #taking the x dataframe "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "GAcmQBboaRZZ"
      },
      "outputs": [],
      "source": [
        "y_df = dwq_norm['quality'] #taking the y dataframe"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "KSHO3ZmVaTW5"
      },
      "outputs": [],
      "source": [
        "x_train = np.zeros((int(x_df.shape[0]*0.8),x_df.shape[1]+1)) # making a xtrain matrix from first 80% of X dataframe\n",
        "for i in x_train:\n",
        "  i[0]=1\n",
        "for i in range(x_train.shape[0]):\n",
        "  for j in range(1,x_train.shape[1]):\n",
        "    x_train[i][j]=x_df.iloc[i][j-1]\n",
        "y_train = np.asarray(list(y_df)[0:int(x_df.shape[0]*0.8)]) # making a y list of values from first 80% of Y dataframe"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 28,
      "metadata": {
        "id": "TyIzfBGqaqym"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[0.2, 0. , 0. , 0. , 0. ],\n",
              "       [0. , 0.2, 0. , 0. , 0. ],\n",
              "       [0. , 0. , 0.2, 0. , 0. ],\n",
              "       [0. , 0. , 0. , 0.2, 0. ],\n",
              "       [0. , 0. , 0. , 0. , 0.2]])"
            ]
          },
          "execution_count": 28,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "#np.shape(np.matmul(x_train.T,x_train))\n",
        "lmda = 0.2*np.identity(np.shape(np.matmul(x_train.T,x_train))[0]) #lammda identity matrix\n",
        "lmda\n",
        "#w = np.matmul((np.matmul(np.linalg.inv(np.matmul(x_train.T,x_train)),x_train.T)),y_train)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 29,
      "metadata": {
        "id": "ql06Q1HVbSgd"
      },
      "outputs": [],
      "source": [
        "w = np.matmul((np.matmul(np.linalg.inv(np.matmul(x_train.T,x_train)+lmda),x_train.T)),y_train) # using Ridge equation"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rC-YDFFr5Vin",
        "outputId": "3b7844a3-e1a2-49df-e887-ba2129ca2500"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([ 0.35976063, -0.22411475,  0.00982858,  0.49098641,  0.12160322])"
            ]
          },
          "execution_count": 30,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "w"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "id": "Sm2dainIbt0S"
      },
      "outputs": [],
      "source": [
        "x_test = np.zeros((x_df.shape[0]-int(x_df.shape[0]*0.8),x_df.shape[1]+1)) # taking last 20% of X dataframe \n",
        "for i in x_test:\n",
        "  i[0]=1\n",
        "for i in range(x_test.shape[0]):\n",
        "  for j in range(1,x_test.shape[1]):\n",
        "    x_test[i][j]=x_df.iloc[i+int(x_df.shape[0]*0.8)][j-1]\n",
        "y_test = np.asarray(list(y_df)[int(x_df.shape[0]*0.8):int(x_df.shape[0])]) # taking the last 20% of Y dataframe"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "id": "vFCytblucRuR"
      },
      "outputs": [],
      "source": [
        "rmse_train = np.sqrt((np.sum((y_train-np.dot(x_train,w))**2))/x_train.shape[0]) # taking rmse of train dataset"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lFECGV8qcWop",
        "outputId": "e1e002ac-6442-4a85-aee8-5fda7058f6d4"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.08707244156506859"
            ]
          },
          "execution_count": 33,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "rmse_train"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Jz4ANJcWcX1O",
        "outputId": "a9003bae-519e-46cb-adb9-4bb4a1060c5e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.09983210553959837"
            ]
          },
          "execution_count": 34,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "rmse_test = np.sqrt((np.sum((y_test-np.dot(x_test,w))**2))/x_test.shape[0]) # rmse of test dataset\n",
        "rmse_test"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 55,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qt_-7d7I4WoK",
        "outputId": "9c590e43-015c-45a9-d788-5c76dafb8fcc"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "9.784000638942029"
            ]
          },
