Elaine_Zhang__MSIS522_Assignment2.ipynb

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      "name": "Elaine Zhang_ MSIS522_Assignment2.ipynb",
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      "source": [
        "# Decision Tree & Ensemble Learning\n",
        "\n",
        "Classification And Regression Trees (CART for short) is a term introduced by [Leo Breiman](https://en.wikipedia.org/wiki/Leo_Breiman) to refer to Decision Tree algorithms that can be used for classification or regression predictive modeling problems.\n",
        "\n",
        "In this lab assignment, you will implement various ways to calculate impurity which is used to split data in constructing the decision trees and apply the Decision Tree and ensemble learning algorithms to solve two real-world problems: a classification one and a regression one. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WsJh8RbLhs1V"
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      "source": [
        "# import packages\n",
        "%matplotlib inline\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "import pandas as pd\n",
        "from matplotlib.legend_handler import HandlerLine2D\n",
        "from sklearn.metrics import accuracy_score\n",
        "from sklearn.metrics import confusion_matrix\n",
        "from sklearn.metrics import mean_squared_error\n",
        "from sklearn.metrics import mean_absolute_error\n",
        "from sklearn.tree import DecisionTreeClassifier\n",
        "from sklearn.tree import DecisionTreeRegressor\n",
        "from sklearn.model_selection import GridSearchCV\n",
        "\n",
        "# make this notebook's output stable across runs\n",
        "np.random.seed(0)"
      ],
      "execution_count": 1,
      "outputs": []
    },
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      "cell_type": "markdown",
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      "source": [
        "## Gini impurity and Entropy\n"
      ]
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      "source": [
        "#### Gini impurity\n",
        "\n",
        "The CART algorithm recursively splits the training set into two subsets using a single feature k and a threshold $t_k$. The best feature and threshold are chosen to produce the purest subsets weighted by their size. **Gini impurity** measures the impurity of the data points in a set and is used to evaluate how good a split is when the CART algorithm searches for the best pair of feature and the threshold.\n",
        "\n",
        "To compute Gini impurity for a set of items with J classes, suppose $i \\in \\{1, 2, \\dots, J\\}$ and let $p_i$ be the fraction of items labeled with class i in the set.\n",
        "\\begin{align}\n",
        "I(p) = 1 - \\sum_{i=1}^J p_i^2\n",
        "\\end{align}\n",
        "\n",
        "The following function calculates the gini impurity for a given set of data points."
      ]
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    {
      "cell_type": "code",
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      "source": [
        "def gini_impurity(x):\n",
        "    \"\"\"\n",
        "    This function calculate the Gini impurity for a given set of data points.\n",
        "\n",
        "    Args:\n",
        "    x: a numpy ndarray\n",
        "    \"\"\"\n",
        "    unique, counts = np.unique(x, return_counts=True)\n",
        "    probabilities = counts / sum(counts)\n",
        "    gini = 1 - sum([p*p for p in probabilities])\n",
        "\n",
        "    return gini"
      ],
      "execution_count": 2,
      "outputs": []
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      "source": [
        "np.testing.assert_equal(0, gini_impurity(np.array([1, 1, 1])))\n",
        "np.testing.assert_equal(0.5, gini_impurity(np.array([1, 0, 1, 0])))\n",
        "np.testing.assert_equal(3/4, gini_impurity(np.array(['a', 'b', 'c', 'd'])))\n",
        "np.testing.assert_almost_equal(2.0/3, gini_impurity(np.array([1, 2, 3, 1, 2, 3])))"
      ],
      "execution_count": 3,
      "outputs": []
    },
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      "source": [
        "#### Entropy\n",
        "\n",
        "Another popular measure of impurity is called **entropy**, which measures the average information content of a message. Entropy is zero when all messages are identical. When it applied to CART, a set's entropy is zero when it contains instances of only one class. Entropy is calculated as follows:\n",
        "\\begin{align}\n",
