Morten Hjorth-Jensen
1775 lines
425 KiB
Plaintext
1775 lines
425 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: 2.7023746599300384\n",
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"first power: 0.03407676546787885\n",
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"second power: 9.208257931205295e-06\n"
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]
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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_1_1.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
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||
},
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||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_1_2.png"
|
||
}
|
||
},
|
||
"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 1 0\n",
|
||
"1 1 0\n",
|
||
"2 1 0\n",
|
||
"3 1 0\n",
|
||
"4 1 0\n",
|
||
".. ... ...\n",
|
||
"564 1 0\n",
|
||
"565 1 0\n",
|
||
"566 1 0\n",
|
||
"567 1 0\n",
|
||
"568 0 1\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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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_24_1.png"
|
||
}
|
||
},
|
||
"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",
|
||
"Test set accuracy with Logistic Regression: 0.94\n",
|
||
"Test set accuracy with SVM: 0.63\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"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"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"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:814: 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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\n",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_42_0.png"
|
||
}
|
||
},
|
||
"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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\n",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_43_0.png"
|
||
}
|
||
},
|
||
"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/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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\n",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_46_0.png"
|
||
}
|
||
},
|
||
"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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\n",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_47_0.png"
|
||
}
|
||
},
|
||
"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."
|
||
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|
||
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|
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