DS10_2021_Wine_Classification_Part_2.ipynb

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      "source": [
        "<a id='top'></a>\n",
        "# DS10 Wine Classification - Part 2\n",
        "Notebook by Rashmi Banthia and Hanspeter Pfister\n",
        "\n",
        "**Make a copy of this notebook before you make any edits.** Add your name and the name of your team and team members in the text cell below. Answer all of the questions inside the notebook using text and code. Add your answers after the **A** in the text cells. Each team will only submit one notebook. \n",
        "\n",
        "In addition to submitting the completed notebook, each team will also submit a PDF with plots and solutions to some of the exercises below. Check the project instructions on Canvas for submission information.\n",
        "\n",
        "This notebook covers the following topics:\n",
        "\n",
        "- Logistic regression, decision tree, SVM, and kNN models \n",
        "- Model Performance Assessment \n",
        "     - Accuracy Score\n",
        "     - Confusion Matrix\n",
        "     - ROC Curve and AUC Score\n",
        "     - Precision-Recall Curve\n",
        "     - F1 Score\n",
        "- Cross-Validation and Grid Search\n",
        "     - SVM - find optimal kernel and parameter C\n",
        "     - kNN - find optimal k\n",
        "     - Decision Tree - find optimal tree depth\n",
        "     - Effects of Optimal Hyperparameters\n",
        "- Advanced Topics\n",
        "     - Feature Importance (Decision Tree Example)\n",
        "     - Visualizing Decision Boundaries\n",
        "     - Balanced vs. Imbalanced Data\n",
        "     - Dealing with Imbalanced Data\n",
        "\n",
        "**Note: The exercises for Effects of Optimal Hyperparameters, Visualizing Decision Boundaries, and Balanced vs. Imbalanced Data at the end will take some time, so please get started early!**"
      ]
    },
    {
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      "source": [
        "\n",
        "--------\n",
        "**Team Name:**\n",
        "\n",
        "**Team Members:**\n",
        "\n",
        "--------"
      ]
    },
    {
      "cell_type": "code",
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      "source": [
        "# Pandas is a powerful package that deals with tables (https://pandas.pydata.org)\n",
        "# You will get a proper introduction to Pandas in the labs.\n",
        "import pandas as pd\n",
        "# Of course we will be using Numpy\n",
        "import numpy as np\n",
        "\n",
        "# We are using scikit-learn for machine learning (https://scikit-learn.org/stable/)\n",
        "# Because scikit-learn is a big package it is good practice to only import the modules we need.\n",
        "from sklearn.tree import DecisionTreeClassifier\n",
        "import graphviz \n",
        "from sklearn.tree import export_graphviz\n",
        "\n",
        "from sklearn.ensemble import RandomForestClassifier\n",
        "from sklearn.model_selection import cross_val_score, GridSearchCV\n",
        "from sklearn.metrics import f1_score, confusion_matrix, plot_confusion_matrix\n",
        "from sklearn.metrics import accuracy_score, precision_score,  recall_score, average_precision_score\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "from sklearn.metrics import precision_recall_curve\n",
        "from sklearn.metrics import plot_precision_recall_curve, roc_auc_score, roc_curve, auc\n",
        "from sklearn.metrics import mean_squared_error\n",
        "\n",
        "from sklearn.svm import SVC \n",
        "from sklearn.neighbors import KNeighborsClassifier\n",
        "from sklearn.linear_model import LogisticRegression \n",
        "\n",
        "# We will be using statsmodels for linear regression (https://www.statsmodels.org/stable/index.html) \n",
        "import statsmodels.api as sm\n",
        "from statsmodels import graphics\n",
        "\n",
        "# Some useful libraries to import data\n",
        "import requests\n",
        "from urllib.request import urlopen\n",
        "from io import BytesIO\n",
        "from zipfile import ZipFile\n",
        "\n",
        "# Libraries for visualizations\n",
        "from matplotlib import pyplot as plt\n",
        "import seaborn as sns\n",
        "# Some settings to make the plots prettier\n",
        "%matplotlib inline\n",
        "sns.set_theme(style=\"ticks\")\n",
        "sns.set_context(\"talk\", font_scale=0.9)\n",
        "sns.set(font_scale = 1)"
      ],
      "execution_count": null,
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          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ],
          "name": "stderr"
        }
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      "source": [
        "### Getting the Data"
      ]
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      "source": [
        "# Reading the dataset into a Pandas dataframe (df)\n",
        "df = pd.read_csv('https://raw.githubusercontent.com/hpfister/ds10/master/winequality-red.csv', sep=';')\n",
        "# 'https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-red.csv' # Alternate URL\n",
        "print(df.shape) # we have 1599 rows and 12 columns\n",
        "df.head()"
      ],
      "execution_count": null,
      "outputs": [
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          "text": [
            "(1599, 12)\n"
          ],
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        },
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          "output_type": "execute_result",
          "data": {
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              "\n",
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              "</style>\n",
              "<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",
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            ],
            "text/plain": [
              "   fixed acidity  volatile acidity  citric acid  ...  sulphates  alcohol  quality\n",
              "0            7.4              0.70         0.00  ...       0.56      9.4        5\n",
              "1            7.8              0.88         0.00  ...       0.68      9.8        5\n",
              "2            7.8              0.76         0.04  ...       0.65      9.8        5\n",
              "3           11.2              0.28         0.56  ...       0.58      9.8        6\n",
              "4            7.4              0.70         0.00  ...       0.56      9.4        5\n",
              "\n",
              "[5 rows x 12 columns]"
            ]
          },
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          "execution_count": 2
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      "source": [
        "### Predicted Value\n",
        "\n",
        "Our target predicted value is `quality`, which is a discrete ordinal value in the range (3, 8). First, lets take a look at the number of wines for each quality level in the dataset. "
      ]
    },
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      "source": [
        "# Our target Predicted value is quality \n",
        "print(df.quality.value_counts())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "5    681\n",
            "6    638\n",
            "7    199\n",
            "4     53\n",
            "8     18\n",
            "3     10\n",
            "Name: quality, dtype: int64\n"
          ],
          "name": "stdout"
        }
      ]
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      "source": [
        "------\n",
        "### Binary Classification\n",
        "\n",
        "We are going to convert this into a binary classification problem. I.e., we will convert the ordinal values of `quality` into a binary class (0, 1) (0 = bad quality, 1 = good quality). \n",
        "\n",
        "We decide that wines with quality `>=6` are good quality (i.e., `quality=1`) and wines with quality `<6` are bad quality (i.e., `quality=0`). Later on you will change this threshold to create an imbalanced dataset. For now, pay attention to where it says \"COME BACK HERE\" in the code. "
      ]
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      "source": [
        "# By convention, the perdictor are stored in the vector Y\n",
        "Y = df.quality\n",
        "\n",
        "# By convention, the features are stored in the vector X\n",
        "X = df[df.columns.difference(['quality'])]\n",
        "print(X.shape, Y.shape)\n",
        "\n",
        "# Original code - leave this for your first run through\n",
        "# Convert Y to a vector with binary values. Ratings 6,7,8 are good quality, <6 are bad quality\n",
        "Y = np.array([1 if y>=6 else 0 for y in Y])\n",
        "\n",
        "# COME BACK HERE: Later on, you will change the ratings threshold to get an imbalanced dataset \n",
        "# Imbalanced: Ratings 7,8 are good quality,  3,4,5,6 are bad quality - comment line 10 and uncomment line 14\n",
        "# Y = np.array([1 if y>=7 else 0 for y in Y])\n",
        "\n",
        "# Print the percentage of samples in each class\n",
        "print(\"\\n\\nBinary Classification (1 = Good quality  , 0 = Bad quality): \")\n",
        "print(pd.Series(Y).value_counts(normalize=True))  "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(1599, 11) (1599,)\n",
            "\n",
            "\n",
            "Binary Classification (1 = Good quality  , 0 = Bad quality): \n",
            "1    0.534709\n",
            "0    0.465291\n",
            "dtype: float64\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "# Basic ML Models\n",
        "\n",
        "We are training the same basic ML models we used in part 1:\n",
        "- Logistic regression\n",
        "- SVM\n",
        "- Decision Tree\n",
        "- k-Nearest Neighbor (kNN)\n",
        "\n",
        "We will first create our training and test data and then standardize the data. \n",
        "\n",
        "In a binary classification problem, we may decide to predict the class values (0 or 1) for each wine directly. However, it is more flexible to predict the probabilities for each class instead. The reason for this is to provide the capability to choose and even calibrate a **threshold** for how to interpret the predicted probabilities. \n",
        "\n",
        "For example, a threshold of 0.5 means that a probability in [0.0, 0.49] is a negative outcome (0=bad quality) and a probability in [0.5, 1.0] is a positive outcome (1=good quality). This threshold can be adjusted to tune the behavior of the model for a specific problem. An example would be to reduce more of one or another type of error.\n",
        "\n",
        "In the following code, we are making sure that all our models output probabilities for each class. We will then compute confusion matrices and then adjust the threshold to compute ROC/AUC and precision / recall curves."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00010-135f7ef5-bea1-4907-a6ee-be7c693d5a7f",
        "deepnote_cell_type": "markdown",
        "id": "hkk69ZI2jE56"
      },
      "source": [
        "**Split and Standardize Data**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00011-9e8d9bbd-6b68-487c-aef2-1fe4cb4e8522",
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        "execution_start": 1615167672905,
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      "source": [
        "# From Part 1 \n",
        "# Split data into train (80%) and test (20%) sets.\n",
        "# random_state: Controls the shuffling applied to the data before applying the split. \n",
        "#              Pass an int for reproducible output across multiple function calls.\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, Y,\n",
        "                                                    test_size=0.2,\n",
        "                                                    random_state=10)\n",
        "\n",
        "\n",
        "# Standardize the features\n",
        "\n",
        "# We standardize training and test data separately to avoid information leakage between them\n",
        "# Also note we do not standardize the predicted value `quality`, just the features\n",
        "scaler = StandardScaler()\n",
        "X_train_s = scaler.fit_transform(X_train)\n",
        "X_test_s = scaler.transform(X_test)\n",
        "\n",
        "# sklearn StandardScaler() returns Numpy arrays. That means your column names are gone. \n",
        "# If we want to preserve the column names we need to convert the array back to a Pandas dataframe and add the column names. \n",
        "X_train_s = pd.DataFrame(X_train_s,columns=X.columns)\n",
        "X_test_s = pd.DataFrame(X_test_s,columns=X.columns)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
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        "deepnote_cell_type": "markdown",
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      },
      "source": [
        "**Logistic Regression**"
      ]
    },
    {
      "cell_type": "code",
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        "tags": [],
        "cell_id": "00011-7769712e-29dc-4955-b80b-24ab1f14acf9",
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        "execution_start": 1615167675302,
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      "source": [
        "# From Part 1 \n",
        "# Creating the logistic regression model\n",
        "# Hyperparamter 'C' controls how much regularization the model uses (smaller C = more regularization)\n",
        "lr_clf = LogisticRegression(solver='liblinear', \n",
        "                           random_state=57,C=10000) \n",
        "\n",
        "# Fitting the model to the data (i.e., training the model)\n",
        "lr_clf.fit(X_train_s, y_train)\n",
        "\n",
        "# Predictions on the test set\n",
        "lr_preds = lr_clf.predict(X_test_s)\n",
        "\n",
        "# Predict probabilities on the test set\n",
        "# Predicted probabilites are required for plotting ROC AUC curve\n",