        "I(p) = - \\sum_{i=1}^J p_i log_2{p_i}\n",
        "\\end{align}\n",
        "\n",
        "<span style=\"color:orange\">**Question 1: In this exercise, you will implement the entropy function.**"
      ]
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      "source": [
        "def entropy(x):\n",
        "    \"\"\"\n",
        "    TODO: This function calculate the entropy of an array.\n",
        "\n",
        "    Args:\n",
        "    x: a numpy ndarray\n",
        "    \"\"\"\n",
        "    e = 0 # TODO\n",
        "    unique, counts = np.unique(x, return_counts=True)\n",
        "    probabilities = counts / sum(counts)\n",
        "    e = 0 - sum([p* np.log2(p) for p in probabilities])\n",
        "    return e"
      ],
      "execution_count": 4,
      "outputs": []
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      "cell_type": "code",
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      "source": [
        "np.testing.assert_equal(0, entropy(np.array([1, 1, 1])))\n",
        "np.testing.assert_equal(1.0, entropy(np.array([1, 0, 1, 0])))\n",
        "np.testing.assert_equal(2.0, entropy(np.array(['a', 'b', 'c', 'd'])))\n",
        "np.testing.assert_almost_equal(1.58496, entropy(np.array([1, 2, 3, 1, 2, 3])), 4)"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4qX1XT12hs1t"
      },
      "source": [
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EZGblkNkhs2g"
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      "source": [
        "## Iris dataset\n",
        "\n",
        "The Iris data set contains the morphologic variation of Iris flowers of three related species (Iris setosa, Iris virginica and Iris versicolor). Four features were measured from each observation (see image below):\n",
        "- Sepal.Length: sepal length in centimeters.\n",
        "- Sepal.Width: sepal width in centimeters.\n",
        "- Petal.Length: petal length in centimeters.\n",
        "- Petal.Width: petal width in centimeters.\n",
        "\n",
        "<table>\n",
        "  <tr>\n",
        "    <td><img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/5/56/Kosaciec_szczecinkowaty_Iris_setosa.jpg/180px-Kosaciec_szczecinkowaty_Iris_setosa.jpg\" style=\"width:250px\"></td>\n",
        "    <td><img src=\"https://www.math.umd.edu/~petersd/666/html/iris_with_labels.jpg\" width=\"250px\"></td>\n",
        "    <td><img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Iris_virginica.jpg/295px-Iris_virginica.jpg\" width=\"250px\"></td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td>Iris setosa</td>\n",
        "    <td>Iris versicolor</td>\n",
        "    <td>Iris virginica</td>\n",
        "  </tr>\n",
        "</table>\n"
      ]
    },
    {
      "cell_type": "code",
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      "source": [
        "# load the iris train and test data from CSV files\n",
        "train = pd.read_csv('https://raw.githubusercontent.com/zariable/data/master/iris_train.csv')\n",
        "test = pd.read_csv('https://raw.githubusercontent.com/zariable/data/master/iris_test.csv')\n",
        "\n",
        "train_x = train.iloc[:,0:4]\n",
        "train_y = train.iloc[:,4]\n",
        "\n",
        "test_x = test.iloc[:,0:4]\n",
        "test_y = test.iloc[:,4]\n",
        "\n",
        "# print the number of instances in each class\n",
        "print(train_y.value_counts().sort_index())\n",
        "print(test_y.value_counts().sort_index())"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iris-setosa        34\n",
            "Iris-versicolor    32\n",
            "Iris-virginica     39\n",
            "Name: species, dtype: int64\n",
            "Iris-setosa        16\n",
            "Iris-versicolor    18\n",
            "Iris-virginica     11\n",
            "Name: species, dtype: int64\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tpe8jv7Qhs2f"
      },
      "source": [
        "### Decision Tree Classifier\n",
        "\n",
        "<span style=\"color:orange\">**In this exercise, we will apply the Decision Tree classifier to classify the Iris flower data.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8JwQoOdPhs2j"
      },
      "source": [
        "#### Train and visualize a simple Decision Tree\n",
        "\n",
        "<span style=\"color:orange\">**Question 2: create a decision tree with max_depth of 2.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
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        "scrolled": true,
