Morten Hjorth-Jensen
1744 lines
428 KiB
Plaintext
1744 lines
428 KiB
Plaintext
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"# Decision trees, overarching aims\n",
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"\n",
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"\n",
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"We start here with the most basic algorithm, the so-called decision\n",
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"tree. With this basic algorithm we can in turn build more complex\n",
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"networks, spanning from homogeneous and heterogenous forests (bagging,\n",
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"random forests and more) to one of the most popular supervised\n",
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"algorithms nowadays, the extreme gradient boosting, or just\n",
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"XGBoost. But let us start with the simplest possible ingredient.\n",
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"\n",
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"Decision trees are supervised learning algorithms used for both,\n",
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"classification and regression tasks.\n",
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"\n",
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"\n",
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"The main idea of decision trees\n",
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"is to find those descriptive features which contain the most\n",
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"**information** regarding the target feature and then split the dataset\n",
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"along the values of these features such that the target feature values\n",
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"for the resulting underlying datasets are as pure as possible.\n",
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"\n",
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"The descriptive features which reproduce best the target/output features are normally said\n",
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"to be the most informative ones. The process of finding the **most\n",
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"informative** feature is done until we accomplish a stopping criteria\n",
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"where we then finally end up in so called **leaf nodes**. \n",
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"\n",
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"## Basics of a tree\n",
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"\n",
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"A decision tree is typically divided into a **root node**, the **interior nodes**,\n",
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"and the final **leaf nodes** or just **leaves**. These entities are then connected by so-called **branches**.\n",
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"\n",
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"The leaf nodes\n",
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"contain the predictions we will make for new query instances presented\n",
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"to our trained model. This is possible since the model has \n",
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"learned the underlying structure of the training data and hence can,\n",
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"given some assumptions, make predictions about the target feature value\n",
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"(class) of unseen query instances.\n",
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"\n",
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"\n",
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"## General Features\n",
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"\n",
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"The overarching approach to decision trees is a top-down approach.\n",
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"\n",
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"* A leaf provides the classification of a given instance.\n",
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"\n",
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"* A node specifies a test of some attribute of the instance.\n",
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"\n",
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"* A branch corresponds to a possible values of an attribute.\n",
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"\n",
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"* An instance is classified by starting at the root node of the tree, testing the attribute specified by this node, then moving down the tree branch corresponding to the value of the attribute in the given example.\n",
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"\n",
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"This process is then repeated for the subtree rooted at the new\n",
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"node.\n",
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"\n",
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"\n",
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"\n",
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"In simplified terms, the process of training a decision tree and\n",
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"predicting the target features of query instances is as follows:\n",
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"\n",
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"1. Present a dataset containing of a number of training instances characterized by a number of descriptive features and a target feature\n",
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"\n",
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"2. Train the decision tree model by continuously splitting the target feature along the values of the descriptive features using a measure of information gain during the training process\n",
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"\n",
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"3. Grow the tree until we accomplish a stopping criteria create leaf nodes which represent the *predictions* we want to make for new query instances\n",
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"\n",
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"4. Show query instances to the tree and run down the tree until we arrive at leaf nodes\n",
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"\n",
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"Then we are essentially done!"
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"text": [
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"2nd degree coefficients:\n",
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"zero power: -3.6801072677808095\n",
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"first power: 0.14054303349959596\n",
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"second power: -0.0002999281168222194\n"
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]
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"%matplotlib inline\n",
|
||
"\n",
