Assignment 4/Ibrahim_Mohamed_A4_DT.ipynb

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    "id": "ee87b09a-445c-44e5-8c46-01cfd49e7b17"
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   "source": [
    "# Assignment_4 DT"
   ]
  },
  {
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   "id": "cde0bee0-be12-489f-b1f5-f501ed213a33",
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   "source": [
    "# Python ≥3.5 is required\n",
    "import sys\n",
    "assert sys.version_info >= (3, 5)\n",
    "\n",
    "# Scikit-Learn ≥0.20 is required\n",
    "import sklearn\n",
    "assert sklearn.__version__ >= \"0.20\"\n",
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "# to make this notebook's output stable across runs\n",
    "np.random.seed(42)\n",
    "\n",
    "# To plot pretty figures\n",
    "%matplotlib inline\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "mpl.rc('axes', labelsize=14)\n",
    "mpl.rc('xtick', labelsize=12)\n",
    "mpl.rc('ytick', labelsize=12)"
   ]
  },
  {
   "cell_type": "markdown",
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   "metadata": {
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    "id": "5678808b-305d-4a22-aa9c-52dcf7871a0e"
   },
   "source": [
    "# Part 1 Decision Tree\n"
   ]
  },
  {
   "cell_type": "code",
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      "text/plain": "DecisionTreeClassifier(criterion='entropy', max_depth=2, random_state=42)",
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     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "\n",
    "iris = load_iris()\n",
    "X = iris.data[:, 2:] # petal length and width\n",
    "y = iris.target\n",
    "\n",
    "feat_names = np.array(iris.feature_names)\n",
    "\n",
    "tree_clf_depth_2 = DecisionTreeClassifier(max_depth=2, random_state=42, criterion='entropy')\n",
    "tree_clf_depth_2.fit(X, y)"
   ]
  },
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    "id": "cf2b341d-f202-4ce4-a2b4-293a1f0a3fef"
   },
   "source": [
    "## Q1 Plot decision tree using export_graphviz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "outputs": [],
   "source": [
    "# Answer:\n",
    "from graphviz import Source\n",
    "from sklearn.tree import export_graphviz\n",
    "import pydotplus\n",
    "\n",
    "def graphiz_output(clf, features_names, class_names , outfile=None, filled=True, rounded=True, special_characters=True):\n",
    "    return export_graphviz(\n",
    "    clf,\n",
    "    out_file=outfile,\n",
    "    feature_names=features_names,\n",
    "    class_names=class_names,\n",
    "    filled=filled,\n",
    "    rounded=rounded,\n",
    "    special_characters=special_characters\n",
    ")\n"
   ],
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    "collapsed": false
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y=\"-290.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">petal length (cm) ≤ 2.45</text>\n<text text-anchor=\"start\" x=\"88\" y=\"-275.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">entropy = 1.585</text>\n<text text-anchor=\"start\" x=\"90.5\" y=\"-260.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 150</text>\n<text text-anchor=\"start\" x=\"77.5\" y=\"-245.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">value = [50, 50, 50]</text>\n<text text-anchor=\"start\" x=\"92\" y=\"-230.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">class = setosa</text>\n</g>\n<!-- 1 -->\n<g id=\"node2\" class=\"node\">\n<title>1</title>\n<path fill=\"#e58139\" stroke=\"black\" d=\"M105,-179.5C105,-179.5 12,-179.5 12,-179.5 6,-179.5 0,-173.5 0,-167.5 0,-167.5 0,-123.5 0,-123.5 0,-117.5 6,-111.5 12,-111.5 12,-111.5 105,-111.5 105,-111.5 111,-111.5 117,-117.5 117,-123.5 117,-123.5 117,-167.5 117,-167.5 117,-173.5 111,-179.5 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   "source": [
    "# Answer:\n",
    "\n",
    "from graphviz import Source\n",
    "from sklearn.tree import export_graphviz\n",
    "import pydotplus\n",
    "\n",
    "# Export decision tree to graphviz format\n",
    "dot_data = graphiz_output(tree_clf_depth_2, feat_names[2:4], iris.target_names)\n",
    "\n",
    "# Create graph from dot data\n",
    "tree_plot_depth_2 = pydotplus.graph_from_dot_data(dot_data)\n",
    "\n",
    "# Show graph in Jupyter Notebook\n",
    "Source(tree_plot_depth_2.to_string())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8f92c0a-e0b6-4431-a484-16d235fb74f0",
   "metadata": {
    "id": "c8f92c0a-e0b6-4431-a484-16d235fb74f0"
   },
   "source": [
    "## Q2 Plotting decision boundaries"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03bc39a1-488c-4ec2-9b27-f514a1109860",
   "metadata": {
    "id": "03bc39a1-488c-4ec2-9b27-f514a1109860"
   },
   "source": [