        "lr_preds_prob = lr_clf.predict_proba(X_test_s)\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00013-f6bf0249-e722-4599-83af-423a79ef53b2",
        "deepnote_cell_type": "markdown",
        "id": "2rRYBnoIjE57"
      },
      "source": [
        "**Support Vector Machine**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00013-ec1d04ed-adff-4204-a5e7-ceccd7d22637",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "5a1f2292",
        "execution_millis": 374,
        "execution_start": 1615167677609,
        "deepnote_cell_type": "code",
        "id": "c1t1FnugjE57"
      },
      "source": [
        "# From Part 1\n",
        "# Creating the SVM model\n",
        "# We are setting probability=True for the model to predict probabilites (this was not in part 1)\n",
        "# Note the hyperparameters 'kernel' and 'C' (smaller C = more regularization) - we will come back to these later\n",
        "# INITIAL CODE\n",
        "svc_clf = SVC( kernel='rbf', C=100.0, probability=True, random_state=10) \n",
        "# OPTIMAL HYPERPARAMETERS\n",
        "# Change your optimal parameters here after you finished the \"Cross-Validation and Grid Search\" section.\n",
        "# svc_clf = SVC( kernel='rbf', C=100.0, probability=True, random_state=10)\n",
        "\n",
        "# Fitting the model to the data (i.e., training the model)\n",
        "svc_clf.fit(X_train_s, y_train) \n",
        "\n",
        "# Predictions on the test set\n",
        "svc_preds = svc_clf.predict(X_test_s)\n",
        "\n",
        "# Predict probabilities on the test set\n",
        "# Predicted probabilites are required for plotting ROC AUC curve\n",
        "svc_preds_prob = svc_clf.predict_proba(X_test_s)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00015-72b99262-1b56-4b12-9337-6f078385a5de",
        "deepnote_cell_type": "markdown",
        "id": "RJ2xv8ZkjE57"
      },
      "source": [
        "**Decision Tree** "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00016-9d2815ad-b191-42da-92bc-919b594cb130",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "c524c6f8",
        "execution_millis": 7,
        "execution_start": 1615167680075,
        "deepnote_cell_type": "code",
        "id": "y2uXp3NHjE59"
      },
      "source": [
        "# From Part 1 \n",
        "# Creating the DT model\n",
        "# Note the hyperparameter 'max_depth' - we will come back to this later\n",
        "# INITIAL CODE\n",
        "clf_dt = DecisionTreeClassifier(max_depth=10, random_state=10) \n",
        "# OPTIMAL HYPERPARAMETERS\n",
        "# Change your optimal parameters here after you finished the \"Cross-Validation and Grid Search\" section.\n",
        "# clf_dt = DecisionTreeClassifier(max_depth=10, random_state=10) \n",
        "\n",
        "# Fitting the model to the data (i.e., training the model)\n",
        "clf_dt.fit(X_train_s, y_train)\n",
        "\n",
        "# Predictions on the test set\n",
        "dt_preds = clf_dt.predict(X_test_s)\n",
        "\n",
        "# Predict probabilities on the test set\n",
        "# Predicted probabilites are required for plotting ROC AUC curve\n",
        "dt_preds_prob = clf_dt.predict_proba(X_test_s)\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00017-6b67c45f-dd02-4e2d-bb60-fd0b508a0069",
        "deepnote_cell_type": "markdown",
        "id": "KEC49wlsjE59"
      },
      "source": [
        "**KNearest Neighbors**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00018-3c6096a8-faab-42b7-b2b6-a86dd5f47f8f",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "68f740cd",
        "execution_millis": 27,
        "execution_start": 1615167681904,
        "deepnote_cell_type": "code",
        "id": "7kwJdDXzjE59"
      },
      "source": [
        "# From Part 1 \n",
        "# Creating the KNN model\n",
        "# Note the hyperparameter 'n_neighbors' (or k) and p - we will come back to this later\n",
        "# INITIAL CODE\n",
        "clf_knn = KNeighborsClassifier(n_neighbors=10, p=2)\n",
        "# OPTIMAL HYPERPARAMETERS\n",
        "# Change your optimal parameters here after you finished the \"Cross-Validation and Grid Search\" section.\n",
        "# clf_knn = KNeighborsClassifier(n_neighbors=10, p=2)\n",
        "\n",
        "# Fitting the model to the data (i.e., training the model)\n",
        "clf_knn.fit(X_train_s, y_train)\n",
        "\n",
        "# Predictions on the test set\n",
        "knn_preds = clf_knn.predict(X_test_s)\n",
        "\n",
        "# Predict probabilities on the test set\n",
        "# Predicted probabilites are required for plotting ROC AUC curve\n",
        "knn_preds_prob = clf_knn.predict_proba(X_test_s)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00011-42d9554f-0bc3-49ee-80b8-2422891a315a",
        "deepnote_cell_type": "markdown",
        "id": "mJ7WypFRjE59"
      },
      "source": [
        "# Model Performance Assessment\n",
        "\n",
        "We will now compare several error metrics to assess the performance of our classification models. Please take note and capture screenshots of the visualizations. Later on you will come back to re-run these cells with an imbalanced dataset, and we would like you to compare the results of the balanced and imbalanced data. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00012-2e569f0c-716e-468a-be63-d80c9dbfacde",
        "deepnote_cell_type": "markdown",
        "id": "a2dgFxNtjE5-"
      },
      "source": [
        "## [Accuracy](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.accuracy_score.html)\n",
        "\n",
        "The most commonly used metric to judge a model is accuracy. Unfortunately, accuracy is a bad indicator of model performance, especially when the classes are imbalanced. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00013-071c85b9-e1b3-4165-8c04-aabb1d1b1978",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "e62c6d13",
        "execution_millis": 21,
        "execution_start": 1615167684303,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AEFxMisPjE5-",
        "outputId": "9d7afd58-8277-40f7-da00-4ead4b09135c"
      },
      "source": [
        "# Setting different colors for the print statements\n",
        "class color:\n",
        "   PURPLE = '\\033[95m'\n",
        "   CYAN = '\\033[96m'\n",
        "   DARKCYAN = '\\033[36m'\n",
        "   BLUE = '\\033[94m'\n",
        "   GREEN = '\\033[92m'\n",
        "   YELLOW = '\\033[93m'\n",
        "   RED = '\\033[91m'\n",
        "   BOLD = '\\033[1m'\n",
        "   UNDERLINE = '\\033[4m'\n",
        "   END = '\\033[0m'\n",
        "\n",
        "\n",
        "# We evaluate each model on the test set with accuracy\n",
        "print(color.BOLD + '\\nLogistic Regression: ') \n",
        "print(\"Accuracy:\", accuracy_score(y_test,lr_preds))\n",
        "\n",
        "print(color.BLUE + '\\nSupport Vector Machine: ')\n",
        "print(\"Accuracy:\", accuracy_score(y_test,svc_preds))\n",
        "\n",
        "\n",
        "print(color.RED + '\\nDecision Tree: ')\n",
        "print(\"Accuracy:\", accuracy_score(y_test,dt_preds))\n",
        "\n",
        "print(color.PURPLE + '\\nKNearest Neighbors: ')\n",
        "print(\"Accuracy:\", accuracy_score(y_test,knn_preds))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[1m\n",
            "Logistic Regression: \n",
            "Accuracy: 0.73125\n",
            "\u001b[94m\n",
            "Support Vector Machine: \n",
            "Accuracy: 0.7375\n",
            "\u001b[91m\n",
            "Decision Tree: \n",
            "Accuracy: 0.778125\n",
            "\u001b[95m\n",
            "KNearest Neighbors: \n",
            "Accuracy: 0.71875\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00014-2bba8738-2cf9-4b96-816a-4bd26049cd86",
        "deepnote_cell_type": "markdown",
        "id": "4sIceTgojE5-"
      },
      "source": [
        "**Q** We said that accuracy is a bad metric for imbalanced data. For example, the chances of having cancer are very low. Let’s say 90 out of 100 patients do not have cancer and the remaining 10 actually have it. What simple, but useless model would get 90% accuracy for this data?\n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vPEMjWlR-Ps7",
        "cell_id": "00030-8cd003be-7f1d-4b26-9551-1b89282c04e5",
        "deepnote_cell_type": "markdown"
      },
      "source": [
        "## [Confusion Matrix](https://scikit-learn.org/stable/modules/model_evaluation.html#confusion-matrix)\n",
        "The confusion matrix nicely summarizes the following quantities:\n",
        "\n",
        "- True positives (TP): Predicted positive and are actually positive.\n",
        "- False positives (FP): Predicted positive and are actually negative.\n",
        "- True negatives (TN): Predicted negative and are actually negative.\n",
        "- False negatives (FN): Predicted negative and are actually positive.\n",
        "\n",
        "See [Wikipedia](#https://en.wikipedia.org/wiki/Confusion_matrix) for a good explanation and a nice figure on how the confusion matrix relates to the different error metrics."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00026-fe29633f-81fd-4c87-b9fe-dae1f8185b6f",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "f6db4935",
        "execution_millis": 911,
        "execution_start": 1615167687772,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 646
        },
        "id": "niAlytbyjE5-",
        "outputId": "11d12ea0-3069-42d7-fbf7-241e41a51f97"
      },
      "source": [
        "# CAREFUL: scikit-learn plots the confusion matrix with TP in the lower right corner unlike \n",
        "# what would be considered the \"standard\" arrangement with TP in the upper left corner. \n",
        "# Alway check the axis in the confusion matrix plot!\n",
        "\n",
        "fig, axs = plt.subplots(2, 2, figsize=(10,10))\n",
        "fig.suptitle('Confusion Matrix')\n",
        "# remove the x and y ticks\n",
        "plt.setp(axs, xticks=[], yticks=[])\n",
        "threshold = 0.5\n",
        "group_names = ['True Neg','False Pos','False Neg','True Pos']\n",
        "\n",
        "all_preds = [lr_preds_prob, svc_preds_prob, dt_preds_prob, knn_preds_prob]\n",
        "titles = ['Logistic Regression', 'Support Vector Machines', 'Decision Tree', 'KNearestNeighors']\n",
        "\n",
        "for i in range(2):\n",
        "    for j in range(2):\n",
        "        cf_matrix =  confusion_matrix(y_test, all_preds[i*2+j][:,1]>threshold) \n",
        "        group_counts = [value for value in  cf_matrix.flatten()]\n",
        "        labels = [f\"{v1}\\n{v2}\" for v1, v2 in  zip(group_names,group_counts)]\n",
        "        labels = np.asarray(labels).reshape(2,2)\n",
        "        axs[i,j].title.set_text(titles[i*2+j])\n",
        "        sns.heatmap(cf_matrix, annot=labels, fmt='', ax=axs[i,j])\n",
        "\n",
        "\n",
        "plt.setp(axs, xticks=[], yticks=[]); #Remove x and y tick labels"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x720 with 8 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00028-2caa2ba8-79cc-47cc-956f-15ff358999d9",
        "deepnote_cell_type": "markdown",
        "id": "Py5My49IjE5_"
      },
      "source": [
        "**Q** Looking at these confusion matrices, rank the models by performance, and explain your ranking. \n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00028-c8795a1f-dfac-4143-a7a8-085d2e7c3af1",
        "deepnote_cell_type": "markdown",
        "id": "jE_kYWrcjE5_"
      },
      "source": [
        "---\n",
        "**Q** Looking at the SVM confusion matrix, how would you feel about this model if this were a medical diagnosis example (0 = disease not present, 1 = disease present)? \n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00018-dc3922ed-ac40-4025-b713-de2e391c38e4",
        "deepnote_cell_type": "markdown",
        "id": "Jdpxq_GEjE5_"
      },
      "source": [
        "## [ROC Curve and AUC Score](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.roc_curve.html?highlight=roc_curve#sklearn.metrics.roc_curve)\n",
        "\n",
        "The ROC (Receiver Operator Characteristics) curve shows the TPR (true positive rate) and FPR (false positive rate) for a number of different threshold values to convert class probabilites to binary classification outputs. Put another way, it plots the false alarm rate (FPR) versus the hit rate (TPR).\n",
        "\n",
        "The true positive rate is calculated as the number of true positives divided by the sum of the number of true positives and the number of false negatives. It describes how good the model is at predicting the positive class when the actual outcome is positive.\n",
        "\n",
        "**True Positive Rate = True Positives / (True Positives + False Negatives)**\n",
        "\n",
        "The false positive rate is calculated as the number of false positives divided by the sum of the number of false positives and the number of true negatives. It is also called the false alarm rate as it summarizes how often a positive class is predicted when the actual outcome is negative.\n",
        "\n",
        "**False Positive Rate = False Positives / (False Positives + True Negatives) = 1 - Specificity**\n",
        "\n",
        "The diagonal line indicates random chance results for all thresholds. The Area Under Curve (AUC) metric computes the area under the ROC curve. The higher the AUC score, the better. It is a better metric than accuracy in case of class imbalance. \n",
        "\n",
        "[Source](https://machinelearningmastery.com/roc-curves-and-precision-recall-curves-for-classification-in-python/)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00026-3ad002db-1675-4756-964c-9625f9a8e293",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "67968a02",
        "execution_millis": 240,
        "execution_start": 1615167692326,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 464
        },
        "id": "oiCo0euojE5_",