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.preprocessing import PolynomialFeatures\n",
|
||
"from sklearn.linear_model import LinearRegression\n",
|
||
"\n",
|
||
"steps=250\n",
|
||
"\n",
|
||
"distance=0\n",
|
||
"x=0\n",
|
||
"distance_list=[]\n",
|
||
"steps_list=[]\n",
|
||
"while x<steps:\n",
|
||
" distance+=np.random.randint(-1,2)\n",
|
||
" distance_list.append(distance)\n",
|
||
" x+=1\n",
|
||
" steps_list.append(x)\n",
|
||
"plt.plot(steps_list,distance_list, color='green', label=\"Random Walk Data\")\n",
|
||
"\n",
|
||
"steps_list=np.asarray(steps_list)\n",
|
||
"distance_list=np.asarray(distance_list)\n",
|
||
"\n",
|
||
"X=steps_list[:,np.newaxis]\n",
|
||
"\n",
|
||
"#Polynomial fits\n",
|
||
"\n",
|
||
"#Degree 2\n",
|
||
"poly_features=PolynomialFeatures(degree=2, include_bias=False)\n",
|
||
"X_poly=poly_features.fit_transform(X)\n",
|
||
"\n",
|
||
"lin_reg=LinearRegression()\n",
|
||
"poly_fit=lin_reg.fit(X_poly,distance_list)\n",
|
||
"b=lin_reg.coef_\n",
|
||
"c=lin_reg.intercept_\n",
|
||
"print (\"2nd degree coefficients:\")\n",
|
||
"print (\"zero power: \",c)\n",
|
||
"print (\"first power: \", b[0])\n",
|
||
"print (\"second power: \",b[1])\n",
|
||
"\n",
|
||
"z = np.arange(0, steps, .01)\n",
|
||
"z_mod=b[1]*z**2+b[0]*z+c\n",
|
||
"\n",
|
||
"fit_mod=b[1]*X**2+b[0]*X+c\n",
|
||
"plt.plot(z, z_mod, color='r', label=\"2nd Degree Fit\")\n",
|
||
"plt.title(\"Polynomial Regression\")\n",
|
||
"\n",
|
||
"plt.xlabel(\"Steps\")\n",
|
||
"plt.ylabel(\"Distance\")\n",
|
||
"\n",
|
||
"#Degree 10\n",
|
||
"poly_features10=PolynomialFeatures(degree=10, include_bias=False)\n",
|
||
"X_poly10=poly_features10.fit_transform(X)\n",
|
||
"\n",
|
||
"poly_fit10=lin_reg.fit(X_poly10,distance_list)\n",
|
||
"\n",
|
||
"y_plot=poly_fit10.predict(X_poly10)\n",
|
||
"plt.plot(X, y_plot, color='black', label=\"10th Degree Fit\")\n",
|
||
"\n",
|
||
"plt.legend()\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"\n",
|
||
"#Decision Tree Regression\n",
|
||
"from sklearn.tree import DecisionTreeRegressor\n",
|
||
"regr_1=DecisionTreeRegressor(max_depth=2)\n",
|
||
"regr_2=DecisionTreeRegressor(max_depth=5)\n",
|
||
"regr_3=DecisionTreeRegressor(max_depth=7)\n",
|
||
"regr_1.fit(X, distance_list)\n",
|
||
"regr_2.fit(X, distance_list)\n",
|
||
"regr_3.fit(X, distance_list)\n",
|
||
"\n",
|
||
"X_test = np.arange(0.0, steps, 0.01)[:, np.newaxis]\n",
|
||
"y_1 = regr_1.predict(X_test)\n",
|
||
"y_2 = regr_2.predict(X_test)\n",
|
||
"y_3=regr_3.predict(X_test)\n",
|
||
"\n",
|
||
"# Plot the results\n",
|
||
"plt.figure()\n",
|
||
"plt.scatter(X, distance_list, s=2.5, c=\"black\", label=\"data\")\n",
|
||
"plt.plot(X_test, y_1, color=\"red\",\n",
|
||
" label=\"max_depth=2\", linewidth=2)\n",
|
||
"plt.plot(X_test, y_2, color=\"green\", label=\"max_depth=5\", linewidth=2)\n",
|
||
"plt.plot(X_test, y_3, color=\"m\", label=\"max_depth=7\", linewidth=2)\n",
|
||
"\n",
|
||
"plt.xlabel(\"Data\")\n",
|
||
"plt.ylabel(\"Darget\")\n",
|
||
"plt.title(\"Decision Tree Regression\")\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Building a tree, regression\n",
|
||
"\n",
|
||
"There are mainly two steps\n",
|
||
"1. We split the predictor space (the set of possible values $x_1,x_2,\\dots, x_p$) into $J$ distinct and non-non-overlapping regions, $R_1,R_2,\\dots,R_J$. \n",
|
||
"\n",
|
||
"2. For every observation that falls into the region $R_j$ , we make the same prediction, which is simply the mean of the response values for the training observations in $R_j$.\n",
|
||
"\n",
|
||
"How do we construct the regions $R_1,\\dots,R_J$? In theory, the\n",
|
||
"regions could have any shape. However, we choose to divide the\n",
|
||
"predictor space into high-dimensional rectangles, or boxes, for\n",
|
||
"simplicity and for ease of interpretation of the resulting predictive\n",
|
||
"model. The goal is to find boxes $R_1,\\dots,R_J$ that minimize the\n",
|
||
"MSE, given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sum_{j=1}^J\\sum_{i\\in R_j}(y_i-\\overline{y}_{R_j})^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $\\overline{y}_{R_j}$ is the mean response for the training observations \n",
|
||
"within box $j$. \n",
|
||
"\n",
|
||
"\n",
|
||
"Unfortunately, it is computationally infeasible to consider every\n",
|
||
"possible partition of the feature space into $J$ boxes. The common\n",
|
||
"strategy is to take a top-down approach\n",
|
||
"\n",
|
||
"The approach is top-down because it begins at the top of the tree (all\n",
|
||
"observations belong to a single region) and then successively splits\n",
|
||
"the predictor space; each split is indicated via two new branches\n",
|
||
"further down on the tree. It is greedy because at each step of the\n",
|
||
"tree-building process, the best split is made at that particular step,\n",
|
||
"rather than looking ahead and picking a split that will lead to a\n",
|
||
"better tree in some future step.\n",
|
||
"\n",
|
||
"\n",
|
||
"### Making a tree\n",
|
||
"\n",
|
||
"In order to implement the recursive binary splitting we start by selecting\n",
|
||
"the predictor $x_j$ and a cutpoint $s$ that splits the predictor space into two regions $R_1$ and $R_2$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\left\\{X\\vert x_j < s\\right\\},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\left\\{X\\vert x_j \\geq s\\right\\},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"so that we obtain the lowest MSE, that is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sum_{i:x_i\\in R_j}(y_i-\\overline{y}_{R_1})^2+\\sum_{i:x_i\\in R_2}(y_i-\\overline{y}_{R_2})^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"which we want to minimize by considering all predictors\n",
|
||
"$x_1,x_2,\\dots,x_p$. We consider also all possible values of $s$ for\n",
|
||
"each predictor. These values could be determined by randomly assigned\n",
|
||
"numbers or by starting at the midpoint and then proceed till we find\n",
|
||
"an optimal value.\n",
|
||
"\n",
|
||
"For any $j$ and $s$, we define the pair of half-planes where\n",
|
||
"$\\overline{y}_{R_1}$ is the mean response for the training\n",
|
||
"observations in $R_1(j,s)$, and $\\overline{y}_{R_2}$ is the mean\n",
|
||
"response for the training observations in $R_2(j,s)$.\n",
|
||
"\n",
|
||
"Finding the values of $j$ and $s$ that minimize the above equation can be\n",
|
||
"done quite quickly, especially when the number of features $p$ is not\n",
|
||
"too large.\n",
|
||
"\n",
|
||
"Next, we repeat the process, looking\n",
|
||
"for the best predictor and best cutpoint in order to split the data\n",
|
||
"further so as to minimize the MSE within each of the resulting\n",
|
||
"regions. However, this time, instead of splitting the entire predictor\n",
|
||
"space, we split one of the two previously identified regions. We now\n",
|
||
"have three regions. Again, we look to split one of these three regions\n",
|
||
"further, so as to minimize the MSE. The process continues until a\n",
|
||
"stopping criterion is reached; for instance, we may continue until no\n",
|
||
"region contains more than five observations.\n",
|
||
"\n",
|
||
"\n",
|
||
"The above procedure is rather straightforward, but leads often to\n",
|
||
"overfitting and unnecessarily large and complicated trees. The basic\n",
|
||
"idea is to grow a large tree $T_0$ and then prune it back in order to\n",
|
||
"obtain a subtree. A smaller tree with fewer splits (fewer regions) can\n",
|
||
