Decision-trees.ipynb

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    "Copyright 2020 Vasile Rus, Andrew M. Olney and made available under [CC BY-SA](https://creativecommons.org/licenses/by-sa/4.0) for text and [Apache-2.0](http://www.apache.org/licenses/LICENSE-2.0) for code.\n"
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    "# Decision Trees\n",
    "\n",
    "So far we have talked about the KNN classifier, which uses *closeness to known points* to classify, and logistic regression, which uses *probability* to classify.\n",
    "Decision trees are a new idea that uses a *tree* to classify.\n",
    "\n",
    "Building a decision tree means, as the name implies, generating a tree in which each internal node of the tree is a decision point, usually deciding which of that node's children to consider next based on the values of the predictor or feature associated with the current node.\n",
    "\n",
    " The goal is to reach a leaf node which corresponds to a prediction, for instance, the category of the object/instance described by the predictors/features.\n",
    " \n",
    "## What you will learn\n",
    "\n",
    "In this notebook, you will learn about decision trees, an original data\n",
    "science paradigm to approach primarily classification tasks, and how it can\n",
    "be used to infer from labeled/annotated data decision tree based\n",
    "classifiers.  We will study the following:\n",
    "\n",
    "- The basics of decision trees\n",
    "- Details about how decision trees are built\n",
    "- Criteria to evaluate features/predictors\n",
    "- Interpreting paths from the root to leaf nodes\n",
    "- Visualization of decision trees\n",
    "- Evaluation of performance for decision trees\n",
    "\n",
    "\n",
    "## When to use decision trees\n",
    "\n",
    "Decision trees are useful when you have a categorical response/outcome\n",
    "variable and there are multiple features/predictors that can be used to\n",
    "predict the correct value of the outcome variable. The ultimate goal is to\n",
    "build automatically a decision tree to predict the\n",
    "correct value of the outcome variable for a new instance described by the\n",
    "set of predictors/features. It can also be used as a feature selection tool\n",
    "to determine which features/predictors are most discriminatory with respect\n",
    "to the outcome variable. Decision trees have the major of being\n",
    "interpretable over many other classification paradigms.\n",
    "\n",
    "## Example\n",
    "\n",
    " An example of such a tree is given below, just for illustration purposes.\n",
    " It uses two decision nodes (the circles/blue nodes): `Rainy`, which has two values Yes and No, and `Fit`, which has two values as well: Yes - meaning being fit to play - and No - not being fit to play for whatever reason, medical or not.\n",
    " The leaf nodes at the bottom correspond to the outcomes: Play or No-Play.\n",
    " \n",
    " Using this tree, if it is NOT `Rainy` and `Fit` is Yes, the decision in the corresponding leaf node is Play.\n",
    " That is, a path from the root/top node to a leaf node illustrates a decision path resulting in the decision shown in the leaf node.\n",
    " Each path in decision trees can be expressed as an IF-THEN, for instance: IF (Rainy == No) AND (Fit == Yes) THEN Play.\n",
    " \n",
    " While this example uses nominal variables that are binary (yes/no), the same approach also works for other variable types.\n",
    " For example, ratio variables can be given a decision threshold such that one path is followed if the value is above that threshold vs. below.\n",
    " Continuing the example below, if we replaced `Rainy` with `Cloud cover`, then we could set a threshold of 50%, so that if `Cloud cover` was above 50%, then we would follow the arrow to No-Play and otherwise we'd follow the arrow to `Fit`."
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's one thing to create a tree by hand - the magic is learning a tree like this from the data.\n",
    "\n",
    "As a simple example, we consider the artificially created dataset below:\n",
    "\n",
    "| Rainy | Fit | Play |\n",
    "|------------|------------|-------------|\n",
    "| 0          | 0          | 0           |\n",
    "| 0          | 1          | 1           |\n",
    "| 1          | 1          | 0           |\n",
    "| 1          | 0          | 0           |\n",
    "\n",
    "<!-- NOTE: trying to simplify\n",
    "In this dataset, there are four instances. Each instances has two predictors, say $predictor_1$ and $predictor_2$, which are the first values in each instance. $Predictor_1$ could indicate whether it is rainy (1) or not (0) whereas $predictor_2$ may indicate whether a person feels fit (1) to play, say, tennis or not (0). The last value in each instance is the class: 0 (no play) or 1 (play).\n",
    "The Python code below illustrates how to build a decision tree based on this simple data. -->\n",
    "Let's build a decision tree using this simple data:\n",
    "- Create variable `X` and set it to a list containing\n",
    "    - a list containing\n",
    "        - 0\n",
    "        - 0\n",
    "    - a list containing\n",
    "        - 0\n",
    "        - 1\n",
    "    - a list containing\n",
    "        - 1\n",
    "        - 1\n",
    "    - a list containing\n",
