Morten Hjorth-Jensen
1772 lines
430 KiB
Plaintext
1772 lines
430 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: -1.5105332296929628\n",
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"first power: 0.08398399377155011\n",
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"second power: -0.0003701342170783489\n"
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]
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",
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||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
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||
"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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",
|
||
"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 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": {
|
||
"image/png": 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uXIX/Qbt48WLs2bMH2dnZ6Ny5M9vhEEIaQckAIUrC3t4ely5dQnZ2NvT09NgOp0HFxcWwsrLC4MGDkZCQwHY4hJBGUDcBIUrg+PHjOHbsGLZv367wiQAA6OnpITg4GEePHsWJEyeQl5eHqqoqtsMihLwHPRkgRMG9evUKPXv2hLW1NX755RelWeGPYRiMHTsW2dnZKC8vR0BAAJydndkOixBSDxrqS4iCW7t2LZ49e4YffvhBaRIBALh79y40NTXx+PFjaGtr4969e2yHRAh5D0oGCFFgWVlZ2LZtG/z9/dGtWze2w5GIrq4u7t+/jzdv3uD169e4ceMG2yERQt6DugkIUVACgQCffPIJiouLkZmZCS0tLbZDktibN2+wdetW+Pn5wcLCAtnZ2WyHRAipByUDhCiYly9fIjQ0FAYGBnBzc8PZs2cxbNgwtsNqlnv37kFdXR1dunRhOxRCSD0oGSBEwfz000+YOnUq2rRpg4kTJ2LPnj0KucAQIaTloKmFhCiYx48fg8Ph4M2bNzhy5IjC7EpICGm5aAAhIQrm0qVLYBgGlZWVWLp0Kezs7OR2bj6fj4KCArmdT9kYGhrCzMyM7TAIkTpKBghRMEZGRujYsSNOnjyJ/v37y+28fD4fVlZWKCsrk9s5lQ2Xy0V2djYlBKTFoTEDhBAAQHp6OmxsbLBv3z5YWVmxHY7Cyc7OhpOTE9LS0jBgwAC2wyFEqujJACFEhJWVFf2wI0TFUDJAVAL1hYuivm9CSF2UDJAWj/rC3yXLvu+UlBQEBgYiLCwM9+/fR1xcHPLz8zF//nzY2dnBx8cHALBp06b3llFRUQEdHZ1Gz/Xdd9/h8OHD+Oeff0SOv3HjBnbs2AEAOH36NO7evQtnZ2doampCXV0d27dvh7a2djOvlJCWg5IB0uIVFBSgrKyM+sL/X23fd0FBgVSSgaNHj+LRo0cwNzfH5cuXYWtri/Hjx8PMzAxmZmb49NNPUVRUhO+//x52dnbg8XiIiIh4p5yioiLEx8fj4sWLcHBwwNixYxs994YNG5Cfn//O13v27ImIiAhkZWXBwMAAQE0CVF1dDQMDA6VczZEQWaJkgKgM6guXDXt7eyxZsgRnzpzBwYMH8eeff4q8HxMTg+joaGzYsOG9Zbi4uKCqqgo8Hg9ubm4AapZjXrhwochxX3/9NQYNGiR2bNHR0fjmm28AQLjR044dO5CUlCRWskGIqqBFhwhphtpH3m+LiIhAbm6uRGX5+vpiyZIl75RZWloKZ2dnuLi4YP/+/U0NVWYYhkFhYSHU1dVRXV39zvvOzs5ITk5GSEjIe8twd3eHsbExdu/ejSNHjqCysrLZcZWXl+Phw4fo0aMHAAh3fGzfvj1evnzZ7PIJaUnoyQAhYsrOzsbatWthYWGBtLQ0nDx5UvgDv0+fPvj666+RmpqK6OhoPH78GBUVFWKXzefzIRAIsGPHDixbtgx5eXno3LkzACAhIQEzZszA2LFjMWPGDDg6Osri8pps+/btmDlzJkxMTLB69Wp88cUXwvd++ukn/PHHHygrK8PMmTPfW0bfvn3Rt29fVFVV4dSpUzhz5gzGjh1bb3dCXUFBQfj777+xePFirF+/HufOnYO2tjbs7Oxw+PBhTJkyRXish4cHysrK8PLlS+zatav5F05IC0LJACFiio6ORmBgIExMTDB+/HiR97p06YKlS5ciJCQEmZmZ73z22bNnWLlypcjXli1bhu7duwMA8vPzhT/8zczM8ODBA+HrBw8eCBcfUsQ9CpYuXSr8t42NDVJSUoSvp0yZIvIDuTEaGhqYMGGC2Md7enrC09NT+HratGnCf8+ePVvk2G3btoldLiGqhroJCBFT3fW53l6rq1WrVgAATU3NJj3iNjU1xYMHDwAAeXl5MDU1rfc9gUAgcdnypq+vj/T0dPD5/Hrfj4mJQbdu3eQcFSGkIfRkgBAxubi4wMvLC+bm5mjdurVEnzUyMmrwkXftqH4PDw9oaWnBzMwMQUFBGDFiBCZPngx3d3ckJiZi3LhxzboGeejXrx+ioqLqfc/Hx6feKYUREREYM2YMunbtKvZ5fH19UVpaCi6XK1JmSkoKVq1ahZ49e8LBwQHDhw+X9BIIUTmUDBAipvbt28Pc3BzPnz8XPoKOj48X+ZvH4wFAk34Avf1Dsu7j75iYmCZEzC62xlhwOBy0adMGFRUVwq8RQhpGyQAhYjIwMIC/vz/bYSgNtsZYDBs2DJ999hmePHkCb29v/PjjjzK4OkJaFhozQIiMxMTEICkpSapl9ujRAzweT/gY/tq1a3BycoKjoyOuXbsm1XM1F1tjLGqnELZt21YqUxQJUQX0ZICQOuLi4pCSkgIul4vNmzfj0KFDyMzMRGlpKUJCQrBhwwYUFxejqKgI1tbWePHiBe7fv499+/bBzs4OQ4cORW5uLhYtWiQs8/79+wgICACHw0H37t0xZswYrF27Fqamppg7dy569eoldny6urooLy9Hly5dAAAhISEIDw+HQCCAt7c3IiMjpV4nTcXWGIu7d+8iKSkJxcXFIv8PhJD3o2SAkDry8/PRu3dvTJo0Cdra2uBwONDS0kJOTo7wcbaDgwMsLS3h7OyMo0ePYsGCBSgqKkJ1dTU8PT1RUlKCFStWYODAgQCAsLAwtGrVClwuF9euXcOQIUPQtm1bzJo1SyQRaOzROFCzzbBAIICdnR2++OILlJSUQFdXFwBQUlIi49qRDFtjLPr374+pU6c2NWxCVBIlA4TUsWzZMmRlZcHb2xv+/v5ISEhAQkIC1qxZg9LSUgCAnp4etLW1oaenBwDQ0tJCZWUlBAIBqqur8fr1a+GjaqBmOqCzszOsra2FXzM1NcXu3buRlZWFOXPmiB0fh8OBuro6dHR0wDAMWrdujZKSEuG/FQmNsSBEeVAyQEgdUVFRuH37NgCgXbt2MDIyQkBAAFJTUxv97VVbWxv+/v64e/cuVq5cidTUVAA1S+36+fmhQ4cO0NXVxbBhw3DixAk8f/4cn3/+ufDzjT0az8nJwcaNGwEAn376KTgcDtzd3eHu7i7sJlBGMTExMDExwZgxY6RWpqurKy5fvoyMjAwANWMrNm3aBIZh4Ovri169er13aiIhqoiSAULqWLBggcjr2j742h+0dROC2ul+oaGhAAAdHR2RzXjqPgl4e0+BESNGSBybpaXlOyPj+/Tpw8poeUUfWxEZGQkHBwfh67fHVnz33XfvnZpIiCqiZIAQKantB1cFij624m1vj61oaGoiIaqIkgFCiMQUfWzF294eW2FqaorExEQANVMTJ06c2OSyCWkJKBkgpB4ODg5S/01/6NCh8Pb2hp2dHXr06IHPP/8cAwYMwIIFC+rt035bU46pXZdg8ODBwpH70qDIYysA4LvvvsOVK1fA4/EQGhr6ztiK+qYmEqLSGEJauLS0NAYAk5aWxjAMwyxYsIB5/vw5U1VVxTg6OjL5+fmMj48Pw+PxmMTERIZhGGbGjBkif4eHhzPJyclMeno6s3DhQobH4zF79+6VKI7ashiGYfr168fMnj2bSUpKEsb08uVL5sWLF8yCBQvq/XxTj0lOTmbCw8PfWx+NfV3a6taDMpFX/RDCBnoyQFTO9OnTcfjwYXz44YcYOXIkNDQ0UFVVBWNjY8TGxsLOzu69nw0KCkK3bt3A4XCQmZmJWbNmCd/z9fVFUVGR8PXEiRMxduzYestpynoB0jqGbao0toIQZUHJAFE5I0aMwO7du5GWloYtW7YgOjoa9vb2sLGxeafvWE2tZsXu2n7wqqoqeHh4QF9fv1kxNGW9AGkdQwghb6NkgKgcNTU1dO7cGQ8fPoSenh5sbW0RGRkJCwsLaGlpiRxrYmKCwMBAnD9/HjY2NvD29oa7uzvat2+Prl27YvHixcJja9cAaIy46wVs2rQJPj4+ws819RhZkvXYCnHWAmjK+Is1a9YgJycH+vr6WLVqFTp27PjOuZKSkrBmzRpcvHhRqtdHiCKiZICopLo/WIYMGYIhQ4aIvF/7Ay4oKAgA4OXlJXxv3759zTq3OOsFvHr1ClVVVc0+pjlcXV2xceNG6OnpYc6cOQgICEBISAhevHiBsWPHinSn1CYFERERsLS0hJ6eHqKjoyEQCGBrayvSndKYTp06wc7OrsFtiutqyn4Nmpqa0NHRgZaWFtq2bVvvucaMGaOUW0cT0hSUDBAiJ23atMHx48cbHJNQq3Xr1lixYkWzj6moqMCxY8cwcuRIiWIF2B9bIe5aAE0Zf+Hn5wcOh4Pjx48jJiYG/fr1o3UHiEqjZICojOzsbFbPXzu1Lz09Xa7nrd0kqPa84tYD22MrxF0LoCnjL2rXN2jfvj2ys7Np3QGi8igZIC2eoaEhuFwunJyc2A5FYXC5XBgaGjZ4DNtjK+pbC+D06dNo164dBgwYAKDp4y/Wr18PPp+PwsJChISEoEOHDu+cixBVwmEYhmE7CEJkjc/no6CggO0wFIahoeE7P/DS09NhY2ODtLQ04Q9bNjQ0KPH777+Hu7s72rRpI3Z5r169QnBwcKNdKo3Foij1Q4gs0JMBohLMzMzot71GKEqy1NDYCj8/P4nLE2dsRX2SkpLA5XIl/hwhyoieDBCi4m7duoWtW7diz549ePPmDfbt2wcrKyu2w1I42dnZcHJywsCBA7Fu3TqMHj1aZG8FQpQZJQOEqKhLly4hICAAR48ehbGxMZydnRESEoKysjK2Q1NYOjo6+M9//oOrV6+iT58+8Pb2xvTp06Gpqcl2aIQ0CyUDhKgQgUCAU6dOISAgAOfOnYO5uTm8vLwwa9Ys6Ojo0NiKRhgaGqJz5844e/YsAgICcOrUKZiZmcHT0xPz5s2jVR+J0qJkgBAV8Pr1axw4cABbtmzB9evX8fHHH2P58uWws7ODuro62+EprX/++QeBgYE4cOAAdHV1sWjRIixevBjGxsZsh0aIRCgZIKQFKykpwc6dO7Ft2zY8ePAA48ePh7e3N4YOHUr93VLE5/Oxbds27Ny5E9XV1Zg7dy48PT3Ro0cPtkMjRCyUDBDSAj1+/Bg7duxAWFgYysrK4OjoCC8vL1hbW7MdWotWWFiI8PBw7NixAwUFBZgyZQqWLVuGgQMHsh0aIQ2iZICQFuTmzZvYunUrfvzxR2hpacHV1RVLly5Fp06d2A5NpZSXl2Pv3r0IDAzEnTt3MGLECHh7e+OLL76gJzJEIVEyQEgLcPHiRQQEBODYsWMwNjbG0qVLwePxmr3VMmme6upqHDt2DJs3b0Zqaip69+4Nb29vzJgxg2YgEIWixnYAhJCmEQgEOHnyJIYNG4YhQ4bg+vXriIqKQm5uLnx8fCgRUADq6uqYMmUKLl26hOTkZHTq1AmzZs1C9+7dERwcjFevXrEdIiEAKBkgROm8fv0aMTEx6N27NyZMmIA3b97g6NGjyM7Oxvz586Gjo8N2iOQtHA4Hw4cPxy+//IKsrCwMHz4cy5Ytg5mZGVasWIGnT5+yHSJRcdRNQIiSePnypXBmQH5+PsaPH4/ly5fjk08+oX5oJcTn8xEcHIyoqChUVVVh7ty5+Pbbb2kGAmEFJQOEKLhHjx5hx44dCA8Pp5kBLVBRURHCw8Oxfft2PHv2DFOmTIG3tzfNQCByRckAIQrq5s2bCAwMxN69e6GtrQ1XV1d88803NDOghaqoqMDevXuxZcsW3LlzB8OHD4e3tzfGjBlDT36IzFEyQIiC+fvvvxEQEIDExES0b98eS5cuhaurKw0IVBH1zUBYtmwZHBwcaAYCkRkaQEiIAqidGfDpp5/C1tYW2dnZ2LlzJ3Jzc7F8+XJKBFRI3RkIKSkp6Ny5M2bPnk0zEIhMUTJACIvenhlQ+1vhjRs3MG/ePGhra7MdImEJh8PBZ599hp9//hn//PMPRowYITID4cmTJ2yHSFoQ6iYghAUvX75EVFQUgoODkZ+fjwkTJgj3DCDkffLy8oQzEN68eQNnZ2d8++23+M9//sN2aETJUTJAiBw9evQI27dvR3h4OMrLy+Hk5AQvLy/07NmT7dCIEnl7BsLkyZPh7e2NQYMGsR0aUVKUDBAiBzdv3sSWLVsQGxsLbW1t8Hg8fPPNNzA1NWU7NKLEamcgBAYG4vbt2/jss8+wfPlymoFAJEZjBgiRob///hv29vawsrLCL7/8gnXr1iEvLw8BAQGUCJBm09HRwYIFC5CdnY2ffvoJ5eXl+PLLL9GnTx/ExsbizZs3bIdIlAQlA4RImUAgwIkTJ4QzA3JychAdHY1///0X3t7e0NPTYztE0sKoq6tj8uTJuHjxIs6ePYsuXboIZyBs27YNJSUlbIdIFBwlA4RISWVlJfbs2YNevXrBzs4OAoEAiYmJuH79Or7++muaGUBkjsPhYNiwYTh58iSuXr0q3DrZzMwM3333Hc1AIO9FYwYIaabi4mLhzICHDx/Czs4O3t7e+OSTT9gOjZB3ZiDMmTMH3377LczNzdkOjSgQSgYIaaKHDx9i+/btiIiIQHl5OWbNmgUvLy9YWVmxHRoh7ygqKkJERAS2b9+Op0+fwt7eHt7e3vj444/ZDo0oAOomIEQM6enpePnyJQAgJycH8+fPx4cffoiIiAjweDzk5uZi165dlAgQhdW2bVv4+voiNzcXkZGRuHr1KgYPHizcWplhGDAMgz///BPV1dVsh0vkjJIBQhqRkpKCQYMGYcuWLZg0aZJwZsD69evB5/OxefNmdOzYke0wCRGLjo4OXFxckJ2djYSEBFRUVGDcuHHo06cPwsPDMXz4cPj5+bEdJpEz6iYgpAG5ubno27cvOBwOiouLYWlpCW9vb3z11Vc0IJC0CAzD4Pz58wgICMDJkyehp6eH4uJi7NmzB87OzmyHR+SEkgECPp+PgoICtsNQCIaGhjAzMxO+NjMzQ15eHjQ1NWFkZIS1a9di/vz5LEZIiGzk5ORg0qRJePDgAUpLSwEABQUFaNeunfAYulf8z9v3CmWnwXYAhF18Ph9WVlYoKytjOxSFwOVykZ2dLfwm9/X1RVZWFoyNjVFeXo5evXqxHCEhsmFoaIipU6cCqJkmW1ZWJrJbJt0rRL19r1B29GRAxaWnp8PGxgb79u1T+cFv2dnZcHJyQlpaGgYMGMB2OIQoFLpX/E9LvFfQkwECALCysmoxjZoQIjt0r2iZaDYBIYQQouIoGSDNkpKSgvHjx4PP5yM6OhoLFiyAnZ0drl69CgDw8fGBj49Pg2VUVFSIfb5NmzbBwcFB5GuPHz/GlClT4ObmhoiICACAs7MzXFxcwOPxUFlZKeFVEUKkTRHuFS9fvsTkyZPh4uKCb7/9FgDdK2pRMkAkcvToUYSFheH333/H999/DwAYP348zMzMMH/+fERFRWHt2rU4ceIEAIDH49VbTu1+7HPmzEFycrJY57548SI6dOjwztcvXLiAKVOmIDw8HMnJyXjz5g24XC7U1NRgYGAALS2tJl4tIaSpFPFe8eTJE1hbW2Pnzp14+vQpANC94v/RmAEiEXt7eyxZsgRnzpzBwYMH8eeff4q8X1VVhdDQUKxevfq9Zbi4uKCqqgo8Hg9ubm4Aanb6W7hwochxX3/9NQYNGgQAKC8vx/79+xESEoJTp06JHDd27FisWLEC6enpKCgoQGFhIX744QdwOBzs2LEDSUlJGDt2rDQunxAiJkW8V3Tq1An//PMPxo4dKzye7hU16MkAkQjDMCgsLIS6uvo7S5a+fv0aCxcuxJIlSxqcbuPu7g5jY2Ps3r0bR44cEevR3JUrV1BcXIylS5ciIyMDFy9eFL73wQcfYOvWrQgMDESrVq1gZGQEDocDAGjfvr1wGWFCiPwo4r3i559/xvTp03Hq1Ck8evQIhYWFdK/4f/RkgEhk+/btmDlzJkxMTLB69Wp88cUXwvd8fHxw69YthIeHY9SoUZg2bVq9ZfTt2xd9+/ZFVVUVTp06hTNnzmDs2LHC/v76fPrpp/j0008B1IwRGDx4MA4fPgxtbW2MGjUKbm5uqK6uhrOzM9TU1ODh4YGysjK8fPkSu3btkm4lEEIapYj3ik8++QSLFy/GX3/9hTdv3qBt27Z0r/h/lAwQiSxdulT4bxsbG6SkpAhfBwUFSVSWhoYGJkyYIHEM8fHxACByA9m7d6/IMdu2bZO4XEKI9CjqveLIkSMix9C9ogZ1E5Bm0dfXR3p6Ovh8fr3vx8TEoFu3bnKOihCiaOheodgoGSDN0q9fP0RFRSEsLKze901MTDB69GiJyvT19cWSJUvemWZ07949zJs3T2S60Pnz5+Hu7o7Fixfj0aNH4PP5mDhxIr7++mts3rxZ8gsihMiEPO8VpaWlwimD+/fvF359165dGDVqFICaVQR5PB6mTp2KyMhICa+m5aFkgEgsOzsbDg4OWL16NcaPHw+gZnc/AOjTpw+Cg4Ph6OiI8vJyPH78WKK5wXw+HwKBADt27EB1dTXy8vKE73Xr1u2dPr2QkBBoaWlBW1sbbdu2xa1bt2BnZ4fdu3fj2rVrzb9YQkiTsXWvSEhIwIwZM7Bz504cP34