        "outputId": "69036fc0-3071-4ed0-88ef-7362af1e8e61"
      },
      "source": [
        "# Compare all classifiers (Logisitic Regression, SVM, Decision Tree and KNN) with ROC curves and AUC\n",
        "plt.figure(figsize=(12,7))\n",
        "labels = ['LR', 'SVM', 'DT', 'KNN']\n",
        "all_preds = [lr_preds_prob, svc_preds_prob, dt_preds_prob, knn_preds_prob]\n",
        "\n",
        "# For all four models:\n",
        "for i in range(4):\n",
        "    # The roc_curve() function takes both the true outcomes (0,1) from the test set and \n",
        "    # the predicted probabilities for the 1 class. The function returns the false positive \n",
        "    # rates for each threshold, true positive rates for each threshold, and the thresholds.\n",
        "    fpr, tpr, roc_thresholds = roc_curve(y_test,all_preds[i][:,1])\n",
        "    \n",
        "    # The auc() function computes the AUC\n",
        "    roc_auc = auc(fpr, tpr)\n",
        "\n",
        "    plt.plot(fpr, tpr, lw=2, label='%s (AUC = %0.2f)' % (labels[i], roc_auc))\n",
        "\n",
        "# Diagonal line for chance predictions\n",
        "plt.plot([0, 1], [0, 1], '--', color=(0.6, 0.6, 0.6), label='Luck'); \n",
        "\n",
        "# Show a bit beyond range [0,1]\n",
        "plt.xlim([-0.05, 1.05])\n",
        "plt.ylim([-0.05, 1.05])\n",
        "\n",
        "# Axis labels and legend\n",
        "plt.xlabel('False Positive Rate')\n",
        "plt.ylabel('True Positive Rate')\n",
        "plt.title('ROC curve for different ML models')\n",
        "plt.legend(loc=\"lower right\")\n",
        "\n",
        "# Show the plot\n",
        "plt.show()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00031-4a4710de-a74d-4498-a512-1d67cd629d49",
        "deepnote_cell_type": "markdown",
        "id": "x4ZqEKNCjE5_"
      },
      "source": [
        "**Q** What do you notice? What do you wonder?\n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00032-74949efb-478e-4de0-aa66-eca5b827d4b2",
        "deepnote_cell_type": "markdown",
        "id": "RC4MkLNQjE5_"
      },
      "source": [
        "-----\n",
        "**Q** Looking at the ROC curve for the SVM model, what values are a desirable balance between the false positives and false negatives? Report the (TPR, FPR) values for the optimal point on the ROC curve and explain your reasoning. \n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00030-e921fb57-6fc5-43b2-80fc-3441d9cc87d7",
        "deepnote_cell_type": "markdown",
        "id": "dtwec1hbjE5_"
      },
      "source": [
        "-----\n",
        "**Q** Are the class predictions that gets passed to `roc_curve()` discrete or continuous? \n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00021-1f84ccf9-abdb-4937-83cd-a04bcfc71b54",
        "deepnote_cell_type": "markdown",
        "id": "9-ouA-w1jE5_"
      },
      "source": [
        "## [Precision-Recall Curve](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.precision_recall_curve.html)\n",
        "\n",
        "A precision-recall curve is a plot of the precision (y-axis) and the recall (x-axis) for different thresholds, much like the ROC curve. \n",
        "\n",
        "Precision is a ratio of the number of true positives divided by the sum of the true positives and false positives. It describes how good a model is at predicting the positive class. Precision is also referred to as the positive predictive value (PPV).\n",
        "\n",
        "**Precision = True Positives / (True Positives + False Positives) = PPV **\n",
        "\n",
        "Recall is calculated as the ratio of the number of true positives divided by the sum of the true positives and the false negatives. Recall is the same as sensitivity.\n",
        "\n",
        "**Recall = True Positives / (True Positives + False Negatives) = Sensitivity**\n",
        "\n",
        "Reviewing both precision and recall is useful in cases where there is an imbalance in the observations between the two classes. Specifically, if there are many examples of no event (class 0) and only a few examples of an event (class 1). \n",
        "\n",
        "Typically, the large number of class 0 examples (i.e., high true negatives) means we are less interested in the skill of the model at predicting class 0 correctly. [Precision and recall are better for imbalanced data](https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0118432) because the calculations do not make use of the true negatives (class 0) and are only concerned with the correct prediction of the minority class (class 1).\n",
        "\n",
        "A no-skill classifier is one that cannot discriminate between the classes and would predict a random class or a constant class in all cases. The no-skill line is a horizontal line that changes based on the value of the ratio of positive to negative cases in the dataset. For a balanced dataset this is line is at y=0.5.\n",
        "\n",
        "A model with perfect skill is depicted as a point at (1,1). A skilful model is represented by a curve that bows towards (1,1) above the flat line of no skill. The AUC summarizes the integral or an approximation of the area under the precision-recall curve across thresholds like the ROC AUC.\n",
        "\n",
        "[Source](https://machinelearningmastery.com/roc-curves-and-precision-recall-curves-for-classification-in-python/)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00036-366190aa-1fc3-4b8e-a070-4bb67ab6f2e7",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "68642bd9",
        "execution_millis": 298,
        "execution_start": 1615167697502,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "xvOM5NN1jE6A",
        "outputId": "bb9f0d7c-7770-4fe8-9b1b-e1fb6430e5be"
      },
      "source": [
        "# Compare all classifiers (Logisitic Regression, SVM, Decision Tree and KNN) with P-R curves and AUC\n",
        "plt.figure(figsize=(12,7))\n",
        "all_preds = [lr_preds_prob, svc_preds_prob, dt_preds_prob, knn_preds_prob]\n",
        "labels = ['LR', 'SVM', 'DT', 'KNN']\n",
        "\n",
        "# For all four models:\n",
        "for i in range(4):\n",
        "    # The precision_recall_curve() function takes the true output values and\n",
        "    # the probabilities for the positive class as input and returns the precision, \n",
        "    # recall and threshold values.\n",
        "    prec, rec, pr_thresholds = precision_recall_curve(y_test, all_preds[i][:,1])\n",
        "\n",
        "    # The auc() function computes the AUC\n",
        "    auc_prec_rec = auc(rec, prec)\n",
        "    plt.plot(rec, prec, marker='.', lw=1, label='%s (AUC = %0.2f)' % (labels[i], auc_prec_rec)); \n",
        "    \n",
        "\n",
        "# Plot chance prediction precision-recall curve\n",
        "chance = len(y_test[y_test==1]) / len(y_test)\n",
        "plt.plot([0, 1], [chance, chance], linestyle='--', label='Luck')\n",
        "\n",
        "# Axis labels & legend\n",
        "plt.xlabel('Recall')\n",
        "plt.ylabel('Precision')\n",
        "plt.legend()\n",
        "\n",
        "# Show the plot\n",
        "plt.show()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00035-dba0705f-fad3-4b84-94b7-225b53e93cea",
        "deepnote_cell_type": "markdown",
        "id": "Z3hG_oyXjE6A"
      },
      "source": [
        "**Q** What do you notice? What do you wonder? \n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IjktJkZxhZbF"
      },
      "source": [
        "## Predicted Probabilites\n",
        "\n",
        "It is instructive to look at the predicted probabilites of each model, and to see how many unique values there are. Below is code for showing the probabilities of the positive predictions (class 1) and the number of unique probabilities for each of the models."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00037-e1aa4b3f-4154-4881-9543-45b9cce782fc",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "e45fdb41",
        "execution_millis": 13,
        "execution_start": 1615167702005,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gkXhVhd8jE6A",
        "outputId": "ad5c50a4-06e0-4e37-fb57-736457f7fb54"
      },
      "source": [
        "lr_preds_prob[:,1]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.55308679, 0.24002594, 0.52553567, 0.63524837, 0.34235874,\n",
              "       0.90289527, 0.85063011, 0.6637669 , 0.25577538, 0.08576731,\n",
              "       0.91225146, 0.33432062, 0.24333971, 0.09385271, 0.27194321,\n",
              "       0.26140051, 0.44799396, 0.64865857, 0.35256899, 0.05364075,\n",
              "       0.21541474, 0.86056089, 0.54086242, 0.44086159, 0.13684722,\n",
              "       0.64285193, 0.79679167, 0.48976519, 0.66298757, 0.34675611,\n",
              "       0.19680862, 0.36156288, 0.80838758, 0.88764206, 0.88019086,\n",
              "       0.27816864, 0.95151553, 0.40326716, 0.74786245, 0.20147156,\n",
              "       0.81265537, 0.80998061, 0.28469746, 0.94339276, 0.0382497 ,\n",
              "       0.85063011, 0.51303393, 0.70443295, 0.97658508, 0.50813153,\n",
              "       0.67956188, 0.96999508, 0.94803227, 0.90953897, 0.48032469,\n",
              "       0.97039192, 0.62547629, 0.00757758, 0.46300733, 0.39733374,\n",
              "       0.74294894, 0.1880337 , 0.91801125, 0.63399926, 0.45251334,\n",
              "       0.29325931, 0.53789136, 0.62671656, 0.33142107, 0.71401779,\n",
              "       0.78471729, 0.1786226 , 0.50438521, 0.36554751, 0.40513463,\n",
              "       0.25379684, 0.54112882, 0.65116341, 0.76803961, 0.88946464,\n",
              "       0.95033249, 0.23115995, 0.94382724, 0.21351734, 0.68300921,\n",
              "       0.79845346, 0.52676334, 0.31463098, 0.51061569, 0.46824618,\n",
              "       0.93925902, 0.77031   , 0.95886256, 0.42101478, 0.43132124,\n",
              "       0.43024261, 0.18610639, 0.27035793, 0.67422996, 0.83392635,\n",
              "       0.88109564, 0.36394952, 0.29670879, 0.76099604, 0.72047276,\n",
              "       0.55692418, 0.3431163 , 0.9144853 , 0.86467484, 0.48321013,\n",
              "       0.32127712, 0.92069792, 0.39932014, 0.29869319, 0.22773694,\n",
              "       0.21309425, 0.15865369, 0.12444469, 0.90724452, 0.81561768,\n",
              "       0.42216429, 0.21555752, 0.64865857, 0.31951179, 0.51457616,\n",
              "       0.28641727, 0.44026563, 0.15754709, 0.07400934, 0.01436425,\n",
              "       0.1215585 , 0.17961208, 0.09637518, 0.57821077, 0.32789491,\n",
              "       0.94861461, 0.92963201, 0.41074987, 0.01660628, 0.73118298,\n",
              "       0.72841899, 0.75970877, 0.33322964, 0.64984683, 0.46657107,\n",
              "       0.65483421, 0.67819797, 0.36811577, 0.41963171, 0.51246322,\n",
              "       0.28910529, 0.71401779, 0.92596725, 0.84844607, 0.54214158,\n",
              "       0.33150434, 0.64180904, 0.39800999, 0.8391188 , 0.97505748,\n",
              "       0.86697016, 0.90320739, 0.91490056, 0.74615528, 0.678526  ,\n",
              "       0.80088962, 0.96419233, 0.96843748, 0.74342051, 0.8492616 ,\n",
              "       0.55571178, 0.98186184, 0.65287678, 0.94608298, 0.27253301,\n",
              "       0.18200919, 0.70542541, 0.45074105, 0.04848965, 0.82144029,\n",
              "       0.74326563, 0.48442762, 0.48649521, 0.50556483, 0.33070667,\n",
              "       0.27806635, 0.55481567, 0.95106204, 0.27449872, 0.50165485,\n",
              "       0.26635616, 0.35692246, 0.83228666, 0.95007014, 0.4100224 ,\n",
              "       0.5406963 , 0.42205477, 0.65624147, 0.9430356 , 0.75379366,\n",
              "       0.84760723, 0.57809551, 0.84268085, 0.28833659, 0.19715076,\n",
              "       0.38297765, 0.47347482, 0.39984831, 0.23026097, 0.9766626 ,\n",
              "       0.4155017 , 0.63242107, 0.60711583, 0.02899913, 0.68076717,\n",
              "       0.4768651 , 0.63519714, 0.31311535, 0.40509794, 0.19388824,\n",
              "       0.63055335, 0.91598623, 0.19829481, 0.52889609, 0.92598572,\n",
              "       0.15453799, 0.91108073, 0.52838206, 0.04408881, 0.25591645,\n",
              "       0.29463173, 0.76762087, 0.06222905, 0.59787612, 0.15752594,\n",
              "       0.51934207, 0.10778968, 0.10732405, 0.19568121, 0.42813784,\n",
              "       0.34593637, 0.42716642, 0.46264728, 0.9793961 , 0.6867925 ,\n",
              "       0.71506284, 0.36865782, 0.23168174, 0.60364605, 0.67755153,\n",
              "       0.39367919, 0.77151207, 0.42148751, 0.12444469, 0.14662789,\n",
              "       0.17663268, 0.98103897, 0.87135494, 0.92514339, 0.85638613,\n",
              "       0.51439563, 0.19900206, 0.90291091, 0.37244822, 0.4454784 ,\n",
              "       0.57931059, 0.10923235, 0.87773555, 0.74229247, 0.49581286,\n",
              "       0.12530527, 0.92019963, 0.72047276, 0.76930361, 0.52785634,\n",
              "       0.31753364, 0.29335716, 0.28469746, 0.60004276, 0.3487799 ,\n",
              "       0.86242403, 0.87221544, 0.74022107, 0.8612767 , 0.65267815,\n",
              "       0.30636565, 0.6820195 , 0.7225676 , 0.15307096, 0.77059415,\n",
              "       0.88352111, 0.21540685, 0.94258852, 0.5250824 , 0.22212646,\n",
              "       0.91934949, 0.09617189, 0.83495014, 0.37772786, 0.69030277,\n",
              "       0.91244698, 0.74073778, 0.84533823, 0.86030311, 0.84621229,\n",
              "       0.90674841, 0.16208424, 0.95253745, 0.8727432 , 0.18860177,\n",
              "       0.51331451, 0.19829481, 0.80122202, 0.25773376, 0.50166467,\n",
              "       0.98456517, 0.90669019, 0.97625541, 0.19200037, 0.4097481 ])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00038-5ce482ef-4ba3-4a87-9580-9332652dcdf6",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "89ca2af0",
        "execution_millis": 14,
        "execution_start": 1615167704839,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FL6HKWKLjE6A",