        "outputId": "0ece1d4b-e1f3-49a9-f1b1-793866876016"
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      "source": [
        "# TODO: read the scikit-learn doc on DecisionTreeClassifier and train a Decision Tree with max depth of 2\n",
        "# TODO\n",
        "dtc = DecisionTreeClassifier(max_depth=2)\n",
        "dtc.fit(train_x, train_y)\n",
        "\n"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "DecisionTreeClassifier(ccp_alpha=0.0, class_weight=None, criterion='gini',\n",
              "                       max_depth=2, max_features=None, max_leaf_nodes=None,\n",
              "                       min_impurity_decrease=0.0, min_impurity_split=None,\n",
              "                       min_samples_leaf=1, min_samples_split=2,\n",
              "                       min_weight_fraction_leaf=0.0, presort='deprecated',\n",
              "                       random_state=None, splitter='best')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Tn25MVpchs2n"
      },
      "source": [
        "Now let's visualize the decision tree we just trained on the iris dataset and see how it makes predictions. Note that if the following code does not work for you because the graphviz is missing, do not worry about it and you should still be able to move on."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 492
        },
        "id": "Y80Nilx1hs2o",
        "scrolled": true,
        "outputId": "3a61182d-bdab-42af-e1ea-68788b953a4b"
      },
      "source": [
        "from sklearn.externals.six import StringIO  \n",
        "from IPython.display import Image  \n",
        "from sklearn.tree import export_graphviz\n",
        "import pydotplus\n",
        "\n",
        "dot_data = StringIO()\n",
        "feature_names = train_x.columns\n",
        "class_names = train_y.unique()\n",
        "class_names.sort()\n",
        "export_graphviz(dtc, out_file=dot_data, feature_names=feature_names, class_names=class_names, filled=True, rounded=True)\n",
        "graph = pydotplus.graph_from_dot_data(dot_data.getvalue())  \n",
        "Image(graph.create_png())"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/sklearn/externals/six.py:31: FutureWarning: The module is deprecated in version 0.21 and will be removed in version 0.23 since we've dropped support for Python 2.7. Please rely on the official version of six (https://pypi.org/project/six/).\n",
            "  \"(https://pypi.org/project/six/).\", FutureWarning)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<IPython.core.display.Image object>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZgqeLw6Lhs2t"
      },
      "source": [
        "Decision trees are easy to inteprete and is often referred to as *whitebox* machine learning algorithm. Let's see how this decision tree represented above makes predictions. Suppose you find an iris flower and want to classify it into setosa, versicolor or virginica. You start at the root node (the very top node in the tree). In this node, we check if the flower's patel length is smaller than or equal to 2.35 cm. If it is, we move to the left child and predict setosa to be its class. Otherwise, we move to the right child node. Then similarly we check if the petal length is smaller than or equal to 4.95 cm. If it is, we move to its left child node and predict versicolor to be its class. Otherwise, we move to its right child and predict virginica to be its class. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W94pWMvIhs2t"
      },
      "source": [
        "#### Prediction with Decision tree\n",
        "\n",
        "With this simple decision tree above, we can apply it to make predictions on the test dataset and evaluate its performance.\n",
        "\n",
        "<span style=\"color:orange\">**Question 3: make prediction using the trained decision tree model on the test data.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ugRPudSThs2u",
        "outputId": "2aa7d760-d493-4a69-e1b8-1341b0012e36"
      },
      "source": [
        "# TODO: use the trained decision tree model to make predictions on the test data and evaluate the model performance.\n",
        "# TODO\n",
        "test_z = dtc.predict(test_x)\n",
        "\n",
        "print(\"model accuracy: {}\".format(accuracy_score(test_y, test_z)))\n",
        "print(\"model confusion matrix:\\n {}\".format(confusion_matrix(test_y, test_z, labels=['Iris-setosa', 'Iris-versicolor', 'Iris-virginica'])))"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "model accuracy: 0.9111111111111111\n",
