DL_regression_regularization_eval.ipynb

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      "source": [
        "# Introduction\n",
        "\n",
        "The purpose of this small project is to compare the performance of dense layer neural networks methods to predict the quality of wine from the [wine quality dataset](https://archive.ics.uci.edu/ml/datasets/wine+quality).\n",
        "\n",
        "Wine's quality can take decimal values (i.e. 7.25), regardless of the fact that only integers are found in the training dataset. Therefore, this is a `regression` task.\n",
        "\n",
        "For the comparison, an evaluation of a base model, a lasso-regularized model, a drop-out regularization and regularized models with early stopping will be compared to see which one provides the best results.\n",
        "\n",
        "### Regularization Techniques in Deep Learning\n",
        "\n",
        "Regularization is a technique used to prevent overfitting in a model. Overfitting occurs when the model performs well on the training data but poorly on the unseen data (like validation or test data). Regularization adds a penalty on the different parameters of the model to reduce the freedom of the model and in other words to avoid overfitting.\n",
        "\n",
        "### L1 and L2 Regularization\n",
        "\n",
        "L1 and L2 are the most common types of regularization. These update the general cost function by adding another term known as the regularization term. For this evaluation, we will focus on L1 Lasso regularization\n",
        "\n",
        "- L1 Regularization (Lasso Regression)\n",
        "In L1, we shrink the parameters to zero, thus removing some features and making the model simpler and interpretable.\n",
        "\n",
        "Here's the formula for L1 Regularization:\n",
        "\n",
        "$$\n",
        "L1 = \\lambda \\sum_{i=1}^{n} |w_{i}|\n",
        "$$\n",
        "\n",
        "### Dropout\n",
        "Dropout is a technique where randomly selected neurons are ignored during training, meaning that their contribution to the activation of downstream neurons is temporally removed on the forward pass and any weight updates are not applied to the neuron on the backward pass. It has the effect of reducing overfitting and improving model performance.\n",
        "\n",
        "### Early Stopping\n",
        "Early stopping is a form of regularization used to avoid overfitting when training a learner with an iterative method, such as gradient descent. These methods update the learner so as to make it better fit the training data with each iteration. Up to a point, this improves the learner's performance on data outside of the training set. Past that point, however, improving the learner's fit to the training data comes at the expense of increased generalization error AKA overfitting."
      ]
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    {
      "cell_type": "markdown",
      "id": "linHt5zeqsiK",
      "metadata": {
        "id": "linHt5zeqsiK"
      },
      "source": [
        "# 0. Import of packages"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "hSLa4hDktAAx",
      "metadata": {
        "id": "hSLa4hDktAAx"
      },
      "source": [
        "#### Import of necessary packages"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "prompt-developer",
      "metadata": {
        "id": "prompt-developer"
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      "source": [
        "import tensorflow as tf\n",
        "from tensorflow import keras\n",
        "from tensorflow.keras import layers, regularizers\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "from sklearn.model_selection import train_test_split, KFold\n",
        "tf.random.set_seed(0)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "xY16JTvAtEKL",
      "metadata": {
        "id": "xY16JTvAtEKL"
      },
      "source": [
        "#### Definition of useful functions"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "gmRf21x3tD0v",
      "metadata": {
        "id": "gmRf21x3tD0v"
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      "source": [
        "def show_loss_accuracy_evolution(history, model_name):\n",
        "\n",
        "    hist = pd.DataFrame(history.history)\n",
        "    hist['epoch'] = history.epoch\n",
        "\n",
        "    fig, (ax1) = plt.subplots(1, figsize=(16, 6))\n",
        "\n",
        "    ax1.set_xlabel('Epoch')\n",
        "    ax1.set_ylabel('MSE')\n",
        "    ax1.set_title(f'Train-val epoch evolution of {model_name}')\n",
        "    ax1.plot(hist['epoch'], hist['loss'], label='Train Error')\n",
        "    ax1.plot(hist['epoch'], hist['val_loss'], label = 'Val Error')\n",
        "    ax1.grid()\n",
        "    ax1.legend()\n",
        "\n",
        "    plt.show()\n",
        "\n",
        "\n",
        "def show_samples(x_test, y_test, model):\n",
        "    predictions = model.predict(x_test)\n",
        "    predicted_classes = np.argmax(predictions, -1)\n",
        "\n",
        "    L = 5\n",
        "    W = 5\n",
        "    fig, axes = plt.subplots(L, W, figsize=(14, 14))\n",
        "    axes = axes.ravel()\n",
        "\n",
        "    for i in np.arange(0, L * W):\n",
        "        ind = np.random.randint(len(y_test))\n",
        "        axes[i].imshow(x_test[ind].reshape(28, 28))\n",
        "        prob_pred = np.max(predictions[ind, :])\n",
        "        class_pred = int(predicted_classes[ind])\n",
        "        original_class = int(y_test[ind])\n",
        "        if class_pred == original_class:\n",
        "            color = 'green'\n",
        "        else:\n",
        "            color = 'red'\n",
        "        title = \"Pred: {0} \\n Target: {1} \\n Prob: {2:.3f}\".format(\n",
        "        class_pred, original_class, prob_pred)\n",
        "        axes[i].set_title(title, color=color)\n",
        "        axes[i].axis('off')\n",
        "\n",
        "    plt.subplots_adjust(wspace=0.5)"
      ]
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    {
      "cell_type": "markdown",
      "id": "mK9wXxYltSEP",
      "metadata": {
        "id": "mK9wXxYltSEP"
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      "source": [
        "# 1. Data import and preparation for modelling"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "qn7KqpD6tX0n",
      "metadata": {
        "id": "qn7KqpD6tX0n"
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      "source": [
        "Given that the purpose of this notebook is merely the comparison of dense-layered neural networks training, the chosen dataset is one that is available in a completely cleaned form.\n",
        "\n",
        "Additionally, although EDA and Feature Engineering are a desirable, or even a must, for data understanding and preparation for modelling, no effort will be dedicated to those tasks with the intention of centering the attention on the topic of interest."