cAPDvv//i+fPnMDIyAlCzkmJERAQOHTqEtLQ0KV2x8qJkgEgsOjoagYGBWLlyJaqqqkTe69KlC5YuXYrBgwcjMzPznc8+e/YMPB5P5M/du3eF7+fn56Nz584AanYMfPDgQYOxpKWlYfPmzfjss88QFxeH/v37Y9++fRg5ciRGjBjR/IslhDQZW/eKBw8eCN9TV1eHQCDA1q1bRcYxAMDx48fx3//+V/i0QJVRMkAkVndvq7f3uWrVqhUAQFNTs0mreZmamgq/qfPy8mBqatrg8VZWVtDU1ES7du1QUlKCPXv2YP369Thz5gx++eUXic9PCJEetu4Vdd8TCAS4d+8enj17Bm9vb2RkZAjvDXZ2dvjjjz9w4MABic/f0tBsAiIxFxcXeHl5wdzcHK1bt5bos0ZGRg1OC6qdc+zh4QEtLS2YmZkhKCgII0aMgJmZGb777jtcuXIFAQEB8Pb2hqOjI9zc3PDq1SsEBQXhyZMnWLt2LWJjY9G1a9fmXCYhpJnYuldMnjwZ7u7uSExMxLhx49CjRw8cPHgQQM10wy+//BIpKSk4dOgQXr9+LfFYhZaItjBWcbXbkkqyFWdhYSGCg4Px/PlzjB49GhMnTpRxlPLRlLogRFXQveJ/WuK9gp4MEIkZGBjA39+f7TAIIQqO7hXKg8YMELmLiYlBUlKSVMvs0aMHeDweoqKihF+7evUqjI2NJRqhTAhRLLK4XwA1GyPVTkl89OgRlixZAnd3d5w/f17q51IG9GSAiCUuLg4pKSngcrnYvHkzDh06hMzMTJSWliIkJAQbNmxAcXExioqKYG1tjRcvXuD+/fvYt28f7OzsMHToUOTm5mLRokXCMu/fv4+AgABwOBx0794dY8aMwdq1a2Fqaoq5c+eiV69eYsenq6uL8vJydOnSBQDw5s0bREdHq+ymI4SwSdHvF0eOHMFHH32EO3fuAKhZEZHL5aK4uLjRQcstFSUDRCz5+fno3bs3Jk2aBG1tbXA4HGhpaSEnJ0c4LcjBwQGWlpZwdnbG0aNHsWDBAhQVFaG6uhqenp4oKSnBihUrMHDgQABAWFgYWrVqBS6Xi2vXrmHIkCFo27YtZs2aJfKN/ezZM6xcuVIknmXLlqF79+7C1+np6RAIBLCzs8MXX3yBwMBALF68GOvXr5d95RBCRCjy/eLJkyfIyMiAi4uLMBm4evUqgoODYWRkBG9vb5Xco4CSASKWZcuWISsrC97e3vD390dCQgISEhKwZs0alJaWAgD09PSgra0NPT09AICWlhYqKyshEAhQXV2N169fC3cIA2qm/Dg7O8Pa2lr4NVNTU+zevRtZWVmYM2eO2PFxOByoq6tDR0cHDMMgMzMTT548weXLlxEeHg4PDw8p1QQhpDGKfL84e/Ysnj59Cn9/f1y9ehW3bt2CqakpDAwM0KZNmyZNc2wJKBkgYomKisLt27cBAO3atYORkRECAgKQmpqK4cOHN/hZbW1t+Pv74+7du1i5ciVSU1MB1GxP6ufnhw4dOkBXVxfDhg3DiRMn8Pz5c3z++efCzzc2xSgnJwcbN24EULNjGYfDEU4jcnZ2Fu6DTgiRD0W+X0yfPh3Tp09Hbm4uIiIiYG5uDk9PTyxbtgxqamoqe7+gqYUqTh5TZBwcHIS7hymyljhdiBBpkdf3hzLcL1rivYJmExCZU/RvbEKI4qD7BTsoGSCEEEJUHCUDRGJ1txCWlqFDhwp3F3vftqRvqztP+MCBA3B0dMS8efOQnZ1d7/Fr1qyBg4MDeDweHj58iIqKCjg7OzfYv0gIaTpFuFe4urqif//+jZZb936iivcKSgaICFdXVxQWFqK6uhpOTk54+PAhfH194ebmJvwGrFX7jR4REYGUlBRkZGRg0aJFcHNzQ2xsrETn7dSpE+zs7BrclrSu2nnCtRITExETE4MtW7Zg69at9X5GU1MTOjo60NLSQtu2baGjowNnZ2eJ4iSE1FCWe0VkZCQsLCwaLPPt+4kq3itoNgERMX36dBw+fBgffvghRo4cCQ0NDVRVVcHY2BixsbGws7N772eDgoLQrVs3cDgcZGZmYtasWcL3fH19UVRUJHw9ceLEehcEqm9b0trXteqbJ+zl5YUlS5bAxMRE5Dx1+fn5gcPh4Pjx44iJiVHZUcOESIMy3CvEUd/9RBXvFZQMEBEjRozA7t27kZaWhi1btiA6Ohr29vawsbF5Z5MRNbWaB0u184arqqrg4eEBfX39Jp/f1NQUiYmJAGq2Ja1vY5P65gl/9NFH+Oijj3D79m28ePGi3rJr5yy3b9/+vV0JhBDxKMO9Qhz13U/Mzc0BqNa9gpIBIkJNTQ2dO3fGw4cPoaenB1tbW+FjNi0tLZFjTUxMEBgYiPPnz8PGxgbe3t5wd3dH+/bt0bVrVyxevFh4bO06AI2pb1vS06dPo127dsIpPPXNEz558iQSExNRVlYm7CbYtGmTSF/i+vXrwefzUVhYiJCQkGbVEyGqThnuFQCE257zeDyEhoYiOTm50fuJSt4rGKLS0tLSGABMWloaq3HMmDHjve9t2LCBKS4ulqi8kpISZt26dY0el5yczISHhzMMozh1QYgiUpTvj+beK5pyP2GYln+voAGERCG0adPmnUFHtfz8/NCmTRuJymvdujVWrFjR4DEVFRU4duwYOnbsKFHZhBD2NPde0ZT7iSrcK6ibgAAA6/1iPB4PQM3KXvI0e/Zs4XnZrgNClAHb3yd0r5ANSgZUnKGhIbhcLpycnNgORSFwuVwYGhqyHQYhCofuFaJa2r2C9iYg4PP5KCgoaPCYR48ewcvLC//++y/WrFmD0aNHyym6psvJycG3336LyspKbNmyRayFRwwNDYUDkwghosS5V0jqt99+g6+vL7Zt24Zhw4ZJrdzy8nJMnToVXbt2RWhoqMgOiNLQ0u4VlAyQRp07dw5Tp04Fl8vFsWPH0K9fP7ZDEtuzZ88wbdo0XLhwASEhIXB1dWU7JELI/ysuLoalpSWGDBmChIQEqZd/8uRJTJgwAfHx8ZgxY4bUy29JaAAheS+GYfDDDz9g1KhRsLa2RmpqqlIlAkDNdqanT5+Gq6sreDweXF1d8fr1a7bDIoSgZtrfq1evsGPHDpmUP378eNjb22Pp0qXvXX+E1KBkgNSrsrISLi4ucHd3x8KFC/Hbb7/ByMiI7bCaRFNTEyEhIdi1axdiYmIwcuRIPH78mO2wCFFpqampCAsLg7+/Pzp16iSz8+zYsQOvXr1qdHaRqqNuAvKOR48eYcqUKUhLS0NERATmzp3LdkhSc/HiRUyePBlqamo4evQoBg4cyHZIhKicqqoqDBo0CAzDIDU1FRoash3Lvm3bNnz77be4ePEiBg0aJNNzKStKBoiIS5cuwd7eHhwOBwkJCfj444/ZDknqHj58iClTpiAjIwNRUVHCKUOEEPkIDg6Gp6en3H44V1VVYeDAgeBwOLh8+bLMkw9lRN0ERGjPnj0YNmwYunbtiitXrrTIRAAAOnbsiJSUFDg6OmLOnDnw8PBAVVUV22ERohIePHiAlStXws3NTW6/pWtoaCAyMhKZmZkIDQ2VyzmVDT0ZIHjz5g2+/fZbhISEwMXFBSEhIdDW1mY7LJljGAbh4eH45ptvMGzYMBw8eLBFzRsmRBFNmTIFFy5cQE5ODvT09OR67kWLFmHv3r3Izs6W6TgFZUTJgIp79uwZpk+fjvPnz2PHjh3g8XhSn4+r6M6ePYtp06ahVatWOHbsGPr27ct2SIS0SLVT/Q4cOAAHBwe5n792KqOtrS1++uknuZ9fkVEyoMIyMzMxadIklJWV4ciRI1Jd8EPZ8Pl8TJo0CTdv3sSePXswffp0tkMipEUpLS2FtbU1LCwskJSUxNovHfHx8Zg5cyZOnDiB8ePHsxKDIqIxAyoqPj4etra2aNeuHdLS0lQ6EQBqtkM9f/48Jk6ciBkzZsDPzw/V1dVsh0VIi7Fu3To8fvwYYWFhrD59nDFjBkaPHg13d3eUlpayFoeioWRAxVRXV2P58uWYOXMmJk+ejPPnz6Nz585sh6UQuFwu9u/fjy1btmDz5s2ws7OjhUoIkYJr165h69atWLFiBbp3785qLBwOBz/88AMeP34Mf39/VmNRJNRNoEKKioowc+ZMnD59GgEBAfD09FS58QHi+vXXX+Hg4ABjY2McO3YMVlZWbIdEiFISCAQYNmwYnj9/jszMTIUZnLx+/XqsXbsW6enp6N27N9vhsI6SARVx/fp1TJo0Cc+fP8fBgwfx3//+l+2QFN6dO3cwadIk8Pl87Nu3D3Z2dmyHRIjSiY6OhouLC5KTkzF8+HC2wxGqrKxEv379YGBggD///BNqaqr9oFy1r15FHDt2DIMHD4aOjg5SU1MpERBTjx498Pfff+Pzzz/HxIkTsW7dOggEArbDIkRpPHv2DN7e3pgzZ45CJQIAoK2tjfDwcFy4cAG7d+9mOxzWUTLQggkEAqxZswb29vb44osv8Pfff7PeX6dsdHV1ceTIEaxduxarVq3CtGnTUFJSwnZYhCgFLy8vcDgcbNmyhe1Q6jV8+HDMmTMH3t7eePr0KdvhsIq6CVqokpISzJ49G4mJiVi3bh38/PxofEAzJSYmwsnJCV26dEFiYiIlVoQ0IDk5GSNHjkR0dDTmzZvHdjjv9ezZM1haWmL8+PH48ccf2Q6HNZQMtEB37tzBxIkTkZeXh/3792PChAlsh9Ri3LhxA5MmTUJBQQGNvSDkPSorK9G3b18YGRnh7NmzCt8fv2vXLsyfPx9nzpzBiBEj2A6HFYr9P0QklpSUhIEDB6KqqgqXL1+mREDKevbsicuXL2Pw4MEYM2YMAgMDQfk0IaICAgJw9+5dREREKHwiAABz587F0KFD4ebmhsrKSrbDYYXi/y8RsTAMg82bN+PLL7+Era0tLl26BEtLS7bDapH09fVx4sQJeHt7Y9myZXByckJZWRnbYRHCOldXV7i6umLDhg3w8vKCtbU12yGJRU1NDREREbh79y4CAgLYDocVlAwoserqasyZMwcXL17EV199BR8fH/j6+uL48ePQ19dnO7wWTV1dHRs3bsTBgwdx7NgxDB06FDk5OZgyZQry8/PZDo8QVly5cgU///wzDAwMYGJiwnY4ErG2toaXlxc2bNiAO3fusB2O3NGYASV25MgRTJs2Debm5njw4AFiYmIwbdo0tsNSOVlZWZg4cSJKS0tRWVmJ+fPnIygoiO2wCJE7AwMDFBUVQU1NDQMHDsSFCxeUopugVllZGaytrfGf//wHv/76q0oNulae/yUigmEYrFy5EmpqaigoKMD06dNhb2/PdlgqqW/fvuDxeGjdujVevXqFsLAwFBUVsR0WIXL34sULqKur4/vvv8e5c+eUKhEAapYk/+GHH3D69GkcPHiQ7XDkSrn+p4jQmTNnkJOTA4FAgLKyMjx+/BivX79mOyyV9fjxYxQXF4NhGFRWVsLPz4/tkAiRu3Xr1iE9PR3Lly+HlpYW2+E0yZdffokpU6Zg6dKluH//Pv766y+2Q5IL6iZQUmVlZVi3bh0mTZqEAQMGQFNTk+2QVB7DMLh9+zb279+PmTNn0gBOQpRUfn4+rKysMHDgQJw/fx5lZWVQV1dnOyyZomSAEEIIqcPDwwNnzpzBP//8AwB48uQJjI2NWY5KtjTYDkAW+Hw+CgoK2A5DIRgaGsLMzIztMFokVW5n1K7kg9oYO21s/PjxOHTokPB1fn4+JQPKhs/nw8rKiuZ9/z8ul4vs7Gy6cUuZqrczaleyR22MvTY2atQo5OTkwNXVFQcOHFCJAcEtLhkoKChAWVkZ9u3bp/J70GdnZ8PJyQkFBQV005YyVW5n1K7kg9oYu21MV1cXcXFx2Lt3LzQ0WtyPyne02Cu0srLCgAED2A6DtHDUzoisURtjlyokAgBNLSSEEEJUnmqkPGJKSUlBYGAgwsLCcP/+fcTFxSE/Px/z58+HnZ0dfHx8AACbNm16bxkVFRXQ0dFp9FzfffcdDh8+jH/++eed47ds2QI+n4+uXbvi22+/hbOzMzQ1NaGuro7t27dDW1u7eRdKWKMIbSw3Nxf29vb4+OOP8d///hdTpkyhNtYC1W1rjx8/xtatW/Hhhx8K25Y029ry5cvx9OlTlJeXIzY2VjjVubi4GB4eHsjLy8Pp06elcFX1U+WBlvVpyuBLlU4Gjh49ikePHsHc3ByXL1+Gra0txo8fDzMzM5iZmeHTTz9FUVERvv/+e9jZ2YHH4yEiIuKdcoqKihAfH4+LFy/CwcEBY8eObfTcGzZsqHcN+4yMDPz999/o3Lkz2rdvD6BmIE11dTUMDAyUdiEPVaWIbQwA2rRpg7KyMnTp0gUAtbGWoLG2tnnzZpG2Jc22tnnzZgCAl5cXSktLhXuj6OnpYffu3XBwcJDORdZD1Qda1qcpgy9VOhmwt7fHkiVLcObMGRw8eBB//vmnyPsxMTGIjo7Ghg0b3luGi4sLqqqqwOPx4ObmBgAQCARYuHChyHFff/01Bg0a1GhMN2/ehLm5OTZt2gRHR0dMnjwZP/zwAzgcDnbs2IGkpCSxvjmJYlDENtalSxecPXsWZWVlcHJyQkJCArWxFqCxtiaOpra1x48fw8/PD+Xl5WjVqlXzLkRCqjzQsj5NHXyp0skAwzAoLCyEuro6qqur33nf2dkZjo6OmDlzJj777LN6y3B3d0dcXBx2796NvLw8TJgwoVmrAZqamoLP5wMAWrdujdevX4PL5QIA2rdvj5cvXza5bCJ/itjGajdfqW1Xdb9GbUx5NdbWxNHUtmZiYoLdu3djy5YtuHz5Mj755JMmnb85ZDHQ0sfHp95ulIiICIwZMwZdu3YVuyxfX1+UlpaCy+WKlFlaWopFixZBU1MTw4cPh6OjozRCl5hKJwPbt2/HzJkzYWJigtWrV+OLL74QvvfTTz/hjz/+QFlZGWbOnPneMvr27Yu+ffuiqqoKp06dwpkzZzB27Nh6H7/VFRQUhL///huLFy/G+vXrce7cOWhra2PChAmIi4uDh4cHTExMoK+vDw8PD5SVleHly5fYtWuX1K6fyJ4itjF9fX3ExMSgvLwcM2bMAABqYy1AQ23t1q1bWLt2LW7cuIH//Oc/mDdvXr1lNKWtVVZWwsPDQ7gvh7u7Ow4fPgxtbW1h19eVK1ewfPlyYXeCIsrOzsbatWthYWGBtLQ0nDx5Erm5uQCAPn364Ouvv0Zqaiqio6Px+PFjVFRUiF02n8+HQCDAjh07sGzZMuTl5aFz584AgISEBMyYMQNjx47FjBkzKBlgw9KlS4X/trGxQUpKivD1lClTMGXKFLHL0tDQwIQJE8Q+3tPTE56ensLXdbceDg8PFzl227ZtYpdLFIuitrFhw4aJHEttTPk11NbMzc2xf/9+scuSpK1pa2sjLCxM5Gt121pjSauiiI6ORmBgIExMTDB+/HiR97p06YKlS5ciJCQEmZmZ73z22bNnWLlypcjXli1bhu7duwOoWcGw9oe/mZkZHjx4IHz94MED9O/fHwBY3f+AphbWoa+vj/T0dOFj+rfFxMSgW7duco6KtCTUxoi8UFuTTN1tet7esqd2HISmpiYqKyslLtvU1BQPHjwAAOTl5cHU1LTe9wQCgcRlSwslA3X069cPUVFRMDMzE067qWvNmjUQCATCR0fi8vX1xZIlS94ps7S0FM7OznBxcRHJ2nft2oVRo0YBAO7du4d58+bJdDQukZ/aNvb2b1K1TExMMHr0aInKfF/7AmramI2NDZKSkoRfq9u+3ncMUX7x8fHC+1ldERERyM3NxZo1a7BgwQKxylKFNubi4gIvLy/4+/ujdevWEn3WyMgIERERIn9qnwoAEP4feHh4gMPhwMzMDEFBQcjIyMDkyZMRHx8PNzc3jBs3TqrXJAlKBlDTV+Tg4IDVq1cLHw/V7SsKDg6Go6MjysvLm9VXVF1djby8POF7tX1FO3fuxPHjxwEA//77L54/fw4jIyMAQLdu3agPV8mx1b6Amilf06dPF75+u33VdwxRPtTGmq99+/YwNzfH8+fPMXv2bAA1CVXdv3k8HoYPH441a9ZIvEX5pk2bsG3bNuG4CU9PT/Tv3x+tW7dGTEwMwsPDMWvWLClekWRUesxALUXpKxIIBNi6dSuCgoKEjZEoP7ba1++//46ePXsKb/z1ta+3jyHKidpY8xkYGMDf35/tMFhDyQBk31eUmJgIoKavaOLEiSLvPXjwAL169YJAIMC9e/fw7NkzeHt7IyMjA7/88gu+/PLLplwSUSBsta/k5GSUlpbixo0baNWqFbp16/ZO+/rrr79Ejhk9ejTU1OiBobKhNiZ/MTExMDExwZgxY6RaLo/Hg76+PjZt2oRjx44hKSkJeXl5WLVqFT7++GOpnqsuSgbwv74ic3PzJvcVvU/dviItLS1hX9GIESMwefJkuLu7IzExEePGjUOPHj1w8OBBADWLeHz55Zd4/vw5vvvuO1y5cgUBAQHw9vZu+oUSVrDVvmoXMqq9aZmbm7/TvmqTzdpjWsJNWhVRGxNPXFwcUlJSwOVysXnzZhw6dAiZmZkoLS1FSEgINmzYgOLiYhQVFcHa2hovXrzA/fv3sW/fPtjZ2WHo0KHIzc3FokWLhGXev38fAQEB4HA46N69O8aMGYO1a9fC1NQUc+fORa9evcSO78iRI/joo49w584dAMCkSZMwadIkZGRk4MKFC5QMyJq4fUUAMHz4cInLf3vRirrTvWJiYur9TO1527VrpzRTc0j92GxfQM3CRm+rPW9DxxDlQW1MPPn5+ejduzcmTZoEbW1tcDgcaGlpIScnR9iF4uDgAEtLSzg7O+Po0aNYsGABioqKUF1dDU9PT5SUlGDFihUYOHAgACAsLAytWrUCl8vFtWvXMGTIELRt2xazZs0SSQQa64558uQJMjIy4OLiIkwGACAwMBBHjx7Fzp07ZVo3lAyA+oqIbFH7IrJGbUw8y5YtQ1ZWFry9veHv74+EhAQkJCRgzZo1KC0tBVCzn4K2tjb09PQAAFpaWqisrIRAIEB1dTVev34tXLETqBkn4ezsDGtra+HXTE1NsXv3bmRlZWHOnDlixXb27Fk8ffoU/v7+uHr1Km7dugVzc3N4eXlhzpw58PPzk2lCQMmAFMij7+iXX37Bnj17wOFwMH/+fImnn5GWQRZtbffu3cjIyICuri6+//57qZVLlJO025hAIICbm5tw34K3F1WTp6ioKNy+fRtAzVNXIyMjBAQEIDU1tdEnJtra2vD398fdu3excuVKpKamAqhZwtnPzw8dOnSArq4uhg0bhhMnTuD58+f4/PPPhZ9vrDtm+vTpmD59OnJzcxEREQFzc3Ps3LkTGRkZKCkpgaura/MroAEqmwwoW9/RhQsXsGnTJnC5XAQHB1MyoEQUua09ffoUhw8fhqWlJYyNjWVVBUTGFLmNqampITIyEgAwf/58mVy/uN5eV6E2rtqxWHUTgtou3NDQUACAjo6OyIZidZ8EvL2644gRI5ocY9euXYXdMi4uLk0uR1IqmwwoW9+Rvb09nJycIBAIEBUVJYcaItKiyG3t3r170NPTw7Zt2+Dl5YW7d++KLJZClIMitzEAuHHjBtatWyey9oCyeXsMREujssmAsvUdBQQE4OzZswBqBuLExcVJqyqIjClyW+vYsSPatWsHoKbf+dWrV9K6bCJHitzGAKBnz544cOAAFi1ahPz8fJHleIliUNlkQNn6juzs7ODi4gKGYaQ+NoHIliK3NTMzM+jr68PT0xOvX79G3759m3/BRO4UuY09fPgQ69evh0AggJaWFjp27Nj8C24mBwcHqf+mP3ToUHh7e8POzu692xXXJc4xQMPrDvTt2xc8Hg+DBw8WzhZpMqaFSUtLYwAwaWlpMjvHjBkzZFa2NMmjLlSVvOpWEdsatSv5oDYm3rW/feyCBQuY58+fM1VVVYyjoyOTn5/P+Pj4MDwej0lMTGQY5n/XXPt3eHg4k5yczKSnpzMLFy5keDwes3fvXoliri3r/v37jLe3N8MwDOPl5cXw+fx3jhXnGIZhmMOHDzM7d+5kli9fLvL19PR0JjQ0lGEYhklOTmbCw8PfWx/iohVGmqCl9x0RxUFtjchaS2tj06dPx+HDh/HHH39g5MiR0NDQQFVVFYyNjREbG9vgZ4OCgmBoaIj27du/s3Szr68veDye8M+pU6fqLaO+5Zubckzt2LG6T2GAmnUH3N3dmzVIsT6UDBBCCGkxRowYgXPnzuHIkSOYMmUKYmNjYW9vDz8/P5SUlIgcW7saYu24iqqqKnh4eGDNmjXYunVrk87f0HbFkhxTd+zYH3/8gVu3bgEAvLy8cOzYMWzbtq1J8b2PyicDstgaeOjQocJdCBva+rMuHo8nPGbXrl3g8XgYN24cfH196z2+dt+C2r66iooKODs702qFCozttnbz5k3MmzcPX331FQIDAxsst257TEpKwuDBg6UbOJEJttsYALi6ugo3YKtPfe1Qmm1MTU0NnTt3RkVFBfT09GBra4uoqCgEBQVBS0tL5FgTExMEBgbizz//BFAzxdDd3R3ffvstQkJCRI7duHGjyBbFY8eOrff89W1XfPr0aaSnp0t0zPTp07Fz506sWrUKo0aNEq47sHDhQnh6eko0gFMsEnUqKIG6/SXK0HfEMO/vF/Lw8GBycnLee563+4qk1XdEGqeM/ZR1TZky5b3v1dce6/YrU7uSD2VuY+KOQ6jbDpvaxhSlPTZ0zRs2bGCKi4sb/Lw4x9SHxgyIQRn6jt7XL1RZWYl///0XFhYWElwxYYsytLVahw4dwqhRo+p9733tkbBPmdqYOBpqh8qoTZs2wicob/Pz80ObNm0a/Lw4x7ytoqICx44dk8oMjRY9tXDEiBHYvXs30tLSsGXLFkRHR8Pe3h42NjYi23AC7+870tfXb/L5G9r6s9b71qNOSEiAvb19k89N5EsZ2hoAHDhwAHl5ee/d/fJ97ZGwT1namDgaa4dNkZ2dLbWymqJ2al/dR/3yULsxVe15m1oPLToZqO07evjwobDvKDIyEhYWFu/tOzp//jxsbGyEfUft27dH165dsXjxYuGxGzduFOv89W39efr0abRr1w4DBgwAUP+aAgBw+PBhkSUuN23aJNJP9/fffyMoKAgvXryAiYkJJk2a1KQ6ItKhDG0tIyMDXl5emDBhAjw9PREUFCR2eyTsU4Y2BkC45TqPx0NoaCiSk5MbbYfNYWhoCC6XCycnp2aV05JwuVwYGhpK9BkOwzCMjOJhRXp6OmxsbJCWlibSQOWpoQUtvv/+e7i7u0v0OOjVq1cIDg7GihUrGjwuJSUFOTk5Ihkq23XRUilK3Ta3rYnbHuueR1GuvaVTlHpWhjbG5/NRUFDQ6HGqwtDQUJi8iatFPxlgS23fkZ2d3Tvv+fn5SVxe69atG00EavuORo4cKXH5RHk1t62Jc0xSUhK4XG6T4iPKTxnamJmZmcQ//IioFpsMsNl/pOx9R0R8bNexPNqasbEx3N3dqV2xhO36pjamGlpcMkD9R6Ka0ndEGqfq7YzalexRG6M2Jk8tbswAIP3+o5KSEkyePBkDBgzA5s2bpVYuUDOVa8qUKRg/fnyjCxM1RVP6joh4pNnOfvnlF6xcuRIhISGwtbWVSpm19u/fj6CgIOzdu1dkB7rmoHYlH9JqYwzDwM3NDQ8fPsShQ4ego6MjhehqVFVVYdasWeBwONi7dy80NKTzOya1MTmTeIUDFeTm5sbo6uoy+fn5Mik/ODiY4XA4zKVLl2RSPlFshYWFjLGxMTNt2jSZlP/mzRumf//+TP/+/Zk3b97I5BxEscXGxjIAmFOnTsmk/IsXLzIcDocJDg6WSflE9lrkkwFpunTpEoYMGYLt27eLTMeRpqqqKgwaNAgMwyA1NVVqmTVRDjweD3FxccjJyZHZ9q6XL1/G4MGDsW3bNnzzzTcyOQdRTEVFRbCwsMCIESNw8OBBmZ1n4cKFiI2NRXZ2Njp16iSz8xDZoGSgAVVVVfjoo4+goaGBS5cuQV1dXWbnSk1Nxccff4ygoCAsXbpUZuchiuXvv/+Gra0tduzYIbNks5a7uzt+/PFHulmrGFdXV8THxyMnJwcdOnSQ2XlevHgBS0tLDB06FEeOHJHZeYiMsPpcQsFt3bqVUVNTY65cuSKX8y1atIhp3bo1k5eXJ5fzEXa9fv2a6d27N/PRRx8xVVVVMj/fixcvGBMTkwb3JSAty19//cUAYEJDQ+Vyvri4OAYAc/LkSbmcj0gPPRl4Dz6fj549e2LevHnYvn27XM5ZXFwMS0tLDBkyBAkJCXI5J2FPYGAgli9fjsuXL8PGxkYu5zx48CAcHBxw8uRJjBs3Ti7nJOx48+YNbGxsoK2tjYsXL8r0yWYthmHwxRdf4NatW7h+/TpatWol83MSKWE5GVFYkyZNYjp27NikXaSaIz4+ngHAnDhxQq7nJfKVm5vLcLlcZsmSJXI9r0AgYEaPHs106dKFKS0tleu5iXwFBAQwampqct/N7/bt24y2tvY7u7ASxUbJQD0SExMZAMzhw4flfm6BQMB88cUXjJmZGfPq1Su5n5/Ih52dHSvJJsMwzJ07dxgdHR26WbdgtcnmN998w8r5/f39GQ0NDebq1ausnJ9IjroJ3vLq1Sv07NkTvXr1ws8//wwOhyP3GO7evYtevXphyZIlUl/XgLDv2LFjsLe3x+HDhzF16lRWYtiwYQPWrFmDjIwM9OrVi5UYiGwwDIOJEyciPT0d2dnZ0NXVlXsMlZWV6Nu3LwwNDXHu3DnhLopEgbGcjCgcLy8v5oMPPmDu3bvHahzr169nNDQ0mH/++YfVOIh0lZSUMJ06dWK+/PJLRiAQsBZHRUUFY2lpyXzyySdMdXU1a3EQ6Tt69CgDgPnpp59YjePMmTMMAGbnzp2sxkHEQ08G6sjKyoKNjQ3Wr18vk9UAJfH69Wv069cPbdu2xZ9//kmZdQvx7bffIjw8HNevX8eHH37Iaixnz57F8OHDsXPnTsyfP5/VWIh0lJSUoGfPnujbty9OnDjBypPNuubMmYMTJ07g5s2bMDIyYjUW0gi2sxFFUV1dzQwePJjp2bMnU1lZyXY4DMMwTEpKCgOAiYqKYjsUIgUZGRmMuro6s3HjRrZDEZozZw7Ttm1b5unTp2yHQqTAw8OD+eCDD5h///2X7VAYhmGYJ0+eMG3btmVmz57NdiikEZQM/L+IiAgGAHPu3Dm2QxHh7OzMtG3blnny5AnboZBmqKqqYj7++GPG2tqaef36NdvhCD19+pQxMDCgm3ULkJ6ezqipqTGbNm1iOxQRO3fuZAAwZ86cYTsU0gDqJkDNZkGWlpaYPHkydu3axXY4IgoKCmBhYYFx48Zh7969bIdDmigiIgJubm74888/MXToULbDEbFr1y7Mnz8fZ86cwYgRI9gOhzRBdXU1bG1tUVZWhvT0dGhqarIdkpBAIMCwYcNQUFCArKwsaGtrsx0SqQ/b2YgicHR0ZNq1a8cUFBSwHUq9du3axQBg/vjjD7ZDIU3w6NEjRk9Pj5k3bx7bodSrurqaGTp0KGNhYcFUVFSwHQ5pgrCwMAYAc/78ebZDqdfVq1cZDQ0Nxt/fn+1QyHuofDJw+vRpBgCzZ88etkN5r9qbtbm5Od2sldBXX33FGBoaKmyyyTAMc+3aNbpZK6naZHP+/Plsh9Kg5cuXM9ra2szt27fZDoXUQ6W7CSoqKtCnTx907NgRycnJrI+8bcj169fRr18/rFy5EqtWrWI7HCKm06dPY/To0YiJicGcOXPYDqdBvr6+2LZtG65du4YePXqwHQ4R08yZM/H777/j5s2bMDAwYDuc9yotLYW1tTXMzc3x66+/KvT9ViWxnY2wafXq1YympiZz48YNtkMRi6+vL6Otrc3cunWL7VCIGMrLy5kePXown332GatrCoirtLSU6dq1K/Pf//5XKeIlDPPrr78yAJgff/yR7VDEcvLkSQYAc+DAAbZDIW9R2ScDN2/eRJ8+fbBs2TKsX7+e7XDEUlZWhl69eqF79+747bffKLNWcKtXr8bGjRvxzz//wNLSku1wxPLLL79g3LhxOHDgAFq3bo3PP/8cOjo6bIdF6lFeXo7evXvDzMwMf/zxh9LcD6ZMmYK//voLOTk