1Bb_Polynomial_Regression_with_Regularization.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
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        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/bharathvariar/FoDS/blob/main/1Bb_Polynomial_Regression_with_Regularization.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "1IMpVg6k2KpD",
      "metadata": {
        "id": "1IMpVg6k2KpD"
      },
      "source": [
        "# Polynomial Regression with Regularization\n",
        "Bharath Variar, 2019B5A70930H <br>\n",
        "Kanika Gandhi, 2019B5A71080H <br>\n",
        "Karan Moza, 2019B4A71372H "
      ]
    },
    {
      "cell_type": "markdown",
      "id": "NiUWrGKR2MPp",
      "metadata": {
        "id": "NiUWrGKR2MPp"
      },
      "source": [
        "## Importing Libraries"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "8dfeada2",
      "metadata": {
        "id": "8dfeada2"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import random\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "from mpl_toolkits import mplot3d\n",
        "\n",
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "IjpUMULg2VL9",
      "metadata": {
        "id": "IjpUMULg2VL9"
      },
      "source": [
        "## Defining Functions"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "d857bb64",
      "metadata": {
        "id": "d857bb64"
      },
      "outputs": [],
      "source": [
        "def pol_feat(mat, deg):\n",
        "    if deg == 1:\n",
        "        mat = mat.to_numpy()\n",
        "        m, n = mat.shape\n",
        "        return mat.reshape(n, m), n\n",
        "\n",
        "    for i in range(0, deg + 1):\n",
        "        mat = pd.concat(\n",
        "            [mat, pd.DataFrame(mat[\"MLOGP\"] ** (deg - i) * mat[\"RDCHI\"] ** i)], axis=1\n",
        "        )\n",
        "\n",
        "    if deg > 1:\n",
        "        return pol_feat(mat, deg - 1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "d08ee056",
      "metadata": {
        "id": "d08ee056"
      },
      "outputs": [],
      "source": [
        "def initialize(dim):\n",
        "    b = random.random()\n",
        "    theta = np.random.rand(1, dim) * 0.01\n",
        "    return b, theta"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "wlIBkX3p3yH_",
      "metadata": {
        "id": "wlIBkX3p3yH_"
      },
      "source": [
        "### Gradient Descent"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "01d91f3f",
      "metadata": {
        "id": "01d91f3f"
      },
      "outputs": [],
      "source": [
        "def r_cost(y, t, theta, l, q):\n",
        "    return 0.5 * np.sum(np.power((t - y), 2)) / y.shape[1] + (l / 2) * np.sum(\n",
        "        np.power(abs(theta), q)\n",
        "    )"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "d1303cfd",
      "metadata": {
        "id": "d1303cfd"
      },
      "outputs": [],
      "source": [
        "def r_gradient_descent(num_epochs, X, t, theta, bias, learning_rate, q, l):\n",
        "    # forward-propagation\n",
        "    costs = []\n",
        "    for iter in range(num_epochs):\n",
        "        y = np.dot(theta, X) + bias\n",
        "\n",
        "        loss = r_cost(y, t, theta, l, q)\n",
        "        costs.append(loss)\n",
        "\n",
        "        # back propagation\n",
        "        r_dW = (1 / y.shape[1]) * np.dot(y - t, X.T) + q * (l / 2) * np.power(\n",
        "            theta, q - 1\n",
        "        )\n",
        "        dBias = (1 / y.shape[1]) * np.sum((y - t))\n",
        "\n",
        "        # updation\n",
        "        theta = theta - learning_rate * r_dW\n",
        "        bias = bias - learning_rate * dBias\n",
        "\n",
        "    return costs"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "8473af42",
      "metadata": {
        "id": "8473af42"
      },
      "outputs": [],
      "source": [
        "def r1_gradient_descent(num_epochs, X, t, theta, bias, learning_rate, q, l):\n",
        "\n",
        "    # forward-prop\n",
        "    costs = []\n",
        "    der = np.array([0, 0])\n",
        "    for iter in range(num_epochs):\n",
        "        y = np.dot(theta, X) + bias\n",
        "\n",
        "        loss = r_cost(y, t, theta, l, q)\n",
        "        costs.append(loss)\n",
        "\n",
        "        # backprop\n",
        "        if q == 0.5:\n",
        "            r_dW = (1 / y.shape[1]) * np.dot(y - t, X.T) + q * (l / 2) * np.power(\n",
        "                abs(theta), q - 1\n",
        "            )\n",
        "        else:\n",
        "            if abs(theta[0][0]) == theta[0][0]:\n",
        "                der[0] = 1\n",
        "            else:\n",
        "                der[0] = -1\n",