      ]
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    {
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              "      <th>fixed acidity</th>\n",
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              "      <th>citric acid</th>\n",
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              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-39801838-115c-4a31-af3d-57c24a6a661b button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "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": 44,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df_red = pd.read_csv(\n",
        "    'https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-red.csv',\n",
        "    sep=';'\n",
        ")\n",
        "df_white = pd.read_csv(\n",
        "    'https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-white.csv',\n",
        "    sep=';'\n",
        ")\n",
        "df = pd.concat([df_red, df_white])\n",
        "\n",
        "df.head()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "CGa_ZDW6xNvh",
      "metadata": {
        "id": "CGa_ZDW6xNvh"
      },
      "source": [
        "### Feature selection"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "f9a547f1",
      "metadata": {
        "id": "f9a547f1"
      },
      "outputs": [],
      "source": [
        "feature_names = [\n",
        "    'fixed acidity', 'volatile acidity', 'citric acid', 'residual sugar', 'chlorides',\n",
        "    'free sulfur dioxide', 'total sulfur dioxide', 'density', 'pH', 'sulphates', 'alcohol'\n",
        "]\n",
        "\n",
        "y = df.pop('quality').values\n",
        "X = df.copy().values"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "mGWW03_BxRDQ",
      "metadata": {
        "id": "mGWW03_BxRDQ"
      },
      "source": [
        "### Train-test split"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "5cfb80ec",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5cfb80ec",
        "outputId": "1efc195b-f2da-40cb-ffb2-9ec856ee9c79"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "x_train, y_train shapes: (4872, 11) (4872,)\n",
            "x_test, y_test shapes: (1625, 11) (1625,)\n"
          ]
        }
      ],
      "source": [
        "x_train, x_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=0)\n",
        "\n",
        "print('x_train, y_train shapes:', x_train.shape, y_train.shape)\n",
        "print('x_test, y_test shapes:', x_test.shape, y_test.shape)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "OD3sFx0HxHjL",
      "metadata": {
        "id": "OD3sFx0HxHjL"
      },
      "source": [
        "### Feature normalization"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "painted-extreme",
      "metadata": {
        "id": "painted-extreme"
      },
      "outputs": [],
      "source": [
        "norm = tf.keras.layers.Normalization(axis=-1)\n",
        "norm.adapt(x_train)\n",
        "norm.adapt(x_test)\n",
        "\n",
        "x_train_norm = norm(x_train).numpy()\n",
        "x_test_norm = norm(x_test).numpy()"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "underlying-planner",
      "metadata": {
        "id": "underlying-planner"
      },
      "source": [
        "# 2. Modelling\n",
        "### 2.1 Definition of functions to build the models\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "working-shade",
      "metadata": {
        "id": "working-shade"
      },
      "outputs": [],
      "source": [
        "def build_base(n_layers=4, neurons=64, opt ='adam', metrics=['mae']):\n",
        "  model = keras.Sequential()\n",
        "\n",
        "  for _ in range(n_layers):\n",
        "    model.add(layers.Dense(neurons, input_shape=(11,), activation='relu'))\n",
        "\n",
        "  model.add(layers.Dense(1, activation='linear'))\n",
        "\n",
        "  model.summary()\n",
        "\n",
        "  model.compile(\n",
        "    optimizer= opt,\n",
        "    loss=tf.keras.losses.MSE,\n",
        "    metrics= metrics\n",
        "  )\n",
        "\n",
        "  return model\n",
        "\n",
        "def build_dropout(n_layers=4, neurons=64, opt ='adam', metrics=['mae'], drop_pct = 0.4):\n",
        "  model = keras.Sequential()\n",
        "\n",
        "  for _ in range(n_layers):\n",
        "    model.add(layers.Dense(neurons, input_shape=(11,), activation='relu'))\n",
        "    model.add(layers.Dropout(drop_pct))\n",
        "\n",
        "  model.add(layers.Dense(1, activation='linear'))\n",
        "\n",
        "  model.summary()\n",
        "\n",
        "  model.compile(\n",
        "    optimizer= opt,\n",
        "    loss=tf.keras.losses.MSE,\n",
        "    metrics= metrics\n",
        "  )\n",
        "\n",
        "  return model\n",
        "\n",
        "def build_lasso(n_layers=4, neurons=64, opt ='adam', metrics=['mae'], reg=5e-4):\n",
        "  kernel_regularizer_lasso = regularizers.l2(reg)\n",
        "  model = keras.Sequential()\n",
        "\n",
        "  for _ in range(n_layers):\n",
        "    model.add(layers.Dense(neurons, input_shape=(11,),kernel_regularizer=kernel_regularizer_lasso, activation='relu'))\n",
        "\n",
        "  model.add(layers.Dense(1, activation='linear'))\n",
        "\n",
        "  model.summary()\n",
        "\n",
        "  model.compile(\n",
        "    optimizer= opt,\n",
        "    loss=tf.keras.losses.MSE,\n",
        "    metrics= metrics\n",
        "  )\n",
        "\n",
        "  return model"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "cb8e071a",
      "metadata": {
        "id": "cb8e071a"
      },
      "source": [
        "### 2.2 Model build and fitting"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "a6564f6f",
      "metadata": {
        "id": "a6564f6f"