    "Use the following function to plot the decision boundaries of DT from Q1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "c5fa8ec6-637f-424d-82fa-5ca8e2efd6ae",
   "metadata": {
    "tags": [],
    "id": "c5fa8ec6-637f-424d-82fa-5ca8e2efd6ae"
   },
   "outputs": [],
   "source": [
    "from matplotlib.colors import ListedColormap\n",
    "\n",
    "def plot_decision_boundary(clf, X, y, axes=[0, 7.5, 0, 3], iris=True, legend=False, plot_training=True):\n",
    "    x1s = np.linspace(axes[0], axes[1], 100)\n",
    "    x2s = np.linspace(axes[2], axes[3], 100)\n",
    "    x1, x2 = np.meshgrid(x1s, x2s)\n",
    "    X_new = np.c_[x1.ravel(), x2.ravel()]\n",
    "    y_pred = clf.predict(X_new).reshape(x1.shape)\n",
    "    custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "    plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)\n",
    "    if not iris:\n",
    "        custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])\n",
    "        plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)\n",
    "    if plot_training:\n",
    "        plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", label=\"Iris setosa\")\n",
    "        plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", label=\"Iris versicolor\")\n",
    "        plt.plot(X[:, 0][y==2], X[:, 1][y==2], \"g^\", label=\"Iris virginica\")\n",
    "        plt.axis(axes)\n",
    "    if iris:\n",
    "        plt.xlabel(\"Petal length\", fontsize=14)\n",
    "        plt.ylabel(\"Petal width\", fontsize=14)\n",
    "    else:\n",
    "        plt.xlabel(r\"$x_1$\", fontsize=18)\n",
    "        plt.ylabel(r\"$x_2$\", fontsize=18, rotation=0)\n",
    "    if legend:\n",
    "        plt.legend(loc=\"lower right\", fontsize=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbf4c59b-aebc-4c10-a1da-69aa6cce0cb9",
   "metadata": {
    "id": "dbf4c59b-aebc-4c10-a1da-69aa6cce0cb9"
   },
   "source": [
    "### Plotting for max_depth = 2"
   ]
  },
  {
   "cell_type": "code",
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   "id": "3025e63c-c904-4cb7-9d77-912fff7e262e",
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    {
     "data": {
      "text/plain": "<Figure size 576x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 4))\n",
    "\n",
    "plot_decision_boundary(tree_clf_depth_2, X, y)\n",
    "\n",
    "plt.plot([2.45, 2.45], [0, 3], \"k-\", linewidth=2)\n",
    "plt.plot([2.45, 7.5], [1.75, 1.75], \"k--\", linewidth=2)\n",
    "plt.plot([4.95, 4.95], [0, 1.75], \"k:\", linewidth=2)\n",
    "plt.plot([4.85, 4.85], [1.75, 3], \"k:\", linewidth=2)\n",
    "plt.text(1.40, 1.0, \"Depth=0\", fontsize=15)\n",
    "plt.text(3.2, 1.80, \"Depth=1\", fontsize=13)\n",
    "plt.text(4.05, 0.5, \"(Depth=2)\", fontsize=11)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Q2.1\n",
    "- Train the decision tree using a maximum depth of 1.\n",
    "- Plot the decision tree using graphviz\n",
    "- Use the above function to plot the decision boundaries"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "outputs": [
    {
     "data": {
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      "text/plain": "<graphviz.sources.Source at 0x28ca1e432e0>"
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree_clf_depth_1 = DecisionTreeClassifier(max_depth=1, random_state=42, criterion='entropy')\n",
    "tree_clf_depth_1.fit(X, y)\n",
    "\n",
    "# Export decision tree to graphviz format\n",
    "dot_data = graphiz_output(tree_clf_depth_1, feat_names[2:4], iris.target_names)\n",
    "\n",
    "# Create graph from dot data\n",
    "tree_plot_depth_1 = pydotplus.graph_from_dot_data(dot_data)\n",
    "\n",
    "# Show graph in Jupyter Notebook\n",
    "Source(tree_plot_depth_1.to_string())"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Plotting for max_depth = 1"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 576x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 4))\n",
    "\n",
    "plot_decision_boundary(tree_clf_depth_1, X, y)\n",
    "\n",
    "plt.plot([2.45, 2.45], [0, 3], \"k-\", linewidth=2)\n",
    "plt.text(1.40, 1.0, \"Depth=0\", fontsize=15)\n",
    "plt.text(3.2, 1.80, \"Depth=1\", fontsize=13)\n",
    "\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "outputs": [
    {
     "data": {