        "outputId": "9df4a52c-3ab4-4248-c275-69d4966ba4f8"
      },
      "source": [
        "svc_preds_prob[:,1]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.77621189, 0.22937074, 0.5       , 0.75807025, 0.66386947,\n",
              "       0.86888307, 0.88087767, 0.7937282 , 0.6918607 , 0.10008513,\n",
              "       0.66798612, 0.28736769, 0.3815453 , 0.2879819 , 0.54804646,\n",
              "       0.36679735, 0.3790928 , 0.69045392, 0.69047262, 0.03918644,\n",
              "       0.30921262, 0.8176574 , 0.72658849, 0.0566502 , 0.29129597,\n",
              "       0.83005601, 0.33953239, 0.36366478, 0.66176613, 0.32865191,\n",
              "       0.3413597 , 0.46132235, 0.95829638, 0.94628987, 0.80432669,\n",
              "       0.27853274, 0.84880898, 0.4698479 , 0.88633523, 0.38808812,\n",
              "       0.71166824, 0.80271403, 0.38455604, 0.68437824, 0.00443843,\n",
              "       0.88087767, 0.79223741, 0.69042655, 0.60946945, 0.76700563,\n",
              "       0.73347976, 0.93319117, 0.99483883, 0.72528681, 0.55939717,\n",
              "       0.93353185, 0.23768428, 0.0276228 , 0.34070997, 0.42439626,\n",
              "       0.31525731, 0.42071471, 0.94249716, 0.61207769, 0.66340217,\n",
              "       0.52991424, 0.67619421, 0.70490339, 0.29778759, 0.45796331,\n",
              "       0.23890783, 0.29381787, 0.21577431, 0.40738086, 0.45744319,\n",
              "       0.06199954, 0.74399544, 0.82757908, 0.50701669, 0.75641246,\n",
              "       0.8870156 , 0.23130258, 0.72996399, 0.04812575, 0.69045665,\n",
              "       0.74333198, 0.55496279, 0.25183196, 0.183636  , 0.68271991,\n",
              "       0.44897089, 0.4308584 , 0.93549568, 0.69045092, 0.3406807 ,\n",
              "       0.61458758, 0.21631206, 0.11577287, 0.87605725, 0.83668532,\n",
              "       0.94926331, 0.43162977, 0.06827273, 0.77513709, 0.75810636,\n",
              "       0.44747649, 0.29851593, 0.7726194 , 0.8021059 , 0.651422  ,\n",
              "       0.37145416, 0.88180965, 0.69964888, 0.67808869, 0.51881854,\n",
              "       0.2695088 , 0.36224351, 0.29620907, 0.61576552, 0.72358264,\n",
              "       0.5905765 , 0.29199664, 0.69045392, 0.69628357, 0.35205915,\n",
              "       0.29466628, 0.55040951, 0.50934294, 0.43205526, 0.36069173,\n",
              "       0.73820996, 0.29407445, 0.53819443, 0.20808987, 0.57672034,\n",
              "       0.80118202, 0.41796795, 0.47726675, 0.01191863, 0.44655925,\n",
              "       0.83308604, 0.89051432, 0.5       , 0.66333852, 0.5465182 ,\n",
              "       0.90048487, 0.39383698, 0.30270382, 0.6287909 , 0.79194689,\n",
              "       0.29397564, 0.45796331, 0.4127821 , 0.98333159, 0.79485093,\n",
              "       0.60174165, 0.34743922, 0.33068488, 0.80983235, 0.6127322 ,\n",
              "       0.44295662, 0.72008919, 0.72384453, 0.3407033 , 0.4689798 ,\n",
              "       0.96564888, 0.96745891, 0.91514169, 0.65016535, 0.34063931,\n",
              "       0.25065864, 0.90448439, 0.53296285, 0.98514535, 0.57517817,\n",
              "       0.10410299, 0.90298152, 0.61582372, 0.03459329, 0.87255549,\n",
              "       0.23281055, 0.59170247, 0.59562491, 0.5754719 , 0.39850072,\n",
              "       0.35867362, 0.74561162, 0.70092583, 0.31407442, 0.37956219,\n",
              "       0.38018939, 0.35215881, 0.82948292, 0.71331039, 0.67920594,\n",
              "       0.77193372, 0.40171937, 0.34067517, 0.85519539, 0.91521741,\n",
              "       0.39768932, 0.65664528, 0.55897848, 0.38247901, 0.01393297,\n",
              "       0.43999775, 0.50852058, 0.24082916, 0.27506514, 0.52960665,\n",
              "       0.26375345, 0.37939567, 0.69698257, 0.00259161, 0.27427289,\n",
              "       0.74355854, 0.46948384, 0.34063334, 0.57342271, 0.2141214 ,\n",
              "       0.34063694, 0.77758273, 0.35291444, 0.76161787, 0.82048592,\n",
              "       0.33741331, 0.38644653, 0.5448258 , 0.00889421, 0.34060779,\n",
              "       0.03970308, 0.70283927, 0.69043667, 0.59473936, 0.31361766,\n",
              "       0.57295027, 0.41473385, 0.11571226, 0.17212674, 0.2378601 ,\n",
              "       0.39468936, 0.65822511, 0.30341397, 0.85458656, 0.79740138,\n",
              "       0.34180748, 0.36724612, 0.46872686, 0.37437821, 0.44806535,\n",
              "       0.27440471, 0.92913309, 0.25540252, 0.29620907, 0.91959   ,\n",
              "       0.47909898, 0.94663945, 0.69042791, 0.79448057, 0.83965318,\n",
              "       0.34067075, 0.16174475, 0.67038663, 0.35282077, 0.62244052,\n",
              "       0.38029944, 0.60374528, 0.68296651, 0.88326715, 0.6069574 ,\n",
              "       0.33846473, 0.88027703, 0.75810636, 0.81864164, 0.5       ,\n",
              "       0.55484874, 0.34068369, 0.38455604, 0.69040954, 0.59327974,\n",
              "       0.77032113, 0.74607478, 0.91273737, 0.72758455, 0.45555409,\n",
              "       0.3787849 , 0.79749631, 0.74886119, 0.37182373, 0.81312383,\n",
              "       0.94041472, 0.34750368, 0.78130339, 0.62318797, 0.38420659,\n",
              "       0.92177036, 0.69157568, 0.91365009, 0.46158184, 0.85066759,\n",
              "       0.96583062, 0.35597001, 0.84364856, 0.85394181, 0.92311612,\n",
              "       0.42182664, 0.33813491, 0.89452169, 0.9193464 , 0.73728926,\n",
              "       0.35880459, 0.35291444, 0.77620073, 0.74420421, 0.47432288,\n",
              "       0.65103801, 0.66918372, 0.85943273, 0.37604695, 0.34575559])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00037-1969cddf-0c19-4023-96e6-3c407aa19a80",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "73571764",
        "execution_millis": 20,
        "execution_start": 1615167708344,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QvjOcOBejE6A",
        "outputId": "5d94bb46-dd1d-4ae3-b3ab-f146040937a4"
      },
      "source": [
        "dt_preds_prob[:,1] "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.93103448, 0.        , 0.        , 1.        , 1.        ,\n",
              "       1.        , 0.96511628, 0.95384615, 0.        , 0.        ,\n",
              "       0.96511628, 0.        , 0.        , 0.        , 1.        ,\n",
              "       0.        , 0.        , 0.93103448, 1.        , 0.        ,\n",
              "       0.        , 0.8       , 1.        , 0.        , 0.        ,\n",
              "       0.5       , 0.        , 1.        , 1.        , 0.        ,\n",
              "       0.        , 0.        , 0.96511628, 0.98601399, 0.98601399,\n",
              "       0.        , 0.98601399, 0.        , 1.        , 0.625     ,\n",
              "       0.96511628, 0.96511628, 0.        , 1.        , 0.        ,\n",
              "       0.96511628, 1.        , 1.        , 1.        , 0.        ,\n",
              "       0.5       , 0.8       , 0.98601399, 0.96511628, 1.        ,\n",
              "       1.        , 0.96511628, 0.        , 0.        , 1.        ,\n",
              "       1.        , 0.        , 0.98601399, 0.28571429, 1.        ,\n",
              "       0.        , 0.5       , 1.        , 1.        , 0.96511628,\n",
              "       1.        , 0.        , 0.        , 0.        , 0.63636364,\n",
              "       0.        , 0.        , 1.        , 0.5       , 1.        ,\n",
              "       0.98601399, 0.        , 0.98601399, 0.        , 1.        ,\n",
              "       0.        , 1.        , 0.        , 0.        , 0.        ,\n",
              "       0.96511628, 0.28571429, 0.98601399, 1.        , 0.        ,\n",
              "       0.        , 0.        , 0.        , 0.83333333, 0.96511628,\n",
              "       0.98601399, 1.        , 0.        , 0.8       , 0.96511628,\n",
              "       0.57142857, 0.        , 0.        , 0.96511628, 0.        ,\n",
              "       0.        , 0.96511628, 0.95384615, 0.        , 0.        ,\n",
              "       0.        , 0.        , 0.        , 1.        , 0.98601399,\n",
              "       1.        , 0.        , 0.93103448, 1.        , 0.        ,\n",
              "       0.        , 0.        , 0.27272727, 0.        , 0.        ,\n",
              "       1.        , 0.        , 0.        , 0.        , 1.        ,\n",
              "       1.        , 0.8       , 0.        , 0.        , 0.28571429,\n",
              "       0.95384615, 0.96511628, 0.        , 0.        , 0.63636364,\n",
              "       0.93103448, 0.        , 0.        , 0.        , 1.        ,\n",
              "       0.        , 0.96511628, 0.8       , 1.        , 1.        ,\n",
              "       1.        , 0.        , 0.        , 0.96511628, 0.98601399,\n",
              "       0.96511628, 0.98601399, 0.96511628, 0.        , 1.        ,\n",
              "       0.        , 0.98601399, 0.98601399, 0.        , 0.        ,\n",
              "       0.27272727, 0.98601399, 1.        , 0.98601399, 1.        ,\n",
              "       0.        , 1.        , 0.        , 0.        , 0.98601399,\n",
              "       1.        , 0.95384615, 0.93103448, 0.93103448, 0.        ,\n",
              "       0.        , 0.        , 1.        , 0.        , 0.        ,\n",
              "       0.        , 0.        , 1.        , 1.        , 0.83333333,\n",
              "       1.        , 0.        , 0.        , 0.98601399, 1.        ,\n",
              "       0.95384615, 0.        , 1.        , 1.        , 0.        ,\n",
              "       0.        , 1.        , 0.        , 0.        , 0.98601399,\n",
              "       0.        , 0.95384615, 0.96511628, 0.        , 0.        ,\n",
              "       1.        , 0.95384615, 0.        , 0.        , 0.        ,\n",
              "       0.        , 0.98601399, 0.        , 0.96511628, 0.98601399,\n",
              "       0.        , 1.        , 0.        , 0.        , 0.        ,\n",
              "       0.        , 1.        , 1.        , 1.        , 0.        ,\n",
              "       1.        , 0.        , 0.        , 0.11764706, 0.        ,\n",
              "       1.        , 0.        , 0.        , 0.96511628, 0.95384615,\n",
              "       0.        , 0.        , 1.        , 0.        , 0.63636364,\n",
              "       0.        , 1.        , 0.        , 0.        , 1.        ,\n",
              "       1.        , 0.98601399, 0.98601399, 0.96511628, 0.96511628,\n",
              "       0.28571429, 0.        , 0.5       , 0.        , 1.        ,\n",
              "       0.        , 1.        , 0.98601399, 0.98601399, 0.93103448,\n",
              "       0.        , 0.98601399, 0.96511628, 0.95384615, 0.        ,\n",
              "       0.93103448, 0.        , 0.        , 1.        , 1.        ,\n",
              "       0.95384615, 0.98601399, 0.98601399, 0.98601399, 0.6       ,\n",
              "       0.        , 0.96511628, 0.95384615, 0.        , 0.95384615,\n",
              "       0.96511628, 0.        , 0.96511628, 0.        , 1.        ,\n",
              "       0.96511628, 1.        , 0.98601399, 0.11764706, 0.5       ,\n",
              "       0.98601399, 1.        , 1.        , 0.92307692, 0.95384615,\n",
              "       0.98601399, 0.        , 1.        , 1.        , 0.        ,\n",
              "       0.11764706, 0.        , 0.98601399, 0.8       , 0.        ,\n",
              "       0.98601399, 0.96511628, 0.96511628, 0.        , 0.        ])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00039-96c69c4e-6ec6-408c-aa1d-54b88758f85b",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "132d57e0",
        "execution_millis": 10,
        "execution_start": 1615167712762,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Xq0xG-nZjE6B",
        "outputId": "a20941cc-c24e-4e22-d019-a681a77b72fc"
      },
      "source": [
        "knn_preds_prob[:,1]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.9, 0.1, 0.7, 0.8, 0.5, 0.9, 1. , 1. , 0.6, 0. , 0.9, 0.6, 0. ,\n",
              "       0.2, 0.7, 0.4, 0.5, 0.8, 0.2, 0.1, 0.5, 0.9, 0.8, 0.3, 0.4, 0.9,\n",
              "       0.8, 0.5, 0.8, 0.4, 0. , 0.5, 0.9, 0.9, 0.9, 0.1, 1. , 0.5, 0.9,\n",
              "       0.2, 0.9, 0.9, 0.3, 0.9, 0. , 1. , 0.6, 0.9, 1. , 0.7, 0.6, 1. ,\n",
              "       0.9, 0.9, 0.8, 0.9, 0.1, 0. , 0.5, 0.3, 0.7, 0.1, 1. , 0.7, 0.2,\n",
              "       0.4, 0.8, 0.7, 0.3, 0.8, 0.3, 0.2, 0.4, 0.5, 0.5, 0.1, 0.7, 0.7,\n",
              "       0.7, 0.9, 1. , 0.1, 0.8, 0.1, 0.8, 0.9, 0.5, 0.1, 0.5, 0.5, 0.8,\n",
              "       0.7, 0.9, 0.5, 0.5, 0.6, 0.4, 0.2, 0.8, 0.9, 0.9, 0.6, 0.3, 0.6,\n",
              "       0.8, 0.7, 0.3, 0.6, 0.9, 0.8, 0.5, 1. , 0.8, 0.5, 0.4, 0.4, 0.2,\n",
              "       0. , 0.9, 0.8, 0.5, 0.1, 0.8, 0.5, 0.6, 0.7, 0.6, 0.5, 0.2, 0.2,\n",
              "       0.7, 0.1, 0.6, 0.5, 0.5, 1. , 0.9, 0.5, 0. , 0.8, 0.8, 0.9, 0.5,\n",
              "       0.6, 0.7, 0.9, 0.4, 0.4, 0. , 0.5, 0.5, 0.8, 0.5, 0.9, 0.7, 0.4,\n",
              "       0.5, 0.1, 0.7, 0.7, 0.6, 0.9, 1. , 0.7, 0.6, 0.3, 1. , 1. , 0.5,\n",
              "       0.9, 0.1, 0.9, 0.6, 1. , 0.9, 0.4, 0.5, 0.7, 0.1, 1. , 0.8, 0.7,\n",
              "       0.8, 0.6, 0.3, 0.4, 0.7, 0.9, 0.3, 0.2, 0.4, 0.5, 0.9, 1. , 0.7,\n",
              "       0.6, 0.7, 0.6, 1. , 0.9, 0.9, 0.7, 0.7, 0.3, 0.1, 0.6, 0.6, 0. ,\n",
              "       0.7, 0.8, 0.5, 0.7, 0.9, 0. , 0.3, 0.5, 0.3, 0.4, 0.4, 0.2, 0.6,\n",
              "       0.9, 0.4, 0.4, 1. , 0.4, 0.6, 0.7, 0. , 0.2, 0. , 0.6, 0.2, 0.4,\n",
              "       0.2, 0.7, 0.2, 0. , 0.3, 0.1, 0. , 0.6, 0.6, 1. , 0.8, 0.6, 0.5,\n",
              "       0.3, 0.4, 0.6, 0.5, 0.8, 0.1, 0. , 0.5, 0.5, 1. , 0.7, 1. , 0.8,\n",
              "       0.5, 0.2, 1. , 0.5, 0.3, 0.4, 0.5, 1. , 0.9, 0.6, 0. , 0.9, 0.8,\n",
              "       0.7, 0.5, 0.5, 0.1, 0.3, 0.6, 0.5, 0.9, 1. , 1. , 0.9, 0.7, 0.2,\n",
              "       0.7, 0.6, 0.1, 0.9, 0.9, 0.4, 1. , 0.7, 0.1, 0.9, 0.2, 1. , 0.3,\n",