      },
      "source": [
        "As said earlier, 3 types of overfitting prevention strategies will be evaluated:\n",
        "- Dropout\n",
        "- Lasso regularization\n",
        "- Early stoppage\n",
        "\n",
        "Early stopagge is compatible with the previous 2 methods of regularization. Thus, 6 models will be evaluated:\n",
        "1. Baseline model\n",
        "2. Model with dropout\n",
        "3. Model with lasso\n",
        "4. Baseline with early stopping callback\n",
        "5. Dropout model with early stopping callback\n",
        "6. Lasso model with early stopping callback\n",
        "\n",
        "To evaluate them in equal conditions, the models will be built upon the same number of hidden layers, with the same number of neurons, optimizer and loss function, while they will have their own regularization terms. On the same line, they will be fitted in batch sizes of 100 and 200 epochs, with a validation size of 20%.\n",
        "\n",
        "For this short evaluation, only 1 value for a regularization term of dropout, lasso and patience for early stopping will be evaluated. However, for rigorous evaluation these parameters should be fine tuned in order to properly compare the best version of each method against the others. That proper evaluation will be performed in future versions of this notebook."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "lTO4BkQoBRGn",
      "metadata": {
        "id": "lTO4BkQoBRGn"
      },
      "source": [
        "#### 2.2.1 Base dense layer model with 4 hidden layers"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "rotary-credits",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rotary-credits",
        "outputId": "22c10b9a-866a-46bc-e7f2-464fc322720b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Model: \"sequential_23\"\n",
            "_________________________________________________________________\n",
            " Layer (type)                Output Shape              Param #   \n",
            "=================================================================\n",
            " dense_115 (Dense)           (None, 64)                768       \n",
            "                                                                 \n",
            " dense_116 (Dense)           (None, 64)                4160      \n",
            "                                                                 \n",
            " dense_117 (Dense)           (None, 64)                4160      \n",
            "                                                                 \n",
            " dense_118 (Dense)           (None, 64)                4160      \n",
            "                                                                 \n",
            " dense_119 (Dense)           (None, 1)                 65        \n",
            "                                                                 \n",
            "=================================================================\n",
            "Total params: 13313 (52.00 KB)\n",
            "Trainable params: 13313 (52.00 KB)\n",
            "Non-trainable params: 0 (0.00 Byte)\n",
            "_________________________________________________________________\n",
            "Epoch 1/100\n",
            "39/39 [==============================] - 2s 8ms/step - loss: 13.2478 - mae: 3.0357 - val_loss: 3.3096 - val_mae: 1.3368\n",
            "Epoch 2/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 2.2240 - mae: 1.1772 - val_loss: 2.2660 - val_mae: 1.0613\n",
            "Epoch 3/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 1.5821 - mae: 0.9839 - val_loss: 1.7379 - val_mae: 0.9475\n",
            "Epoch 4/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 1.2815 - mae: 0.8885 - val_loss: 1.3900 - val_mae: 0.8496\n",
            "Epoch 5/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 1.0312 - mae: 0.7951 - val_loss: 1.1219 - val_mae: 0.7780\n",
            "Epoch 6/100\n",
            "39/39 [==============================] - 0s 8ms/step - loss: 0.8521 - mae: 0.7247 - val_loss: 0.9321 - val_mae: 0.7106\n",
            "Epoch 7/100\n",
            "39/39 [==============================] - 0s 7ms/step - loss: 0.7114 - mae: 0.6577 - val_loss: 0.7912 - val_mae: 0.6672\n",
            "Epoch 8/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.6224 - mae: 0.6117 - val_loss: 0.6882 - val_mae: 0.6195\n",
            "Epoch 9/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.5577 - mae: 0.5767 - val_loss: 0.6291 - val_mae: 0.5935\n",
            "Epoch 10/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.5309 - mae: 0.5640 - val_loss: 0.5682 - val_mae: 0.5627\n",
            "Epoch 11/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.4880 - mae: 0.5367 - val_loss: 0.5643 - val_mae: 0.5653\n",
            "Epoch 12/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.4796 - mae: 0.5325 - val_loss: 0.5663 - val_mae: 0.5637\n",
            "Epoch 13/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.4605 - mae: 0.5248 - val_loss: 0.5603 - val_mae: 0.5692\n",
            "Epoch 14/100\n",
            "39/39 [==============================] - 0s 7ms/step - loss: 0.4477 - mae: 0.5165 - val_loss: 0.5314 - val_mae: 0.5564\n",
            "Epoch 15/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.4402 - mae: 0.5123 - val_loss: 0.5624 - val_mae: 0.5713\n",
            "Epoch 16/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.4349 - mae: 0.5077 - val_loss: 0.5306 - val_mae: 0.5534\n",
            "Epoch 17/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.4293 - mae: 0.5065 - val_loss: 0.5208 - val_mae: 0.5533\n",
            "Epoch 18/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.4254 - mae: 0.5026 - val_loss: 0.5108 - val_mae: 0.5451\n",