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427,-104 433,-104 433,-104 568,-104 568,-104 574,-104 580,-110 580,-116 580,-116 580,-175 580,-175 580,-181 574,-187 568,-187\"/>\n<text text-anchor=\"start\" x=\"429\" y=\"-171.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">petal length (cm) ≤ 5.45</text>\n<text text-anchor=\"start\" x=\"453\" y=\"-156.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">entropy = 0.918</text>\n<text text-anchor=\"start\" x=\"463\" y=\"-141.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 3</text>\n<text text-anchor=\"start\" x=\"453.5\" y=\"-126.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">value = [0, 2, 1]</text>\n<text text-anchor=\"start\" x=\"448\" y=\"-111.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">class = versicolor</text>\n</g>\n<!-- 7&#45;&gt;9 -->\n<g id=\"edge9\" class=\"edge\">\n<title>7&#45;&gt;9</title>\n<path fill=\"none\" stroke=\"black\" d=\"M406.46,-222.91C418.19,-213.38 430.78,-203.15 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712,-242.5 712,-286.5 712,-286.5 712,-292.5 706,-298.5 700,-298.5\"/>\n<text text-anchor=\"start\" x=\"613.5\" y=\"-283.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">entropy = 0.0</text>\n<text text-anchor=\"start\" x=\"612.5\" y=\"-268.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">samples = 43</text>\n<text text-anchor=\"start\" x=\"603\" y=\"-253.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">value = [0, 0, 43]</text>\n<text text-anchor=\"start\" x=\"605\" y=\"-238.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\">class = virginica</text>\n</g>\n<!-- 12&#45;&gt;14 -->\n<g id=\"edge14\" class=\"edge\">\n<title>12&#45;&gt;14</title>\n<path fill=\"none\" stroke=\"black\" d=\"M570.56,-341.91C583.38,-330.1 597.36,-317.22 610.14,-305.45\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"612.52,-308.02 617.5,-298.67 607.77,-302.87 612.52,-308.02\"/>\n</g>\n<!-- \\n -->\n<g id=\"node16\" class=\"node\">\n<title>\\n</title>\n<path fill=\"black\" stroke=\"black\" d=\"M500.5,-639.5C500.5,-639.5 470.5,-639.5 470.5,-639.5 464.5,-639.5 458.5,-633.5 458.5,-627.5 458.5,-627.5 458.5,-615.5 458.5,-615.5 458.5,-609.5 464.5,-603.5 470.5,-603.5 470.5,-603.5 500.5,-603.5 500.5,-603.5 506.5,-603.5 512.5,-609.5 512.5,-615.5 512.5,-615.5 512.5,-627.5 512.5,-627.5 512.5,-633.5 506.5,-639.5 500.5,-639.5\"/>\n</g>\n</g>\n</svg>\n",
      "text/plain": "<graphviz.sources.Source at 0x28ca19d4b50>"
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree_clf_depth_10 = DecisionTreeClassifier(max_depth=10, random_state=42, criterion='entropy')\n",
    "tree_clf_depth_10.fit(X, y)\n",
    "\n",
    "# Export decision tree to graphviz format\n",
    "dot_data = graphiz_output(tree_clf_depth_10, feat_names[2:4], iris.target_names)\n",
    "\n",
    "# Create graph from dot data\n",
    "tree_plot_depth_10 = pydotplus.graph_from_dot_data(dot_data)\n",
    "\n",
    "# Show graph in Jupyter Notebook\n",
    "Source(tree_plot_depth_10.to_string())"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "**Question**\n",
    "1. After plotting the resulting tree.\n",
    "    - What's the output entropy in each block?\n",
    "    - Comment on the entropy values in each block.\n",
    "2. What's the difference in decision trees between using max_depth = 1, max_depth = 2, max_depth = 10? *Hint: Plot the tree in each case*"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "**Answer**"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "1.\n",
    "- Depth 1 => Petal Length (1.585)\n",
    "- Depth 2 => Petal Length True (0), Petal Length False (Petal Width) (1.0)\n",
    "- Depth 3=> Petal Width True (0.445), Petal Width False (0.151)\n",
    "\n",
    "2.\n",
    "- The complexity and accuracy of the models in decision trees varies whether max_depth is set to 1, 2, or 10. With max_depth = 1, a decision tree will have just one split, resulting in a very simple model with low complexity but potentially inferior accuracy. The decision tree plot shows this as a single root node with only one decision rule.\n",
    "- With max_depth = 2 (Accuracy Increased), a decision tree will have two splits, resulting in a somewhat more sophisticated model that can capture more subtle correlations between the input characteristics and the target variable. This may be visualised as a root node with two child nodes in the decision tree plot.\n",
    "- With max_depth = 10, a decision tree will have numerous splits, resulting in a very complicated model that may overfit the training data and generalise poorly to new data. The decision tree plot shows this as an extremely deep tree with many decision rules."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Q2.2"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "**Question**\n",
    "1. Calculate probabilities of all classes on this data point X = [[5, 1.5]] using decision tree with max_depth = 2\n",
    "2. Compare your result with \"predict_proba\" function."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def calculate_probability(clf, data_point):\n",
    "    # get the leaf node reached by the input data point\n",
    "    leaf_id = clf.apply(data_point)\n",
    "\n",
    "    # get the class distribution for the leaf node\n",
    "    class_counts = clf.tree_.value[leaf_id][0]\n",
    "\n",
    "    # get the total number of samples that reached the leaf node\n",