              "       0.8, 1. , 0.7, 0.8, 1. , 0.8, 0.7, 0.1, 1. , 0.9, 0.4, 0.4, 0.4,\n",
              "       0.8, 0.6, 0.2, 0.8, 0.7, 1. , 0.4, 0.6])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00036-fb573f33-346c-439f-ac04-07c5353389c2",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "17ba0812",
        "execution_millis": 37,
        "execution_start": 1615167715508,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ADglrCv6jE6B",
        "outputId": "09359d92-ccf8-47e6-ebbb-6ae39e1a6814"
      },
      "source": [
        "# Here is the number of unique positive predictions (class 1)\n",
        "print(color.BOLD + 'Number of elements in the positive class (class 1): ') \n",
        "\n",
        "print(color.BOLD + '\\nLogistic Regression: ') \n",
        "print(\"count:\", np.unique( lr_preds_prob[:,1]).shape) \n",
        "\n",
        "print(color.BLUE + '\\nSupport Vector Machine: ')\n",
        "print(\"count:\", np.unique( svc_preds_prob[:,1]).shape) \n",
        "\n",
        "print(color.RED + '\\nDecision Tree: ')\n",
        "print(\"count:\", np.unique( dt_preds_prob[:,1]).shape) \n",
        "\n",
        "print(color.PURPLE + '\\nKNearest Neighbors: ')\n",
        "print(\"count:\", np.unique( knn_preds_prob[:,1]).shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[1mNumber of elements in the positive class (class 1): \n",
            "\u001b[1m\n",
            "Logistic Regression: \n",
            "count: (313,)\n",
            "\u001b[94m\n",
            "Support Vector Machine: \n",
            "count: (311,)\n",
            "\u001b[91m\n",
            "Decision Tree: \n",
            "count: (17,)\n",
            "\u001b[95m\n",
            "KNearest Neighbors: \n",
            "count: (11,)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00038-3e588483-a48e-41cb-a331-a939cd5758d3",
        "deepnote_cell_type": "markdown",
        "id": "hOHYsy3SjE6A"
      },
      "source": [
        "-----\n",
        "**Q** What do you notice? Would this explain something you might have wondered about in the ROC and P-R plots?\n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00039-4eca26c4-e3c8-4f41-a7f6-11871a3f701f",
        "deepnote_cell_type": "markdown",
        "id": "zLzpg-VTjE6B"
      },
      "source": [
        "## [F1 Score](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.f1_score.html?highlight=f1_score#sklearn.metrics.f1_score)\n",
        "There are also composite scores that attempt to summarize the precision and recall; the most notable example is the F-measure or F1 score. It calculates the weighted average of precision and recall for a specific probability threshold (e.g. 0.5):\n",
        "\n",
        "**F1 = 2 x (Precision x Recall) / (Precision + Recall)**\n",
        "\n",
        "In the multi-class and multi-label case, we compute the average of the F1 score of each class with weighting depending on the `average` parameter.\n",
        "\n",
        "F1 Score is a good measure to use to seek a balance between precision and recall, especially if there is an uneven class distribution (e.g., large number of negatives).\n",
        "\n",
        "[Source](https://machinelearningmastery.com/roc-curves-and-precision-recall-curves-for-classification-in-python/)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00040-f17bdba9-f5de-4390-b4cd-40c69f6670aa",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "fd105d1c",
        "execution_millis": 21,
        "execution_start": 1615167718463,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rIjBv1q1jE6B",
        "outputId": "2b0a040c-f43e-4d86-e779-e8fc839e4c82"
      },
      "source": [
        "# Printing F-1 scores for the different models\n",
        "print(color.BOLD + '\\nLogistic Regression: ') \n",
        "print(\"F1-Score: {0:0.5f}\".format(f1_score(y_test,lr_preds)))\n",
        "\n",
        "print(color.BLUE + '\\nSupport Vector Machine: ')\n",
        "print(\"F1-Score: {0:0.5f}\".format(f1_score(y_test,svc_preds)))\n",
        "\n",
        "print(color.RED + '\\nDecision Tree: ')\n",
        "print(\"F1-Score: {0:0.5f}\".format(f1_score(y_test,dt_preds)))\n",
        "\n",
        "print(color.PURPLE + '\\nKNearest Neighbors: ')\n",
        "print(\"F1-Score: {0:0.5f}\".format(f1_score(y_test,knn_preds)) + color.END)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[1m\n",
            "Logistic Regression: \n",
            "F1-Score: 0.75568\n",
            "\u001b[94m\n",
            "Support Vector Machine: \n",
            "F1-Score: 0.75862\n",
            "\u001b[91m\n",
            "Decision Tree: \n",
            "F1-Score: 0.79656\n",
            "\u001b[95m\n",
            "KNearest Neighbors: \n",
            "F1-Score: 0.74576\u001b[0m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cJE7r0wCh78I"
      },
      "source": [
        "---\n",
        "**Q** How do the F1 scores compare with what you noticed before about the ROC and P-R curves? How do they compare with the accuracy scores? Does this change your mind about which model is best?\n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00022-b010ba21-2617-4718-b4a2-9355047c9efb",
        "deepnote_cell_type": "markdown",
        "id": "G1CkC9CMjE6B"
      },
      "source": [
        "# [Cross-Validation and Grid Search](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html)\n",
        "\n",
        "A model **hyperparameter** is a characteristic of a model that is external to the model and whose value cannot be estimated from data. The value of the hyperparameter has to be set before the learning process begins. For example, C in Support Vector Machines, k in k-Nearest Neighbors, the depth of the tree for decision trees, etc.\n",
        "\n",
        "We can use cross-validation and grid search to find the optimal hyperparameters of a model which results in the most ‘accurate’ predictions. Grid search builds a model for every combination of the hyperparameters we specify and evaluates each model. The grid search provided by GridSearchCV() exhaustively generates candidates from a grid of parameter values specified with the `param_grid` parameter. \n",
        "\n",
        "Remember that in Part 1 we had split the data into training and test sets using an 80% / 20% split. For cross validation, we will use the full datasets again, i.e., `X` for the features and `Y` for the predicted binary variable `quality`."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00040-7decfb1b-adfd-4cc1-a0ae-95d0e3e1c5f7",
        "deepnote_cell_type": "markdown",
        "id": "i7peYUC4jE6B"
      },
      "source": [
        "## [Support Vector Machine](https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html#sklearn.svm.SVC)\n",
        "\n",
        "As you know from Chapter 3 in the ML book and the lecture video (on Canvas), SVMs have two important hyperparamters. One is the **kernel** that we apply to the data to deal with non-linear decision boundaries. Popular choices are `linear` to use a linear hpyerplane as the decision boundary and `rbf` to transform the data using a [radial basis function kernel](https://en.wikipedia.org/wiki/Radial_basis_function_kernel). \n",
        "\n",
        "The hyperparameter **C** determines the tradeoff between increasing the size of the decision boundary (i.e., its margin) and making sure each examples is classified correctly (accuracy). C is a *regularization* parameter, where the strength of the regularization is inversely proportional to C. **Regularization** is an umbrella term that encompasses methods that force the learning algorithm to build a less complex model. In practice, that oftern leads to slighly higher bias but significantly reduces the variance. \n",
        "\n",
        "We are now going to use using grid search to find optimal values for `kernel` and `C`. \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00040-04045c4e-e663-4501-8fdb-87a6164d3a16",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "6b631b59",
        "execution_millis": 10931,
        "execution_start": 1615167722682,
        "deepnote_cell_type": "code",
        "id": "vsiaWPI4jE6B"
      },
      "source": [
        "# We search over SVM kernels (linear or RBF) and values of C (1, 10, or 100).\n",
        "param_grid = {'kernel':('linear', 'rbf'), 'C':[1, 10, 100]}\n",
        "\n",
        "# Defining our model\n",
        "svc = SVC()\n",
        "\n",
        "# Initializing grid search\n",
        "clf = GridSearchCV(svc, param_grid, n_jobs=-1 ) # n_jobs=-1 will utilize all the processors\n",
        "\n",
        "# Fitting the model to the full feature data X and predicted variable Y\n",
        "# Note: the grid search is actually run when you call GridSearchCV.fit()\n",
        "clf.fit(StandardScaler().fit_transform(X), Y);\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00042-6a5f0d28-3a44-48d9-86c6-8ca5d19cd6bb",
        "deepnote_cell_type": "markdown",
        "id": "LkTUHDx6jE6C"
      },
      "source": [
        "**Q** Read [documentation](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html) and find out what type of cross validation strategy GridSearchCV() uses. \n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00043-4dffde54-b806-49e6-abf5-3c3315e1e000",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "8ff9a5c5",
        "execution_millis": 20,
        "execution_start": 1615167733622,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 235
        },
        "id": "XsJ95UjKjE6C",
        "outputId": "9e3b0c1b-78ad-4410-d4cd-1fe88b9af3c1"
      },
      "source": [
        "# Gather grid search information stored in `clf.cv_results_` into a dataframe\n",
        "grid_df = pd.DataFrame(clf.cv_results_['params'])\n",
        "grid_df['mean_test_score'] = clf.cv_results_['mean_test_score']\n",
        "grid_df['plot_label'] = 'C:' + grid_df.C.astype('str') + ' Kernel: ' + grid_df.kernel\n",
        "grid_df = grid_df.sort_values('mean_test_score')\n",
        "# Display the dataframe\n",
        "grid_df"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>C</th>\n",
              "      <th>kernel</th>\n",
              "      <th>mean_test_score</th>\n",
              "      <th>plot_label</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>100</td>\n",
              "      <td>rbf</td>\n",
              "      <td>0.668527</td>\n",
              "      <td>C:100 Kernel: rbf</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>10</td>\n",
              "      <td>rbf</td>\n",
              "      <td>0.717951</td>\n",
              "      <td>C:10 Kernel: rbf</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>100</td>\n",
              "      <td>linear</td>\n",
              "      <td>0.719212</td>\n",
              "      <td>C:100 Kernel: linear</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>10</td>\n",
              "      <td>linear</td>\n",
              "      <td>0.720462</td>\n",
              "      <td>C:10 Kernel: linear</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>linear</td>\n",
              "      <td>0.721087</td>\n",
              "      <td>C:1 Kernel: linear</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>rbf</td>\n",
              "      <td>0.737332</td>\n",
              "      <td>C:1 Kernel: rbf</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "     C  kernel  mean_test_score            plot_label\n",
              "5  100     rbf         0.668527     C:100 Kernel: rbf\n",
              "3   10     rbf         0.717951      C:10 Kernel: rbf\n",
              "4  100  linear         0.719212  C:100 Kernel: linear\n",
              "2   10  linear         0.720462   C:10 Kernel: linear\n",
              "0    1  linear         0.721087    C:1 Kernel: linear\n",
              "1    1     rbf         0.737332       C:1 Kernel: rbf"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00048-922fea8d-b943-4417-957d-d6bacdd639eb",
        "deepnote_cell_type": "markdown",
        "id": "k6tT0ONCjE6C"
      },
      "source": [
        "**Q** Look at the documentation of the results returned in `cv_results_` by [GridSearchCV](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html) and do some internet sleuthing (e.g., on [StackOverflow](https://stackoverflow.com/), a great community forum for programmers). How exactly is `mean_test_score` computed, and what other information does `cv_results_` provide?\n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00043-7b8e5f92-bbfc-4c98-9482-c941f3bdb0eb",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "9bf9ec20",
        "execution_millis": 283,
        "execution_start": 1615167737663,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        },
        "id": "8kO9vQh6jE6C",
        "outputId": "9a96514f-b305-4ebb-c119-7ba0f7d1e04c"
      },
      "source": [
        "# Let's display the mean test scores as a bar chart\n",
        "fig, ax = plt.subplots(figsize=(9,6))\n",
        "p = sns.barplot(x='plot_label', y='mean_test_score', data=grid_df,ax=ax, palette=\"Blues_d\")\n",
        "p.set_xticklabels(labels=grid_df.plot_label,rotation=60);\n",
        "p.set_xlabel(\"SVM Parameters\");\n",
        "p.set_ylabel(\"Mean test score\"); # Notice the semicolon, this avoids extraneous output"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 648x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00045-efaeb442-d067-4b79-982d-0738250a865a",
        "deepnote_cell_type": "markdown",
        "id": "84kgszZejE6C"
      },
      "source": [
        "**Q** What do you notice? What do you wonder? What are the optimal SVM hyperparameters for this data?\n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00051-efb24e91-642c-4f37-8c9c-9058919e5f94",
        "deepnote_cell_type": "markdown",
        "id": "ktLHXACpjE6C"
      },
      "source": [
        "### KNN\n",
        "\n",