"lead to smaller variance and better interpretation at the cost of a\n",
|
||
"little more bias.\n",
|
||
"\n",
|
||
"The so-called Cost complexity pruning algorithm gives us a\n",
|
||
"way to do just this. Rather than considering every possible subtree,\n",
|
||
"we consider a sequence of trees indexed by a nonnegative tuning\n",
|
||
"parameter $\\alpha$.\n",
|
||
"\n",
|
||
"Read more at the following [Scikit-Learn link on pruning](https://scikit-learn.org/stable/auto_examples/tree/plot_cost_complexity_pruning.html#sphx-glr-auto-examples-tree-plot-cost-complexity-pruning-py).\n",
|
||
"\n",
|
||
"\n",
|
||
"For each value of $\\alpha$ there corresponds a subtree $T \\in T_0$ such that"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sum_{m=1}^{\\overline{T}}\\sum_{i:x_i\\in R_m}(y_i-\\overline{y}_{R_m})^2+\\alpha\\overline{T},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"is as small as possible. Here $\\overline{T}$ is \n",
|
||
"the number of terminal nodes of the tree $T$ , $R_m$ is the\n",
|
||
"rectangle (i.e. the subset of predictor space) corresponding to the $m$-th terminal node.\n",
|
||
"\n",
|
||
"The tuning parameter $\\alpha$ controls a trade-off between the subtree’s\n",
|
||
"complexity and its fit to the training data. When $\\alpha = 0$, then the\n",
|
||
"subtree $T$ will simply equal $T_0$, \n",
|
||
"because then the above equation just measures the\n",
|
||
"training error. \n",
|
||
"However, as $\\alpha$ increases, there is a price to pay for\n",
|
||
"having a tree with many terminal nodes. The above equation will\n",
|
||
"tend to be minimized for a smaller subtree. \n",
|
||
"\n",
|
||
"\n",
|
||
"It turns out that as we increase $\\alpha$ from zero\n",
|
||
"branches get pruned from the tree in a nested and predictable fashion,\n",
|
||
"so obtaining the whole sequence of subtrees as a function of $\\alpha$ is\n",
|
||
"easy. We can select a value of $\\alpha$ using a validation set or using\n",
|
||
"cross-validation. We then return to the full data set and obtain the\n",
|
||
"subtree corresponding to $\\alpha$. \n",
|
||
"\n",
|
||
"\n",
|
||
"### Schematic Regression Procedure\n",
|
||
"\n",
|
||
"Building a Regression Tree\n",
|
||
"\n",
|
||
"1. Use recursive binary splitting to grow a large tree on the training data, stopping only when each terminal node has fewer than some minimum number of observations.\n",
|
||
"\n",
|
||
"2. Apply cost complexity pruning to the large tree in order to obtain a sequence of best subtrees, as a function of $\\alpha$.\n",
|
||
"\n",
|
||
"3. Use for example $K$-fold cross-validation to choose $\\alpha$. Divide the training observations into $K$ folds. For each $k=1,2,\\dots,K$ we: \n",
|
||
"\n",
|
||
" * repeat steps 1 and 2 on all but the $k$-th fold of the training data. \n",
|
||
"\n",
|
||
" * Then we valuate the mean squared prediction error on the data in the left-out $k$-th fold, as a function of $\\alpha$.\n",
|
||
"\n",
|
||
" * Finally we average the results for each value of $\\alpha$, and pick $\\alpha$ to minimize the average error.\n",
|
||
"\n",
|
||
"\n",
|
||
"4. Return the subtree from Step 2 that corresponds to the chosen value of $\\alpha$. \n",
|
||
"\n",
|
||
"!eblock\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"## A Classification Tree\n",
|
||
"\n",
|
||
"A classification tree is very similar to a regression tree, except\n",
|
||
"that it is used to predict a qualitative response rather than a\n",
|
||
"quantitative one. Recall that for a regression tree, the predicted\n",
|
||
"response for an observation is given by the mean response of the\n",
|
||
"training observations that belong to the same terminal node. In\n",
|
||
"contrast, for a classification tree, we predict that each observation\n",
|
||
"belongs to the most commonly occurring class of training observations\n",
|
||
"in the region to which it belongs. In interpreting the results of a\n",
|
||
"classification tree, we are often interested not only in the class\n",
|
||
"prediction corresponding to a particular terminal node region, but\n",
|
||
"also in the class proportions among the training observations that\n",
|
||
"fall into that region. \n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"The task of growing a\n",
|
||
"classification tree is quite similar to the task of growing a\n",
|
||
"regression tree. Just as in the regression setting, we use recursive\n",
|
||
"binary splitting to grow a classification tree. However, in the\n",
|
||
"classification setting, the MSE cannot be used as a criterion for making\n",
|
||
"the binary splits. A natural alternative to MSE is the **classification\n",
|
||
"error rate**. Since we plan to assign an observation in a given region\n",
|
||
"to the most commonly occurring error rate class of training\n",
|
||
"observations in that region, the classification error rate is simply\n",
|
||
"the fraction of the training observations in that region that do not\n",
|
||
"belong to the most common class. \n",
|
||
"\n",
|
||
"When building a classification tree, either the Gini index or the\n",
|
||
"entropy are typically used to evaluate the quality of a particular\n",
|
||
"split, since these two approaches are more sensitive to node purity\n",
|
||
"than is the classification error rate. \n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"If our targets are the outcome of a classification process that takes\n",
|
||
"for example $k=1,2,\\dots,K$ values, the only thing we need to think of\n",
|
||
"is to set up the splitting criteria for each node.\n",
|
||
"\n",
|
||
"We define a PDF $p_{mk}$ that represents the number of observations of\n",
|
||
"a class $k$ in a region $R_m$ with $N_m$ observations. We represent\n",
|
||
"this likelihood function in terms of the proportion $I(y_i=k)$ of\n",
|
||
"observations of this class in the region $R_m$ as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i=k).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We let $p_{mk}$ represent the majority class of observations in region\n",
|
||
"$m$. The three most common ways of splitting a node are given by\n",
|
||
"\n",
|
||
"* Misclassification error"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i\\ne k) = 1-p_{mk}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* Gini index $g$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"g = \\sum_{k=1}^K p_{mk}(1-p_{mk}).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* Information entropy or just entropy $s$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"s = -\\sum_{k=1}^K p_{mk}\\log{p_{mk}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Visualizing the Tree, Classification"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
" mean radius mean texture mean perimeter mean area mean smoothness \\\n",
|
||
"0 17.99 10.38 122.80 1001.0 0.11840 \n",
|
||
"1 20.57 17.77 132.90 1326.0 0.08474 \n",
|
||
"2 19.69 21.25 130.00 1203.0 0.10960 \n",
|
||
"3 11.42 20.38 77.58 386.1 0.14250 \n",
|
||
"4 20.29 14.34 135.10 1297.0 0.10030 \n",
|
||
".. ... ... ... ... ... \n",
|
||
"564 21.56 22.39 142.00 1479.0 0.11100 \n",
|
||
"565 20.13 28.25 131.20 1261.0 0.09780 \n",
|
||
"566 16.60 28.08 108.30 858.1 0.08455 \n",
|
||
"567 20.60 29.33 140.10 1265.0 0.11780 \n",
|
||
"568 7.76 24.54 47.92 181.0 0.05263 \n",
|
||
"\n",
|
||
" mean compactness mean concavity mean concave points mean symmetry \\\n",
|
||
"0 0.27760 0.30010 0.14710 0.2419 \n",
|
||
"1 0.07864 0.08690 0.07017 0.1812 \n",