    "    total_samples = np.sum(class_counts)\n",
    "\n",
    "    # calculate class probabilities for the input data point\n",
    "    class_probabilities = class_counts / total_samples\n",
    "\n",
    "    # print the resulting class probabilities\n",
    "    return class_probabilities"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Question 3 Sensitivity to data"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Q3.1 Decision Tree\n",
    "**Question**\n",
    "1. Fit a decision tree classifier max_depth = 2, to the original data\n",
    "2. Plot the resulting decision boundaries\n",
    "3. Print the clasifier score on training data"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classifier score on Original training data: 0.960\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## we have already made a tree with max_depth = 2 on the original data and plotted the decision boundaries so we will skip that part\n",
    "# calculate the score of the classifier on the training data\n",
    "score = tree_clf_depth_2.score(X, y)\n",
    "print(\"Classifier score on Original training data: {:.3f}\".format(score))\n",
    "plot_decision_boundary(tree_clf_depth_2, X, y)"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "id": "a5305987-08db-4353-a1dd-aff97449219a",
   "metadata": {
    "id": "a5305987-08db-4353-a1dd-aff97449219a"
   },
   "source": [
    "The following cell rotates the data by angle 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "d6298947-acd2-45b1-945e-9170470f3264",
   "metadata": {
    "tags": [],
    "id": "d6298947-acd2-45b1-945e-9170470f3264"
   },
   "outputs": [],
   "source": [
    "angle = np.pi / 180 * 20\n",
    "rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])\n",
    "Xr = X.dot(rotation_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38645586-6b98-4c22-aca8-bc7587d8eab1",
   "metadata": {
    "id": "38645586-6b98-4c22-aca8-bc7587d8eab1"
   },
   "source": [
    "**Question**\n",
    "1. Fit another decision tree classifier max_depth = 2, to the rotated data\n",
    "2. Plot the resulting decision boundaries\n",
    "3. Print the clasifier score on training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "b73bd7f0-093f-468d-972a-a55123da9054",
   "metadata": {
    "tags": [],
    "id": "b73bd7f0-093f-468d-972a-a55123da9054"
   },
   "outputs": [
    {
     "data": {
      "text/plain": "DecisionTreeClassifier(criterion='entropy', max_depth=2, random_state=42)",
      "text/html": "<style>#sk-container-id-6 {color: black;background-color: white;}#sk-container-id-6 pre{padding: 0;}#sk-container-id-6 div.sk-toggleable {background-color: white;}#sk-container-id-6 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-6 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-6 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-6 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-6 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-6 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-6 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-6 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-6 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-6 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-6 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-6 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-6 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-6 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-6 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-6 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-6 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-6 div.sk-item {position: relative;z-index: 1;}#sk-container-id-6 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-6 div.sk-item::before, #sk-container-id-6 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-6 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-6 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-6 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-6 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-6 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-6 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-6 div.sk-label-container {text-align: center;}#sk-container-id-6 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-6 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-6\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>DecisionTreeClassifier(criterion=&#x27;entropy&#x27;, max_depth=2, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-6\" type=\"checkbox\" checked><label for=\"sk-estimator-id-6\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">DecisionTreeClassifier</label><div class=\"sk-toggleable__content\"><pre>DecisionTreeClassifier(criterion=&#x27;entropy&#x27;, max_depth=2, random_state=42)</pre></div></div></div></div></div>"