    "        - 1\n",
    "        - 0\n",
    "- Create a variable `Y` and set it to a list containing\n",
    "    - 0\n",
    "    - 1\n",
    "    - 0\n",
    "    - 0\n",
    "    \n",
    "As you can see, we've recreated the table above using these lists.\n",
    "Normally we work with larger dataframes, so you may not have thought of it this way, but ultimately all our data is just lists of numbers like this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = [[0, 0], [0, 1], [1, 1], [1, 0]]\n",
    "Y = [0, 1, 0, 0]\n",
    "\n",
    "#<xml xmlns=\"https://developers.google.com/blockly/xml\"><variables><variable id=\"_z/H/tTnOYS1Lla2~;*0\">X</variable><variable id=\"o8#tp%!,_Okj2aVwX(DL\">Y</variable></variables><block type=\"variables_set\" id=\"Iwb#y?nx(@|hrx`dPD21\" x=\"225\" y=\"122\"><field name=\"VAR\" id=\"_z/H/tTnOYS1Lla2~;*0\">X</field><value name=\"VALUE\"><block type=\"lists_create_with\" id=\"M(r*hCGi-1+FP3$9I/jI\"><mutation items=\"4\"></mutation><value name=\"ADD0\"><block type=\"lists_create_with\" id=\"!mtX-`LPTj2ek-kix54P\"><mutation items=\"2\"></mutation><value name=\"ADD0\"><block type=\"math_number\" id=\"w@E:*IEeZ_vb.xt/W.1`\"><field name=\"NUM\">0</field></block></value><value name=\"ADD1\"><block type=\"math_number\" id=\"m1Q];BPvl{pmtXT^T9*u\"><field name=\"NUM\">0</field></block></value></block></value><value name=\"ADD1\"><block type=\"lists_create_with\" id=\"/G|.+K|h9-p~!!LHIkw}\"><mutation items=\"2\"></mutation><value name=\"ADD0\"><block type=\"math_number\" id=\"Q=zSR?(Ysp[S{hh_0}t@\"><field name=\"NUM\">0</field></block></value><value name=\"ADD1\"><block type=\"math_number\" id=\"KT4OlB?BCwAy~6VyG0oh\"><field name=\"NUM\">1</field></block></value></block></value><value name=\"ADD2\"><block type=\"lists_create_with\" id=\"^_N6We|_:gx(xQiFu]aW\"><mutation items=\"2\"></mutation><value name=\"ADD0\"><block type=\"math_number\" id=\"O+U8]nd%wt}c-:C#Ho1D\"><field name=\"NUM\">1</field></block></value><value name=\"ADD1\"><block type=\"math_number\" id=\":*9[$?!#gwbPt69dmLo|\"><field name=\"NUM\">1</field></block></value></block></value><value name=\"ADD3\"><block type=\"lists_create_with\" id=\"edXG56R~rZt/}bb9.FNe\"><mutation items=\"2\"></mutation><value name=\"ADD0\"><block type=\"math_number\" id=\"#2(OH@:RIQG-221lz|Nc\"><field name=\"NUM\">1</field></block></value><value name=\"ADD1\"><block type=\"math_number\" id=\"tgFCw4(dD*iA^?h`{xP-\"><field name=\"NUM\">0</field></block></value></block></value></block></value><next><block type=\"variables_set\" id=\"Hb9H-%nIxKc,UMwINy57\"><field name=\"VAR\" id=\"o8#tp%!,_Okj2aVwX(DL\">Y</field><value name=\"VALUE\"><block type=\"lists_create_with\" id=\"qk~BgitfP@aj/2oa+`W(\"><mutation items=\"4\"></mutation><value name=\"ADD0\"><block type=\"math_number\" id=\"IV{G{Q+%sJS#Nv)XO4;I\"><field name=\"NUM\">0</field></block></value><value name=\"ADD1\"><block type=\"math_number\" id=\"DinOCv.!$Vk[!{j5WaW;\"><field name=\"NUM\">1</field></block></value><value name=\"ADD2\"><block type=\"math_number\" id=\"DEjz[VWhV:(ZleV{V(Y1\"><field name=\"NUM\">0</field></block></value><value name=\"ADD3\"><block type=\"math_number\" id=\"2EzEW`TvJ(5/i@?`.Kh;\"><field name=\"NUM\">0</field></block></value></block></value></block></next></block></xml>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next the imports for creating the decision tree model and graphing it:\n",
    "\n",
    "- `import sklearn.tree as tree`\n",
    "- `import graphviz as graphviz`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sklearn.tree as tree\n",
    "import graphviz as graphviz\n",
    "\n",
    "#<xml xmlns=\"https://developers.google.com/blockly/xml\"><variables><variable id=\"tkeU~z;dQ]^6[?rbF?)9\">tree</variable><variable id=\"rrXqQ:9R(~X0,}F[1UD]\">graphviz</variable></variables><block type=\"importAs_Python\" id=\"g[,/=2yYgO?4Bv[OrVf;\" x=\"16\" y=\"10\"><field name=\"libraryName\">sklearn.tree</field><field name=\"libraryAlias\" id=\"tkeU~z;dQ]^6[?rbF?)9\">tree</field><next><block type=\"importAs_Python\" id=\"5j3UPoKQcO/bU0u!@P06\"><field name=\"libraryName\">graphviz</field><field name=\"libraryAlias\" id=\"rrXqQ:9R(~X0,}F[1UD]\">graphviz</field></block></next></block></xml>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the model:\n",
    "\n",
    "- Create `decisionTreeExample`\n",
    "- Set it to `with tree create DecisionTreeClassifier using`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "decisionTreeExample = tree.DecisionTreeClassifier()\n",
    "\n",
    "#<xml xmlns=\"https://developers.google.com/blockly/xml\"><variables><variable id=\"@[.K6R7D##dBf3mu(%2`\">decisionTreeExample</variable><variable id=\"tkeU~z;dQ]^6[?rbF?)9\">tree</variable></variables><block type=\"variables_set\" id=\"}:yCB*e+[r5M{rIc($M]\" x=\"84\" y=\"299\"><field name=\"VAR\" id=\"@[.K6R7D##dBf3mu(%2`\">decisionTreeExample</field><value name=\"VALUE\"><block type=\"varCreateObject_Python\" id=\"bcO!l)K~/m6oq}xWIulv\"><field name=\"VAR\" id=\"tkeU~z;dQ]^6[?rbF?)9\">tree</field><field name=\"MEMBER\">DecisionTreeClassifier</field><data>tree:DecisionTreeClassifier</data></block></value></block></xml>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And fit the model\n",
    "\n",
    "- `with decisionTreeExample do fit using` a list containing\n",
    "    - `X`\n",
    "    - `Y`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeClassifier(ccp_alpha=0.0, class_weight=None, criterion='gini',\n",