            "model confusion matrix:\n",
            " [[16  0  0]\n",
            " [ 0 17  1]\n",
            " [ 0  3  8]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RMzcZjQQhs2x"
      },
      "source": [
        "#### Hyper-parameters\n",
        "\n",
        "Hyper-parameter controls the complexity of the decision tree model. For example, the deeper the tree is, the more complex patterns the model will be able to capture. In this exercise, we train the decision trees with increasing number of maximum depth and plot its performance. We should see the accuracy of the training data increase as the tree grows deeper, but the accuracy on the test data might not as the model will eventually start to overfit and does not generalize well on the unseen test data.\n",
        "\n",
        "<span style=\"color:orange\">**Question 4: for each value of max_depth, we train a decision tree model and evaluate its accuracy on both train and test data, and plot both accuracies in the figure.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "uw23r_MXhs2x",
        "outputId": "4589a41b-29bc-4bd1-a1f2-07cf5edb168f"
      },
      "source": [
        "# TODO: train the decision tree model with various max_depth, make predictions and evaluate on both train and test data.\n",
        "#max_depth = 2\n",
        "dtcQ4_2 = DecisionTreeClassifier(max_depth=2)\n",
        "dtcQ4_2.fit(train_x, train_y)\n",
        "train_z_2 = dtcQ4_2.predict(train_x)\n",
        "test_z_2 = dtcQ4_2.predict(test_x)\n",
        "\n",
        "atrain2 = accuracy_score(train_y, train_z_2)\n",
        "atest2 = accuracy_score(test_y, test_z_2)\n",
        "\n",
        "#max_depth = 3\n",
        "dtcQ4_3 = DecisionTreeClassifier(max_depth=3)\n",
        "dtcQ4_3.fit(train_x, train_y)\n",
        "train_z_3 = dtcQ4_3.predict(train_x)\n",
        "test_z_3 = dtcQ4_3.predict(test_x)\n",
        "\n",
        "atrain3 = accuracy_score(train_y, train_z_3)\n",
        "atest3 = accuracy_score(test_y, test_z_3)\n",
        "\n",
        "#max_depth = 4\n",
        "dtcQ4_4 = DecisionTreeClassifier(max_depth=4)\n",
        "dtcQ4_4.fit(train_x, train_y)\n",
        "train_z_4 = dtcQ4_4.predict(train_x)\n",
        "test_z_4 = dtcQ4_4.predict(test_x)\n",
        "\n",
        "atrain4 = accuracy_score(train_y, train_z_4)\n",
        "atest4 = accuracy_score(test_y, test_z_4)\n",
        "\n",
        "#plot\n",
        "train_accuracy = [atrain2,atrain3,atrain4]\n",
        "test_accuracy = [atest2,atest3,atest4]\n",
        "\n",
        "N = 3\n",
        "ind = np.arange(N) \n",
        "width = 0.35       \n",
        "\n",
        "plt.bar(ind, train_accuracy, width, label='train accuracy')\n",
        "plt.bar(ind + width, test_accuracy, width,\n",
        "    label='test accuracy')\n",
        "plt.ylabel('Accuracy')\n",
        "plt.xlabel('Max depth')\n",
        "\n",
        "plt.xticks(ind + width / 2, ('2', '3', '4'))\n",
        "plt.legend(loc='center')\n",
        "plt.show()\n"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2iaLr1ufhs20"
      },
      "source": [
        "#### Fine-tune the decision tree classifier\n",
        "\n",
        "Decision tree is a very powerful model with very few assumptions about the incoming training data (unlike linear models, which assume the data linear), however, it is more likely to overfit the data and won't generalize well to unseen data. To void overfitting, we need to restrict the decision tree's freedom during training via regularization (e.g. max_depth, min_sample_split, max_leaf_nodes and etc.).\n",
        "\n",
        "To fine-tune the model and combat overfitting, use grid search with cross-validation (with the help of the GridSearchCV class) to find the best hyper-parameter settings for the DecisionTreeClassifier. In particular, we would like to fine-tune the following hyper-parameters:\n",
        "- **criteria**: this defines how we measure the quality of a split. we can choose either \"gini\" for the Gini impurity or \"entropy\" for the information gain.\n",
        "- **max_depth**: the maximum depth of the tree. This indicates how deep the tree can be. The deeper the tree, the more splits it has and it captures more information about the data. But meanwhile, deeper trees are more likely to overfit the data. For this practice, we will choose from {1, 2, 3} given there are only 4 features in the iris dataset.\n",