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fit a decision tree classifier to the rotated data\n",
    "tree_clf_depth_2_rotated = DecisionTreeClassifier(max_depth=2, random_state=42, criterion='entropy')\n",
    "tree_clf_depth_2_rotated.fit(Xr, y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classifier score on Rotated training data: 0.973\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# calculate the score of the classifier on the rotated data\n",
    "\n",
    "score_Xr = tree_clf_depth_2_rotated.score(Xr, y)\n",
    "print(\"Classifier score on Rotated training data: {:.3f}\".format(score_Xr))\n",
    "plot_decision_boundary(tree_clf_depth_2_rotated, Xr, y)\n"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "id": "1c012442-5bef-48ff-9674-60aba0010168",
   "metadata": {
    "id": "1c012442-5bef-48ff-9674-60aba0010168"
   },
   "source": [
    "### Q3.2 Logistic Regression\n",
    "The following function plots the decision boundaries for a logistic regression classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "8232066b-2388-4296-b4ea-11c4dc2821ef",
   "metadata": {
    "tags": [],
    "id": "8232066b-2388-4296-b4ea-11c4dc2821ef"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def plot_logistic_regression(clf, X, y, iris=True):\n",
    "\n",
    "  x_min, x_max = X[:, 0].min() - 0.5, X[:, 0].max() + 0.5\n",
    "  y_min, y_max = X[:, 1].min() - 0.5, X[:, 1].max() + 0.5\n",
    "  h = 0.02  # step size in the mesh\n",
    "  xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n",
    "  Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "\n",
    "  # Put the result into a color plot\n",
    "  Z = Z.reshape(xx.shape)\n",
    "  plt.pcolormesh(xx, yy, Z, cmap=plt.cm.Paired)\n",
    "\n",
    "  plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", label=\"Iris setosa\")\n",
    "  plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", label=\"Iris versicolor\")\n",
    "  plt.plot(X[:, 0][y==2], X[:, 1][y==2], \"g^\", label=\"Iris virginica\")\n",
    "  \n",
    "  plt.xlim(xx.min(), xx.max())\n",
    "  plt.ylim(yy.min(), yy.max())\n",
    "  if iris:\n",
    "        plt.xlabel(\"Petal length\", fontsize=14)\n",
    "        plt.ylabel(\"Petal width\", fontsize=14)\n",
    "  else:\n",
    "        plt.xlabel(r\"$x_1$\", fontsize=18)\n",
    "        plt.ylabel(r\"$x_2$\", fontsize=18, rotation=0)\n",
    "  plt.legend(loc=\"lower right\", fontsize=14)\n",
    "  plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc414d90-b10d-4d3b-a198-5ecd2781e835",
   "metadata": {
    "id": "bc414d90-b10d-4d3b-a198-5ecd2781e835"
   },
   "source": [
    "**Question**\n",
    "\n",
    "1. Fit a logistic regression classifier to the original data\n",
    "2. Plot the resulting decision boundaries\n",
    "3. Print the clasifier score on training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "22136243-8687-4413-b5f8-4ae7a979a142",
   "metadata": {
    "tags": [],
    "id": "22136243-8687-4413-b5f8-4ae7a979a142"
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classifier score on Original data: 0.9666666666666667\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "# Fit a logistic regression classifier to the original data\n",
    "LR_original = LogisticRegression(random_state=42)\n",
    "LR_original.fit(X, y)\n",
    "\n",
    "# Plot the decision boundaries\n",
    "plot_logistic_regression(LR_original, X, y)\n",
    "\n",
    "# Print the classifier score on the original data\n",
    "print('Classifier score on Original data:', LR_original.score(X, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f0357b4-70fa-47a7-929c-144ca3ece41d",
   "metadata": {
    "id": "9f0357b4-70fa-47a7-929c-144ca3ece41d"
   },
   "source": [
    "**Question**\n",
    "1. Fit another logistic regression classifier to the rotated data\n",
    "2. Plot the resulting decision boundaries\n",
    "3. Print the classifier score on training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "e315a031-b001-447e-beec-1fb7bfc06269",
   "metadata": {
    "id": "e315a031-b001-447e-beec-1fb7bfc06269"
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classifier score on Rotated data: 0.9666666666666667\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# Fit a logistic regression classifier to the rotated data\n",
    "LR_rotated = LogisticRegression(random_state=42)\n",
    "LR_rotated.fit(X, y)\n",
    "\n",
    "# Plot the decision boundaries\n",
    "plot_logistic_regression(LR_rotated, X, y)\n",
    "\n",
    "# Print the classifier score on the rotated data\n",
    "print('Classifier score on Rotated data:', LR_rotated.score(X, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c18142e-f4f4-458b-96cb-cf9c3dec8223",
   "metadata": {
    "id": "2c18142e-f4f4-458b-96cb-cf9c3dec8223"
   },
   "source": [
    "### Q3.3\n",