       "                       max_depth=None, 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')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decisionTreeExample.fit(X, Y)\n",
    "\n",
    "#<xml xmlns=\"https://developers.google.com/blockly/xml\"><variables><variable id=\"@[.K6R7D##dBf3mu(%2`\">decisionTreeExample</variable><variable id=\"_z/H/tTnOYS1Lla2~;*0\">X</variable><variable id=\"o8#tp%!,_Okj2aVwX(DL\">Y</variable></variables><block type=\"varDoMethod_Python\" id=\",S.=/_X:;`m5Ahy=!xmE\" x=\"40\" y=\"235\"><field name=\"VAR\" id=\"@[.K6R7D##dBf3mu(%2`\">decisionTreeExample</field><field name=\"MEMBER\">fit</field><data>decisionTreeExample:fit</data><value name=\"INPUT\"><block type=\"lists_create_with\" id=\"}F0@!:1xqW/}(Dj%-V78\"><mutation items=\"2\"></mutation><value name=\"ADD0\"><block type=\"variables_get\" id=\"2:V:wGJK%j=I8yZEc^o}\"><field name=\"VAR\" id=\"_z/H/tTnOYS1Lla2~;*0\">X</field></block></value><value name=\"ADD1\"><block type=\"variables_get\" id=\"BG#`Opts05WCR={8qe{k\"><field name=\"VAR\" id=\"o8#tp%!,_Okj2aVwX(DL\">Y</field></block></value></block></value></block></xml>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize the tree and interpret how the algorithm fit the tree to the data.\n",
    "This is a little complicated to set up, but the results are worth it:\n",
    "\n",
    "- Create `dot_data` and set to `with tree do export_graphviz using` a list containing\n",
    "    - `decisionTreeExample`\n",
    "    - freestyle `out_file=None`\n",
    "    - freestyle `feature_names=['Rainy','Fit']`\n",
    "    - freestyle `class_names=['NoPlay','Play']`\n",
    "    - freestyle `filled=True`\n",
    "    - freestyle `rounded=True`\n",
    "    - freestyle `special_characters=True`\n",
    "    \n",
    "- `with graphviz create Source using` a list containing `dot_data`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot_data = tree.export_graphviz(decisionTreeExample, out_file=None, feature_names=['Rainy','Fit'], class_names=['NoPlay','Play'], filled=True, rounded=True, special_characters=True)\n",
    "\n",
    "graphviz.Source(dot_data)\n",
    "\n",
    "#<xml xmlns=\"https://developers.google.com/blockly/xml\"><variables><variable id=\"F.ej=Hud7vT9uozVaF5C\">dot_data</variable><variable id=\"rrXqQ:9R(~X0,}F[1UD]\">graphviz</variable><variable id=\"tkeU~z;dQ]^6[?rbF?)9\">tree</variable><variable id=\"@[.K6R7D##dBf3mu(%2`\">decisionTreeExample</variable></variables><block type=\"variables_set\" id=\":6*zm74#9$!O3?QVUukE\" x=\"209\" y=\"280\"><field name=\"VAR\" id=\"F.ej=Hud7vT9uozVaF5C\">dot_data</field><value name=\"VALUE\"><block type=\"varDoMethod_Python\" id=\"jsRyzb,9t~G^G@G@SMkS\"><field name=\"VAR\" id=\"tkeU~z;dQ]^6[?rbF?)9\">tree</field><field name=\"MEMBER\">export_graphviz</field><data>dot_data:</data><value name=\"INPUT\"><block type=\"lists_create_with\" id=\"r2_rY*ef1v:96w)e_B6K\"><mutation items=\"7\"></mutation><value name=\"ADD0\"><block type=\"variables_get\" id=\"x$]b$%X#}qjO@0H/!O|N\"><field name=\"VAR\" id=\"@[.K6R7D##dBf3mu(%2`\">decisionTreeExample</field></block></value><value name=\"ADD1\"><block type=\"dummyOutputCodeBlock_Python\" id=\"K!=:ty3DMPs#b^ziH=5p\"><field name=\"CODE\">out_file=None</field></block></value><value name=\"ADD2\"><block type=\"dummyOutputCodeBlock_Python\" id=\"by]EM[Y$kMG~MfF0{q^,\"><field name=\"CODE\">feature_names=['Rainy','Fit']</field></block></value><value name=\"ADD3\"><block type=\"dummyOutputCodeBlock_Python\" id=\"2hz~E.{8:W9-wWb*9Ut~\"><field name=\"CODE\">class_names=['NoPlay','Play']</field></block></value><value name=\"ADD4\"><block type=\"dummyOutputCodeBlock_Python\" id=\"^IJ3b3Eg7K9k^6Of_4i%\"><field name=\"CODE\">filled=True</field></block></value><value name=\"ADD5\"><block type=\"dummyOutputCodeBlock_Python\" id=\"VH!NxdBRgItjnN]Zs^Uh\"><field name=\"CODE\">rounded=True</field></block></value><value name=\"ADD6\"><block type=\"dummyOutputCodeBlock_Python\" id=\"f*|7fCy,K/0{_WzfribG\"><field name=\"CODE\">special_characters=True</field></block></value></block></value></block></value></block><block type=\"varCreateObject_Python\" id=\"-a(nDg:Sgtf)Ey5vB4(x\" x=\"187\" y=\"513\"><field name=\"VAR\" id=\"rrXqQ:9R(~X0,}F[1UD]\">graphviz</field><field name=\"MEMBER\">Source</field><data>graphviz:Source</data><value name=\"INPUT\"><block type=\"variables_get\" id=\"!M}@xBlLyRkl~Us)Smh%\"><field name=\"VAR\" id=\"F.ej=Hud7vT9uozVaF5C\">dot_data</field></block></value></block></xml>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's pause for a moment and look at the tree.\n",
    "The first node *splits* on whether `Rainy` is &le; 0.05 (i.e is 0 or 1).\n",
    "If it isn't (i.e. is 1), then we go to the right and `NoPlay`.\n",
    "If it is, we go to the left and test whether `Fit` is &le; 0.05 (i.e is 0 or 1).\n",
    "If it isn't (i.e. is 1), we go to the right and `Play`.\n",
    "If it is, we go to the left and `NoPlay`.\n",
    "\n",
    "Underneath the split rule for each node are several properties with an = :\n",
    "\n",
    "- `samples=` describes how many datapoints fall under that node. So at the top, we have 4 because all samples fall under that node. When we get to the bottom nodes, or **leaves** (which are all fully shaded), `samples` shows how many datapoints fell into each leaf, and those numbers *sum* to 4.\n",