        "As you know from Chapter 3 in the ML book and the lecture video (on Canvas), KNN also has two important hyperparamters. The first one is the value of **k**, the number of nearest neighbors for each example in the test data. The second is the **distance metric** that we use to find the k-nearest neighbors. There are [many choices](https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.DistanceMetric.html) for distance metrics in machine learning. We are going to use the [Minkowski](https://en.wikipedia.org/wiki/Minkowski_distance) norm. Mikowski is known as the Lp norm, and it is a generalization of the [Manhattan](https://en.wikipedia.org/wiki/Taxicab_geometry) (L1) and [Euclidan](https://en.wikipedia.org/wiki/Euclidean_distance) (L2) norms. The parameter p changes the shape of the distance metric as shown here:\n",
        "\n",
        "[](https://en.wikipedia.org/wiki/File:2D_unit_balls.svg)\n",
        "\n",
        "Similar to the SVM model, we are going to use grid search to find the optimal value of k and p (for the Lp norm) for our data.\n",
        "\n",
        "KNN is sensitive to differences in scales between the features, so we have to standardize the data first. This will lead to [data leakage](https://scikit-learn.org/stable/common_pitfalls.html#data-leakage-during-pre-processing), which occurs when information that would not be available at prediction time is used when building the model. \n",
        "\n",
        "A common cause is not keeping the test and train data subsets separate. Test data should never be used to make choices about the model. The general rule is to never call fit on the test data. While this may sound obvious, this is easy to miss in some cases, for example when applying certain pre-processing steps. To prevent data leakage, it is good practice to split your data into train and test subsets first. Feature selection can then be formed using just the train dataset. Notice that whenever we use fit or fit_transform, we only use the train dataset. ([Source](https://scikit-learn.org/stable/common_pitfalls.html#data-leakage-during-pre-processing))\n",
        "\n",
        "So in our case we are using the full data (X, Y) for cross validation we will have data leakage. We had the same issue above when doing cross-validation for the SVM model. To avoid this, we should be using [scikit-learn pipelines](https://scikit-learn.org/stable/modules/generated/sklearn.pipeline.Pipeline.html), which are an advanced topic. For pedagogical purposes we are keeping it simple."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00055-9128496d-1b15-4a62-80a8-0041f97a908a",
        "deepnote_cell_type": "markdown",
        "id": "EaeysGnejE6D"
      },
      "source": [
        "---\n",
        "**Q** What is the proper procedure to avoid feature leakage in your final projects ?\n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00051-42ba2346-9e4e-40c3-9589-599fc6fd6e2f",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "4b8c2192",
        "execution_millis": 19939,
        "execution_start": 1615167742222,
        "deepnote_cell_type": "code",
        "id": "2YxArUvEjE6C"
      },
      "source": [
        "# We search over these discrete values of k\n",
        "n_list = [50,100,200,300]\n",
        " \n",
        "# Power parameter p for the Minkowski metric (Lp). When p = 1, this is equivalent to using manhattan_distance (L1), \n",
        "# and euclidean_distance (L2) for p = 2. For arbitrary p, minkowski_distance (Lp) is used. \n",
        "p_list = [1, 1.4, 2, 2.8, 4, 10 ] \n",
        "\n",
        "param_grid = {'n_neighbors': n_list, 'p': p_list}\n",
        "\n",
        "# Defining our model\n",
        "knn_clf = KNeighborsClassifier()\n",
        "\n",
        "# Initializing grid search\n",
        "clf = GridSearchCV(knn_clf, param_grid,n_jobs=-1,cv=10)\n",
        "\n",
        "# KNN is sensitive to differences in scales between the features, so we have to standardize.\n",
        "# Since our dataset is small and we have only one hyperparameter, this will run a lot faster \n",
        "# than grid search for SVM\n",
        "clf.fit(StandardScaler().fit_transform(X), Y);"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00055-5cf0fe0c-f9aa-4a30-8c6b-e7c38afab8d8",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "451d61a5",
        "execution_millis": 651,
        "execution_start": 1615167765645,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 642
        },
        "id": "h3DMftedjE6D",
        "outputId": "cb4c6add-4dc5-4a14-f384-0cc79a54e6d9"
      },
      "source": [
        "all_scores = []\n",
        "for i in range(10): \n",
        "    key = 'split'+str(i)+'_test_score'\n",
        "    all_scores.append(clf.cv_results_[key])\n",
        "\n",
        "# Add back the column names\n",
        "col_names = []\n",
        "for i in n_list: \n",
        "    for j in p_list:\n",
        "        col_names.append(\"K=\" +str(i)+' p='+str(j))\n",
        "\n",
        "\n",
        "# Add column names to a dataframe\n",
        "df_boxplot = pd.DataFrame(all_scores,columns=col_names)\n",
        "\n",
        "# Use df_boxplot to create our plot\n",
        "plt.figure(figsize=(10,10))\n",
        "\n",
        "plt.title('Grid Search Boxplot (KNN) - Accuracy vs. Parameters\\n')\n",
        "\n",
        "df_boxplot = pd.DataFrame(df_boxplot).melt()\n",
        "\n",
        "df_boxplot.columns = ['KNN Parameters','Accuracy']\n",
        "df_boxplot['mean_col'] = df_boxplot.groupby('KNN Parameters').transform(np.mean)  \n",
        "df_boxplot = df_boxplot.sort_values('mean_col',ascending=False)\n",
        "df_boxplot.drop('mean_col',axis=1,inplace=True)\n",
        "\n",
        "sns.boxplot(y='KNN Parameters' , x='Accuracy',data = df_boxplot, showmeans=True,palette='vlag', orient='h');\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00057-32e5c879-1b3d-49bc-b792-bc8f1179f14c",
        "deepnote_cell_type": "markdown",
        "id": "-fjmgVlYjE6D"
      },
      "source": [
        "**Q** What are the optimal hyperparameter values, and why? Does this surprise you?\n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00043-8f536e4f-f0f7-4498-80a0-7eb14a350814",
        "deepnote_cell_type": "markdown",
        "id": "R5UHBmgQjE6D"
      },
      "source": [
        "### [Decision Tree Classifier](https://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeClassifier.html)\n",
        "\n",
        "We are now going to find the optimal tree depth for our decision tree classifier using grid search and 10-fold cross-validation. We will use **pruning**, which reduces the size of decision trees by removing sections of the tree that are non-critical and redundant to classify instances. Pruning reduces the complexity of the final classifier, and hence improves predictive accuracy by the reduction of overfitting.\n",
        "\n",
        "One of the questions that arises in a decision tree algorithm is the optimal size of the final tree. A tree that is too large risks overfitting the training data and poorly generalizing to new samples. A small tree might not capture important structural information about the sample space. However, it is hard to tell when a tree algorithm should stop because it is impossible to tell if the addition of a single extra node will dramatically decrease error. A common strategy is to grow the tree until each node contains a small number of instances then use pruning to remove nodes that do not provide additional information. ([Source](https://en.wikipedia.org/wiki/Decision_tree_pruning))\n",
        "\n",
        "In our case, since our data is relatively small, we will train different decision tree models by varying their maximum depth.  "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00043-77df5463-15ab-4d23-b649-8077ddcc87f6",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "16a157dc",
        "execution_millis": 677,
        "execution_start": 1615167770930,
        "deepnote_cell_type": "code",
        "id": "RCQH4anvjE6D"
      },
      "source": [
        "# We change the maximum tree depth (max_depth) using 10-fold cross validation.\n",
        "scores = []\n",
        "\n",
        "# Check tree depths in the range [2, 20]\n",
        "for depth in np.arange(2,21):\n",
        "    # Initialize the decision tree\n",
        "    dt_clf = DecisionTreeClassifier(max_depth=depth, random_state=10)\n",
        "\n",
        "    # We are using the cross_val_score() function for 10-fold CV\n",
        "    # The default scoring metric is accuracy\n",
        "    score_list = cross_val_score(dt_clf, X, Y, cv=10)  \n",
        "    scores.append(score_list)\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00053-b7813be9-5d68-47d1-945a-e6ff4e18e190",
        "deepnote_cell_type": "markdown",
        "id": "V9dbZn_hjE6D"
      },
      "source": [
        "---\n",
        "**Q** What are the reasons to prune a decision tree in terms of the bias-variance tradeoff?\n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00053-58f5424c-7063-4dfe-9246-cbe5fbe4b749",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "6d0f0e0b",
        "execution_millis": 335,
        "execution_start": 1615167773983,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 339
        },
        "id": "kAG8QQ2ojE6D",
        "outputId": "66ffe1f6-2237-4b18-d951-d6162c6fb0bc"
      },
      "source": [
        "# Draw box and whisker plots of the accuracy scores for each tree depth\n",
        "# https://seaborn.pydata.org/generated/seaborn.boxplot.html \n",
        "# Plot shows median (line), mean (triangle), and quartiles (box, 25%/50%)\n",
        "# Whiskers show extent of the data distribution, dark dots (diamonds) show outliers\n",
        "plt.figure(figsize=(14,5))\n",
        "df_boxplot = pd.DataFrame(scores).T.melt()\n",
        "df_boxplot.columns = ['max_depth','Accuracy']\n",
        "df_boxplot['max_depth'] = (df_boxplot['max_depth']+2)\n",
        "sns.boxplot(x='max_depth' , y='Accuracy',data = df_boxplot, showmeans=True,palette='husl');"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1008x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00046-09bac486-178f-4e4c-ab3b-138d0ffaaa34",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "b65184f6",
        "execution_millis": 27,
        "execution_start": 1615167779392,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 638
        },
        "id": "B5cuWWB2jE6D",
        "outputId": "7e5799ba-ee9d-486e-9713-89dc31e3d276"
      },
      "source": [
        "# Print the values for mean accuracy and std_dev as well\n",
        "tree_scores = pd.DataFrame([np.arange(2,21), np.mean(scores,axis=1), np.std(scores,axis=1)]).T\n",
        "tree_scores.columns = ['max_depth', 'accuracy', 'std_dev']\n",
        "tree_scores.sort_values('max_depth',ascending=True).iloc[0:20,]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>max_depth</th>\n",
              "      <th>accuracy</th>\n",
              "      <th>std_dev</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>2.0</td>\n",
              "      <td>0.681678</td>\n",
              "      <td>0.093006</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>3.0</td>\n",
              "      <td>0.677932</td>\n",
              "      <td>0.062906</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>4.0</td>\n",
              "      <td>0.696694</td>\n",
              "      <td>0.079035</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>5.0</td>\n",
              "      <td>0.691686</td>\n",
              "      <td>0.060512</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>6.0</td>\n",
              "      <td>0.685401</td>\n",
              "      <td>0.072807</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>7.0</td>\n",
              "      <td>0.691061</td>\n",
              "      <td>0.075043</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>8.0</td>\n",
              "      <td>0.666034</td>\n",
              "      <td>0.078850</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>9.0</td>\n",
              "      <td>0.656651</td>\n",
              "      <td>0.077271</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>10.0</td>\n",
              "      <td>0.634764</td>\n",
              "      <td>0.082390</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>11.0</td>\n",
              "      <td>0.640385</td>\n",
              "      <td>0.074302</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>12.0</td>\n",
              "      <td>0.644123</td>\n",
              "      <td>0.078182</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>13.0</td>\n",
              "      <td>0.638518</td>\n",
              "      <td>0.064790</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>14.0</td>\n",
              "      <td>0.637893</td>\n",
              "      <td>0.060008</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>15.0</td>\n",
              "      <td>0.641655</td>\n",
              "      <td>0.057326</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>16.0</td>\n",
              "      <td>0.648526</td>\n",
              "      <td>0.056260</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>17.0</td>\n",
              "      <td>0.646038</td>\n",
              "      <td>0.059383</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>18.0</td>\n",
              "      <td>0.646038</td>\n",
              "      <td>0.059383</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>19.0</td>\n",
              "      <td>0.646647</td>\n",
              "      <td>0.059677</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>20.0</td>\n",
              "      <td>0.646647</td>\n",
              "      <td>0.059677</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    max_depth  accuracy   std_dev\n",
              "0         2.0  0.681678  0.093006\n",
              "1         3.0  0.677932  0.062906\n",
              "2         4.0  0.696694  0.079035\n",
              "3         5.0  0.691686  0.060512\n",