    "1. Comment on the differences between the logistic regression and decision trees classifiers scores to the original and rotated data\n",
    "2. Explain why that happened?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7563c051-da7a-4038-a8cb-60763a629bda",
   "metadata": {
    "id": "7563c051-da7a-4038-a8cb-60763a629bda"
   },
   "source": [
    "**Answer**\n",
    "\n",
    "1. When it comes to sensitivity, the decision tree are more sensitive to data since when we used the rotated data on the DT the accuracy changed while the logistic regression it stayed the same.\n",
    "\n",
    "2. As Decision Tree applies concept learning So it is more affected by the distribution of the data as the model as the model is built by this way. While Logistic Regression transforms the data anyway to another domain and apply the maximum likelihood to get the final model, So it is not so affected by the transformation of data to it."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9185fdd-aebc-4266-ba6c-432809a92763",
   "metadata": {
    "id": "d9185fdd-aebc-4266-ba6c-432809a92763"
   },
   "source": [
    "## Question 4 GridSearch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0a07c83-b9ad-4b36-8565-b60140d79ace",
   "metadata": {
    "id": "d0a07c83-b9ad-4b36-8565-b60140d79ace"
   },
   "source": [
    "1. Generate a moons dataset using `make_moons(n_samples=10000, noise=0.4)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "f0e27b3b-e44b-401c-afec-e61c9a37a9d8",
   "metadata": {
    "id": "f0e27b3b-e44b-401c-afec-e61c9a37a9d8"
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_moons"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f498d10-ba3d-4a08-9190-17eb3afdbd51",
   "metadata": {
    "id": "5f498d10-ba3d-4a08-9190-17eb3afdbd51"
   },
   "source": [
    "2. Split it into a training set and a test set using train_test_split()."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "912c9c1b-f781-4a8e-9749-cd8b3450418d",
   "metadata": {
    "id": "912c9c1b-f781-4a8e-9749-cd8b3450418d"
   },
   "outputs": [],
   "source": [
    "moon_x, moon_y = make_moons(n_samples=10000, noise=0.4, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb2bb873-baf4-40cd-b6f1-a23c61e78160",
   "metadata": {
    "id": "cb2bb873-baf4-40cd-b6f1-a23c61e78160"
   },
   "source": [
    "3. Use grid search with cross-validation (with the help of the GridSearchCV class) to find best hyperparameter (max_depth, max_leaf_nodes, min_samples_split) values for a DecisionTreeClassifier. \n",
    "    - Choose reasonable values for each hyperparameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "dc7d9e5e-16b0-4acd-8a3e-3f2f51bb1949",
   "metadata": {
    "id": "dc7d9e5e-16b0-4acd-8a3e-3f2f51bb1949"
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(moon_x, moon_y, test_size=0.2, random_state=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "ede295ff-e343-4d7e-9c2c-0320fbde9df1",
   "metadata": {
    "id": "ede295ff-e343-4d7e-9c2c-0320fbde9df1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best Hyper Parameters:  {'max_depth': 2, 'max_leaf_nodes': 4, 'min_samples_split': 2}\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\I1bra\\anaconda3\\lib\\site-packages\\sklearn\\model_selection\\_validation.py:378: FitFailedWarning: \n",
      "360 fits failed out of a total of 1260.\n",
      "The score on these train-test partitions for these parameters will be set to nan.\n",
      "If these failures are not expected, you can try to debug them by setting error_score='raise'.\n",
      "\n",
      "Below are more details about the failures:\n",
      "--------------------------------------------------------------------------------\n",
      "210 fits failed with the following error:\n",
      "Traceback (most recent call last):\n",
      "  File \"C:\\Users\\I1bra\\anaconda3\\lib\\site-packages\\sklearn\\model_selection\\_validation.py\", line 686, in _fit_and_score\n",
      "    estimator.fit(X_train, y_train, **fit_params)\n",
      "  File \"C:\\Users\\I1bra\\anaconda3\\lib\\site-packages\\sklearn\\tree\\_classes.py\", line 889, in fit\n",
      "    super().fit(\n",
      "  File \"C:\\Users\\I1bra\\anaconda3\\lib\\site-packages\\sklearn\\tree\\_classes.py\", line 177, in fit\n",
      "    self._validate_params()\n",
      "  File \"C:\\Users\\I1bra\\anaconda3\\lib\\site-packages\\sklearn\\base.py\", line 600, in _validate_params\n",
      "    validate_parameter_constraints(\n",
      "  File \"C:\\Users\\I1bra\\anaconda3\\lib\\site-packages\\sklearn\\utils\\_param_validation.py\", line 97, in validate_parameter_constraints\n",
      "    raise InvalidParameterError(\n",
      "sklearn.utils._param_validation.InvalidParameterError: The 'max_leaf_nodes' parameter of DecisionTreeClassifier must be an int in the range [2, inf) or None. Got 1 instead.\n",
      "\n",