|
||
"2 0.15990 0.19740 0.12790 0.2069 \n",
|
||
"3 0.28390 0.24140 0.10520 0.2597 \n",
|
||
"4 0.13280 0.19800 0.10430 0.1809 \n",
|
||
".. ... ... ... ... \n",
|
||
"564 0.11590 0.24390 0.13890 0.1726 \n",
|
||
"565 0.10340 0.14400 0.09791 0.1752 \n",
|
||
"566 0.10230 0.09251 0.05302 0.1590 \n",
|
||
"567 0.27700 0.35140 0.15200 0.2397 \n",
|
||
"568 0.04362 0.00000 0.00000 0.1587 \n",
|
||
"\n",
|
||
" mean fractal dimension ... worst radius worst texture \\\n",
|
||
"0 0.07871 ... 25.380 17.33 \n",
|
||
"1 0.05667 ... 24.990 23.41 \n",
|
||
"2 0.05999 ... 23.570 25.53 \n",
|
||
"3 0.09744 ... 14.910 26.50 \n",
|
||
"4 0.05883 ... 22.540 16.67 \n",
|
||
".. ... ... ... ... \n",
|
||
"564 0.05623 ... 25.450 26.40 \n",
|
||
"565 0.05533 ... 23.690 38.25 \n",
|
||
"566 0.05648 ... 18.980 34.12 \n",
|
||
"567 0.07016 ... 25.740 39.42 \n",
|
||
"568 0.05884 ... 9.456 30.37 \n",
|
||
"\n",
|
||
" worst perimeter worst area worst smoothness worst compactness \\\n",
|
||
"0 184.60 2019.0 0.16220 0.66560 \n",
|
||
"1 158.80 1956.0 0.12380 0.18660 \n",
|
||
"2 152.50 1709.0 0.14440 0.42450 \n",
|
||
"3 98.87 567.7 0.20980 0.86630 \n",
|
||
"4 152.20 1575.0 0.13740 0.20500 \n",
|
||
".. ... ... ... ... \n",
|
||
"564 166.10 2027.0 0.14100 0.21130 \n",
|
||
"565 155.00 1731.0 0.11660 0.19220 \n",
|
||
"566 126.70 1124.0 0.11390 0.30940 \n",
|
||
"567 184.60 1821.0 0.16500 0.86810 \n",
|
||
"568 59.16 268.6 0.08996 0.06444 \n",
|
||
"\n",
|
||
" worst concavity worst concave points worst symmetry \\\n",
|
||
"0 0.7119 0.2654 0.4601 \n",
|
||
"1 0.2416 0.1860 0.2750 \n",
|
||
"2 0.4504 0.2430 0.3613 \n",
|
||
"3 0.6869 0.2575 0.6638 \n",
|
||
"4 0.4000 0.1625 0.2364 \n",
|
||
".. ... ... ... \n",
|
||
"564 0.4107 0.2216 0.2060 \n",
|
||
"565 0.3215 0.1628 0.2572 \n",
|
||
"566 0.3403 0.1418 0.2218 \n",
|
||
"567 0.9387 0.2650 0.4087 \n",
|
||
"568 0.0000 0.0000 0.2871 \n",
|
||
"\n",
|
||
" worst fractal dimension \n",
|
||
"0 0.11890 \n",
|
||
"1 0.08902 \n",
|
||
"2 0.08758 \n",
|
||
"3 0.17300 \n",
|
||
"4 0.07678 \n",
|
||
".. ... \n",
|
||
"564 0.07115 \n",
|
||
"565 0.06637 \n",
|
||
"566 0.07820 \n",
|
||
"567 0.12400 \n",
|
||
"568 0.07039 \n",
|
||
"\n",
|
||
"[569 rows x 30 columns]\n",
|
||
" malignant benign\n",
|
||
"0 True False\n",
|
||
"1 True False\n",
|
||
"2 True False\n",
|
||
"3 True False\n",
|
||
"4 True False\n",
|
||
".. ... ...\n",
|
||
"564 True False\n",
|
||
"565 True False\n",
|
||
"566 True False\n",
|
||
"567 True False\n",
|
||
"568 False True\n",
|
||
"\n",
|
||
"[569 rows x 2 columns]\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0"
|
||
]
|
||
},
|
||
"execution_count": 2,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"import os\n",
|
||
"from sklearn.datasets import load_breast_cancer\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.metrics import confusion_matrix\n",
|
||
"from sklearn.tree import export_graphviz\n",
|
||
"\n",
|
||
"from IPython.display import Image \n",
|
||
"from pydot import graph_from_dot_data\n",
|
||
"import pandas as pd\n",
|
||
"import numpy as np\n",
|
||
"\n",
|
||
"\n",
|
||
"cancer = load_breast_cancer()\n",
|
||
"X = pd.DataFrame(cancer.data, columns=cancer.feature_names)\n",
|
||
"print(X)\n",
|
||
"y = pd.Categorical.from_codes(cancer.target, cancer.target_names)\n",
|
||
"y = pd.get_dummies(y)\n",
|
||
"print(y)\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)\n",
|
||
"tree_clf = DecisionTreeClassifier(max_depth=5)\n",
|
||
"tree_clf.fit(X_train, y_train)\n",
|
||
"\n",
|
||
"export_graphviz(\n",
|
||
" tree_clf,\n",
|
||
" out_file=\"DataFiles/cancer.dot\",\n",
|
||
" feature_names=cancer.feature_names,\n",
|
||
" class_names=cancer.target_names,\n",
|
||
" rounded=True,\n",
|
||
" filled=True\n",
|
||
")\n",
|
||
"cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'\n",
|
||
"os.system(cmd)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0"
|
||
]
|
||
},
|
||
"execution_count": 3,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Common imports\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.model_selection import train_test_split \n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.datasets import make_moons\n",
|
||
"from sklearn.tree import export_graphviz\n",
|
||
"from pydot import graph_from_dot_data\n",
|
||
"import pandas as pd\n",
|
||
"import os\n",
|
||
"\n",
|
||
"np.random.seed(42)\n",
|
||
"X, y = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X,y,random_state=0)\n",
|
||
"tree_clf = DecisionTreeClassifier(max_depth=5)\n",
|
||
"tree_clf.fit(X_train, y_train)\n",
|
||
"\n",
|
||
"export_graphviz(\n",
|
||
" tree_clf,\n",
|
||
" out_file=\"DataFiles/moons.dot\",\n",
|
||
" rounded=True,\n",
|
||
" filled=True\n",
|
||
")\n",
|
||
"cmd = 'dot -Tpng DataFiles/moons.dot -o DataFiles/moons.png'\n",
|
||
"os.system(cmd)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Other ways of visualizing the trees\n",
|
||
"\n",
|
||
"**Scikit-Learn** has also another way to visualize the trees which is very useful, here with the Iris data."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"[Text(0.5, 0.9166666666666666, 'x[2] <= 2.45\\ngini = 0.667\\nsamples = 150\\nvalue = [50, 50, 50]'),\n",
|
||
" Text(0.4230769230769231, 0.75, 'gini = 0.0\\nsamples = 50\\nvalue = [50, 0, 0]'),\n",
|
||
" Text(0.5769230769230769, 0.75, 'x[3] <= 1.75\\ngini = 0.5\\nsamples = 100\\nvalue = [0, 50, 50]'),\n",
|
||
" Text(0.3076923076923077, 0.5833333333333334, 'x[2] <= 4.95\\ngini = 0.168\\nsamples = 54\\nvalue = [0, 49, 5]'),\n",
|
||
" Text(0.15384615384615385, 0.4166666666666667, 'x[3] <= 1.65\\ngini = 0.041\\nsamples = 48\\nvalue = [0, 47, 1]'),\n",
|
||
" Text(0.07692307692307693, 0.25, 'gini = 0.0\\nsamples = 47\\nvalue = [0, 47, 0]'),\n",
|
||
" Text(0.23076923076923078, 0.25, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 0, 1]'),\n",
|
||
" Text(0.46153846153846156, 0.4166666666666667, 'x[3] <= 1.55\\ngini = 0.444\\nsamples = 6\\nvalue = [0, 2, 4]'),\n",
|
||
" Text(0.38461538461538464, 0.25, 'gini = 0.0\\nsamples = 3\\nvalue = [0, 0, 3]'),\n",
|
||
" Text(0.5384615384615384, 0.25, 'x[2] <= 5.45\\ngini = 0.444\\nsamples = 3\\nvalue = [0, 2, 1]'),\n",
|
||
" Text(0.46153846153846156, 0.08333333333333333, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 2, 0]'),\n",
|
||
" Text(0.6153846153846154, 0.08333333333333333, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 0, 1]'),\n",
|
||
" Text(0.8461538461538461, 0.5833333333333334, 'x[2] <= 4.85\\ngini = 0.043\\nsamples = 46\\nvalue = [0, 1, 45]'),\n",
|
||
" Text(0.7692307692307693, 0.4166666666666667, 'x[1] <= 3.1\\ngini = 0.444\\nsamples = 3\\nvalue = [0, 1, 2]'),\n",
|
||
" Text(0.6923076923076923, 0.25, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 0, 2]'),\n",
|
||
" Text(0.8461538461538461, 0.25, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 1, 0]'),\n",
|
||
" Text(0.9230769230769231, 0.4166666666666667, 'gini = 0.0\\nsamples = 43\\nvalue = [0, 0, 43]')]"
|
||
]
|
||
},
|
||
"execution_count": 4,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
},
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.datasets import load_iris\n",
|
||
"from sklearn import tree\n",
|
||
"X, y = load_iris(return_X_y=True)\n",
|
||
"tree_clf = tree.DecisionTreeClassifier()\n",
|
||
"tree_clf = tree_clf.fit(X, y)\n",
|
||
"# and then plot the tree\n",
|
||
"tree.plot_tree(tree_clf)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Alternatively, the tree can also be exported in textual format with the function exporttext.\n",