        "            if abs(theta[0][1]) == theta[0][1]:\n",
        "                der[1] = 1\n",
        "            else:\n",
        "                der[1] = -1\n",
        "            r_dW = (1 / y.shape[1]) * np.dot(y - t, X.T) + (l / 2) * der\n",
        "\n",
        "        dBias = (1 / y.shape[1]) * np.sum((y - t))\n",
        "\n",
        "        # updation\n",
        "        theta = theta - learning_rate * r_dW\n",
        "        bias = bias - learning_rate * dBias\n",
        "\n",
        "    return costs"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "4e7c4780",
      "metadata": {
        "id": "4e7c4780"
      },
      "outputs": [],
      "source": [
        "def testing(X, t, theta, bias, learning_rate, q, l):\n",
        "    y = np.dot(theta, X) + bias\n",
        "    error = r_cost(y, t, theta, l, q)\n",
        "    return error"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "N1PTWSER2b50",
      "metadata": {
        "id": "N1PTWSER2b50"
      },
      "source": [
        "## Dataset handling"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "7cc66fd1",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "7cc66fd1",
        "outputId": "36451685-68bf-4c46-bf4f-644b16dd77db"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "<div>\n",
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              "    }\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>MLOGP</th>\n",
              "      <th>RDCHI</th>\n",
              "      <th>quantitative response of LC50</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>2.419</td>\n",
              "      <td>1.225</td>\n",
              "      <td>3.740</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2.638</td>\n",
              "      <td>1.401</td>\n",
              "      <td>4.330</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>5.799</td>\n",
              "      <td>2.930</td>\n",
              "      <td>7.019</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>5.453</td>\n",
              "      <td>2.887</td>\n",
              "      <td>6.723</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4.068</td>\n",
              "      <td>2.758</td>\n",
              "      <td>5.979</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   MLOGP  RDCHI  quantitative response of LC50\n",
              "0  2.419  1.225                          3.740\n",
              "1  2.638  1.401                          4.330\n",
              "2  5.799  2.930                          7.019\n",
              "3  5.453  2.887                          6.723\n",
              "4  4.068  2.758                          5.979"
            ]
          },
          "execution_count": 8,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df = pd.read_csv(\"fods_1.csv\")\n",
        "df.head()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "XcW14gSt3nw-",
      "metadata": {
        "id": "XcW14gSt3nw-"
      },
      "source": [
        "### Shuffling and splitting data into training and testing subsets"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "19366a6a",
      "metadata": {
        "id": "19366a6a"
      },
      "outputs": [],
      "source": [
        "# Shuffling the dataset\n",
        "shuffled_df = df.sample(frac=1, random_state=42)\n",
        "\n",
        "# Define a size for your train set\n",
        "training_data_size = int(0.8 * len(df))\n",
        "\n",
        "# Split your dataset\n",
        "training_data = shuffled_df[:training_data_size]\n",
        "testing_data = shuffled_df[training_data_size:]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "e0d7ecc7",
      "metadata": {
        "id": "e0d7ecc7"
      },
      "outputs": [],
      "source": [
        "X_train = training_data[[\"MLOGP\", \"RDCHI\"]]\n",
        "y_train = training_data[\"quantitative response of LC50\"]\n",
        "X_test = testing_data[[\"MLOGP\", \"RDCHI\"]]\n",
        "y_test = testing_data[\"quantitative response of LC50\"]"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "BTbP-RNj06_H",
      "metadata": {
        "id": "BTbP-RNj06_H"
      },
      "source": [
        "Polynomial of the form:\n",
        "$$ y = w_0 + w_1.x + w_2.x^2 +\\dots+ w_9.x^9 $$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "3658752e",
      "metadata": {
        "id": "3658752e"
      },
      "outputs": [],
      "source": [
        "data, num_features = pol_feat(X_train, 1)\n",
        "test_data, num_features = pol_feat(X_test, 1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "2e9e844b",
      "metadata": {
        "id": "2e9e844b"
      },
      "outputs": [],
      "source": [
        "# normalizing training data\n",
        "mean = np.mean(data, axis=1, keepdims=True)\n",