      "--------------------------------------------------------------------------------\n",
      "150 fits failed with the following error:\n",
      "Traceback (most recent call last):\n",
      "  File \"C:\\Users\\I1bra\\anaconda3\\lib\\site-packages\\sklearn\\model_selection\\_validation.py\", line 686, in _fit_and_score\n",
      "    estimator.fit(X_train, y_train, **fit_params)\n",
      "  File \"C:\\Users\\I1bra\\anaconda3\\lib\\site-packages\\sklearn\\tree\\_classes.py\", line 889, in fit\n",
      "    super().fit(\n",
      "  File \"C:\\Users\\I1bra\\anaconda3\\lib\\site-packages\\sklearn\\tree\\_classes.py\", line 177, in fit\n",
      "    self._validate_params()\n",
      "  File \"C:\\Users\\I1bra\\anaconda3\\lib\\site-packages\\sklearn\\base.py\", line 600, in _validate_params\n",
      "    validate_parameter_constraints(\n",
      "  File \"C:\\Users\\I1bra\\anaconda3\\lib\\site-packages\\sklearn\\utils\\_param_validation.py\", line 97, in validate_parameter_constraints\n",
      "    raise InvalidParameterError(\n",
      "sklearn.utils._param_validation.InvalidParameterError: The 'min_samples_split' parameter of DecisionTreeClassifier must be an int in the range [2, inf) or a float in the range (0.0, 1.0]. Got 1 instead.\n",
      "\n",
      "  warnings.warn(some_fits_failed_message, FitFailedWarning)\n",
      "C:\\Users\\I1bra\\anaconda3\\lib\\site-packages\\sklearn\\model_selection\\_search.py:952: UserWarning: One or more of the test scores are non-finite: [     nan      nan      nan      nan      nan      nan      nan      nan\n",
      " 0.774    0.774    0.774    0.774    0.774    0.774         nan 0.774\n",
      " 0.774    0.774    0.774    0.774    0.774         nan 0.774    0.774\n",
      " 0.774    0.774    0.774    0.774         nan 0.774    0.774    0.774\n",
      " 0.774    0.774    0.774         nan 0.774    0.774    0.774    0.774\n",
      " 0.774    0.774         nan      nan      nan      nan      nan      nan\n",
      "      nan      nan 0.774    0.774    0.774    0.774    0.774    0.774\n",
      "      nan 0.8165   0.8165   0.8165   0.8165   0.8165   0.8165        nan\n",
      " 0.854625 0.854625 0.854625 0.854625 0.854625 0.854625      nan 0.854625\n",
      " 0.854625 0.854625 0.854625 0.854625 0.854625      nan 0.854625 0.854625\n",
      " 0.854625 0.854625 0.854625 0.854625      nan      nan      nan      nan\n",
      "      nan      nan      nan      nan 0.774    0.774    0.774    0.774\n",
      " 0.774    0.774         nan 0.8165   0.8165   0.8165   0.8165   0.8165\n",
      " 0.8165        nan 0.854625 0.854625 0.854625 0.854625 0.854625 0.854625\n",
      "      nan 0.854625 0.854625 0.854625 0.854625 0.854625 0.854625      nan\n",
      " 0.854625 0.854625 0.854625 0.854625 0.854625 0.854625      nan      nan\n",
      "      nan      nan      nan      nan      nan      nan 0.774    0.774\n",
      " 0.774    0.774    0.774    0.774         nan 0.8165   0.8165   0.8165\n",
      " 0.8165   0.8165   0.8165        nan 0.854625 0.854625 0.854625 0.854625\n",
      " 0.854625 0.854625      nan 0.854625 0.854625 0.854625 0.854625 0.854625\n",
      " 0.854625      nan 0.854625 0.854625 0.854625 0.854625 0.854625 0.854625\n",
      "      nan      nan      nan      nan      nan      nan      nan      nan\n",
      " 0.774    0.774    0.774    0.774    0.774    0.774         nan 0.8165\n",
      " 0.8165   0.8165   0.8165   0.8165   0.8165        nan 0.854625 0.854625\n",
      " 0.854625 0.854625 0.854625 0.854625      nan 0.854625 0.854625 0.854625\n",
      " 0.854625 0.854625 0.854625      nan 0.854625 0.854625 0.854625 0.854625\n",
      " 0.854625 0.854625      nan      nan      nan      nan      nan      nan\n",
      "      nan      nan 0.774    0.774    0.774    0.774    0.774    0.774\n",
      "      nan 0.8165   0.8165   0.8165   0.8165   0.8165   0.8165        nan\n",
      " 0.854625 0.854625 0.854625 0.854625 0.854625 0.854625      nan 0.854625\n",
      " 0.854625 0.854625 0.854625 0.854625 0.854625      nan 0.854625 0.854625\n",
      " 0.854625 0.854625 0.854625 0.854625]\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import GridSearchCV\n",
    "\n",
    "param_grid = {\n",
    "    'max_depth': [1,2,3,4,5,8],\n",
    "    'max_leaf_nodes': [1,2,3,4,5,6],\n",
    "    'min_samples_split': [1,2,3,4,6,8,10]\n",
    "}\n",
    "\n",
    "tree_1 = DecisionTreeClassifier()\n",
    "\n",
    "grid_search = GridSearchCV(tree_1, param_grid, cv=5, scoring='accuracy')\n",
    "\n",
    "grid_search.fit(X_train, y_train)\n",
    "\n",
    "print(\"Best Hyper Parameters: \", grid_search.best_params_)"
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "4. Train it on the full training set using the best hyperparameters, and measure your model's performance on the test set."