|
||
"This method doesn’t require the installation of external libraries and is more compact:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"|--- petal width (cm) <= 0.80\n",
|
||
"| |--- class: 0\n",
|
||
"|--- petal width (cm) > 0.80\n",
|
||
"| |--- petal width (cm) <= 1.75\n",
|
||
"| | |--- class: 1\n",
|
||
"| |--- petal width (cm) > 1.75\n",
|
||
"| | |--- class: 2\n",
|
||
"\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.datasets import load_iris\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.tree import export_text\n",
|
||
"iris = load_iris()\n",
|
||
"decision_tree = DecisionTreeClassifier(random_state=0, max_depth=2)\n",
|
||
"decision_tree = decision_tree.fit(iris.data, iris.target)\n",
|
||
"r = export_text(decision_tree, feature_names=iris['feature_names'])\n",
|
||
"print(r)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Algorithms for Setting up Decision Trees\n",
|
||
"\n",
|
||
"Two algorithms stand out in the set up of decision trees:\n",
|
||
"1. The CART (Classification And Regression Tree) algorithm for both classification and regression\n",
|
||
"\n",
|
||
"2. The ID3 algorithm based on the computation of the information gain for classification\n",
|
||
"\n",
|
||
"We discuss both algorithms with applications here. The popular library\n",
|
||
"**Scikit-Learn** uses the CART algorithm. For classification problems\n",
|
||
"you can use either the **gini** index or the **entropy** to split a tree\n",
|
||
"in two branches.\n",
|
||
"\n",
|
||
"### The CART algorithm for Classification\n",
|
||
"\n",
|
||
"For classification, the CART algorithm splits the data set in two subsets using a single feature $k$ and a threshold $t_k$.\n",
|
||
"This could be for example a threshold set by a number below a certain circumference of a malign tumor.\n",
|
||
"\n",
|
||
"How do we find these two quantities?\n",
|
||
"We search for the pair $(k,t_k)$ that produces the purest subset using for example the **gini** factor $G$.\n",
|
||
"The cost function it tries to minimize is then"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"C(k,t_k) = \\frac{m_{\\mathrm{left}}}{m}G_{\\mathrm{left}}+ \\frac{m_{\\mathrm{right}}}{m}G_{\\mathrm{right}},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $G_{\\mathrm{left/right}}$ measures the impurity of the left/right subset and $m_{\\mathrm{left/right}}$\n",
|
||
" is the number of instances in the left/right subset\n",
|
||
"\n",
|
||
"Once it has successfully split the training set in two, it splits the subsets using the same logic, then the subsubsets\n",
|
||
"and so on, recursively. It stops recursing once it reaches the maximum depth (defined by the\n",
|
||
"$max\\_depth$ hyperparameter), or if it cannot find a split that will reduce impurity. A few other\n",
|
||
"hyperparameters control additional stopping conditions such as the $min\\_samples\\_split$,\n",
|
||
"$min\\_samples\\_leaf$, $min\\_weight\\_fraction\\_leaf$, and $max\\_leaf\\_nodes$.\n",
|
||
"\n",
|
||
"\n",
|
||
"### The CART algorithm for Regression\n",
|
||
"\n",
|
||
"The CART algorithm for regression works is similar to the one for classification except that instead of trying to split the\n",
|
||
"training set in a way that minimizes say the **gini** or **entropy** impurity, it now tries to split the training set in a way that minimizes our well-known mean-squared error (MSE). The cost function is now"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"C(k,t_k) = \\frac{m_{\\mathrm{left}}}{m}\\mathrm{MSE}_{\\mathrm{left}}+ \\frac{m_{\\mathrm{right}}}{m}\\mathrm{MSE}_{\\mathrm{right}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Here the MSE for a specific node is defined as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathrm{MSE}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}(\\overline{y}_{\\mathrm{node}}-y_i)^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"with"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\overline{y}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}y_i,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"the mean value of all observations in a specific node.\n",
|
||
"\n",
|
||
"Without any regularization, the regression task for decision trees, \n",
|
||
"just like for classification tasks, is prone to overfitting.\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"### Computing the Gini index\n",
|
||
"\n",
|
||
"The example we will look at is a classical one in many Machine\n",
|
||
"Learning applications. Based on various meteorological features, we\n",
|
||
"have several so-called attributes which decide whether we at the end\n",
|
||
"will do some outdoor activity like skiing, going for a bike ride etc\n",
|
||
"etc. The table here contains the feautures **outlook**, **temperature**,\n",
|
||
"**humidity** and **wind**. The target or output is whether we ride\n",
|
||
"(True=1) or whether we do something else that day (False=0). The\n",
|
||
"attributes for each feature are then sunny, overcast and rain for the\n",
|
||
"outlook, hot, cold and mild for temperature, high and normal for\n",
|
||
"humidity and weak and strong for wind.\n",
|
||
"\n",
|
||
"The table here summarizes the various attributes and\n",
|
||
"<table border=\"1\">\n",
|
||
"<thead>\n",
|
||
"<tr><th align=\"center\">Day</th> <th align=\"center\">Outlook </th> <th align=\"center\">Temperature</th> <th align=\"center\">Humidity</th> <th align=\"center\"> Wind </th> <th align=\"center\">Ride</th> </tr>\n",
|
||
"</thead>\n",
|
||
"<tbody>\n",
|
||
"<tr><td align=\"center\"> 1 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Hot </td> <td align=\"center\"> High </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 0 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 2 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Hot </td> <td align=\"center\"> High </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 3 </td> <td align=\"center\"> Overcast </td> <td align=\"center\"> Hot </td> <td align=\"center\"> High </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 4 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Mild </td> <td align=\"center\"> High </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 5 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Cool </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 6 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Cool </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 0 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 7 </td> <td align=\"center\"> Overcast </td> <td align=\"center\"> Cool </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 8 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Mild </td> <td align=\"center\"> High </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 0 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 9 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Cool </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 10 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Mild </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 11 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Mild </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 12 </td> <td align=\"center\"> Overcast </td> <td align=\"center\"> Mild </td> <td align=\"center\"> High </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 13 </td> <td align=\"center\"> Overcast </td> <td align=\"center\"> Hot </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 14 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Mild </td> <td align=\"center\"> High </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 0 </td> </tr>\n",