    "- `value=` describes how many of each class (`NoPlay`, `Play`) fall under that node. Notice the leaf nodes only contain one class or the other - this is important as we'll discuss later.\n",
    "- `class=` is the class that will be returned for datapoints in the node, but it only has meaning for the leaves."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Theoretical Background"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Building a decision tree means deciding which predictor/feature should correspond to which node of the tree and which predictions should correspond to which terminal nodes or leaf nodes of the tree.\n",
    " The predictions in the leaf nodes in our case are class label.\n",
    " Decision trees are commonly used for classification.\n",
    " The tree is constructed so that predictors that better split the instances according to some criterion such as information gain (IG; to be discussed shortly) are placed higher in the decision tree.\n",
    " The net effect of such a strategy is to minimize the depth of the tree, i.e., to make the tree as flat as possible.\n",
    "\n",
    "The general algorithm to infer a particular Decision Tree (i.e., a particular configuration of internal and leaf nodes arranged in a tree) for a given dataset is the following:\n",
    "\n",
    "1. Select the best predictor based on some criterion such as Information Gain (discussed shortly)\n",
    "2. Split the data set into subsets based on the values of the chosen predictor in Step 1.\n",
    "3. Repeat the above process for the subsets until one of the following conditions is met:\n",
    " - all the instances in the subset belong to the same class.\n",
    " - there are no more predictors/features left.\n",
    " - no more instances.\n",
    "\n",
    "The most widely used predictor selection criteria are:\n",
    " - Entropy\n",
    " - Information Gain\n",
    " - Gain Ratio\n",
    " - Gini Index\n",
    " - Chi-square\n",
    " - Reduction in Variance"
   ]
  },
  {
   "attachments": {
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"
    }
   },
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   "source": [
    "### Entropy and Information Gain\n",
    "\n",
    "One of the most widely used criteria to guide the construction of Decision Trees is $Information Gain (IG)$ which relies on another fundamental concept called $Entropy (E)$.\n",
    "We will define first entropy E and then IG.\n",
    "\n",
    "*Entropy*\n",
    "\n",
    "Entropy is a measure of uncertainty or impurity of a set of items.\n",
    " It can also be regarded as a measure of the diversity of a set of items.\n",
    " For instance, in the left urn (Urn A) below there are only red balls.\n",
    " The impurity of this set of balls is 0 - the purity is perfect as all the balls are of the same color (red) or we can say they all belong to class 'red'.\n",
    " The urn on the right (Urn B) has two types of balls - red and blue - and therefore is less pure or more diverse.\n",
    " When drawing balls from Urn A we are certain that the ball is red.\n",
    " When we draw balls from urn B we are less certain whether the ball will be red as we may also draw a blue ball.\n",
    "\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "In order to measure this degree of uncertainty, the following formula has been proposed which accounts for the distribution of the possible values/labels/classes/categories C in a set of items S:\n",
    "\n",
    "$$ E (S) =  \\sum \\limits _{j=1} ^{C} P(c_j)log_2 P(c_j) $$"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In general, the more balanced the distribution of categories in a set of items the higher the entropy. You can see the entropy for a set of items with two categories. \n",
    "\n",
    "<!-- NOTE: on this image, the y-axis is H(X); should we make E(S) to match the equations? -->\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "As you can see, the entropy is maximum when the two categories have an equal probability 50-50, e.g., 50% chance of drawing a red ball versus 50% chance of drawing a blue ball.\n",
    "For instance, a set of 30 red balls and 30 blue balls is perfectly balanced and therefore has maximum entropy as opposed to a set with 50 red balls and 10 blue balls in which case the chances/probability of drawing a red balls are much higher.\n",
    "\n",
    "When we have a set S of items (X,Y) where Y describes possible outcomes and X are the predictors/features/attributes then we can compute the entropy of a partition of S according to the values $v$ of a particular predictor $x$ as in the following:\n",
    "\n",
    "$$ E (S, x) =  \\sum \\limits _{v \\in x} P(x=v) E(S_v) $$\n",
    "\n",
    "where $x$ is a predictor from the set of predictors $X$ and $E(S,x)$ is the entropy of the split of the set S into subsets ${S_v}$ according to the values of $x$.\n",
    "As it can be seen, the entropy $E(S,x)$ of such as split is computed as the weighted average of the entropies of each of the subsets $S_v$ corresponding to each of the values $v$ of predictor $x$.\n",
    "The weight corresponds to the probability of that value $P(x=v)$ and is computed as $\\frac {|S_v|} {|S|}$. "
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Information Gain*\n",
    "\n",