            "Epoch 19/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.4157 - mae: 0.4987 - val_loss: 0.5208 - val_mae: 0.5506\n",
            "Epoch 20/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.4142 - mae: 0.4955 - val_loss: 0.5657 - val_mae: 0.5825\n",
            "Epoch 21/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.4191 - mae: 0.4994 - val_loss: 0.5463 - val_mae: 0.5737\n",
            "Epoch 22/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.4074 - mae: 0.4904 - val_loss: 0.5334 - val_mae: 0.5596\n",
            "Epoch 23/100\n",
            "39/39 [==============================] - 0s 8ms/step - loss: 0.3963 - mae: 0.4868 - val_loss: 0.5012 - val_mae: 0.5426\n",
            "Epoch 24/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.3965 - mae: 0.4886 - val_loss: 0.5191 - val_mae: 0.5508\n",
            "Epoch 25/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.3917 - mae: 0.4848 - val_loss: 0.5329 - val_mae: 0.5695\n",
            "Epoch 26/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.3842 - mae: 0.4788 - val_loss: 0.5033 - val_mae: 0.5421\n",
            "Epoch 27/100\n",
            "39/39 [==============================] - 0s 8ms/step - loss: 0.3829 - mae: 0.4784 - val_loss: 0.5067 - val_mae: 0.5506\n",
            "Epoch 28/100\n",
            "39/39 [==============================] - 0s 7ms/step - loss: 0.3807 - mae: 0.4772 - val_loss: 0.5060 - val_mae: 0.5502\n",
            "Epoch 29/100\n",
            "39/39 [==============================] - 0s 7ms/step - loss: 0.3752 - mae: 0.4727 - val_loss: 0.5097 - val_mae: 0.5510\n",
            "Epoch 30/100\n",
            "39/39 [==============================] - 0s 8ms/step - loss: 0.3683 - mae: 0.4659 - val_loss: 0.5139 - val_mae: 0.5474\n",
            "Epoch 31/100\n",
            "39/39 [==============================] - 0s 7ms/step - loss: 0.3642 - mae: 0.4642 - val_loss: 0.5057 - val_mae: 0.5423\n",
            "Epoch 32/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.3641 - mae: 0.4655 - val_loss: 0.4941 - val_mae: 0.5414\n",
            "Epoch 33/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.3604 - mae: 0.4635 - val_loss: 0.4925 - val_mae: 0.5406\n",
            "Epoch 34/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.3626 - mae: 0.4647 - val_loss: 0.5090 - val_mae: 0.5485\n",
            "Epoch 35/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.3517 - mae: 0.4570 - val_loss: 0.5163 - val_mae: 0.5550\n",
            "Epoch 36/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.3515 - mae: 0.4571 - val_loss: 0.5048 - val_mae: 0.5450\n",
            "Epoch 37/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.3404 - mae: 0.4491 - val_loss: 0.4982 - val_mae: 0.5443\n",
            "Epoch 38/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.3422 - mae: 0.4526 - val_loss: 0.5163 - val_mae: 0.5534\n",
            "Epoch 39/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.3477 - mae: 0.4557 - val_loss: 0.5577 - val_mae: 0.5712\n",
            "Epoch 40/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.3418 - mae: 0.4506 - val_loss: 0.4873 - val_mae: 0.5406\n",
            "Epoch 41/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.3428 - mae: 0.4526 - val_loss: 0.5329 - val_mae: 0.5703\n",
            "Epoch 42/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.3400 - mae: 0.4485 - val_loss: 0.5226 - val_mae: 0.5548\n",
            "Epoch 43/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.3409 - mae: 0.4511 - val_loss: 0.4867 - val_mae: 0.5330\n",
            "Epoch 44/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.3193 - mae: 0.4353 - val_loss: 0.5043 - val_mae: 0.5403\n",
            "Epoch 45/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.3308 - mae: 0.4411 - val_loss: 0.4921 - val_mae: 0.5393\n",
            "Epoch 46/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.3429 - mae: 0.4512 - val_loss: 0.5130 - val_mae: 0.5501\n",
            "Epoch 47/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.3238 - mae: 0.4395 - val_loss: 0.5257 - val_mae: 0.5679\n",
            "Epoch 48/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.3236 - mae: 0.4393 - val_loss: 0.4977 - val_mae: 0.5401\n",
            "Epoch 49/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.3090 - mae: 0.4280 - val_loss: 0.4893 - val_mae: 0.5394\n",
            "Epoch 50/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.3033 - mae: 0.4239 - val_loss: 0.5118 - val_mae: 0.5430\n",
            "Epoch 51/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.3003 - mae: 0.4211 - val_loss: 0.5155 - val_mae: 0.5500\n",
            "Epoch 52/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.3030 - mae: 0.4253 - val_loss: 0.4866 - val_mae: 0.5366\n",
            "Epoch 53/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.2907 - mae: 0.4129 - val_loss: 0.5121 - val_mae: 0.5469\n",
            "Epoch 54/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.2988 - mae: 0.4220 - val_loss: 0.5299 - val_mae: 0.5606\n",
            "Epoch 55/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.3086 - mae: 0.4273 - val_loss: 0.5023 - val_mae: 0.5463\n",
            "Epoch 56/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.2926 - mae: 0.4147 - val_loss: 0.5260 - val_mae: 0.5588\n",
            "Epoch 57/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.2995 - mae: 0.4212 - val_loss: 0.5147 - val_mae: 0.5444\n",
            "Epoch 58/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.2889 - mae: 0.4122 - val_loss: 0.5239 - val_mae: 0.5535\n",
            "Epoch 59/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.2949 - mae: 0.4188 - val_loss: 0.6260 - val_mae: 0.6062\n",