          "execution_count": 55,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "loss_train = np.sum((y_train-np.dot(x_train, w))**2)+0.2*(w.T@w) # Ridge loss of train dataset\n",
        "loss_train"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2V53FCuH4cHp",
        "outputId": "0b8b2e7b-bf6f-4397-ec75-6d00a76ef456"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "3.276385121361451"
            ]
          },
          "execution_count": 43,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "loss_test = np.sum((y_test-np.dot(x_test,w))**2)+0.2*(w.T@w) # Ridge loss of test dataset\n",
        "loss_test"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "fig= plt.figure(figsize=(10,10))\n",
        "ypred = list(map(lambda x: x@w, x_train))\n",
        "\n",
        "index = np.argsort(ypred) #sorting predictions to obtain smooth line \n",
        "xplot = np.arange(len(ypred))\n",
        "yplot = list(map(lambda x : ypred[x],index))\n",
        "yplot_train = list(map(lambda x: y_train[x], index))\n",
        "#plt.scatter(xplot,yplot)\n",
        "\n",
        "plt.scatter(xplot,yplot, color = 'r', label = \"Prediction\")\n",
        "plt.scatter(xplot, yplot_train, color='b' , label = \"Actual\") # plotting corresponding actual data\n",
        "plt.ylim(0,1.5)\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## BONUS"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5C6RygRQi5WY",
        "outputId": "29582a48-87c7-4c10-bb04-b1be61d5c473"
      },
      "outputs": [],
      "source": [
        "alpha = 0.00001\n",
        "lam = 0.2\n",
        "w_gradient = np.ones(5) # initializing w gradient as array of ones \n",
        "# checking l2 norm of gradient J(w) below a particular value to stop the gradient descent\n",
        "while np.linalg.norm((-2*np.matmul(x_train.T, y_train))+(2*np.matmul(np.matmul(x_train.T, x_train), w_gradient))+(2*lam * w_gradient)) > 0.001:\n",
        "  \n",
        "  w_gradient -= alpha*((-2*np.matmul(x_train.T,y_train))+(2*np.matmul(np.matmul(x_train.T,x_train),w_gradient))+(2*lam *w_gradient))#update w gradient "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_GJnonKloH39",
        "outputId": "50f0ae1c-92e6-4128-971b-993810eef711"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.09983087574639984"
            ]
          },
          "execution_count": 51,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "rmse_test = np.sqrt((np.sum((y_test-np.dot(x_test,w_gradient))**2))/x_test.shape[0])\n",
        "rmse_test"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aJ6USrpLqGfP",
        "outputId": "6e774251-2f56-4143-cf53-fc6ebfcbe379"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.087072438340697"
            ]
          },
          "execution_count": 52,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "rmse_train = np.sqrt((np.sum((y_train-np.dot(x_train,w_gradient))**2))/x_train.shape[0])\n",
        "rmse_train"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yfWgzEQS0Lwk",
        "outputId": "401c41a2-aae1-4057-8f1c-e520eb5e25ca"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "9.784000685764532"
            ]
          },
          "execution_count": 54,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "loss_train = np.sum((y_train-np.dot(x_train,w_gradient))**2)+ lam*(w_gradient.T@w_gradient)\n",
        "loss_train"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DCGIXKNy4j00",
        "outputId": "ad326494-eaca-4c76-ed27-b1d195f8093d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "3.276307312215992"
            ]
          },
          "execution_count": 53,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "loss_test = np.sum((y_test-np.dot(x_test,w_gradient))**2)+ lam*(w_gradient.T@w_gradient)\n",
        "loss_test"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "colab": {
      "name": "CSE574-assignment2-part3.ipynb",
      "provenance": []
    },
    "interpreter": {
      "hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6"
    },
    "kernelspec": {
      "display_name": "Python 3.8.9 64-bit",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8.9"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}