    "Information Gain is a selection criterion for predictors and measures how well a predictor can separate the dataset with respect to outcome categories Y.\n",
    "Predictors that separate the dataset into more pure subsets are preferred as they are more informative, i.e., they will lead to more flat (less deep), simpler trees which should generalize better to new instances.\n",
    "Intuitively, you can see in the image below two splits of a set S according to one predictor ($P_i$, bottom left split in the figure) or another ($P_j$, bottom right split).\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "The partition on the right is better as it leads to purer subsets, i.e., the resulting subsets have more balls of the same color.\n",
    "\n",
    "Information Gain for a predictor $x$ and items set S is defined as:\n",
    "\n",
    "$$ IG (S,x) = E(S) - E(S,x) $$\n",
    "\n",
    "which can be expanded based on the previous formulas as follows:\n",
    "\n",
    "$$ IG (S,x) = E(S) - E(S,x) = \\sum \\limits _{j=1} ^{C} P(c_j)log_2 P(c_j) - \\sum \\limits _{v \\in x} P(x=v) E(S_v) = \\sum \\limits _{j=1} ^{C} P(c_j)log_2 P(c_j) - \\sum \\limits _{v \\in x} \\frac {|S_v|} {|S|} E(S_v) $$\n",
    "\n",
    "From the definition, IG can be viewed as a measure quantifying the reduction in entropy of the original dataset versus the entropy of the subsets resulting from splitting the original dataset into subsets based on the values of the predictor $x$.\n",
    "\n",
    "*ID3 Algorithm*\n",
    "\n",
    "The ID3  (Iterative Dichotomizer) algorithm selects a decision tree using a top-down greedy search strategy through the space of possible decision trees, i.e., the set or space of all possible trees that can be arranged by assigning the predictors to nodes in all possible combinations.\n",
    "The greedy strategy in ID3 can be summarized as below:\n",
    "\n",
    "- Give the set of unselected predictors, select the predictor with the highest Information Gain (IG)\n",
    "- Divide the dataset, i.e., the set of instances, into subsets based on the values of the selected attribute\n",
    "- Repeat the above process for each of the subsets until the subset is empty or the subset is homogeneous (contains instances belonging to on class), or no more predictors are available.\n",
    "\n",
    "We will illustrate the ID3 algorithm on the Iris data set next."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Iris Example\n",
    "\n",
    "We will now exemplify how to build a decision tree for the Iris dataset. \n",
    "The goal is to classify each instance in the dataset using the predictors corresponding to each such instance.\n",
    "\n",
    "| Variable    | Type    | Description           |\n",
    "|:-------------|:---------|:-----------------------|\n",
    "| SepalLength | Ratio   | the sepal length (cm) |\n",
    "| SepalWidth  | Ratio   | the sepal width (cm)  |\n",
    "| PetalLength | Ratio   | the petal length (cm) |\n",
    "| PetalWidth  | Ratio   | the petal width (cm)  |\n",
    "| Species     | Nominal | the flower species    |\n",
    "\n",
    "<div style=\"text-align:center;font-size: smaller\">\n",
    " <b>Source:</b> This dataset was taken from the <a href=\"https://archive.ics.uci.edu/ml/datasets/iris\">UCI Machine Learning Repository library\n",
    "    </a></div>\n",
    "<br>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load data\n",
    "\n",
    "Import `pandas` to work with dataframes:\n",
    "\n",
    "- `import pandas as pd`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "#<xml xmlns=\"https://developers.google.com/blockly/xml\"><variables><variable id=\"/%IFN5#t2uAm}E`8:KV:\">pd</variable></variables><block type=\"importAs_Python\" id=\"_@5-r*j4E`}d?=DXLinf\" x=\"16\" y=\"10\"><field name=\"libraryName\">pandas</field><field name=\"libraryAlias\" id=\"/%IFN5#t2uAm}E`8:KV:\">pd</field></block></xml>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the dataframe with the `iris` dataset:\n",
    "\n",
    "- Create variable `iris` and set it to `with pd do read_csv using \"datasets/iris.csv\"`\n",
    "- `iris` (to display)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "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>SepalLength</th>\n",
       "      <th>SepalWidth</th>\n",
       "      <th>PetalLength</th>\n",
       "      <th>PetalWidth</th>\n",
       "      <th>Species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     SepalLength  SepalWidth  PetalLength  PetalWidth    Species\n",
       "0            5.1         3.5          1.4         0.2     setosa\n",
       "1            4.9         3.0          1.4         0.2     setosa\n",
       "2            4.7         3.2          1.3         0.2     setosa\n",
       "3            4.6         3.1          1.5         0.2     setosa\n",
       "4            5.0         3.6          1.4         0.2     setosa\n",
       "..           ...         ...          ...         ...        ...\n",
       "145          6.7         3.0          5.2         2.3  virginica\n",
       "146          6.3         2.5          5.0         1.9  virginica\n",
       "147          6.5         3.0          5.2         2.0  virginica\n",
       "148          6.2         3.4          5.4         2.3  virginica\n",
       "149          5.9         3.0          5.1         1.8  virginica\n",
       "\n",