        "- **min_samples_split**: This value represents the minimum number of samples required to split an internal node. The smaller this value is, the deeper the tree will grow, thus more likely to overfit. On the other hand, if the value is really large (the size of the training data in the extreme case), the tree will be very shallow and could suffer from underfit. In this practice, we choose from {0.01, 0.05, 0.1, 0.2}.\n",
        "\n",
        "<span style=\"color:orange\">**Question 5: Use grid search with 3-fold cross-validation to fine-tune the decision tree model and output the best hyper-parameters.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9fuI5TWkhs21",
        "outputId": "e812a7f0-68f0-4aec-901d-ae706c39deaf"
      },
      "source": [
        "# TODO: fine-tune the model, use grid search with 3-fold cross-validation.\n",
        "parameters = {# TODO\n",
        "    \"max_depth\": [1, 2, 3],    \n",
        "    \"min_samples_split\": [0.01, 0.05,0.1, 0.2]\n",
        "}\n",
        "\n",
        "dt = DecisionTreeClassifier() # TODO\n",
        "grid = GridSearchCV(dt, parameters, cv=3)# TODO\n",
        "grid.fit(train_x, train_y)\n",
        "\n",
        "# summarize the results of the grid search\n",
        "print(\"The best score is {}\".format(grid.best_score_))\n",
        "print(\"The best hyper parameter setting is {}\".format(grid.best_params_))"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The best score is 0.9619047619047619\n",
            "The best hyper parameter setting is {'max_depth': 3, 'min_samples_split': 0.01}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZXeHA4TThs24"
      },
      "source": [
        "#### Prediction and Evaluation\n",
        "\n",
        "Now we have a fine-tuned decision tree classifier based on the training data, let's apply this model to make predictions on the test data and evaluate its performance."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pzGEUWFPhs24",
        "outputId": "66797ea9-072e-4517-b890-5d66e7f4b901"
      },
      "source": [
        "grid.predict(test_x)\n",
        "\n",
        "print(\"model accuracy: {}\".format(accuracy_score(test_y, test_z)))\n",
        "print(\"model confusion matrix:\\n {}\".format(confusion_matrix(test_y, test_z, labels=['Iris-setosa', 'Iris-versicolor', 'Iris-virginica'])))"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "model accuracy: 0.9111111111111111\n",
            "model confusion matrix:\n",
            " [[16  0  0]\n",
            " [ 0 17  1]\n",
            " [ 0  3  8]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fLrLCXpbIHI2"
      },
      "source": [
        "### Random Forest\n",
        "\n",
        "**Question 6: Apply Random Forest together with Gridsearch to the Iris dataset and evaluate its accuracy.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UTzDdKnoIDM1",
        "outputId": "dce2218d-6869-49f5-de76-f84d086f3f37"
      },
      "source": [
        "### TODO \n",
        "from sklearn.ensemble import RandomForestClassifier\n",
        "from sklearn.ensemble import RandomForestRegressor\n",
        "parameters = {\n",
        "    \"n_estimators\": [20, 40],\n",
        "    \"max_depth\": [2, 4], \n",
        "    \"min_samples_split\": [0.01, 0.05,0.1, 0.2]\n",
        "}\n",
        "\n",
        "rfc_grid = GridSearchCV(RandomForestClassifier(n_jobs=-1, random_state=0), parameters, cv=3)\n",
        "rfc_grid.fit(train_x, train_y)\n",
        "\n",
        "print(\"The best score is {}\".format(rfc_grid.best_score_))\n",
        "print(\"The best hyper parameter setting is {}\".format(rfc_grid.best_params_))"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The best score is 0.9619047619047619\n",
            "The best hyper parameter setting is {'max_depth': 2, 'min_samples_split': 0.01, 'n_estimators': 40}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VKgNC7kzIWNC"
      },
      "source": [
        "### Adaboost\n",
        "\n",
        "**Question 7: Apply Adaboost together with Gridsearch to the Iris dataset and evaluate its accuracy.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hDcP-xy_IXFF",
        "outputId": "25d495ab-c93f-49f9-afde-10821bf6a171"
      },
      "source": [
        "### TODO \n",
        "from sklearn.ensemble import AdaBoostClassifier\n",
        "parameters = {\n",
        "    \"n_estimators\": [20, 40],\n",
        "    \"learning_rate\": [0.01, 0.1, 1, 10]\n",
        "}\n",
        "\n",
        "adaboost = AdaBoostClassifier(DecisionTreeClassifier(max_depth=4), random_state=0)\n",