        "std = np.std(data, axis=1, keepdims=True)\n",
        "data = (data - mean) / std"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "f8099653",
      "metadata": {
        "id": "f8099653"
      },
      "outputs": [],
      "source": [
        "# normalizing testing data\n",
        "test_data = (test_data - mean) / std"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "0becb990",
      "metadata": {
        "id": "0becb990"
      },
      "outputs": [],
      "source": [
        "train_err_arr = []\n",
        "test_err_arr = []"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "xiByihi34GXu",
      "metadata": {
        "id": "xiByihi34GXu"
      },
      "source": [
        "## Implementation"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "56bd1a9a",
      "metadata": {
        "id": "56bd1a9a"
      },
      "source": [
        "### `q` = 0.5, \n",
        "`learning_rate` = 0.1 <br>\n",
        "`lambda(l)` = $1.0 \\times 10^{-4}$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "49c1f4f5",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "id": "49c1f4f5",
        "outputId": "97e908e2-274e-40eb-863b-c6b9709919f4"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Training error = 1.44985873\n"
          ]
        },
        {
          "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": [
        "b, theta = initialize(num_features)\n",
        "costs_q1 = r1_gradient_descent(\n",
        "    300, data, y_train.to_numpy().reshape(1, -1), theta, b, 0.1, 0.5, 1.0e-4\n",
        ")\n",
        "print(f\"Training error = {costs_q1[-1]:0.8f}\")\n",
        "train_err_arr.append(costs_q1[-1])\n",
        "fig, ax = plt.subplots(1, 1, sharex=True)\n",
        "ax.plot(costs_q1)\n",
        "t = ax.set_title(f\"Training Error vs. Epochs\", fontsize=18)\n",
        "x = ax.set_xlabel(\"Number of Epochs\", fontsize=16, fontweight=\"bold\", color=\"gray\")\n",
        "y = ax.set_ylabel(\"Mean Squared Error\", fontsize=16, fontweight=\"bold\", color=\"gray\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "9bfecac8",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9bfecac8",
        "outputId": "43833d06-ae35-41ad-f2d1-d1b48dc7d5c2"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Testing error = 7.63266510\n"
          ]
        }
      ],
      "source": [
        "test_error = testing(\n",
        "    test_data, y_test.to_numpy().reshape(1, -1), theta, b, 0.1, 0.5, 1.0e-4\n",
        ")\n",
        "print(f\"Testing error = {test_error:.8f}\")\n",
        "test_err_arr.append(test_error)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "a4bfbb2c",
      "metadata": {
        "id": "a4bfbb2c"
      },
      "source": [
        "### `q` = 1, \n",
        "`learning_rate` = 0.1 <br>\n",
        "`l` = $1.0 \\times 10^{-4}$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "7cfc7e1c",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "id": "7cfc7e1c",
        "outputId": "d2f14ca6-8c1b-43c9-fa34-409d4d8895d7"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Training error = 1.44984179\n"
          ]
        },
        {
          "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": [
        "b, theta = initialize(num_features)\n",
        "costs_q2 = r1_gradient_descent(\n",
        "    300, data, y_train.to_numpy().reshape(1, -1), theta, b, 0.1, 1, 1.0e-4\n",
        ")\n",
        "print(f\"Training error = {costs_q2[-1]:0.8f}\")\n",
        "train_err_arr.append(costs_q2[-1])\n",
        "fig, ax = plt.subplots(1, 1, sharex=True)\n",
        "ax.plot(costs_q2)\n",
        "t = ax.set_title(f\"Training Error vs. Epochs\", fontsize=18)\n",
        "x = ax.set_xlabel(\"Number of Epochs\", fontsize=16, fontweight=\"bold\", color=\"gray\")\n",
        "y = ax.set_ylabel(\"Mean Squared Error\", fontsize=16, fontweight=\"bold\", color=\"gray\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "ec0c6984",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ec0c6984",
        "outputId": "95b05dc2-649c-4315-b493-1d09b40d6d84"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Testing error = 7.47012114\n"
          ]
        }
      ],
      "source": [
        "test_error = testing(\n",
        "    test_data, y_test.to_numpy().reshape(1, -1), theta, b, 0.1, 1, 1.0e-4\n",
        ")\n",
        "print(f\"Testing error = {test_error:.8f}\")\n",
        "test_err_arr.append(test_error)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "da45a9c4",
      "metadata": {
        "id": "da45a9c4"
      },
      "source": [
        "### `q` = 2, \n",
        "`learning_rate` = 0.1 <br>\n",
        "`l` = $1.0 \\times 10^{-4}$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "c86f2c61",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "id": "c86f2c61",