       "[150 rows x 5 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris = pd.read_csv('datasets/iris.csv')\n",
    "\n",
    "iris\n",
    "\n",
    "#<xml xmlns=\"https://developers.google.com/blockly/xml\"><variables><variable id=\"@dNx?X?Zd[|UZ.PI?OJ2\">iris</variable><variable id=\"/%IFN5#t2uAm}E`8:KV:\">pd</variable></variables><block type=\"variables_set\" id=\"gM*jw`FfIR3)8=g0iEB7\" x=\"11\" y=\"186\"><field name=\"VAR\" id=\"@dNx?X?Zd[|UZ.PI?OJ2\">iris</field><value name=\"VALUE\"><block type=\"varDoMethod_Python\" id=\"ny0sjvqTnn2B]K2za7Li\"><field name=\"VAR\" id=\"/%IFN5#t2uAm}E`8:KV:\">pd</field><field name=\"MEMBER\">read_csv</field><data>pd:read_csv</data><value name=\"INPUT\"><block type=\"text\" id=\"dfrpI5b@DHr+DQ:|@vpv\"><field name=\"TEXT\">datasets/iris.csv</field></block></value></block></value></block><block type=\"variables_get\" id=\"dn{+Q#DO%lN;G_tFGJ#B\" x=\"8\" y=\"304\"><field name=\"VAR\" id=\"@dNx?X?Zd[|UZ.PI?OJ2\">iris</field></block></xml>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model\n",
    "\n",
    "### Prepare data\n",
    "\n",
    "Separate the predictor variables (`X`) from the class label (`Y`):\n",
    "\n",
    "- Set `X` to `with iris do drop using` a list containing\n",
    "    - freestyle `columns=['Species']`\n",
    "- Set `Y` to `iris[` a list containing `'Species'` `]`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris.drop(columns=['Species'])\n",
    "Y = iris[['Species']]\n",
    "\n",
    "#<xml xmlns=\"https://developers.google.com/blockly/xml\"><variables><variable id=\"_z/H/tTnOYS1Lla2~;*0\">X</variable><variable id=\"o8#tp%!,_Okj2aVwX(DL\">Y</variable><variable id=\"@dNx?X?Zd[|UZ.PI?OJ2\">iris</variable></variables><block type=\"variables_set\" id=\"M9g^9:hbZQ0Cb9jKq9V6\" x=\"14\" y=\"218\"><field name=\"VAR\" id=\"_z/H/tTnOYS1Lla2~;*0\">X</field><value name=\"VALUE\"><block type=\"varDoMethod_Python\" id=\"HF9HKI:lNqY;?[|G]m=P\"><field name=\"VAR\" id=\"@dNx?X?Zd[|UZ.PI?OJ2\">iris</field><field name=\"MEMBER\">drop</field><data>iris:drop</data><value name=\"INPUT\"><block type=\"lists_create_with\" id=\"Mm^0W8}3,2|YO6m+rQ1Z\"><mutation items=\"1\"></mutation><value name=\"ADD0\"><block type=\"dummyOutputCodeBlock_Python\" id=\"WkdEs~{tWz~8u4:XkYHO\"><field name=\"CODE\">columns=['Species']</field></block></value></block></value></block></value><next><block type=\"variables_set\" id=\":eCC|=CT/c:_fzcI.h5%\"><field name=\"VAR\" id=\"o8#tp%!,_Okj2aVwX(DL\">Y</field><value name=\"VALUE\"><block type=\"indexer_Python\" id=\"i*OWk(?KoBxj{6v-G8RH\"><field name=\"VAR\" id=\"@dNx?X?Zd[|UZ.PI?OJ2\">iris</field><value name=\"INDEX\"><block type=\"lists_create_with\" id=\"H3L8XKx]~iB1,]H3b2H(\"><mutation items=\"1\"></mutation><value name=\"ADD0\"><block type=\"text\" id=\"64q(iYfgFHZZK4?N%T@y\"><field name=\"TEXT\">Species</field></block></value></block></value></block></value></block></next></block></xml>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Split the data into train/test sets:\n",
    "\n",
    "- `import sklearn.model_selection as model_selection`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sklearn.model_selection as model_selection\n",
    "\n",
    "#<xml xmlns=\"https://developers.google.com/blockly/xml\"><variables><variable id=\"-q~R*yx.VGQ@%!0Q+!gh\">model_selection</variable></variables><block type=\"importAs_Python\" id=\"E{QJ$O@lc8u.;OTWdVgf\" x=\"-89\" y=\"168\"><field name=\"libraryName\">sklearn.model_selection</field><field name=\"libraryAlias\" id=\"-q~R*yx.VGQ@%!0Q+!gh\">model_selection</field></block></xml>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And do the actual split:\n",
    "\n",
    "- Create `splits` and set to `with model_selection do train_test_split using` a list containing:\n",
    "    - `X` (the features in an array)\n",
    "    - `Y` (the labels in an array)\n",
    "    - freestyle `random_state=1` (this will make your random split the same as mine)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "splits = model_selection.train_test_split(X, Y, random_state=1)\n",
    "\n",
    "#<xml xmlns=\"https://developers.google.com/blockly/xml\"><variables><variable id=\"{Yt*9=2tTC$JepE9BcRz\">splits</variable><variable id=\"-q~R*yx.VGQ@%!0Q+!gh\">model_selection</variable><variable id=\"_z/H/tTnOYS1Lla2~;*0\">X</variable><variable id=\"o8#tp%!,_Okj2aVwX(DL\">Y</variable></variables><block type=\"variables_set\" id=\"HpD!.HSC`PPRg]21i*7c\" x=\"-102\" y=\"134\"><field name=\"VAR\" id=\"{Yt*9=2tTC$JepE9BcRz\">splits</field><value name=\"VALUE\"><block type=\"varDoMethod_Python\" id=\"fUetl3$Ak=SI~T6T5!6c\"><field name=\"VAR\" id=\"-q~R*yx.VGQ@%!0Q+!gh\">model_selection</field><field name=\"MEMBER\">train_test_split</field><data>model_selection:train_test_split</data><value name=\"INPUT\"><block type=\"lists_create_with\" id=\"uUY%r2L/7acQcS/KbQvx\"><mutation items=\"3\"></mutation><value name=\"ADD0\"><block type=\"variables_get\" id=\"jN^;NIVaV%22*W_^|!uK\"><field name=\"VAR\" id=\"_z/H/tTnOYS1Lla2~;*0\">X</field></block></value><value name=\"ADD1\"><block type=\"variables_get\" id=\"OOZSj;YDm{T6q%{~5?B1\"><field name=\"VAR\" id=\"o8#tp%!,_Okj2aVwX(DL\">Y</field></block></value><value name=\"ADD2\"><block type=\"dummyOutputCodeBlock_Python\" id=\"Gg*^%q4qIJwc*of,V|rb\"><field name=\"CODE\">random_state=1</field></block></value></block></value></block></value></block></xml>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First create the model:\n",