            "Epoch 60/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.2950 - mae: 0.4187 - val_loss: 0.5033 - val_mae: 0.5452\n",
            "Epoch 61/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.2944 - mae: 0.4171 - val_loss: 0.5198 - val_mae: 0.5489\n",
            "Epoch 62/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.2894 - mae: 0.4134 - val_loss: 0.5170 - val_mae: 0.5473\n",
            "Epoch 63/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.2809 - mae: 0.4071 - val_loss: 0.5133 - val_mae: 0.5457\n",
            "Epoch 64/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.2666 - mae: 0.3936 - val_loss: 0.5205 - val_mae: 0.5453\n",
            "Epoch 65/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.2695 - mae: 0.3989 - val_loss: 0.5253 - val_mae: 0.5571\n",
            "Epoch 66/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.2762 - mae: 0.4034 - val_loss: 0.5395 - val_mae: 0.5692\n",
            "Epoch 67/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.2735 - mae: 0.4006 - val_loss: 0.5113 - val_mae: 0.5442\n",
            "Epoch 68/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.2604 - mae: 0.3907 - val_loss: 0.5186 - val_mae: 0.5493\n",
            "Epoch 69/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.2557 - mae: 0.3887 - val_loss: 0.5424 - val_mae: 0.5638\n",
            "Epoch 70/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.2629 - mae: 0.3929 - val_loss: 0.5309 - val_mae: 0.5483\n",
            "Epoch 71/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.2519 - mae: 0.3828 - val_loss: 0.5561 - val_mae: 0.5684\n",
            "Epoch 72/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.2555 - mae: 0.3859 - val_loss: 0.5289 - val_mae: 0.5506\n",
            "Epoch 73/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.2477 - mae: 0.3828 - val_loss: 0.5455 - val_mae: 0.5623\n",
            "Epoch 74/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.2506 - mae: 0.3831 - val_loss: 0.5391 - val_mae: 0.5528\n",
            "Epoch 75/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.2483 - mae: 0.3792 - val_loss: 0.5627 - val_mae: 0.5721\n",
            "Epoch 76/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.2581 - mae: 0.3912 - val_loss: 0.5314 - val_mae: 0.5510\n",
            "Epoch 77/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.2416 - mae: 0.3738 - val_loss: 0.5441 - val_mae: 0.5607\n",
            "Epoch 78/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.2393 - mae: 0.3757 - val_loss: 0.5239 - val_mae: 0.5499\n",
            "Epoch 79/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.2415 - mae: 0.3768 - val_loss: 0.5375 - val_mae: 0.5540\n",
            "Epoch 80/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.2452 - mae: 0.3792 - val_loss: 0.5644 - val_mae: 0.5662\n",
            "Epoch 81/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.2320 - mae: 0.3692 - val_loss: 0.5586 - val_mae: 0.5619\n",
            "Epoch 82/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.2396 - mae: 0.3755 - val_loss: 0.5830 - val_mae: 0.5769\n",
            "Epoch 83/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.2467 - mae: 0.3833 - val_loss: 0.5566 - val_mae: 0.5666\n",
            "Epoch 84/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.2284 - mae: 0.3648 - val_loss: 0.5715 - val_mae: 0.5739\n",
            "Epoch 85/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.2253 - mae: 0.3607 - val_loss: 0.5543 - val_mae: 0.5679\n",
            "Epoch 86/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.2235 - mae: 0.3592 - val_loss: 0.5414 - val_mae: 0.5543\n",
            "Epoch 87/100\n",
            "39/39 [==============================] - 0s 7ms/step - loss: 0.2296 - mae: 0.3674 - val_loss: 0.5472 - val_mae: 0.5531\n",
            "Epoch 88/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.2207 - mae: 0.3572 - val_loss: 0.5704 - val_mae: 0.5717\n",
            "Epoch 89/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.2252 - mae: 0.3629 - val_loss: 0.5439 - val_mae: 0.5564\n",
            "Epoch 90/100\n",
            "39/39 [==============================] - 0s 8ms/step - loss: 0.2210 - mae: 0.3565 - val_loss: 0.5580 - val_mae: 0.5640\n",
            "Epoch 91/100\n",
            "39/39 [==============================] - 0s 8ms/step - loss: 0.2228 - mae: 0.3615 - val_loss: 0.5513 - val_mae: 0.5637\n",
            "Epoch 92/100\n",
            "39/39 [==============================] - 0s 7ms/step - loss: 0.2169 - mae: 0.3569 - val_loss: 0.5820 - val_mae: 0.5782\n",
            "Epoch 93/100\n",
            "39/39 [==============================] - 0s 7ms/step - loss: 0.2114 - mae: 0.3518 - val_loss: 0.5559 - val_mae: 0.5570\n",
            "Epoch 94/100\n",
            "39/39 [==============================] - 0s 8ms/step - loss: 0.2057 - mae: 0.3453 - val_loss: 0.5657 - val_mae: 0.5671\n",
            "Epoch 95/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.2065 - mae: 0.3475 - val_loss: 0.5374 - val_mae: 0.5565\n",
            "Epoch 96/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.2091 - mae: 0.3473 - val_loss: 0.5695 - val_mae: 0.5781\n",
            "Epoch 97/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.1983 - mae: 0.3389 - val_loss: 0.5827 - val_mae: 0.5741\n",
            "Epoch 98/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.2061 - mae: 0.3460 - val_loss: 0.5851 - val_mae: 0.5748\n",
            "Epoch 99/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.2020 - mae: 0.3430 - val_loss: 0.5859 - val_mae: 0.5750\n",
            "Epoch 100/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.2031 - mae: 0.3423 - val_loss: 0.5550 - val_mae: 0.5616\n"