|
||
"</tbody>\n",
|
||
"</table>\n",
|
||
"\n",
|
||
"### Simple Python Code to read in Data and perform Classification"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
" (0, 0)\t1.0\n",
|
||
" (0, 7)\t1.0\n",
|
||
" (0, 9)\t1.0\n",
|
||
" (0, 13)\t1.0\n",
|
||
" (1, 3)\t1.0\n",
|
||
" (1, 5)\t1.0\n",
|
||
" (1, 8)\t1.0\n",
|
||
" (1, 12)\t1.0\n",
|
||
" (2, 3)\t1.0\n",
|
||
" (2, 5)\t1.0\n",
|
||
" (2, 8)\t1.0\n",
|
||
" (2, 11)\t1.0\n",
|
||
" (3, 1)\t1.0\n",
|
||
" (3, 5)\t1.0\n",
|
||
" (3, 8)\t1.0\n",
|
||
" (3, 12)\t1.0\n",
|
||
" (4, 2)\t1.0\n",
|
||
" (4, 6)\t1.0\n",
|
||
" (4, 8)\t1.0\n",
|
||
" (4, 12)\t1.0\n",
|
||
" (5, 2)\t1.0\n",
|
||
" (5, 4)\t1.0\n",
|
||
" (5, 10)\t1.0\n",
|
||
" (5, 12)\t1.0\n",
|
||
" (6, 2)\t1.0\n",
|
||
" :\t:\n",
|
||
" (8, 12)\t1.0\n",
|
||
" (9, 3)\t1.0\n",
|
||
" (9, 4)\t1.0\n",
|
||
" (9, 10)\t1.0\n",
|
||
" (9, 12)\t1.0\n",
|
||
" (10, 2)\t1.0\n",
|
||
" (10, 6)\t1.0\n",
|
||
" (10, 10)\t1.0\n",
|
||
" (10, 12)\t1.0\n",
|
||
" (11, 3)\t1.0\n",
|
||
" (11, 6)\t1.0\n",
|
||
" (11, 10)\t1.0\n",
|
||
" (11, 11)\t1.0\n",
|
||
" (12, 1)\t1.0\n",
|
||
" (12, 6)\t1.0\n",
|
||
" (12, 8)\t1.0\n",
|
||
" (12, 11)\t1.0\n",
|
||
" (13, 1)\t1.0\n",
|
||
" (13, 5)\t1.0\n",
|
||
" (13, 10)\t1.0\n",
|
||
" (13, 12)\t1.0\n",
|
||
" (14, 2)\t1.0\n",
|
||
" (14, 6)\t1.0\n",
|
||
" (14, 8)\t1.0\n",
|
||
" (14, 11)\t1.0\n",
|
||
"Train set accuracy with Decision Tree: 0.73\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0"
|
||
]
|
||
},
|
||
"execution_count": 6,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Common imports\n",
|
||
"import numpy as np\n",
|
||
"import pandas as pd\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.tree import export_graphviz\n",
|
||
"from sklearn.preprocessing import StandardScaler, OneHotEncoder\n",
|
||
"from sklearn.compose import ColumnTransformer\n",
|
||
"from IPython.display import Image \n",
|
||
"from pydot import graph_from_dot_data\n",
|
||
"import os\n",
|
||
"\n",
|
||
"# Where to save the figures and data files\n",
|
||
"PROJECT_ROOT_DIR = \"Results\"\n",
|
||
"FIGURE_ID = \"Results/FigureFiles\"\n",
|
||
"DATA_ID = \"DataFiles/\"\n",
|
||
"\n",
|
||
"if not os.path.exists(PROJECT_ROOT_DIR):\n",
|
||
" os.mkdir(PROJECT_ROOT_DIR)\n",
|
||
"\n",
|
||
"if not os.path.exists(FIGURE_ID):\n",
|
||
" os.makedirs(FIGURE_ID)\n",
|
||
"\n",
|
||
"if not os.path.exists(DATA_ID):\n",
|
||
" os.makedirs(DATA_ID)\n",
|
||
"\n",
|
||
"def image_path(fig_id):\n",
|
||
" return os.path.join(FIGURE_ID, fig_id)\n",
|
||
"\n",
|
||
"def data_path(dat_id):\n",
|
||
" return os.path.join(DATA_ID, dat_id)\n",
|
||
"\n",
|
||
"def save_fig(fig_id):\n",
|
||
" plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
|
||
"\n",
|
||
"infile = open(data_path(\"rideclass.csv\"),'r')\n",
|
||
"\n",
|
||
"# Read the experimental data with Pandas\n",
|
||
"from IPython.display import display\n",
|
||
"ridedata = pd.read_csv(infile,names = ('Outlook','Temperature','Humidity','Wind','Ride'))\n",
|
||
"ridedata = pd.DataFrame(ridedata)\n",
|
||
"\n",
|
||
"# Features and targets\n",
|
||
"X = ridedata.loc[:, ridedata.columns != 'Ride'].values\n",
|
||
"y = ridedata.loc[:, ridedata.columns == 'Ride'].values\n",
|
||
"\n",
|
||
"# Create the encoder.\n",
|
||
"encoder = OneHotEncoder(handle_unknown=\"ignore\")\n",
|
||
"# Assume for simplicity all features are categorical.\n",
|
||
"encoder.fit(X) \n",
|
||
"# Apply the encoder.\n",
|
||
"X = encoder.transform(X)\n",
|
||
"print(X)\n",
|
||
"# Then do a Classification tree\n",
|
||
"tree_clf = DecisionTreeClassifier(max_depth=2)\n",
|
||
"tree_clf.fit(X, y)\n",
|
||
"print(\"Train set accuracy with Decision Tree: {:.2f}\".format(tree_clf.score(X,y)))\n",
|
||
"#transfer to a decision tree graph\n",
|
||
"export_graphviz(\n",
|
||
" tree_clf,\n",
|
||
" out_file=\"DataFiles/ride.dot\",\n",
|
||
" rounded=True,\n",
|
||
" filled=True\n",
|
||
")\n",
|
||
"cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'\n",
|
||
"os.system(cmd)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"The above functions (gini, entropy and misclassification error) are\n",
|
||
"important components of the so-called CART algorithm. We will discuss\n",
|
||
"this algorithm below after we have discussed the information gain\n",
|
||
"algorithm ID3.\n",
|
||
"\n",
|
||
"In the example here we have converted all our attributes into numerical values $0,1,2$ etc."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 1.000 Gini=0.394\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X1 < 1.000 Gini=0.394\n",
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 1.000 Gini=0.394\n",
|
||
"X1 < 1.000 Gini=0.394\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X2 < 0.000 Gini=0.408\n",
|
||
"X2 < 0.000 Gini=0.408\n",
|
||
"X2 < 0.000 Gini=0.408\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 2.000 Gini=0.407\n",
|
||
"X2 < 2.000 Gini=0.407\n",
|
||
"X2 < 2.000 Gini=0.407\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 2.000 Gini=0.407\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 0.000 Gini=0.408\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"Split: [X3 < 1.000]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"# Split a dataset based on an attribute and an attribute value\n",
|
||
"def test_split(index, value, dataset):\n",
|
||
"\tleft, right = list(), list()\n",
|
||
"\tfor row in dataset:\n",
|
||
"\t\tif row[index] < value:\n",
|
||
"\t\t\tleft.append(row)\n",
|
||
"\t\telse:\n",
|
||
"\t\t\tright.append(row)\n",
|
||
"\treturn left, right\n",
|
||
" \n",
|
||
"# Calculate the Gini index for a split dataset\n",
|
||
"def gini_index(groups, classes):\n",
|
||
"\t# count all samples at split point\n",
|
||
"\tn_instances = float(sum([len(group) for group in groups]))\n",
|
||
"\t# sum weighted Gini index for each group\n",
|
||
"\tgini = 0.0\n",
|
||
"\tfor group in groups:\n",
|
||
"\t\tsize = float(len(group))\n",
|
||
"\t\t# avoid divide by zero\n",
|
||
"\t\tif size == 0:\n",
|
||
"\t\t\tcontinue\n",
|
||
"\t\tscore = 0.0\n",
|
||
"\t\t# score the group based on the score for each class\n",
|
||
"\t\tfor class_val in classes:\n",
|
||
"\t\t\tp = [row[-1] for row in group].count(class_val) / size\n",
|
||
"\t\t\tscore += p * p\n",
|
||
"\t\t# weight the group score by its relative size\n",
|
||
"\t\tgini += (1.0 - score) * (size / n_instances)\n",
|
||
"\treturn gini\n",
|
||
"\n",
|
||
"# Select the best split point for a dataset\n",
|
||
"def get_split(dataset):\n",
|
||
"\tclass_values = list(set(row[-1] for row in dataset))\n",
|
||
"\tb_index, b_value, b_score, b_groups = 999, 999, 999, None\n",
|
||
"\tfor index in range(len(dataset[0])-1):\n",
|
||
"\t\tfor row in dataset:\n",
|
||
"\t\t\tgroups = test_split(index, row[index], dataset)\n",
|
||
"\t\t\tgini = gini_index(groups, class_values)\n",
|
||
"\t\t\tprint('X%d < %.3f Gini=%.3f' % ((index+1), row[index], gini))\n",
|
||
"\t\t\tif gini < b_score:\n",
|
||
"\t\t\t\tb_index, b_value, b_score, b_groups = index, row[index], gini, groups\n",
|
||
"\treturn {'index':b_index, 'value':b_value, 'groups':b_groups}\n",
|
||
" \n",
|
||
"dataset = [[0,0,0,0,0],\n",
|
||
" [0,0,0,1,1],\n",
|
||
" [1,0,0,0,1],\n",
|
||
" [2,1,0,0,1],\n",
|
||
" [2,2,1,0,1],\n",
|
||