    "\n",
    "- Create variable `decisionTree` and set to `with tree create DecisionTreeClassifier using`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "decisionTree = tree.DecisionTreeClassifier()\n",
    "\n",
    "#<xml xmlns=\"https://developers.google.com/blockly/xml\"><variables><variable id=\"fYtGc,k9LOv^%_9|[cfE\">decisionTree</variable><variable id=\"tkeU~z;dQ]^6[?rbF?)9\">tree</variable></variables><block type=\"variables_set\" id=\"0{MIimjRn(`+`5M$0_U7\" x=\"-90\" y=\"132\"><field name=\"VAR\" id=\"fYtGc,k9LOv^%_9|[cfE\">decisionTree</field><value name=\"VALUE\"><block type=\"varCreateObject_Python\" id=\"?`dwaKnOBjnrd}`doxhF\"><field name=\"VAR\" id=\"tkeU~z;dQ]^6[?rbF?)9\">tree</field><field name=\"MEMBER\">DecisionTreeClassifier</field><data>tree:DecisionTreeClassifier</data></block></value></block></xml>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit it, and get predictions:\n",
    "\n",
    "- `with decisionTree do fit` a list containing:\n",
    "    - `in list splits get # 1` (this is Xtrain)\n",
    "    - `in list splits get # 3` (this is Ytrain)\n",
    "- Create variable `predictions` and set to `with decisionTree do predict using` a list containing:\n",
    "    - `in list splits get # 2` (this is Xtest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "decisionTree.fit(splits[0], splits[2])\n",
    "\n",
    "predictions = decisionTree.predict(splits[1])\n",
    "\n",
    "#<xml xmlns=\"https://developers.google.com/blockly/xml\"><variables><variable id=\"fYtGc,k9LOv^%_9|[cfE\">decisionTree</variable><variable id=\".hU+?FvKPIm~!dS$d-nj\">predictions</variable><variable id=\"{Yt*9=2tTC$JepE9BcRz\">splits</variable></variables><block type=\"varDoMethod_Python\" id=\"-@fm,911cJiCu@jkys%R\" x=\"-94\" y=\"192\"><field name=\"VAR\" id=\"fYtGc,k9LOv^%_9|[cfE\">decisionTree</field><field name=\"MEMBER\">fit</field><data>decisionTree:fit</data><value name=\"INPUT\"><block type=\"lists_create_with\" id=\"qj[~!aNmN}=v;xQ.=$%L\"><mutation items=\"2\"></mutation><value name=\"ADD0\"><block type=\"lists_getIndex\" id=\"W~.ZU([-)(,-i3=bTsB|\"><mutation statement=\"false\" at=\"true\"></mutation><field name=\"MODE\">GET</field><field name=\"WHERE\">FROM_START</field><value name=\"VALUE\"><block type=\"variables_get\" id=\"GIJn[jpD_~wa}#7IO!1K\"><field name=\"VAR\" id=\"{Yt*9=2tTC$JepE9BcRz\">splits</field></block></value><value name=\"AT\"><block type=\"math_number\" id=\"Rh[;nrMLN$[cFFsZC~T|\"><field name=\"NUM\">1</field></block></value></block></value><value name=\"ADD1\"><block type=\"lists_getIndex\" id=\"YkCD57xF*SSN3[`_op{u\"><mutation statement=\"false\" at=\"true\"></mutation><field name=\"MODE\">GET</field><field name=\"WHERE\">FROM_START</field><value name=\"VALUE\"><block type=\"variables_get\" id=\"M@?wn}aoHxJYan0=AE3$\"><field name=\"VAR\" id=\"{Yt*9=2tTC$JepE9BcRz\">splits</field></block></value><value name=\"AT\"><block type=\"math_number\" id=\"jNUa2BdXPG?H8|.br*@e\"><field name=\"NUM\">3</field></block></value></block></value></block></value></block><block type=\"variables_set\" id=\"W2#bH~%cZ$JYTYX@t`OJ\" x=\"-89\" y=\"291\"><field name=\"VAR\" id=\".hU+?FvKPIm~!dS$d-nj\">predictions</field><value name=\"VALUE\"><block type=\"varDoMethod_Python\" id=\"uF}tgd}f*m!CoCE6Vnfc\"><field name=\"VAR\" id=\"fYtGc,k9LOv^%_9|[cfE\">decisionTree</field><field name=\"MEMBER\">predict</field><data>decisionTree:predict</data><value name=\"INPUT\"><block type=\"lists_create_with\" id=\"g4~yox0A5a]I|VUV:ff9\"><mutation items=\"1\"></mutation><value name=\"ADD0\"><block type=\"lists_getIndex\" id=\"D[QG~pcCO~@%*GRtEXGC\"><mutation statement=\"false\" at=\"true\"></mutation><field name=\"MODE\">GET</field><field name=\"WHERE\">FROM_START</field><value name=\"VALUE\"><block type=\"variables_get\" id=\"k]*6kE_B2NOcRC4T2DMa\"><field name=\"VAR\" id=\"{Yt*9=2tTC$JepE9BcRz\">splits</field></block></value><value name=\"AT\"><block type=\"math_number\" id=\"nwBf+AnSmiv.DN_wSPy(\"><field name=\"NUM\">2</field></block></value></block></value></block></value></block></value></block></xml>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Measure performance\n",
    "\n",
    "Import the evaluation metrics:\n",
    "\n",
    "- `import sklearn.metrics as metrics`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sklearn.metrics as metrics\n",
    "\n",
    "#<xml xmlns=\"https://developers.google.com/blockly/xml\"><variables><variable id=\"jpz]0=,hLYv~rN^#0dFO\">metrics</variable></variables><block type=\"importAs_Python\" id=\"CEkPf]fPOl]|@Gl1lho[\" x=\"-101\" y=\"139\"><field name=\"libraryName\">sklearn.metrics</field><field name=\"libraryAlias\" id=\"jpz]0=,hLYv~rN^#0dFO\">metrics</field></block></xml>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get the accuracy:\n",
    "\n",
    "- `with metrics do accuracy_score using` a list containing\n",
    "    - `in list splits get # 4`  (this is `Ytest`)\n",
    "    - `predictions`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9736842105263158\n"
     ]
    }
   ],
   "source": [
    "print(metrics.accuracy_score(splits[3], predictions))\n",
    "\n",