          ]
        }
      ],
      "source": [
        "n_epochs = 200\n",
        "batch = 100\n",
        "val_pct = 0.2\n",
        "\n",
        "model_base = build_base()\n",
        "model_base_fitted = model_base.fit(x_train_norm,\n",
        "          y_train,\n",
        "          epochs=n_epochs,\n",
        "          batch_size=batch,\n",
        "          validation_split=val_pct,\n",
        "          verbose=1)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "QFq4hQ9rDn-T",
      "metadata": {
        "id": "QFq4hQ9rDn-T"
      },
      "source": [
        "#### 2.2.2 Dense layer model with 4 hidden layers with dropout regularization"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "id": "HR8kaC65B-un",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 211
        },
        "id": "HR8kaC65B-un",
        "outputId": "cbea6936-ad0f-4183-f004-b23f06158f97"
      },
      "outputs": [
        {
          "output_type": "error",
          "ename": "NameError",
          "evalue": "name 'build_dropout' is not defined",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-1-d2f080b431e8>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mmodel_dropout\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbuild_dropout\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m model_dropout_fitted = model_dropout.fit(x_train_norm,\n\u001b[1;32m      3\u001b[0m           \u001b[0my_train\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m           \u001b[0mepochs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mn_epochs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m           \u001b[0mbatch_size\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mbatch\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mNameError\u001b[0m: name 'build_dropout' is not defined"
          ]
        }
      ],
      "source": [
        "model_dropout = build_dropout()\n",
        "model_dropout_fitted = model_dropout.fit(x_train_norm,\n",
        "          y_train,\n",
        "          epochs=n_epochs,\n",
        "          batch_size=batch,\n",
        "          validation_split=val_pct,\n",
        "          verbose=1)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "_yV-zWSPDoXT",
      "metadata": {
        "id": "_yV-zWSPDoXT"
      },
      "source": [
        "#### 2.2.3 Dense layer model with 4 hidden layers with lasso regularization"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "wOMqKD56CERl",
      "metadata": {
        "id": "wOMqKD56CERl"
      },
      "outputs": [],
      "source": [
        "model_lasso = build_lasso()\n",
        "model_lasso_fitted = model_lasso.fit(x_train_norm,\n",
        "          y_train,\n",
        "          epochs=n_epochs,\n",
        "          batch_size=batch,\n",
        "          validation_split=val_pct,\n",
        "          verbose=1)"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "jk-XKXHYDo7x",
      "metadata": {
        "id": "jk-XKXHYDo7x"
      },
      "source": [
        "#### 2.2.4 Base dense layer model with 4 hidden layers with callback"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "Q5ZV30C3CXn6",
      "metadata": {
        "id": "Q5ZV30C3CXn6"
      },
      "outputs": [],
      "source": [
        "es_callback = keras.callbacks.EarlyStopping(\n",
        "    monitor='val_loss',\n",
        "    patience=5,\n",
        "    verbose=1)\n",
        "\n",
        "model_base_callback = build_base()\n",
        "model_base_callback_fitted = model_base_callback.fit(x_train_norm,\n",
        "          y_train,\n",
        "          epochs=n_epochs,\n",
        "          batch_size=batch,\n",
        "          validation_split=val_pct,\n",
        "          verbose=1,\n",
        "          callbacks=[es_callback])"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "pbkJkFi0DpZx",
      "metadata": {
        "id": "pbkJkFi0DpZx"
      },
      "source": [
        "#### 2.2.5 Base dense layer model with 4 hidden layers with dropout and callback"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "0CsdDFXxCmlD",
      "metadata": {
        "id": "0CsdDFXxCmlD"
      },
      "outputs": [],
      "source": [
        "model_dropout_callback = build_dropout()\n",
        "model_dropout_callback_fitted = model_dropout_callback.fit(x_train_norm,\n",
        "          y_train,\n",
        "          epochs=n_epochs,\n",
        "          batch_size=batch,\n",
        "          validation_split=val_pct,\n",
        "          verbose=1,\n",
        "          callbacks=[es_callback])"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "mWNRIehLDp1G",
      "metadata": {
        "id": "mWNRIehLDp1G"
      },
      "source": [
        "#### 2.2.6 Base dense layer model with 4 hidden layers with lasso regularization and callback"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "M9qW5ysTCnXC",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "M9qW5ysTCnXC",
        "outputId": "15e6a08c-86f5-40d2-8168-4705fb1c6abe"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Model: \"sequential_28\"\n",
            "_________________________________________________________________\n",
            " Layer (type)                Output Shape              Param #   \n",
            "=================================================================\n",
            " dense_140 (Dense)           (None, 64)                768       \n",
            "                                                                 \n",
            " dense_141 (Dense)           (None, 64)                4160      \n",
            "                                                                 \n",
            " dense_142 (Dense)           (None, 64)                4160      \n",