        "adaboost_grid = GridSearchCV(adaboost, parameters, cv=3)\n",
        "adaboost_grid.fit(train_x, train_y)\n",
        "\n",
        "# summarize the results of the grid search\n",
        "print(\"The best score is {}\".format(adaboost_grid.best_score_))\n",
        "print(\"The best hyper parameter setting is {}\".format(adaboost_grid.best_params_))"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The best score is 0.9523809523809522\n",
            "The best hyper parameter setting is {'learning_rate': 0.01, 'n_estimators': 20}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tpZFN60NIWdK"
      },
      "source": [
        "### Gradient Boosting\n",
        "\n",
        "**Question 8: Apply Boosting together with Gridsearch to the Iris dataset and evaluate its accuracy.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mmRcvEkSIXrR",
        "outputId": "f8f828bb-7985-482e-a528-484300e95572"
      },
      "source": [
        "### TODO \n",
        "from sklearn.ensemble import GradientBoostingClassifier\n",
        "from sklearn.ensemble import GradientBoostingRegressor\n",
        "\n",
        "parameters = {\n",
        "    \"loss\":[\"deviance\"],\n",
        "    \"learning_rate\": [0.01, 0.1, 1, 10],\n",
        "    \"min_samples_split\": [0.01,0.05,0.1, 0.2],\n",
        "    \"max_depth\":[1,2,3],\n",
        "    \"n_estimators\":[100]\n",
        "}\n",
        "\n",
        "gbc_grid = GridSearchCV(GradientBoostingClassifier(), parameters, cv=3, n_jobs=-1)\n",
        "gbc_grid.fit(train_x, train_y)\n",
        "\n",
        "# summarize the results of the grid search\n",
        "print(\"The best score is {}\".format(gbc_grid.best_score_))\n",
        "print(\"The best hyper parameter setting is {}\".format(gbc_grid.best_params_))"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The best score is 0.9619047619047619\n",
            "The best hyper parameter setting is {'learning_rate': 0.01, 'loss': 'deviance', 'max_depth': 2, 'min_samples_split': 0.1, 'n_estimators': 100}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aTlPSt2Uhs26"
      },
      "source": [
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oyoZxHnxHknE"
      },
      "source": [
        "**BONUS POINT: we will apply the supervised learning models we learnt so far to predict the California housing prices.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3odrweXdhs28"
      },
      "source": [
        "## California Housing Dataset\n",
        "\n",
        "The California Housing dataset appeared in a 1997 paper titled Sparse Spatial Autoregressions by Pace, R. Kelley and Ronald Barry, published in the Statistics and Probability Letters journal. They built it using the 1990 California census data. It contains one row per census block group. A block group is the smallest geographical unit for which the U.S. Census Bureau publishes sample data (a block group typically has a population of 600 to 3,000 people). "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8zXK2RFshs29"
      },
      "source": [
        "# Load train and test data from CSV files.\n",
        "train = pd.read_csv('https://raw.githubusercontent.com/zariable/data/master/housing_train.csv')\n",
        "test = pd.read_csv('https://raw.githubusercontent.com/zariable/data/master/housing_test.csv')\n",
        "\n",
        "train_x = train.iloc[:,0:8]\n",
        "train_y = train.iloc[:,8]\n",
        "\n",
        "test_x = test.iloc[:,0:8]\n",
        "test_y = test.iloc[:,8]"
      ],
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 328
        },
        "id": "KBkB2AmyfGqD",
        "outputId": "ccfffde5-09fa-4ce6-e66e-1dba797d7105"
      },
      "source": [
        "#describe data\n",
        "train.corr()"
      ],
      "execution_count": 17,
      "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>longitude</th>\n",
              "      <th>latitude</th>\n",
              "      <th>housing_median_age</th>\n",
              "      <th>total_rooms</th>\n",
              "      <th>total_bedrooms</th>\n",
              "      <th>population</th>\n",
              "      <th>households</th>\n",
              "      <th>median_income</th>\n",
              "      <th>median_house_value</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>longitude</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.925158</td>\n",
              "      <td>-0.117501</td>\n",
              "      <td>0.057288</td>\n",
              "      <td>0.079141</td>\n",