        "outputId": "1b0ef40e-fb09-4b2b-9558-92a2fa64df40"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Training error = 1.44983705\n"
          ]
        },
        {
          "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": [
        "b, theta = initialize(num_features)\n",
        "costs_q3 = r_gradient_descent(\n",
        "    300, data, y_train.to_numpy().reshape(1, -1), theta, b, 0.1, 2, 1.0e-4\n",
        ")\n",
        "print(f\"Training error = {costs_q3[-1]:0.8f}\")\n",
        "train_err_arr.append(costs_q3[-1])\n",
        "fig, ax = plt.subplots(1, 1, sharex=True)\n",
        "ax.plot(costs_q3)\n",
        "t = ax.set_title(f\"Training Error vs. Epochs\", fontsize=18)\n",
        "x = ax.set_xlabel(\"Number of Epochs\", fontsize=16, fontweight=\"bold\", color=\"gray\")\n",
        "y = ax.set_ylabel(\"Mean Squared Error\", fontsize=16, fontweight=\"bold\", color=\"gray\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "2d5077f4",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2d5077f4",
        "outputId": "9818a45e-68ec-432d-db1b-8d7adda195aa"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Testing error = 7.58703214\n"
          ]
        }
      ],
      "source": [
        "test_error = testing(\n",
        "    test_data, y_test.to_numpy().reshape(1, -1), theta, b, 0.1, 2, 1.0e-4\n",
        ")\n",
        "print(f\"Testing error = {test_error:.8f}\")\n",
        "test_err_arr.append(test_error)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "f5c9c08c",
      "metadata": {
        "id": "f5c9c08c"
      },
      "source": [
        "### `q` = 4, \n",
        "`learning_rate` = 0.1 <br>\n",
        "`l` = $1.0 \\times 10^{-4}$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "7caca0cd",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "id": "7caca0cd",
        "outputId": "8352230b-be8d-4b2f-c4d0-15ab8f3634a9"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Training error = 1.44983654\n"
          ]
        },
        {
          "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": [
        "b, theta = initialize(num_features)\n",
        "costs_q4 = r_gradient_descent(\n",
        "    300, data, y_train.to_numpy().reshape(1, -1), theta, b, 0.1, 4, 1.0e-4\n",
        ")\n",
        "print(f\"Training error = {costs_q4[-1]:0.8f}\")\n",
        "train_err_arr.append(costs_q4[-1])\n",
        "fig, ax = plt.subplots(1, 1, sharex=True)\n",
        "ax.plot(costs_q4)\n",
        "t = ax.set_title(f\"Training Error vs. Epochs\", fontsize=18)\n",
        "x = ax.set_xlabel(\"Number of Epochs\", fontsize=16, fontweight=\"bold\", color=\"gray\")\n",
        "y = ax.set_ylabel(\"Mean Squared Error\", fontsize=16, fontweight=\"bold\", color=\"gray\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "92624c48",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "92624c48",
        "outputId": "d44ae0cc-da9a-466d-95a7-401cb1b45e21"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Testing error = 10.32667100\n"
          ]
        }
      ],
      "source": [
        "test_error = testing(\n",
        "    test_data, y_test.to_numpy().reshape(1, -1), theta, b, 0.1, 4, 1.0e-4\n",
        ")\n",
        "print(f\"Testing error = {test_error:.8f}\")\n",
        "test_err_arr.append(test_error)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "dcdbcc94",
      "metadata": {
        "id": "dcdbcc94"
      },
      "source": [
        "## Visualization"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "8912a579",
      "metadata": {
        "id": "8912a579",
        "outputId": "2e535a48-55ca-4a90-b7b5-016e643160eb"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1080x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "q_val = [0.5, 1, 2, 4]\n",
        "fig, (ax1, ax2) = plt.subplots(1, 2, sharex=True, figsize=(15, 4))\n",
        "ax1.plot(q_val, train_err_arr, \"bo-\")\n",
        "t = ax1.set_title(f\"Training Error vs. q\", fontsize=18)\n",
        "x = ax1.set_xlabel(\"q\", fontsize=16, fontweight=\"bold\", color=\"gray\")\n",
        "y = ax1.set_ylabel(\"Mean Squared Error\", fontsize=16, fontweight=\"bold\", color=\"gray\")\n",
        "ax2.plot(q_val, test_err_arr, \"ro-\")\n",
        "t = ax2.set_title(f\"Testing Error vs. q\", fontsize=18)\n",
        "x = ax2.set_xlabel(\"q\", fontsize=16, fontweight=\"bold\", color=\"gray\")\n",
        "y = ax2.set_ylabel(\"Mean Squared Error\", fontsize=16, fontweight=\"bold\", color=\"gray\")"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "toc_visible": true,
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "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": "3.8.12"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}