            "                                                                 \n",
            " dense_143 (Dense)           (None, 64)                4160      \n",
            "                                                                 \n",
            " dense_144 (Dense)           (None, 1)                 65        \n",
            "                                                                 \n",
            "=================================================================\n",
            "Total params: 13313 (52.00 KB)\n",
            "Trainable params: 13313 (52.00 KB)\n",
            "Non-trainable params: 0 (0.00 Byte)\n",
            "_________________________________________________________________\n",
            "Epoch 1/100\n",
            "39/39 [==============================] - 2s 8ms/step - loss: 14.0791 - mae: 3.1437 - val_loss: 3.4006 - val_mae: 1.2829\n",
            "Epoch 2/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 2.3715 - mae: 1.1725 - val_loss: 2.2426 - val_mae: 1.0506\n",
            "Epoch 3/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 1.7068 - mae: 0.9856 - val_loss: 1.7523 - val_mae: 0.9424\n",
            "Epoch 4/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 1.3807 - mae: 0.8825 - val_loss: 1.4069 - val_mae: 0.8459\n",
            "Epoch 5/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 1.1187 - mae: 0.7908 - val_loss: 1.1502 - val_mae: 0.7650\n",
            "Epoch 6/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.9143 - mae: 0.7073 - val_loss: 0.9151 - val_mae: 0.6776\n",
            "Epoch 7/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.7543 - mae: 0.6346 - val_loss: 0.8222 - val_mae: 0.6522\n",
            "Epoch 8/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.6781 - mae: 0.5965 - val_loss: 0.7334 - val_mae: 0.6075\n",
            "Epoch 9/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.6271 - mae: 0.5679 - val_loss: 0.7013 - val_mae: 0.5937\n",
            "Epoch 10/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.6046 - mae: 0.5590 - val_loss: 0.6531 - val_mae: 0.5677\n",
            "Epoch 11/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.5743 - mae: 0.5397 - val_loss: 0.6567 - val_mae: 0.5695\n",
            "Epoch 12/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.5717 - mae: 0.5354 - val_loss: 0.6521 - val_mae: 0.5688\n",
            "Epoch 13/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.5562 - mae: 0.5312 - val_loss: 0.6910 - val_mae: 0.6008\n",
            "Epoch 14/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.5442 - mae: 0.5222 - val_loss: 0.6299 - val_mae: 0.5642\n",
            "Epoch 15/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.5317 - mae: 0.5166 - val_loss: 0.6370 - val_mae: 0.5641\n",
            "Epoch 16/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.5225 - mae: 0.5116 - val_loss: 0.6102 - val_mae: 0.5530\n",
            "Epoch 17/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.5165 - mae: 0.5057 - val_loss: 0.6086 - val_mae: 0.5548\n",
            "Epoch 18/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.5166 - mae: 0.5071 - val_loss: 0.6078 - val_mae: 0.5528\n",
            "Epoch 19/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.5039 - mae: 0.5004 - val_loss: 0.6098 - val_mae: 0.5537\n",
            "Epoch 20/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.5080 - mae: 0.5028 - val_loss: 0.6807 - val_mae: 0.6047\n",
            "Epoch 21/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.5132 - mae: 0.5040 - val_loss: 0.6668 - val_mae: 0.5996\n",
            "Epoch 22/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.4904 - mae: 0.4913 - val_loss: 0.5948 - val_mae: 0.5497\n",
            "Epoch 23/100\n",
            "39/39 [==============================] - 0s 7ms/step - loss: 0.4792 - mae: 0.4853 - val_loss: 0.5844 - val_mae: 0.5464\n",
            "Epoch 24/100\n",
            "39/39 [==============================] - 0s 8ms/step - loss: 0.4775 - mae: 0.4844 - val_loss: 0.6001 - val_mae: 0.5542\n",
            "Epoch 25/100\n",
            "39/39 [==============================] - 0s 8ms/step - loss: 0.4766 - mae: 0.4854 - val_loss: 0.6085 - val_mae: 0.5647\n",
            "Epoch 26/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.4707 - mae: 0.4808 - val_loss: 0.5937 - val_mae: 0.5501\n",
            "Epoch 27/100\n",
            "39/39 [==============================] - 0s 7ms/step - loss: 0.4654 - mae: 0.4776 - val_loss: 0.5767 - val_mae: 0.5462\n",
            "Epoch 28/100\n",
            "39/39 [==============================] - 0s 7ms/step - loss: 0.4637 - mae: 0.4778 - val_loss: 0.5823 - val_mae: 0.5472\n",
            "Epoch 29/100\n",
            "39/39 [==============================] - 0s 8ms/step - loss: 0.4610 - mae: 0.4737 - val_loss: 0.5746 - val_mae: 0.5446\n",
            "Epoch 30/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.4541 - mae: 0.4703 - val_loss: 0.5822 - val_mae: 0.5465\n",
            "Epoch 31/100\n",
            "39/39 [==============================] - 0s 6ms/step - loss: 0.4525 - mae: 0.4711 - val_loss: 0.5848 - val_mae: 0.5497\n",
            "Epoch 32/100\n",
            "39/39 [==============================] - 0s 8ms/step - loss: 0.4513 - mae: 0.4698 - val_loss: 0.5769 - val_mae: 0.5452\n",
            "Epoch 33/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.4481 - mae: 0.4685 - val_loss: 0.5702 - val_mae: 0.5437\n",
            "Epoch 34/100\n",
            "39/39 [==============================] - 0s 4ms/step - loss: 0.4438 - mae: 0.4671 - val_loss: 0.5752 - val_mae: 0.5442\n",
            "Epoch 35/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.4386 - mae: 0.4632 - val_loss: 0.5859 - val_mae: 0.5493\n",