              "      <td>0.108161</td>\n",
              "      <td>0.064218</td>\n",
              "      <td>-0.010093</td>\n",
              "      <td>-0.045777</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>latitude</th>\n",
              "      <td>-0.925158</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.020830</td>\n",
              "      <td>-0.048514</td>\n",
              "      <td>-0.076412</td>\n",
              "      <td>-0.117704</td>\n",
              "      <td>-0.080046</td>\n",
              "      <td>-0.085176</td>\n",
              "      <td>-0.143957</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>housing_median_age</th>\n",
              "      <td>-0.117501</td>\n",
              "      <td>0.020830</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.367868</td>\n",
              "      <td>-0.328137</td>\n",
              "      <td>-0.299736</td>\n",
              "      <td>-0.312394</td>\n",
              "      <td>-0.120396</td>\n",
              "      <td>0.103863</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>total_rooms</th>\n",
              "      <td>0.057288</td>\n",
              "      <td>-0.048514</td>\n",
              "      <td>-0.367868</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.929925</td>\n",
              "      <td>0.853460</td>\n",
              "      <td>0.919292</td>\n",
              "      <td>0.199549</td>\n",
              "      <td>0.131972</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>total_bedrooms</th>\n",
              "      <td>0.079141</td>\n",
              "      <td>-0.076412</td>\n",
              "      <td>-0.328137</td>\n",
              "      <td>0.929925</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.872138</td>\n",
              "      <td>0.975760</td>\n",
              "      <td>-0.004139</td>\n",
              "      <td>0.045712</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>population</th>\n",
              "      <td>0.108161</td>\n",
              "      <td>-0.117704</td>\n",
              "      <td>-0.299736</td>\n",
              "      <td>0.853460</td>\n",
              "      <td>0.872138</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.905061</td>\n",
              "      <td>0.006284</td>\n",
              "      <td>-0.026183</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>households</th>\n",
              "      <td>0.064218</td>\n",
              "      <td>-0.080046</td>\n",
              "      <td>-0.312394</td>\n",
              "      <td>0.919292</td>\n",
              "      <td>0.975760</td>\n",
              "      <td>0.905061</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.016365</td>\n",
              "      <td>0.061581</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>median_income</th>\n",
              "      <td>-0.010093</td>\n",
              "      <td>-0.085176</td>\n",
              "      <td>-0.120396</td>\n",
              "      <td>0.199549</td>\n",
              "      <td>-0.004139</td>\n",
              "      <td>0.006284</td>\n",
              "      <td>0.016365</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.693273</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>median_house_value</th>\n",
              "      <td>-0.045777</td>\n",
              "      <td>-0.143957</td>\n",
              "      <td>0.103863</td>\n",
              "      <td>0.131972</td>\n",
              "      <td>0.045712</td>\n",
              "      <td>-0.026183</td>\n",
              "      <td>0.061581</td>\n",
              "      <td>0.693273</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                    longitude  latitude  ...  median_income  median_house_value\n",
              "longitude            1.000000 -0.925158  ...      -0.010093           -0.045777\n",
              "latitude            -0.925158  1.000000  ...      -0.085176           -0.143957\n",
              "housing_median_age  -0.117501  0.020830  ...      -0.120396            0.103863\n",
              "total_rooms          0.057288 -0.048514  ...       0.199549            0.131972\n",
              "total_bedrooms       0.079141 -0.076412  ...      -0.004139            0.045712\n",
              "population           0.108161 -0.117704  ...       0.006284           -0.026183\n",
              "households           0.064218 -0.080046  ...       0.016365            0.061581\n",
              "median_income       -0.010093 -0.085176  ...       1.000000            0.693273\n",