              "4         6.0  0.685401  0.072807\n",
              "5         7.0  0.691061  0.075043\n",
              "6         8.0  0.666034  0.078850\n",
              "7         9.0  0.656651  0.077271\n",
              "8        10.0  0.634764  0.082390\n",
              "9        11.0  0.640385  0.074302\n",
              "10       12.0  0.644123  0.078182\n",
              "11       13.0  0.638518  0.064790\n",
              "12       14.0  0.637893  0.060008\n",
              "13       15.0  0.641655  0.057326\n",
              "14       16.0  0.648526  0.056260\n",
              "15       17.0  0.646038  0.059383\n",
              "16       18.0  0.646038  0.059383\n",
              "17       19.0  0.646647  0.059677\n",
              "18       20.0  0.646647  0.059677"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00047-3351c6d5-8b32-479f-88ad-194c4afc7f59",
        "deepnote_cell_type": "markdown",
        "id": "lJLC23xPjE6E"
      },
      "source": [
        "**Q** What optimal tree depth would you choose, and why? Is there anything that surprises you about the plot and data?\n",
        "\n",
        "**A** \n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00059-82a2f429-f365-4c34-b084-dcc8c97418b2",
        "deepnote_cell_type": "markdown",
        "id": "LaFgRnQ8jE6E"
      },
      "source": [
        "-----\n",
        "**Q** What effect on these results would a small change in training data have?\n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dhwIjxwrbtl1"
      },
      "source": [
        "## Effects of Optimal Hyperparameters\n",
        "\n",
        "You are now going to look at the effects of hyperparameter tuning on the error metrics and plots you created so far. From this point on we are only going to consider the SVM, kNN, and decision tree models."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2YBNWFaKQ2fD"
      },
      "source": [
        "---\n",
        "**Q** In your solutions Google doc, collect all of the error metrics (accuracy, F1) and plots (confusion matrix, ROC curves, P-R curves) for the different classification models **before and after** hyperparameter tuning by following these steps:\n",
        "\n",
        "**Before:** Create a title called \"Before Hyperparameter Tuning\" in your Google doc.\n",
        "- Go back to the \"Basic ML Models\" at the beginning of the notebook \n",
        "- Capture the hyperparameters for each model by copy / pasting their initialization code (one line) into the Google doc\n",
        "- Save all of the error metrics and plots *before* \"Cross-Validation and Grid Search\"\n",
        "- Write down the optimal hyperparamters for each model *after* \"Cross-Validation and Grid Search\"\n",
        "\n",
        "**After:** Create a title called \"After Hyperparameter Tuning\" in your Google doc.\n",
        "- Go back to the \"Basic ML Models\" and change the hyperparameters of each model to their optimal values\n",
        "- Capture the new hyperparameters for each model by copy / pasting their initialization code (one line) into the Google doc\n",
        "- Re-run the code to train each model in \"Basic ML Models\"\n",
        "- Re-run the \"Model Error Metrics\" part of the notebook and capture the new error metrics and plots in your Google doc\n",
        "\n",
        "How did the error metrics and plots change for each model? Describe the changes in a short paragraph in your Google doc. It may be easier to put the respective plots next to each other for comparison. Make sure to clearly label everything.\n",
        "\n",
        "**A** Put your answers into a solutions Google doc.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00066-38c87486-b35c-4edb-9f04-da91778ecb76",
        "deepnote_cell_type": "markdown",
        "id": "SA09_oz0jE6E"
      },
      "source": [
        "# Advanced Topics"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00059-c16a86e2-5727-4efc-a301-589570a9a6e1",
        "deepnote_cell_type": "markdown",
        "id": "xD7tSTnQjE6E"
      },
      "source": [
        "## Feature Importance (Decision Tree Example)\n",
        "\n",
        "So far, we have used all of our features in the dataset for wine quality classification. However, as you noticed during EDA in Part 1, not all features are equally important. We can compute the **feature importance** for all our features. \n",
        "\n",
        "Feature importance refers to techniques that assign a score to input features based on how useful they are at predicting a target variable. There are many types and sources of feature importance scores. Popular examples include statistical correlation scores, coefficients calculated as part of linear models and decision trees, and permutation importance scores. See [this blog post](https://machinelearningmastery.com/calculate-feature-importance-with-python/) for more information and how to compute feature importance metrics in scikit-learn. \n",
        "\n",
        "In this example, we are going to use the function `compute_feature_importances()` by the `DecisionTreeClassifier()`. The higher the score, the more important the feature."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00060-4eb6f5bf-12ed-4158-a230-ca97b69a42a7",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "3aef2c37",
        "execution_millis": 1,
        "execution_start": 1615167785548,
        "deepnote_cell_type": "code",
        "id": "sjw7S70RjE6E"
      },
      "source": [
        "# Fit a new decision tree classifier\n",
        "dt_clf = DecisionTreeClassifier(random_state=10, max_depth=5)\n",
        "dt_clf.fit(X, Y)\n",
        "\n",
        "# Capture the feature importance scores returned by compute_feature_importances()\n",
        "feat_importance = dt_clf.tree_.compute_feature_importances()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00061-85103cf3-9d70-4920-8552-e7d372a89de6",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "d1434871",
        "execution_millis": 259,
        "execution_start": 1615167788097,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 410
        },
        "id": "W5I7G8SwjE6E",
        "outputId": "d0bee790-04c0-44b0-beba-ca77b77c21f6"
      },
      "source": [
        "# Create a dataframe to tabulate the importance scores for each of our features\n",
        "df_imp = pd.DataFrame({'feature_importance':feat_importance, 'feature_names': X.columns}).sort_values('feature_importance',ascending=False)\n",
        "\n",
        "# Plot them in a bar chart\n",
        "fig, ax = plt.subplots(figsize=(9,6))\n",
        "sns.barplot(y='feature_names', x='feature_importance',data=df_imp, orient='h',ax=ax);\n",
        "ax.set_title('Feature Importance - Decision Tree');\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 648x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00062-59ef7fea-c09e-4ff1-b444-aca55a21a8a8",
        "deepnote_cell_type": "markdown",
        "id": "IUe5c8iwjE6E"
      },
      "source": [
        "**Q** Which features are most important for the classification of wine quality using a decision tree model?\n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00052-c580dfeb-c6a2-42d5-baff-2870aabaeef3",
        "deepnote_cell_type": "markdown",
        "id": "RceW7yvZjE6E"
      },
      "source": [
        "## Visualizing Decision Boundaries\n",
        "\n",
        "Lastly, we may want to get a better handle on what our decision boundaries look like. Unfortunately, using all of our eight features means that the decision boundary lives in an eight-dimensional hyperspace. To visualize higher-dimensional spaces we would need a dimensionality reduction method to project the samples into 2D. This could be done in scikit-learn using a linear method such as [PCA](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html?highlight=pca#sklearn.decomposition.PCA) or a non-linear method such as [Isomap](https://scikit-learn.org/stable/modules/generated/sklearn.manifold.Isomap.html).\n",
        "\n",
        "Instead of using dimensionality reduction, we will train a new decision tree on the `alcohol` and `sulphates` features. We can then visualize the decision boundary in that two-dimensional feature space. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00052-17c24ccc-0dff-4e7a-9060-5fd52feda563",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "8e702adf",
        "execution_millis": 1,
        "execution_start": 1615167792836,
        "deepnote_cell_type": "code",
        "id": "SccjV_ybjE6F"
      },
      "source": [
        "# We first define the plotting function for decision boundaries for the wine data\n",
        "def plot_wine_2d_boundaries(X_data, y_data, predictors, model, xx_1, xx_2):\n",
        "    \"\"\"Plots 2-dimensional decision boundaries for a fitted sklearn model\n",
        "    \n",
        "    :param X_data: pd.DataFrame object containing your predictor variables\n",
        "    :param y_data: pd.Series object containing your response variable\n",
        "    :param predictors: list of predictor names corresponding with X_data columns\n",
        "    :param model: sklearn fitted model object\n",
        "    :param xx_1: np.array object of 2-dimensions, generated using np.meshgrid\n",
        "    :param xx_2: np.array object of 2-dimensions, generated using np.meshgrid\n",
        "    \"\"\"\n",
        "\n",
        "    def plot_points(ax):\n",
        "        for i, y_class in enumerate(set(y_data.flatten())):\n",
        "            index = (y_data == y_class)\n",
        "            ax.scatter(\n",
        "                X_data[index][predictors[0]],\n",
        "                X_data[index][predictors[1]],\n",
        "                c=colors[i],\n",
        "                marker=markers[i],\n",
        "                s=65, \n",
        "                edgecolor='w',\n",
        "                label=\"class {}\".format(i),\n",
        "            )\n",
        "    colors = [\"tab:blue\", \"tab:orange\"] # Add more colors for more than 2 classes here\n",
        "    markers = [\"s\", \"o\", \"D\"]\n",
        "\n",
        "    # Plotting decision regions\n",
        "    f, ax = plt.subplots(1, 1, figsize=(7, 6))\n",
        "\n",
        "    X_mesh = np.stack((xx_1.ravel(), xx_2.ravel()), axis=1)\n",
        "\n",
        "    Z = model.predict_proba(X_mesh)[:,1]\n",
        "    Z = Z.reshape(xx_1.shape)\n",
        "\n",
        "    ax.contourf(xx_1, xx_2, Z, alpha=0.3, colors=colors, levels=2)\n",
        "\n",
        "    plot_points(ax)\n",
        "\n",
        "    ax.legend(bbox_to_anchor=(1, 1), loc='upper left', ncol=1)\n",
        "\n",
        "    ax.set_title(\n",
        "        'Wine  class prediction\\nDecision boundaries',\n",
        "        fontsize=16\n",
        "    )\n",
        "    ax.set_xlabel(predictors[0], fontsize=12)\n",
        "    ax.set_ylabel(predictors[1], fontsize=12)\n",
        "\n",
        "    plt.tight_layout()\n",
        "    plt.show()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00054-52cf8966-69af-4f6c-9031-279552041aa8",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "b5f62a1a",
        "execution_millis": 499,
        "execution_start": 1615168037138,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 441
        },
        "id": "pTRHdM2_jE6F",
        "outputId": "b0593f52-d94f-4575-e916-bed9319861ec"
      },
      "source": [
        "# Model fit on just two features - alcohol, sulphates - since we can only \n",
        "# visualize two features in the 2D plot\n",
        "predictors = ['alcohol','sulphates']  \n",
        "\n",
        "# You will explore different models by uncommenting one of these lines\n",
        "model1 = DecisionTreeClassifier(max_depth=3, random_state=10).fit(X[predictors],Y)   \n",
        "# model1 = SVC(kernel='rbf', C=10, probability=1, random_state=10).fit(X[predictors], Y)  \n",
        "# model1 = LogisticRegression(C=10000, random_state=10).fit(X[predictors],Y)   \n",
        "\n",
        "# Identify appropriate boundaries for our meshgrid by\n",
        "# referencing the actual wine data\n",
        "x_1_wine = X['alcohol']     \n",
        "x_2_wine = X['sulphates']  \n",
        "alpha = 0.01 #0.1\n",
        "x_1_min_wine, x_1_max_wine = x_1_wine.min() - alpha, x_1_wine.max() + alpha\n",
        "x_2_min_wine, x_2_max_wine = x_2_wine.min() - alpha, x_2_wine.max() + alpha\n",
        "\n",
        "# Use np.arange to generate our interval arrays\n",
        "# and np.meshgrid to generate our actual grids\n",
        "xx_1_wine, xx_2_wine = np.meshgrid(\n",
        "    np.arange(x_1_min_wine, x_1_max_wine, 0.003),\n",
        "    np.arange(x_2_min_wine, x_2_max_wine, 0.003)\n",
        ")\n",
        "\n",
        "# Now we have everything we need to generate our plot\n",
        "plot_wine_2d_boundaries(\n",
        "    X,  \n",
        "    Y,\n",
        "    predictors,\n",
        "    model1,\n",
        "    xx_1_wine,\n",
        "    xx_2_wine,\n",
        ")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00072-4f3491a8-5ed4-401e-8b06-3ad7eefbc717",
        "deepnote_cell_type": "markdown",
        "id": "UpJqZYBZjE6F"
      },
      "source": [
        "**Q** Change the model from decision tree to KNN, SVM, and logistic regression by uncommenting code in lines 6-9 above. For each model, change the models hyperparameters to find values that create optimal decision boundaries. Note that each run may take some time for the SVM model. \n",
        "\n",
        "Save the images of the optimal decision boundaries for each model and put them in your solutions document. Label each with the name of the model and the optimal hyperparameters. Below each plot describe why you chose these particular hyperparameter values.\n",
        "\n",
        "**A** Put your answers into a solutions Google doc."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00073-526befe3-464d-4ce1-899e-1f15938d6c1b",
        "deepnote_cell_type": "markdown",