    "#<xml xmlns=\"https://developers.google.com/blockly/xml\"><variables><variable id=\"jpz]0=,hLYv~rN^#0dFO\">metrics</variable><variable id=\".hU+?FvKPIm~!dS$d-nj\">predictions</variable><variable id=\"{Yt*9=2tTC$JepE9BcRz\">splits</variable></variables><block type=\"text_print\" id=\"u8M]eo-vRBhX!L/a@4+J\" x=\"-102\" y=\"208\"><value name=\"TEXT\"><shadow type=\"text\" id=\")gVsrXo+bq|?9m0cIU/Y\"><field name=\"TEXT\">abc</field></shadow><block type=\"varDoMethod_Python\" id=\"0B;?~qgT4?Xe8I|O=P)%\"><field name=\"VAR\" id=\"jpz]0=,hLYv~rN^#0dFO\">metrics</field><field name=\"MEMBER\">accuracy_score</field><data>metrics:</data><value name=\"INPUT\"><block type=\"lists_create_with\" id=\"qe7YbU#WU/F|Iuks0C:c\"><mutation items=\"2\"></mutation><value name=\"ADD0\"><block type=\"lists_getIndex\" id=\"13J^-{z`P=,aau/j:VF~\"><mutation statement=\"false\" at=\"true\"></mutation><field name=\"MODE\">GET</field><field name=\"WHERE\">FROM_START</field><value name=\"VALUE\"><block type=\"variables_get\" id=\"m^Z6y-8@L:s!oS)`%iJW\"><field name=\"VAR\" id=\"{Yt*9=2tTC$JepE9BcRz\">splits</field></block></value><value name=\"AT\"><block type=\"math_number\" id=\"u}VxLP~*Dbl0g4[AO,bL\"><field name=\"NUM\">4</field></block></value></block></value><value name=\"ADD1\"><block type=\"variables_get\" id=\"|3h,TPit9wg+a;bR[r$P\"><field name=\"VAR\" id=\".hU+?FvKPIm~!dS$d-nj\">predictions</field></block></value></block></value></block></value></block></xml>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And get the recall and precision:\n",
    "\n",
    "- `print with metrics do classification_report using` a list containing\n",
    "    - `in list splits get # 4`  (this is `Ytest`)\n",
    "    - `predictions`\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "      setosa       1.00      1.00      1.00        13\n",
      "  versicolor       1.00      0.94      0.97        16\n",
      "   virginica       0.90      1.00      0.95         9\n",
      "\n",
      "    accuracy                           0.97        38\n",
      "   macro avg       0.97      0.98      0.97        38\n",
      "weighted avg       0.98      0.97      0.97        38\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(metrics.classification_report(splits[3], predictions))\n",
    "\n",
    "#<xml xmlns=\"https://developers.google.com/blockly/xml\"><variables><variable id=\"jpz]0=,hLYv~rN^#0dFO\">metrics</variable><variable id=\".hU+?FvKPIm~!dS$d-nj\">predictions</variable><variable id=\"{Yt*9=2tTC$JepE9BcRz\">splits</variable></variables><block type=\"text_print\" id=\"jFo8knaDn;JRZ=Fj7Tzo\" x=\"57\" y=\"316\"><value name=\"TEXT\"><shadow type=\"text\" id=\"QWuxwm12CzEZ-r2sdwCR\"><field name=\"TEXT\">abc</field></shadow><block type=\"varDoMethod_Python\" id=\"(y`#h=AgNH6X+ahL$2L$\"><field name=\"VAR\" id=\"jpz]0=,hLYv~rN^#0dFO\">metrics</field><field name=\"MEMBER\">classification_report</field><data>metrics:classification_report</data><value name=\"INPUT\"><block type=\"lists_create_with\" id=\"A/#8KhfiGd[(@p,uaFFl\"><mutation items=\"2\"></mutation><value name=\"ADD0\"><block type=\"lists_getIndex\" id=\"*N[l.zzXc*IdHJ-Ur0D)\"><mutation statement=\"false\" at=\"true\"></mutation><field name=\"MODE\">GET</field><field name=\"WHERE\">FROM_START</field><value name=\"VALUE\"><block type=\"variables_get\" id=\"fQYj?Tz[y/t|%9~{2Pf[\"><field name=\"VAR\" id=\"{Yt*9=2tTC$JepE9BcRz\">splits</field></block></value><value name=\"AT\"><block type=\"math_number\" id=\"V(5k43YOsHPep%LEEd9Q\"><field name=\"NUM\">4</field></block></value></block></value><value name=\"ADD1\"><block type=\"variables_get\" id=\"mX(20KX!C)d_,/ddeysr\"><field name=\"VAR\" id=\".hU+?FvKPIm~!dS$d-nj\">predictions</field></block></value></block></value></block></value></block></xml>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, both the accuracy and the average precision, recall, and f1 are all very good."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Display the Tree\n",
    "\n",
    "Copy the blocks above and the necessary changes:\n",
    "\n",
    "- Create `dot_data` and set to `with tree do export_graphviz using` a list containing\n",
    "    - `decisionTree`\n",
    "    - freestyle `out_file=None`\n",
    "    - freestyle `feature_names=[\"SepalLength\",\"SepalWidth\",\"PetalLength\",\"PetalWidth\"]`\n",
    "    - freestyle `class_names=['setosa','versicolor','virginica']`\n",
    "    - freestyle `filled=True`\n",
    "    - freestyle `rounded=True`\n",
    "    - freestyle `special_characters=True`\n",
    "    \n",
    "- `with graphviz create Source using` a list containing `dot_data`\n",
    "\n",
    "**To get the feature names, we just used the columns from the data frame displayed above \n",
    "To get the class names, we copied the names in the classification report above.\n",
    "It is important that both of these lists be in the right order.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
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    "The learning algorithm decided that `PetalWidth` was the most important variable (or feature).\n",
    "If the value of `PetalWidth` is less than .8, the iris will be classified as `setosa`.\n",
    "Notice that all 37 `setosa` are classified by this one decision!\n",
    "For `PetalWidth` &ge; .8 but &le 1.65 AND has `PetalLength` &le; 4.95 most iris are `versicolor` (32 of 34).\n",
    "We can see some complexity here with `versicolor` that don't quite fit as nicely lower in the tree.\n",
    "Everything else, more or less, is `virginica`."
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