              "median_house_value  -0.045777 -0.143957  ...       0.693273            1.000000\n",
              "\n",
              "[9 rows x 9 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GLuEmU1yflfO",
        "outputId": "ecc9f70c-4c38-4526-a4b3-d0c03f71216a"
      },
      "source": [
        "#test null values\n",
        "print(train.isnull().sum())\n",
        "print(test.isnull().sum())"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "longitude             0\n",
            "latitude              0\n",
            "housing_median_age    0\n",
            "total_rooms           0\n",
            "total_bedrooms        0\n",
            "population            0\n",
            "households            0\n",
            "median_income         0\n",
            "median_house_value    0\n",
            "dtype: int64\n",
            "longitude             0\n",
            "latitude              0\n",
            "housing_median_age    0\n",
            "total_rooms           0\n",
            "total_bedrooms        0\n",
            "population            0\n",
            "households            0\n",
            "median_income         0\n",
            "median_house_value    0\n",
            "dtype: int64\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DiHztTEbf2ct"
      },
      "source": [
        "\n",
        "from sklearn.metrics import mean_squared_error\n",
        "from sklearn.metrics import r2_score\n",
        "from sklearn.metrics import accuracy_score\n",
        "from sklearn.metrics import roc_auc_score\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.tree import DecisionTreeRegressor\n",
        "from sklearn.ensemble import RandomForestRegressor"
      ],
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "C-Xv_wdQJob8",
        "outputId": "e3e46e0c-0252-43ae-f233-7b9287ac8976"
      },
      "source": [
        "# TODO \n",
        "#decision tree regression\n",
        "dtc_housing = DecisionTreeRegressor(max_depth=3)\n",
        "dtc_housing.fit(train_x, train_y)\n",
        "test_z = dtc_housing.predict(test_x)\n",
        "mse = mean_squared_error(test_y, test_z)\n",
        "r2 = r2_score(test_y, test_z)\n",
        "print('Decision tree regression mean squared error: {}'.format(mse))\n",
        "print('Decision tree regression R2 score: {}'.format(r2))"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Decision tree regression mean squared error: 7132549714.033251\n",
            "Decision tree regression R2 score: 0.46502003749193555\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SckzGNerOw8w",
        "outputId": "90a6294f-0bf3-427c-d3b0-490ad2828a8d"
      },
      "source": [
        "#linear regression\n",
        "\n",
        "linear_regression_model = LinearRegression()\n",
        "linear_regression_model.fit(train_x, train_y)\n",
        "test_z = linear_regression_model.predict(test_x)\n",
        "\n",
        "mse = mean_squared_error(test_y, test_z)\n",
        "r2 = r2_score(test_y, test_z)\n",
        "\n",
        "print('Linear regression mean squared error: {}'.format(mse))\n",
        "print('Linear regression R2 score: {}'.format(r2))"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Linear regression mean squared error: 4953092025.125008\n",
            "Linear regression R2 score: 0.6284911999019238\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-NNI3nxCSy0o",
        "outputId": "3f297ad5-88c9-4912-d3e5-ab0d8a1b4185"
      },
      "source": [
        "#random forest regression\n",
        "rf_housing = RandomForestRegressor(max_depth=3)\n",
        "rf_housing.fit(train_x, train_y)\n",
        "test_z = rf_housing.predict(test_x)\n",
        "mse = mean_squared_error(test_y, test_z)\n",
        "r2 = r2_score(test_y, test_z)\n",
        "print('Random forest regression mean squared error: {}'.format(mse))\n",
        "print('Random forest regression R2 score: {}'.format(r2))"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Random forest regression mean squared error: 6710600771.753896\n",
            "Random forest regression R2 score: 0.4966684995947368\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4aPSUI90hFfu"
      },
      "source": [
        "#linear regression is the best model among those three, with the lowest MSE and highest R2 score. "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q-zitGTxhs3E"
      },
      "source": [
        "### End of Assignment 2\n",
        "---\n"
      ]
    }
  ]
}