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Accuracy is: 0.8585\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "# create a decision tree classifier with the best hyper parameters found by the grid search\n",
    "tree = DecisionTreeClassifier(max_depth=2, max_leaf_nodes=4, min_samples_split=2)\n",
    "\n",
    "# train the classifier on the full training set\n",
    "tree.fit(X_train, y_train)\n",
    "y_pred = tree.predict(X_test)\n",
    "\n",
    "# Print the accuracy or mean squared error of the model on the test set\n",
    "print(\"The Accuracy is:\", accuracy_score(y_test, y_pred))"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "markdown",
   "id": "95536d76-2750-40aa-b2a1-3fa462602f76",
   "metadata": {
    "id": "95536d76-2750-40aa-b2a1-3fa462602f76"
   },
   "source": [
    "## Question 4 Regression Tree"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9e110ad-7b47-4bb5-b439-5241c04a3ecb",
   "metadata": {
    "id": "d9e110ad-7b47-4bb5-b439-5241c04a3ecb"
   },
   "source": [
    "### Question\n",
    "For the following plot of the two decision tree regressors:\n",
    "1. Comment on the results\n",
    "2. Which model has a higher variance error? why?\n",
    "3. Which model has a higher bias error? why?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "036b8fe9-84d6-4be6-b928-74e57bb9b516",
   "metadata": {
    "id": "036b8fe9-84d6-4be6-b928-74e57bb9b516"
   },
   "source": [
    "**Answer**\n",
    "\n",
    "1.  The make-depth = 2 tree has acceptable general representation of data while the max-depth = 5 has some sort of over-fitting to the data. for sure the 2 depth has less complexity while the 5 depth tree is more complexm\n",
    "2. The max-depth = 5 tree has more variance since it has overfitting which cause high error due to noise.\n",
    "3. The max-depth = 2 tree has more bias error since it's not complex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "486b6e48-87ae-4133-ab82-b36abbc76bad",
   "metadata": {
    "id": "486b6e48-87ae-4133-ab82-b36abbc76bad",
    "outputId": "9558f0c7-a93d-4b9d-e832-b9db6138aae0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 1200x800 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "# Create a random dataset\n",
    "rng = np.random.RandomState(1)\n",
    "X = np.sort(5 * rng.rand(80, 1), axis=0)\n",
    "y = np.sin(X).ravel()\n",
    "y[::5] += 3 * (0.5 - rng.rand(16))\n",
    "\n",
    "# Fit regression model\n",
    "regr_1 = DecisionTreeRegressor(max_depth=2)\n",
    "regr_2 = DecisionTreeRegressor(max_depth=5)\n",
    "regr_1.fit(X, y)\n",
    "regr_2.fit(X, y)\n",
    "\n",
    "# Predict\n",
    "X_test = np.arange(0.0, 5.0, 0.01)[:, np.newaxis]\n",
    "y_1 = regr_1.predict(X_test)\n",
    "y_2 = regr_2.predict(X_test)\n",
    "\n",
    "# Plot the results\n",
    "plt.figure(figsize=(15,10),dpi=80)\n",
    "plt.scatter(X, y, s=20, edgecolor=\"black\",\n",
    "            c=\"darkorange\", label=\"data\")\n",
    "plt.plot(X_test, y_1, color=\"cornflowerblue\",\n",
    "         label=\"max_depth=2\", linewidth=2)\n",
    "plt.plot(X_test, y_2, color=\"yellowgreen\", label=\"max_depth=5\", linewidth=2)\n",
    "plt.xlabel(\"data\")\n",
    "plt.ylabel(\"target\")\n",
    "plt.title(\"Decision Tree Regression\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.10"
  },
  "colab": {
   "provenance": []
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}