        "id": "393u2n8djE6F"
      },
      "source": [
        "-----\n",
        "**Q** Looking at these decision boundaries, which model is optimal, and why?\n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00074-20ba6633-419b-4901-a8c5-cf52c8de010a",
        "deepnote_cell_type": "markdown",
        "id": "N-7wVZqOjE6F"
      },
      "source": [
        "---\n",
        "**Please make sure to finish all of the parts above before you change to imbalanced data in the next section.** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00014-d298f61d-566a-4d3f-aba1-77dd92d0bf35",
        "deepnote_cell_type": "markdown",
        "id": "dGxRZfePjE6F"
      },
      "source": [
        "## Balanced vs. Imbalanced Data\n",
        "\n",
        "To demonstrate the difference between error metrics you will re-run these measures for imbalanced training and test data with more negative examples (class 0). In your solutions Google doc, collect all of the error metrics (accuracy, F1) and plots (confusion matrix, ROC curves, P-R curves) for the different classification models **before and after** making the data imbalanced by following these steps:\n",
        "\n",
        "**Before:** Create a title called \"Before Data Imbalance\" in your Google doc.\n",
        "- Go back to the \"Binary Classification\" at the beginning of the notebook \n",
        "- Capture the ratio of negative (class 0) to positive (class 1) examples in your Google doc\n",
        "- Capture the error metrics and plots in your Google doc. You already did this for the \"Effects of Optimal Hyperparameter\" exercise above. Copy those results here for easier comparison.  \n",
        "\n",
        "**After:** Create a title called \"After Data Imbalance\" in your Google doc.\n",
        "- Go back to \"COME BACK HERE\" in the \"Binary Classification\" section at the beginning of the notebook.\n",
        "- Change the binary classification to make the dataset imbalanced.\n",
        "- Capture the ratio of negative (class 0) to positive (class 1) examples in your Google doc\n",
        "- Re-run the code to train each model in \"Basic ML Models\"\n",
        "- Re-run the \"Model Error Metrics\" part of the notebook and capture the new error metrics and plots in your Google doc\n",
        "\n",
        "How did the error metrics and plots change for each model? Describe the changes in a short paragraph in your Google doc. It may be easier to put the respective plots next to each other for comparison. Make sure to clearly label everything.\n",
        "\n",
        "**A** Put your answers into a solutions Google doc."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00046-b835533c-9fd1-45ed-9adf-7a0c81f0a51b",
        "deepnote_cell_type": "markdown",
        "id": "kWZR7RmAjE6F"
      },
      "source": [
        "___\n",
        "**Q** Which error metrics perform better in showing the difference between balanced and imbalanced classes? Which ones do not show a difference? \n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00081-780bd238-87aa-42f7-b71f-cb8c15c7bfa5",
        "deepnote_cell_type": "markdown",
        "id": "aXv6hWpdjE6G"
      },
      "source": [
        "---\n",
        "**Q** Based on this example, why does imbalanced data pose a danger for machine learning models?\n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00081-55e656d6-46d7-4d3a-940a-fa38522e3a15",
        "deepnote_cell_type": "markdown",
        "id": "UwO4cJHzjE6G"
      },
      "source": [
        "## Handling Imbalanced Data\n",
        "\n",
        "Since it happens quite often that the minority class has much less data (e.g., in health care applications) we need to know how to handle imbalanced data. We are going to continue with our example of imbalanced data between good quality (class 1) wines and the rest (class 0), so make sure you completed the previous exercise to create imbalanced data and rerunning the code cells. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00082-a504877b-c3a6-4f5e-90ca-3572336822e5",
        "deepnote_cell_type": "markdown",
        "id": "FLGKrrZijE6G"
      },
      "source": [
        "### Penalized SVM\n",
        "\n",
        "The first approach is to use a **penalized** model that uses penalized learning algorithms to increase the cost of classification mistakes on the minority class. We will use penalized SVM, a popular algorithm for this technique, that uses class weights to penalize the majority class."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00082-c755aeb5-a29a-4815-a401-b48820cd435c",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "c29245aa",
        "execution_millis": 240,
        "execution_start": 1615166739380,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cv8eOYAwjE6G",
        "outputId": "d88e40b2-7ed0-47c2-9bb8-4a8c298c330e"
      },
      "source": [
        "# From Part 1\n",
        "# Creating the SVM model\n",
        "# We are setting probability=True for the model to predict probabilites (this was not in part 1)\n",
        "# Note the hyperparameters 'kernel' and 'C' - we will come back to these later\n",
        "# class_weight is the parameter that helps with class imbalance \n",
        "svc_clf = SVC( kernel='rbf', random_state=10, C=1.0, probability=True, class_weight='balanced') \n",
        "\n",
        "# Fitting the model to the data (i.e., training the model)\n",
        "svc_clf.fit(X_train_s, y_train) \n",
        "\n",
        "# Predictions on the test set\n",
        "svc_preds = svc_clf.predict(X_test_s)\n",
        "\n",
        "# Predict probabilities on the test set\n",
        "# Predicted probabilites are required for plotting ROC AUC curve\n",
        "svc_preds_prob = svc_clf.predict_proba(X_test_s)\n",
        "\n",
        "print(color.BLUE + '\\nPenalized SVM: ')\n",
        "print(\"Accuracy:\", accuracy_score(y_test,svc_preds))\n",
        "print(\"F1-Score: {0:0.5f}\".format(f1_score(y_test,svc_preds)))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[94m\n",
            "Penalized SVM: \n",
            "Accuracy: 0.765625\n",
            "F1-Score: 0.78134\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00084-c10f85fb-6636-4c78-a965-ac9b8e00231f",
        "deepnote_cell_type": "markdown",
        "id": "zfGzcrFZjE6G"
      },
      "source": [
        "**Q** What are the different accuracy and F1 scores for the SVM model with and without class weights ? \n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00085-ac16226b-f643-42cd-8f9f-f4152b2243e2",
        "deepnote_cell_type": "markdown",
        "id": "7HAc5myAjE6G"
      },
      "source": [
        "### Minority Upsampling\n",
        "\n",
        "Our second, more general approach is to balance our data using upsampling of the minority class. **Upsampling** is the process of randomly duplicating observations from a class in order to reinforce its signal. There are several heuristics for doing so, but the most common way is to simply resample with replacement. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00085-77ca085b-b28a-4e55-9f39-a46f02138fd0",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "7483172",
        "execution_millis": 22,
        "execution_start": 1615167170035,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sXGQHk8-jE6G",
        "outputId": "23227795-8916-4185-c03b-ad0ced106381"
      },
      "source": [
        "# We first upsample our minority class\n",
        "from sklearn.utils import resample\n",
        "\n",
        "# Separate majority and minority classes\n",
        "X['target'] = Y\n",
        "df_majority = X[Y==0]\n",
        "df_minority = X[Y==1]\n",
        "\n",
        "print(\"Current Ratio:\\n\", pd.Series(Y).value_counts())\n",
        "\n",
        "print(\"\\nMajority and Minority Dataframe shapes: \",df_majority.shape, df_minority.shape, \"\\n\")\n",
        "\n",
        "# Upsample minority class\n",
        "df_minority_upsampled = resample(df_minority, \n",
        "                                 replace=True,     # sample with replacement\n",
        "                                 n_samples=df_majority.shape[0],    # to match majority class\n",
        "                                 random_state=123) # reproducible results\n",
        "\n",
        "# Combine majority class with upsampled minority class\n",
        "df_upsampled = pd.concat([df_majority, df_minority_upsampled])\n",
        "\n",
        "print(\"New ratio:\\n\",df_upsampled.target.value_counts())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Current Ratio:\n",
            " 1    855\n",
            "0    744\n",
            "dtype: int64\n",
            "\n",
            "Majority and Minority Dataframe shapes:  (744, 12) (855, 12) \n",
            "\n",
            "New ratio:\n",
            " 1    744\n",
            "0    744\n",
            "Name: target, dtype: int64\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00087-c177704c-9005-4d49-9d7e-c5b4c893e5dd",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "12e99a46",
        "execution_millis": 1,
        "execution_start": 1615167172313,
        "deepnote_cell_type": "code",
        "id": "IDYpImZ-jE6G"
      },
      "source": [
        "\n",
        "target_upsampled = df_upsampled['target']\n",
        "df_upsampled.drop('target', axis=1, inplace=True)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00087-1f2fbd1e-15a7-49f8-887d-debfc16f2f8b",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "9a24c825",
        "execution_millis": 5,
        "execution_start": 1615167205713,
        "deepnote_cell_type": "code",
        "id": "tVGL2mCBjE6G"
      },
      "source": [
        "# From Part 1 - Standardize the data\n",
        "# Split data into train (80%) and test (20%) sets.\n",
        "# random_state: Controls the shuffling applied to the data before applying the split. \n",
        "#              Pass an int for reproducible output across multiple function calls.\n",
        "X_train_upsampled, X_test_upsampled, y_train_upsampled, y_test_upsampled = train_test_split(df_upsampled, target_upsampled,\n",
        "                                                    test_size=0.2,\n",
        "                                                    random_state=10)\n",
        "\n",
        "\n",
        "# Standardize the features\n",
        "\n",
        "# We standardize training and test data separately to avoid information leakage between them\n",
        "# Also note we do not standardize the predicted value `quality`, just the features\n",
        "scaler = StandardScaler()\n",
        "X_train_upsampled_std = scaler.fit_transform(X_train_upsampled)\n",
        "X_test_upsampled_std = scaler.transform(X_test_upsampled)\n",
        "\n",
        "# sklearn StandardScaler() returns Numpy arrays. That means your column names are gone. \n",
        "# If we want to preserve the column names we need to convert the array back to a Pandas dataframe and add the column names. \n",
        "X_train_upsampled_std = pd.DataFrame(X_train_upsampled_std,columns=df_upsampled.columns)\n",
        "X_test_upsampled_std = pd.DataFrame(X_test_upsampled_std,columns=df_upsampled.columns)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "cell_id": "00087-d1839736-8db5-432b-9cea-4e3bf846743c",
        "deepnote_to_be_reexecuted": false,
        "source_hash": "a0dd2ea8",
        "execution_millis": 740,
        "execution_start": 1615167241982,
        "deepnote_cell_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "S8A5uyv_jE6H",
        "outputId": "3511c00b-f55c-4cd8-f6b9-25e863fd0125"
      },
      "source": [
        "# Now we are going to use the the df_upsampled dataset to create the SVM model \n",
        "svc_clf = SVC( kernel='rbf', random_state=10, C=1.0, probability=True, class_weight='balanced') \n",
        "\n",
        "# Fitting the model to the data (i.e., training the model)\n",
        "svc_clf.fit(X_train_upsampled_std, y_train_upsampled) \n",
        "\n",
        "# Predictions on the test set\n",
        "svc_preds = svc_clf.predict(X_test_upsampled_std)\n",
        "\n",
        "# Predict probabilities on the test set\n",
        "# Predicted probabilites are required for plotting ROC AUC curve\n",
        "svc_preds_prob = svc_clf.predict_proba(X_test_upsampled_std)\n",
        "\n",
        "print(color.BLUE + '\\nSupport Vector Machine: ')\n",
        "print(\"Accuracy:\", accuracy_score(y_test_upsampled,svc_preds))\n",
        "\n",
        "#SVM with no class weight results - accuracy \n",
        "#Support Vector Machine: \n",
        "#Accuracy: 0.871875\n",
        "\n",
        "#SVM with no class weight - f1 score\n",
        "print(color.BLUE + '\\nSupport Vector Machine: ')\n",
        "print(\"F1-Score: {0:0.5f}\".format(f1_score(y_test_upsampled,svc_preds)))\n",
        "\n",
        "# Support Vector Machine: \n",
        "# F1-Score: 0.38806"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[94m\n",
            "Support Vector Machine: \n",
            "Accuracy: 0.7718120805369127\n",
            "\u001b[94m\n",
            "Support Vector Machine: \n",
            "F1-Score: 0.77181\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "tags": [],
        "cell_id": "00088-d1ca579c-8183-447c-9e4c-0388f7a95ca1",
        "deepnote_cell_type": "markdown",
        "id": "Xw62RdVZjE6H"
      },
      "source": [
        "**Q** Summarize the accuracy and F1 score results here and discuss what method to deal with the imbalanced data worked best.\n",
        "\n",
        "**A** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V-XNgTGlvWUI"
      },
      "source": [
        "---\n",
        "\n",
        "Congratulations, you have made it to the end of this notebook. This concludes our wine classification example. We hope it was instructive and that you learned some valuable lessons for your final projects. Do not hesitate to ask questions about the code on EdStem or in TF office hours."
      ]
    }
  ]
}