" [2,2,1,1,0],\n",
|
||
" [1,2,1,1,1],\n",
|
||
" [0,1,0,0,0],\n",
|
||
" [0,2,1,0,1],\n",
|
||
" [2,1,1,0,1],\n",
|
||
" [0,1,1,1,1],\n",
|
||
" [1,1,0,1,1],\n",
|
||
" [1,0,1,0,1],\n",
|
||
" [2,1,0,1,0]]\n",
|
||
"\n",
|
||
"split = get_split(dataset)\n",
|
||
"print('Split: [X%d < %.3f]' % ((split['index']+1), split['value']))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Entropy and the ID3 algorithm\n",
|
||
"\n",
|
||
"The ID3 algorithm learns decision trees by constructing\n",
|
||
"them in a top down way, beginning with the question **which attribute should be tested at the root of the tree**?\n",
|
||
"\n",
|
||
"1. Each instance attribute is evaluated using a statistical test to determine how well it alone classifies the training examples.\n",
|
||
"\n",
|
||
"2. The best attribute is selected and used as the test at the root node of the tree.\n",
|
||
"\n",
|
||
"3. A descendant of the root node is then created for each possible value of this attribute.\n",
|
||
"\n",
|
||
"4. Training examples are sorted to the appropriate descendant node.\n",
|
||
"\n",
|
||
"5. The entire process is then repeated using the training examples associated with each descendant node to select the best attribute to test at that point in the tree.\n",
|
||
"\n",
|
||
"6. This forms a greedy search for an acceptable decision tree, in which the algorithm never backtracks to reconsider earlier choices. \n",
|
||
"\n",
|
||
"The ID3 algorithm selects which attribute to test at each node in the\n",
|
||
"tree.\n",
|
||
"\n",
|
||
"We would like to select the attribute that is most useful for classifying\n",
|
||
"examples.\n",
|
||
"\n",
|
||
"What is a good quantitative measure of the worth of an attribute?\n",
|
||
"\n",
|
||
"Information gain measures how well a given attribute separates the\n",
|
||
"training examples according to their target classification.\n",
|
||
"\n",
|
||
"The ID3 algorithm uses this information gain measure to select among the candidate\n",
|
||
"attributes at each step while growing the tree.\n",
|
||
"\n",
|
||
"\n",
|
||
"### Cancer Data again now with Decision Trees and other Methods"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"(426, 30)\n",
|
||
"(143, 30)\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Test set accuracy with Logistic Regression: 0.94\n",
|
||
"Test set accuracy with SVM: 0.63\n",
|
||
"Test set accuracy with Decision Trees: 0.90\n",
|
||
"Test set accuracy Logistic Regression with scaled data: 0.96\n",
|
||
"Test set accuracy SVM with scaled data: 0.96\n",
|
||
"Test set accuracy with Decision Trees and scaled data: 0.89\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:460: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
|
||
"STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
|
||
"\n",
|
||
"Increase the number of iterations (max_iter) or scale the data as shown in:\n",
|
||
" https://scikit-learn.org/stable/modules/preprocessing.html\n",
|
||
"Please also refer to the documentation for alternative solver options:\n",
|
||
" https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
|
||
" n_iter_i = _check_optimize_result(\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.model_selection import train_test_split \n",
|
||
"from sklearn.datasets import load_breast_cancer\n",
|
||
"from sklearn.svm import SVC\n",
|
||
"from sklearn.linear_model import LogisticRegression\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"\n",
|
||
"# Load the data\n",
|
||
"cancer = load_breast_cancer()\n",
|
||
"\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
|
||
"print(X_train.shape)\n",
|
||
"print(X_test.shape)\n",
|
||
"# Logistic Regression\n",
|
||
"logreg = LogisticRegression(solver='lbfgs')\n",
|
||
"logreg.fit(X_train, y_train)\n",
|
||
"print(\"Test set accuracy with Logistic Regression: {:.2f}\".format(logreg.score(X_test,y_test)))\n",
|
||
"# Support vector machine\n",
|
||
"svm = SVC(gamma='auto', C=100)\n",
|
||
"svm.fit(X_train, y_train)\n",
|
||
"print(\"Test set accuracy with SVM: {:.2f}\".format(svm.score(X_test,y_test)))\n",
|
||
"# Decision Trees\n",
|
||
"deep_tree_clf = DecisionTreeClassifier(max_depth=None)\n",
|
||
"deep_tree_clf.fit(X_train, y_train)\n",
|
||
"print(\"Test set accuracy with Decision Trees: {:.2f}\".format(deep_tree_clf.score(X_test,y_test)))\n",
|
||
"#now scale the data\n",
|
||
"from sklearn.preprocessing import StandardScaler\n",
|
||
"scaler = StandardScaler()\n",
|
||
"scaler.fit(X_train)\n",
|
||
"X_train_scaled = scaler.transform(X_train)\n",
|
||
"X_test_scaled = scaler.transform(X_test)\n",
|
||
"# Logistic Regression\n",
|
||
"logreg.fit(X_train_scaled, y_train)\n",
|
||
"print(\"Test set accuracy Logistic Regression with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
|
||
"# Support Vector Machine\n",
|
||
"svm.fit(X_train_scaled, y_train)\n",
|
||
"print(\"Test set accuracy SVM with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
|
||
"# Decision Trees\n",
|
||
"deep_tree_clf.fit(X_train_scaled, y_train)\n",
|
||
"print(\"Test set accuracy with Decision Trees and scaled data: {:.2f}\".format(deep_tree_clf.score(X_test_scaled,y_test)))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Another example, the moons again"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"from __future__ import division, print_function, unicode_literals\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",
|
||
"import matplotlib\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from matplotlib.colors import ListedColormap\n",
|
||
"plt.rcParams['axes.labelsize'] = 14\n",
|
||
"plt.rcParams['xtick.labelsize'] = 12\n",
|
||
"plt.rcParams['ytick.labelsize'] = 12\n",
|
||
"\n",
|
||
"\n",
|
||
"from sklearn.svm import SVC\n",
|
||
"from sklearn import datasets\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.datasets import make_moons\n",
|
||
"from sklearn.tree import export_graphviz\n",
|
||
"\n",
|
||
"Xm, ym = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
|
||
"\n",
|
||
"deep_tree_clf1 = DecisionTreeClassifier(random_state=42)\n",
|
||
"deep_tree_clf2 = DecisionTreeClassifier(min_samples_leaf=4, random_state=42)\n",
|
||
"deep_tree_clf1.fit(Xm, ym)\n",
|
||
"deep_tree_clf2.fit(Xm, ym)\n",
|
||
"\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)\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"plt.subplot(121)\n",
|
||
"plot_decision_boundary(deep_tree_clf1, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
|
||
"plt.title(\"No restrictions\", fontsize=16)\n",
|
||
"plt.subplot(122)\n",
|
||
"plot_decision_boundary(deep_tree_clf2, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
|
||
"plt.title(\"min_samples_leaf = {}\".format(deep_tree_clf2.min_samples_leaf), fontsize=14)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"np.random.seed(6)\n",
|
||
"Xs = np.random.rand(100, 2) - 0.5\n",
|
||
"ys = (Xs[:, 0] > 0).astype(np.float32) * 2\n",
|
||
"\n",
|
||
"angle = np.pi/4\n",
|
||
"rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])\n",
|
||
"Xsr = Xs.dot(rotation_matrix)\n",
|
||
"\n",
|
||
"tree_clf_s = DecisionTreeClassifier(random_state=42)\n",
|
||
"tree_clf_s.fit(Xs, ys)\n",
|
||
"tree_clf_sr = DecisionTreeClassifier(random_state=42)\n",
|
||
"tree_clf_sr.fit(Xsr, ys)\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"plt.subplot(121)\n",
|
||
"plot_decision_boundary(tree_clf_s, Xs, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
|
||
"plt.subplot(122)\n",
|
||