            "Epoch 36/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.4368 - mae: 0.4614 - val_loss: 0.5819 - val_mae: 0.5476\n",
            "Epoch 37/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.4336 - mae: 0.4586 - val_loss: 0.6029 - val_mae: 0.5589\n",
            "Epoch 38/100\n",
            "39/39 [==============================] - 0s 5ms/step - loss: 0.4319 - mae: 0.4599 - val_loss: 0.5821 - val_mae: 0.5497\n",
            "Epoch 38: early stopping\n"
          ]
        }
      ],
      "source": [
        "model_lasso_callback = build_lasso()\n",
        "model_lasso_callback_fitted = model_lasso_callback.fit(x_train_norm,\n",
        "          y_train,\n",
        "          epochs=n_epochs,\n",
        "          batch_size=batch,\n",
        "          validation_split=val_pct,\n",
        "          verbose=1,\n",
        "          callbacks=[es_callback])"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "vej1CColIimg",
      "metadata": {
        "id": "vej1CColIimg"
      },
      "source": [
        "### 3. Evaluation"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "6e3ea46a",
      "metadata": {
        "id": "6e3ea46a"
      },
      "source": [
        "After having built and fitted the 6 variations, let's plot their loss function values in Mean Squared Error evolution along each epoch for the training and validation set. Additionally, let's evaluate the MSE and MAE results for all variations,"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "DZO5zk1as3Hx",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "DZO5zk1as3Hx",
        "outputId": "ec49eefa-1bbc-4954-bfa0-828b9d158b4a"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1600x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1600x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1600x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1600x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1600x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1600x600 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "fitted_models = {\n",
        "    'base': model_base_fitted,\n",
        "    'dropout': model_dropout_fitted,\n",
        "    'lasso': model_lasso_fitted,\n",
        "    'base_callback': model_base_callback_fitted,\n",
        "    'dropout_callback': model_dropout_callback_fitted,\n",
        "    'lasso_callback': model_lasso_callback_fitted\n",
        "}\n",
        "\n",
        "for model_name, model in fitted_models.items():\n",
        "    show_loss_accuracy_evolution(model, model_name)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "descending-letters",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "descending-letters",
        "outputId": "55922da9-7446-41c1-ff56-752bf6071b80"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Test loss (MSE) of base: 0.5970089435577393. MAE: 0.5638329982757568\n",
            "Test loss (MSE) of dropout: 0.5398067831993103. MAE: 0.5584486722946167\n",
            "Test loss (MSE) of lasso: 0.6082820296287537. MAE: 0.5608219504356384\n",
            "Test loss (MSE) of base_callback: 0.5298696756362915. MAE: 0.5632451772689819\n",
            "Test loss (MSE) of dropout_callback: 0.6343355774879456. MAE: 0.6327802538871765\n",
            "Test loss (MSE) of lasso_callback: 0.5986592769622803. MAE: 0.553979218006134\n"
          ]
        }
      ],
      "source": [
        "models = {\n",
        "    'base': model_base,\n",
        "    'dropout': model_dropout,\n",
        "    'lasso': model_lasso,\n",
        "    'base_callback': model_base_callback,\n",
        "    'dropout_callback': model_dropout_callback,\n",
        "    'lasso_callback': model_lasso_callback\n",
        "}\n",
        "\n",
        "for model_name, model in models.items():\n",
        "  test_loss, test_mae = model.evaluate(x_test_norm, y_test, verbose=0)\n",
        "  print(f'Test loss (MSE) of {model_name}: {np.mean(test_loss)}. MAE: {np.mean(test_mae)}')"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The MSE in the training set represents the bias error, while the difference in validation/test vs. training error represents the variance. A low variance and high bias indicates that the model might be underfitting, while the opposite, a low bias and high variance, means the model might be overfitting.\n",
        "\n",
        "The results drawn from the test evaluation indicate that the full version and early stopped version of lasso regularization perform worse than the base model in these forms, respectively. However, as stated earlier, lasso heavily depends on the regularization term which should be tuned to perform at its best, therefore this lack of improvement could be solved by finding the optimal value for this term.\n",
        "\n",
        "The dropout regularization method, on the other hand, performs better than the base model just without the early stoppage, which performs the poorest out of all methods. Observing the plots above, it can be seen that both bias and variance decrease over epoch though slowly. Thus, given the better test results from the not stopped version, it indicates that rather than overfitting prevention, underfitting is achieved and the patience parameter from the early stopping callback should be relaxed perhaps improving it beyond base model.\n",
        "\n",
        "Finally, it can be affirmed than a simple early stopping strategy can greatly reduce overfitting in a base linear regression model.\n",
        "\n",
        "On an additional final note, these comparisons could be more rigorously made through CV, having optimized each regularization method to perform a fair assessement."
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