"plot_decision_boundary(tree_clf_sr, Xsr, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Quadratic training set + noise\n",
|
||
"np.random.seed(42)\n",
|
||
"m = 200\n",
|
||
"X = np.random.rand(m, 1)\n",
|
||
"y = 4 * (X - 0.5) ** 2\n",
|
||
"y = y + np.random.randn(m, 1) / 10"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/html": [
|
||
"<style>#sk-container-id-1 {color: black;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 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-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 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-1 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-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 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-1 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-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 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-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 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-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 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-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>DecisionTreeRegressor(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-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">DecisionTreeRegressor</label><div class=\"sk-toggleable__content\"><pre>DecisionTreeRegressor(max_depth=2, random_state=42)</pre></div></div></div></div></div>"
|
||
],
|
||
"text/plain": [
|
||
"DecisionTreeRegressor(max_depth=2, random_state=42)"
|
||
]
|
||
},
|
||
"execution_count": 12,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.tree import DecisionTreeRegressor\n",
|
||
"\n",
|
||
"tree_reg = DecisionTreeRegressor(max_depth=2, random_state=42)\n",
|
||
"tree_reg.fit(X, y)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 13,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.tree import DecisionTreeRegressor\n",
|
||
"\n",
|
||
"tree_reg1 = DecisionTreeRegressor(random_state=42, max_depth=2)\n",
|
||
"tree_reg2 = DecisionTreeRegressor(random_state=42, max_depth=3)\n",
|
||
"tree_reg1.fit(X, y)\n",
|
||
"tree_reg2.fit(X, y)\n",
|
||
"\n",
|
||
"def plot_regression_predictions(tree_reg, X, y, axes=[0, 1, -0.2, 1], ylabel=\"$y$\"):\n",
|
||
" x1 = np.linspace(axes[0], axes[1], 500).reshape(-1, 1)\n",
|
||
" y_pred = tree_reg.predict(x1)\n",
|
||
" plt.axis(axes)\n",
|
||
" plt.xlabel(\"$x_1$\", fontsize=18)\n",
|
||
" if ylabel:\n",
|
||
" plt.ylabel(ylabel, fontsize=18, rotation=0)\n",
|
||
" plt.plot(X, y, \"b.\")\n",
|
||
" plt.plot(x1, y_pred, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"plt.subplot(121)\n",
|
||
"plot_regression_predictions(tree_reg1, X, y)\n",
|
||
"for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
|
||
" plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
|
||
"plt.text(0.21, 0.65, \"Depth=0\", fontsize=15)\n",
|
||
"plt.text(0.01, 0.2, \"Depth=1\", fontsize=13)\n",
|
||
"plt.text(0.65, 0.8, \"Depth=1\", fontsize=13)\n",
|
||
"plt.legend(loc=\"upper center\", fontsize=18)\n",
|
||
"plt.title(\"max_depth=2\", fontsize=14)\n",
|
||
"\n",
|
||
"plt.subplot(122)\n",
|
||
"plot_regression_predictions(tree_reg2, X, y, ylabel=None)\n",
|
||
"for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
|
||
" plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
|
||
"for split in (0.0458, 0.1298, 0.2873, 0.9040):\n",
|
||
" plt.plot([split, split], [-0.2, 1], \"k:\", linewidth=1)\n",
|
||
"plt.text(0.3, 0.5, \"Depth=2\", fontsize=13)\n",
|
||
"plt.title(\"max_depth=3\", fontsize=14)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"tree_reg1 = DecisionTreeRegressor(random_state=42)\n",
|
||
"tree_reg2 = DecisionTreeRegressor(random_state=42, min_samples_leaf=10)\n",
|
||
"tree_reg1.fit(X, y)\n",
|
||
"tree_reg2.fit(X, y)\n",
|
||
"\n",
|
||
"x1 = np.linspace(0, 1, 500).reshape(-1, 1)\n",
|
||
"y_pred1 = tree_reg1.predict(x1)\n",
|
||
"y_pred2 = tree_reg2.predict(x1)\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"\n",
|
||
"plt.subplot(121)\n",
|
||
"plt.plot(X, y, \"b.\")\n",
|
||
"plt.plot(x1, y_pred1, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
|
||
"plt.axis([0, 1, -0.2, 1.1])\n",
|
||
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
|
||
"plt.ylabel(\"$y$\", fontsize=18, rotation=0)\n",
|
||
"plt.legend(loc=\"upper center\", fontsize=18)\n",
|
||
"plt.title(\"No restrictions\", fontsize=14)\n",
|
||
"\n",
|
||
"plt.subplot(122)\n",
|
||
"plt.plot(X, y, \"b.\")\n",
|
||
"plt.plot(x1, y_pred2, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
|
||
"plt.axis([0, 1, -0.2, 1.1])\n",
|
||
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
|
||
"plt.title(\"min_samples_leaf={}\".format(tree_reg2.min_samples_leaf), fontsize=14)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Pros and cons of trees, pros\n",
|
||
"\n",
|
||
"* White box, easy to interpret model. Some people believe that decision trees more closely mirror human decision-making than do the regression and classification approaches discussed earlier (think of support vector machines)\n",
|
||
"\n",
|
||
"* Trees are very easy to explain to people. In fact, they are even easier to explain than linear regression!\n",
|
||
"\n",
|
||
"* No feature normalization needed\n",
|
||
"\n",
|
||
"* Tree models can handle both continuous and categorical data (Classification and Regression Trees)\n",
|
||
"\n",
|
||
"* Can model nonlinear relationships\n",
|
||
"\n",
|
||
"* Can model interactions between the different descriptive features\n",
|
||
"\n",
|
||
"* Trees can be displayed graphically, and are easily interpreted even by a non-expert (especially if they are small)\n",
|
||
"\n",
|
||
"### Disadvantages\n",
|
||
"\n",
|
||
"* Unfortunately, trees generally do not have the same level of predictive accuracy as some of the other regression and classification approaches\n",
|
||
"\n",
|
||
"* If continuous features are used the tree may become quite large and hence less interpretable\n",
|
||
"\n",
|
||
"* Decision trees are prone to overfit the training data and hence do not well generalize the data if no stopping criteria or improvements like pruning, boosting or bagging are implemented\n",
|
||
"\n",
|
||
"* Small changes in the data may lead to a completely different tree. This issue can be addressed by using ensemble methods like bagging, boosting or random forests\n",
|
||
"\n",
|
||
"* Unbalanced datasets where some target feature values occur much more frequently than others may lead to biased trees since the frequently occurring feature values are preferred over the less frequently occurring ones. \n",
|
||
"\n",
|
||
"* If the number of features is relatively large (high dimensional) and the number of instances is relatively low, the tree might overfit the data\n",
|
||
"\n",
|
||
"* Features with many levels may be preferred over features with less levels since for them it is *more easy* to split the dataset such that the sub datasets only contain pure target feature values. This issue can be addressed by preferring for instance the information gain ratio as splitting criteria over information gain\n",
|
||
"\n",
|
||
"However, by aggregating many decision trees, using methods like\n",
|
||
"bagging, random forests, and boosting, the predictive performance of\n",
|
||
"trees can be substantially improved."
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.9.15"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 4
|
||
} |