50NfXZzscUovtbIQNAoGAGTlyJNOtWzemrKyM7XAk8vPPPzMAmLi4OLZDIQ3IyclhtLS0mBUrVrAdisSmTp3KGBsbMxwOh9m/fz/b4ZD3WLlyJaOlpcXk5OSwHYpE8vLymNatWzMLFy5kOxRSh0oua7d//36cOXMGYWFh+OCDD9gORyJffvklpk6dCg8PD7x48YLtcEg9GIaBm5sbOnfuDD8/P7bDkciZM2eQlZWFly9fQkNDA48ePWI7JFKPnJwcbNq0CcuXL4eFhQXb4UikU6dOWL9+PcLDw3H58mW2wyH/T+W6CYqKimBhYYGRI0ciPj6e7XCa5OHDh7C0tISjoyPCw8PZDoe8JTY2FrNnz8avv/6K0aNHsx2ORF68eIG5c+fi2LFjAABHR0fs27eP3aCICIZhMHLkSOTl5eHatWtK2Y1TVVWFQYMGgWEYpKamQkNDg+2QVJ7KPRnw8fFBZWUltm3bxnYoTdaxY0ds2LABkZGRuHjxItvhkDoKCwvx7bffwsHBQekSAQDQ19fH0aNHcfToUejo6OD58+dsh0TeEhsbi5SUFISHhytlIgAAGhoaiIyMRFZWFkJCQtgOh0CFngy4uLjA1tYWX3/9NUJDQ7Fo0SK2Q2qW6upqfPzxx6iqqsK0adNgYWHB2na4BMjOzsb69evB5XJx6NAh5OTkoEOHDmyH1SwCgQAcDkdpBqa1dNu2bYOOjg5WrVqF//73v4iLi2M7pGZzd3dHTEwMtm/fjgcPHmD16tVsh6SyVCIZKC8vB5fLRadOnWBgYIAjR47gP//5D9thNVtMTAy+/vprdOvWDYMGDWoRNwdlFRoaCg8PD1RVVcHb2xtr1qxRuvEoRLENGDAA5eXlePjwIX766Sd8/vnnbIfUbBcvXsTEiROhr6+PiooK3L9/n+2QVJZKdBM8efIEAPDgwQPcvHkTa9euZTmi5isuLgaPx4O+vj7u3btH30Qse/jwIQQCAfT09BAQEIC///6b7ZBIC5OXl4ecnBxwOBy4uLigJfwe5+7ujvLycty6dQuPHj1qEdekrFRi1MbNmzcBAGpqavjmm29axAp+enp6uHz5MhYsWIBLly7h+vXrbIek0s6dOweBQAAul4vY2FiMHDmS1Xj4fD4KCgpYjYEthoaGMDMzYzsMqWIYRvj/OXLkSGzfvr1FdN/88ssv8PLyQmxsLN68eYPi4mJae4AlKpEMWFlZoX///ggLC8PgwYPZDkdq+vTpgwsXLsDPzw///vsv2+GotHHjxsHIyAj79u1Dq1atWI2Fz+fDysoKZWVlrMbBFi6Xi+zs7BaVEHA4HAwbNgwODg5wc3NjOxypMTY2xt69e/Hll18iKCgIurq6bIekslRizAAhqiQ9PR02NjbYt28frKys2A5HrrKzs+Hk5IS0tDQMGDCA7XAIURoq8WSAEFVkZWVFPxAJIWJpcjKgyn2S9ZGkn1KV664p/blUXy3ncbeiojZG35Piaqnfk01KBlS9T7I+4vZTqnrdSdqfS/Uln/7vlJQUBAYGIiwsDL/99hsuX76Mx48fY8OGDejduzd8fHwAAJs2bXpvGRUVFWItgvPxxx+jf//+6NKlC3x9fUXeEwgEmDBhAiZMmAAejwdnZ2doampCXV0d27dvh7a2dvMutB7Uxuh7UhItcUwK0MRkoKCgAGVlZSrZJ1mf2n7KgoKCRhuIKtedJPVUi+pLsvoS19GjR/Ho0SOYm5vj8uXLsLW1xfjx42FmZob58+dj/vz5yMjIwIkTJ9C7d2/weDxERES8U05RURHi4+Nx8eJFODg4YOzYsY2eW1dXF69fv0anTp3eeS80NBTjxo0TvuZyuaiuroaBgQG0tLSad9HvQW2MvifFJcvvSbY1a8wA9Uk2HdWdZKi+pMve3h5LlizBmTNncPDgQfz5558i71dVVSE0NLTBFeFcXFxQVVUFHo8nHOEuEAiwcOFCkeO+/vprDBo0SPj69OnT4HA4cHBwgJ2dHfT09AAA169fR3V1Nfr06YOcnBwAwA8//AAOh4MdO3YgKSlJrGSjqaiNSYbqq2VRuEWHah9Hvi0iIgK5ubkSleXr64slS5a8U2ZpaSmcnZ3h4uKC/fv3NzVUhUD1JTmqs5p564WFhVBXV0d1dbXIe69fv8bChQuxZMmSBn/7cXd3h7GxMXbv3o0jR46gsrJSrHPXzo9v27YtKioqhF///fffcffuXYSGhuLw4cMoKCgQHtu+fXu8fPlS0stkBbUvyVB9KQZWk4Hs7Gw4ODhg9erVGD9+PAAI//P79OmD4OBgODo6ory8HI8fPxa5cTSGz+dDIBBgx44dqK6uRl5envC9hIQEzJgxAzt37sTx48elek2yRPUlOaqz+m3fvh0zZ86Et7f3O7/9+/j44NatWwgPD8fhw4ffW0bfvn2xefNm/PDDD9DW1saZM2egpqaGiIgIkT91nwoUFRXByckJ8+bNg76+Ptq3b4/Dhw/j+PHj+OabbxAaGgp3d3dMmzYNhoaG8PDwgKurK44dO4YJEybIrD6aitqXZKi+FBerUwujo6MRGBgIExMTYcOo1aVLFyxduhQhISHIzMx857PPnj3DypUrRb62bNkydO/eHQCQn5+Pzp07AwDMzMzw4MED4esHDx6gf//+AAB1dXVpX5bMUH1JjuqsfkuXLhX+28bGBikpKcLXQUFBEpWloaEh9g/qtm3bvrMl8rRp00ReDx8+HMOHDwcAhd9dlNqXZKi+FBerTwbqrnf09tpHtau4aWpqiv34sS5TU1M8ePAAQM2a3qampvW+JxAIJC6bLVRfkqM6E4++vj7S09PB5/PrfT8mJgbdunWTc1SKj9qXZKi+FBerTwZcXFzg5eUFc3NztG7dWqLPGhkZ1Tu6uVZtX6eHhwe0tLRgZmaGoKAgjBgxApMnT4a7uzsSExNFRi4rOqovyVGdiadfv36IioqCj49PvdMHTUxMMHr0aInK9PX1RWlpKbhc7jtllpaWYtiwYdiwYQPGjBkDANi1axfi4uLwxx9/vPcYRUPtSzJUXwqMaYK0tDQGAJOWltaUjws9f/6cWblyJbNw4ULm2LFjzSqLTZLUR3PqTtnrqynX3ty2psx11tRrF/dzN27cYGbMmMGsWrWKGTduHMMwDDNjxgyGYRimd+/ezLZt25ivvvqKKSsrY1avXs1kZ2eLHcP9+/cZb29vhmEYxsvLi+Hz+SLvr1y5ktm0aRNz6tQphmEY5t69e8zmzZuF56/vGHHIu40pc/tiGKovSUnrZ58iYvXJgIGBAfz9/dkMQalQfUmO6uz92Oq//f3339GzZ0/h4DCBQICtW7ciKCgIs2fPrvcYRUXtSzJUX4pLqfYmiImJgYmJidQfGfJ4POjr62PTpk3YtWsXUlNTkZeXhz59+mDjxo1SPRdbZFF3rq6uuHz5MjIyMqRWpqKQdn0JBAK4ubmhvLwcrVq1Qnh4uFTKbQ5Gxv23iYmJAGr6bydOnCh8Lzk5GaWlpbhx4wZatWqFbt264dmzZ/D29kZGRgZ++eUX/PXXXyLHjB49GmpqCjcTulmk3cZu3ryJgIAAlJeXY8CAAfDy8pJKuYqC7mGyJfNkIC4uDikpKeByudi8eTMOHTqEzMxMlJaWIiQkBBs2bEBxcTGKiopgbW2NFy9e4P79+9i3bx/s7OwwdOhQ5ObmYtGiRcIy79+/j4CAAHA4HHTv3h1jxozB2rVrYWpqirlz56JXr15ix3fkyBF89NFHuHPnDgBg3rx5mDdvHjw9PeHs7Czt6pCIotddZGQkHBwcZHHpTaLI9aWmpobIyEgAwPz582Vy/ZJiq/92w4YNAP53czc3N8fBgwcBAI8fP8aXX36JL7/8UuQYRUkEFLmNWVhYYNeuXQCAqVOnyuT6JaXI9QUo3j2MTTJPBvLz89G7d29MmjQJ2tra4HA40NLSQk5OjvDxo4ODAywtLeHs7IyjR49iwYIFKCoqQnV1NTw9PVFSUoIVK1Zg4MCBAICwsDC0atUKXC4X165dw5AhQ9C2bVvMmjVLpCE09ijzyZMnyMjIgIuLizAZAIDKykr8+++/sLCwkHHtNEyR604RKXp93bhxA+vWrYORkZHsK0MM7du3h7m5OZ4/fy58PB8fHy/yN4/HAwDhVD9JvD1o0NPTU+R1fcl27XkbOoZNit7GAODQoUMYNWqUbCtCTMpQX6SGzJOBZcuWISsrC97e3vD390dCQgISEhKwZs0alJaWAgD09PSgra0tXJZUS0sLlZWVEAgEqK6uxuvXr4UrkQE1j1ydnZ1hbW0t/JqpqSl2796NrKwszJkzR6zYzp49i6dPn8Lf3x9Xr17FrVu3YG5ujoSEBNjb20uxFppGketOESl6ffXs2RMHDhzAokWLkJ+fLzL1iQ3Ufys5RW9jBw4cQF5eHry9vaV0xc2j6PVF/kfmyUBUVBRu374NAGjXrh2MjIwQEBCA1NTURn/b0NbWhr+/P+7evYuVK1ciNTUVQM0yqH5+fujQoQN0dXUxbNgwnDhxAs+fP8fnn38u/HxjjzKnT5+O6dOnIzc3FxERETA3NwcAHD58WCGWrFTkugOA7777DleuXAGPx0NoaCg0NNgdgqLI9fXw4UOsX78eAoEAWlpa6NixY/MvWIGowhgLQLHbWEZGBry8vDBhwgR4enpKvHiULChyfQGKdw9jVVOmIMhrekXdaUaKTF5TCyWhiHXHxtRCcbWU+pLkc/v372dcXFyYb775hqmoqGD27t3LeHp6Mq6urszr16+Z1atXM0uXLmXmzJnDBAQEMH5+foyjoyPDMAwzYcIEZvPmzYybmxtz7do1Zs+ePcypU6eY3NxcZuHChcyiRYuYoKAg4fRFT09P5urVq02qh3nz5kn92pv7maZoKW2M6oumFsrd2/2HRHxUd5JRxfpS9P5cRRtj0Vyq2Maag+pLvhQ6GSCEyI6i9+cq2hgLQloyuc3XkcX0jaFDhwp3oHrf1pVv4/F4wmN27doFHo+HcePGwdfXt97jr127BicnJzg6OuLatWuoqKiAs7Nzo31R0qQIdSfOMa6ursLNQAAgKSkJgwcPll7QYlKG+hIIBHB1dcXs2bPh5uYGQP71FRUVJdw06O3+3MbU9ud+8803wviBmv7c77//Hl5eXli7di2Sk5Oxbds23Lt3Dz169BAeV9ufW/dP3acCDx8+xMKFC8Hj8aCurq5wYyyUoY3dvHkT8+bNw1dffYXAwEAAqv09+fb9qT5vl8NWfbFBKsmAq6srCgsLUV1dDScnJzx8+BC+vr5wc3N7Z7vI2kYRERGBlJQUZGRkYNGiRXBzc0NsbKxE5+3UqRPs7Owa3Lqyrto1BWrNmzcPERERsLCweO8UppCQEISHhyMsLAwhISHQ0dGR6nQnZag7ces3MjJSZDrmmDFj0LVrV4niakxLqa/adQf27t2LN2/eAJBNfTVkwYIF2LJlCw4cOAADAwNERkbC29sbP//8M4YPH441a9bA0tISOjo6iImJAQCEhobCxMQEOjo62LBhA+Lj42FtbQ1nZ2eMGTMGXbp0wf79+xEYGIjVq1djxIgRCAoKwo8//ohPPvlE7Ng6duyIsLAwREREYMeOHSJPH2StpbSx2nUH4uLicPHiRQCq+z0JvHt/elt95cj7e5JNUukmmD59Og4fPowPP/wQI0eOhIaGBqqqqmBsbIzY2FjY2dm997NBQUHo1q0bOBwOMjMzMWvWLOF7vr6+KCoqEr6eOHEixo4d+04ZDS19WqupawqUlJRAV1dX+G9pU4a6E+cYeWlJ9aXMfeItuT+3JbUxQPbrDihDfYlDke5zbJDKk4ERI0bg3LlzOHLkCKZMmYLY2FjY29vDz8/vnR+gtSuJ1fZJVlVVwcPDA2vWrMHWrVubdP6Gtq6sVXdNgT/++AO3bt0CgEbXFGjdujVKSkrw8uVLiVdpE4cy1J04x8hLS6qv2j7x6upq5OfnNykeaWD7EW59j7PrI69uqJbUxg4cOIDc3FyRrhxpU4b6kmc5ykoqTwbU1NTQuXNnPHz4EHp6erC1tRU+ktHS0hI51sTEBIGBgTh//jxsbGzg7e0Nd3d3tG/fHl27dsXixYuFx4q7L0B9S5+ePn0a7dq1w4ABAwCIv6bApk2bRG5a7u7ucHd3h0AgkMlCHspQd+IcA8hnzm5LqS95rTvg6uqKjRs3Qk9PD3PmzEFAQABCQkLw4sULjB07VuS3NgcHB8THxyMiIgKWlpbQ09NDdHQ0BAIBbG1tRX5ra0x9j3CXLVuGvLy8d37bEncZ3beXjh0zZoyw+0KaWkobk9e6A8pQX8C796fk5ORG61SlNGU+oqLMtWxoHuqGDRuY4uJiicorKSlh1q1b1+hxycnJTHh4uPC1Iq4z0Jjm1p249Vv3PIo8p7kxylJfb3/u999/ZyIiIphff/2V2bVrF/PkyRPGy8uLWbVqFTN16lSRc9b+HR4eziQnJzNOTk7MqlWrmNWrVzOenp4i5/Dx8WFcXV2Ff3755Zd6r+PChQtMSEgIwzAMs2PHDubChQvvjfvgwYNMWFhYg9f29v/D26+pjdH3JMMoVn0pC8XY/aOJ2rRp884AlVp+fn5o06aNROW1bt0aK1asaPCYiooKHDt2TOFGN0uquXUnzjFJSUngcrlNjlGRKGt9KcsjXHk8zlZ0ytrG2EL1JV3Neo6bnZ0trTiapHYTlfT0dLmet3ZTl9rzNqUeVKHujI2N4e7u3qx6qkX11TTK8Ai3vsfZbHRDURuTDNVXC9OUxwn3799nuFwuA4D+/P8fLpfL3L9/n+pOSvVE9dW0+mIYxXiUycYjXIZp2rVTG6PvSVl/TyqDJqXWZmZmyM7ORkFBQVM+3iIZGhqKNeBE1etO3HqqRfUlWX0pitpHuPVNK/Pz82v08+IcI61HuNTG6HtSEsr6PdkYDsMwDNtBEEKkJz09HTY2NkhLSxN5zK4KVPnaCWkO2puAkBaqRfdvvocqXjMh0kDJACEtjKGhIbhcLpycnNgOhRVcLheGhoZsh0GIUqFuAkJaID6fL5U+3djYWGzfvh2xsbGwsrKSQmT/8+zZM0yZMgWjR49udEqvJFpqny4hskTJACGkXnw+H1ZWVpg/fz62b98uk3OEhYVh0aJF+Ouvv2BrayuTcxBCGkfJACGkXpMmTUJqaiqys7MlXsBLXNXV1RgyZAjKy8uRnp4OTU1NmZyHENIwpV6BkBAiG4mJiUhMTMT27dtllggAgLq6OiIjI3Hjxg1s27ZNZuchhDSMngwQQkS8evUKPXv2RO/evXHy5ElwOByZn9PDw0OYFKjK/vGEKBJKBgghIry8vBAWFobr16/jww8/lMs5S0pKYGVlhX79+uHEiRNySUAIIf9D3QSEEKGsrCwEBwdj1apVcksEAEBXVxc7duzAzz//jGPHjsntvISQGvRkgBACABAIBLC1tUVJSQkyMjLe2chI1hiGgZ2dHTIyMpCdnQ1dXV25np8QVUZPBgghAICoqChcunQJkZGRck8EAIDD4SAkJASFhYVYvXq13M9PiCqjJwOEEDx58gQWFhaYOnUqoqOjWY0lICAAvr6+uHLlCvr3789qLISoCkoGCCFwdHTEb7/9hpycHLRr147VWN68eYMBAwbggw8+wN9//w11dXVW4yFEFVA3ASEq7vfff0dcXBwCAwNZTwQAQFNTE5GRkUhNTUVkZCTb4RCiEujJACEqrKKiAn369EHHjh2RnJysUFP6FixYgIMHD+LmzZswMTFhOxxCWjR6MkCICtu0aRNyc3MRHh6uUIkAUBObtrY2PDw82A6FkBaPkgFCVNTNmzexceNGeHt7S31HQmkwMDDA1q1bER8fj99++43tcAhp0aibgBAVxDAMPv/8c9y/fx9Xr17FBx98wHZI9WIYBqNGjQKfz1foOAlRdvRkgBAVtH//fpw5cwY//PCDQv+A5XA4CA8PR15eHjZu3Mh2OIS0WPRkgBAVU1hYCEtLS4wcORLx8fFshyOWVatWYdOmTfjnn39gaWnJdjiEtDiUDBCiYlxdXREfH4+cnBx06NCB7XDEUlFRgV69eqFz5844c+aMwg12JETZUTcBISrkwoULiIqKwvfff680iQAA6OjoIDw8HCkpKYiNjWU7HEJaHHoyQIiKePPmDWxsbKCjo6O0K/t99dVXOH36NG7evAkDAwO2wyGkxaAnA4SoiODgYFy/fh0RERFKmQgAQFBQEN68eYPly5ezHQohLQo9GSCkhXv06BFev36Nnj17YsGCBdi2bRvbITVLeHg4Fi5ciPPnz6N79+5o3749jSEgpJkoGSCkBbtx4wZ69eqFUaNGITs7G9nZ2dDV1WU7rGYRCASwtbXFq1evcP/+fcTGxmLSpElsh0WIUqNuAkJasLt374JhGPz+++/o27cvLl26xHZIzVY7CyI7Oxtv3rzBnTt32A6JEKVHyQAhLVhubi4AQENDA5cuXQKXy2U3ICn44IMPkJWVBQ6Hg8rKSty6dYvtkAhRepQMENKCXb58GQAwefJk5OTkwNbWluWImu/DDz/EtWvXhBsYpaensxwRIcqPxgwQ0oIVFRXh6tWrGDZsGNuhyERGRgb09fXx4Ycfsh0KIUqNkgFCCCFExVE3ASGEEKLiNNgOgBBlxefzUVBQwHYYrDA0NISZmZnEn6M6k7zOCJEHSgYIaQI+nw8rKyuUlZWxHQoruFwusrOzJfrhRnUmeZ0RIi+UDBDSBAUFBSgrK8O+fftgZWXFdjhylZ2dDScnJxQUFEj0g43qTPI6I0ReKBkgpBmsrKwwYMAAqZTl4+ODTZs2vfP1iIgIjBkzBl27dhW7LF9fX5SWloLL5YqUWVpaikWLFkFTUxPDhw+Ho6OjNEKXiLTqTFXqixB5oAGEhLAgOzsbDg4OWL16NcaPHw/gfwsE9enTB8HBwXB0dER5eTkeP36MiooKscvm8/kQCATYsWMHqqurkZeXJ3wvISEBM2bMwM6dO3H8+HGpXpMsUX0RIlv0ZIAQFkRHRyMwMBAmJibCH261unTpgqVLlyIkJASZmZnvfPbZs2dYuXKlyNeWLVuG7t27AwDy8/PRuXNnAICZmRkePHggfP3gwQP0798fAJRq50KqL0Jki54MEMKCust7vL3UR6tWrQAAmpqaqKyslLhsU1NTPHjwAACQl5cHU1PTet8TCAQSl80Wqi9CZIueDBDCAhcXF3h5ecHc3BytW7eW6LNGRkaIiIh47/u1A9Q8PDygpaUFMzMzBAUFYcSIEZg8eTLc3d2RmJiIcePGNesa5InqixDZohUICWmC9PR02NjYIC0trUmD4QoLCxEcHIznz59j9OjRmDhxogyilI2mXntz6kyZ6wtofnshRNboyQAhLDAwMIC/vz/bYSgNqi9CZIvGDBCiRGJiYpCUlCS18m7evIl58+bhq6++QmBgoNTKVRTSri8AcHV1FQ4qJKSloCcDhMhYXFwcUlJSwOVysXnzZhw6dAiZmZkoLS1FSEgINmzYgOLiYhQVFcHa2hovXrzA/fv3sW/fPtjZ2WHo0KHIzc3FokWLhGXev38fAQEB4HA46N69O8aMGYO1a9fC1NQUc+fORa9evcSKzcLCArt27QIATJ06VSbXLylFri8AiIyMhIODgywunRDWUDJAiIzl5+ejd+/emDRpErS1tcHhcKClpYWcnBzhVDgHBwdYWlrC2dkZR48exYIFC1BUVITq6mp4enqipKQEK1aswMCBAwEAYWFhaNWqFbhcLq5du4YhQ4agbdu2mDVrlsgPtsam1dU6dOgQRo0aJduKEJMy1BchLQ0lA4TI2LJly5CVlQVvb2/4+/sjISEBCQkJWLNmDUpLSwEAenp60NbWhp6eHgBAS0sLlZWVEAgEqK6uxuvXr8HhcIRlCgQCODs7w9raWvg1U1NT7N69G1lZWZgzZ47Y8R04cAB5eXnw9vaW0hU3j6LXFyEtESUDhMhYVFQUbt++DQBo164djIyMEBAQgNTUVAwfPrzBz2pra8Pf3x93797FypUrkZqaCgBwd3eHn58fOnToAF1dXQwbNgwnTpzA8+fP8fnnnws/39i0uoyMDHh5eWHChAnw9PREUFBQ8y+4mRS5vgDgu+++w5UrV8Dj8RAaGgoNDbqNEuVHUwsJaQJ5TRVzcHBAfHy8zMpvCjamFopLEesLoKmFRPHRbAJCFJgi/mBTZFRfhDQNJQOEEEKIiqNkgBA5kcV0tKFDhwp30/P19cWSJUvg4+NT77HirinwdjlJSUkYPHiw1GNvDNv1Je4xb687wFZ9EdIclAwQIgWurq4oLCxEdXU1nJyc8PDhQ/j6+sLNze2drW9rf8hFREQgJSUFGRkZWLRoEdzc3BAbGyvReTt16gQ7O7sGt+GtVbumQFxcHC5evFhvefWVM2bMGHTt2lWiuBqjDPUlzjFAzboDFhYWwteyqC9CZI2GwRIiBdOnT8fhw4fx4YcfYuTIkdDQ0EBVVRWMjY0RGxsLOzu79342KCgI3bp1A4fDQWZmJmbNmiV8z9fXF0VFRcLXEydOxNixY98po6FteN/W0JoCkpTTHMpQX/KqC0IUAT0ZIEQKRowYgXPnzuHIkSOYMmUKYmNjYW9vDz8/P5SUlIgcq6ZW821XO2e+qqoKHh4eWLNmDbZu3dqk8ze0DW9dBw4cQG5uLtzc3JpVTnMpQ33Jqy4IUQT0ZIAQKVBTU0Pnzp3x8OFD6OnpwdbWVvj4WEtLS+RYExMTBAYG4vz587CxsYG3tzfc3d3Rvn17dO3aFYsXLxYeu3HjRrHOX982vKdPn0a7du2EU9nqW1Pg7WPqK0cWlKG+xDkGoHUHSAvBEEIklpaWxgBg0tLSWI1jxowZ731vw4YNTHFxcYOfF+eYt8/T1GtXhDpjo74YRjGunZCGUDcBIUqsTZs27wy4q+Xn54c2bdo0+HlxjklKSgKXy21yjIqE6ouQ+tHzLEKaITs7m9Xz83g8ADUr3MmKsbEx3N3dhedo7jWzWWds1BfAfjshpDGUDBDSBIaGhuByuXBycmI7FFZwuVwYGhpK9BmqM8nrjBB5ob0JCGkiPp+PgoICtsNghaGhYZMGF1KdyWZAJiHNRckAIYQQouJoACEhhBCi4igZIIQQQlQcJQOEEEKIiqNkgBBCCFFxlAwQQgghKo6SAUIIIUTFUTJACCGEqDhKBgghhBAVR8kAIYQQouIoGSCEEEJUHCUDhBBCiIqjZIAQQghRcZQMEEIIISqOkgFCCCFExVEyQAghhKg4SgYIIYQQFUfJACGEEKLiKBkghBBCVBwlA4QQQoiKo2SAEEIIUXGUDBBCCCEqjpIBQgghRMVRMkAIIYSoOEoGCCGEEBVHyQAhhBCi4v4PMP5Jj5JOjDoAAAAASUVORK5CYII=",
|
||
"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"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"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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hZIyNPf744ygtLcU///nPFraO/IFFK5EDU6ZMwfPPP49jx47hX//6F6ZNm2Z3P0uhkpCQ4LAQSUpKAtAwyN9djmawKy0tBdBQ+B0/ftzpY1RXV1v/vWzZMqSmpuLVV1/Fzp07sXPnTgBAVFQUHn74YSxatAh6vd7tdjprqyOW2Y1jYmJa9HzusvytHAWs5e8ENPytGhetjl6fZbIucdkySRqNBlu2bMHixYuxevVqbNy4ERs3bgQApKenY9GiRS4HKhFRS1111VVNtiUnJwOA3YngLLfl5eW5VLTGxMRYZ3W/XNu2bfHNN9+411gAQ4YMQZs2bbB06VLs378fo0ePxuDBg9GjR48mGSuEwKpVq5CVlYWDBw+itLQUZrPZertlwp/GGr8nWq0WiYmJqKysbDLJ4OXvR2OhoaEYMGBAk+3XXXcdXn31Vezfv99p0WqZsf7o0aN218A9f/48zGYzfv75Z/Tt2xd33HEHXn75ZYwbNw533nknbrjhBgwePNjuxIgtVVVVhQMHDiAlJcU6ueTl6urqrG2+3Pr16/HPf/4Te/fuRXFxMUwmk/U2R38Hd0ydOtUnmbllyxasWrUKr7/+Otq2bev1xyfvYdFK5IBWq8WCBQtw9913Y8mSJbj33nvt7meZzffixYsQQtgtXC9cuACg6VliT1ied+XKlbj//vtdvp9Go8Fjjz2Gxx57DCdPnsSOHTuwZcsWrF+/HsuWLUN5eTleeeUVr7XTGcv74a+lXyIiIlBaWor8/Hy7V00tf6fL2+aJ1q1b4+WXX8ZLL72EH3/8ETt27MDHH3+M//73v5g2bRoiIiJwxx13ePw8RESOND75BsB69czZbZbipDnR0dF2t4eEhNgUkK6Kjo7GN998g4ULF+LTTz/F5s2bATQUwXPnzsXDDz9s3XfWrFl45ZVX0K5dO9x2221ITk62nnRdvHgxamtr7T6Ho9dt77U4ez/i4uLsrjBgOQFqObnsSFFREYCGGfSdqaysBNDQg+c///kPli5dijVr1liXkLv66qvx4osvYvjw4U4fxxXFxcUQQiAvL8/plU1LmwDgr3/9K/7whz8gISEBN954I9q2bWu9Gvzyyy87/DvIraqqCg888ACGDx+OBx98UO7mUDNYtBI5MWnSJDz//PM4fPiww/VFMzMzodFoUFtbi19++cVuMXTo0CEAQKdOnbzWtm7duuHjjz/GwYMHW/wYGRkZyMjIwO9+9zv8+9//xqhRo/D222/j73//uzWIfdmN9YorroBOp0NJSQmOHTvmUhdhT9rTqVMn7NmzB4cPH8bAgQOb3G75OyUlJdk9qGkpSZLQu3dv9O7dG7NmzbIuj7Ry5UoWrUREjWRkZCA7OxsmkwkHDhzAF198gb///e/4/e9/j9atW2Py5MnIz8/Hq6++ip49e+Kbb75BeHi49f7nz593qytpSxUWFsJsNjcpXC0nQB0V9BaWnPn0008xZswYl55z6NChGDp0KKqrq5GTk4NPP/0Ur732GkaPHm1dts4TljZdffXV+P7775vdv76+HkuWLEFKSgr279+PhIQE621CCLzwwgsetcdi//79+Pjjj13ePyMjo9krs/n5+cjLy0NeXp7D5Q0tV9r37dvHJepkxqKVyAmNRoOFCxfirrvuwnPPPYf09PQm+0RERGDQoEH4+uuv8X//9394+eWXbW6vrq7Gm2++CQC46aabvNa28ePH489//jNWr16N+fPnezyexdLFqbq6GsXFxdbHs5wtvbyLsbeEhYXhxhtvxGeffYbly5dj5cqVLt2npe256aabsGfPHrzyyiuYMWNGk9v//ve/W/fzJct77Y0uU0REgUqr1VpP+A0cOBBDhgzBJ598gsmTJ+OXX36BEAIjR460KVgBWIe9+FpdXR2+/fZbDBo0yO7zN1fk9O/fHwDwzTffuFy0WoSFhWHYsGEYNmwYYmJisGDBAmzdutXjojUyMhJdu3bFkSNHUFJS0uzwnYKCApSWlmLEiBE2BSsAfP/99147dvDFmNbIyEi7xwIAsGnTJpw/fx5TpkxBWFiYV8cMU8vYP61ARFYTJ05Ejx49cOrUKezatcvuPk8//TQA4LXXXsN7771n3V5eXo7f/e53uHjxIjIyMjBp0iSvtatv37648847UVhYiBtuuAH79u2zud1kMmH79u24++67rV1zDh8+jIceegh79uyxGX9ZW1uL559/HkDDeMvLv5wtk0vt2LHD5j7esnDhQoSGhuLNN9/EH//4R1RVVVlvq6urwwcffICvv/7aui0hIQGRkZHIz8/HkSNH3HqumTNnIioqCvv378cTTzwBo9EIADCbzXjhhRewadMmhIaG4qmnnvL4db377rtYsmQJTp48abO9sLDQWhz36dPH4+chIgokBw8etE4ieDnL1UvLiUvLSeTdu3fbdEM+c+YMnnnmGT+0tMH8+fNtug4fPXoUb7/9NqKjo20mwLJn7NixSEtLw9/+9jfs2LGjye11dXU2+bdz507rXBCXa/zeeGrWrFnWrrOXdwO2OHHihDXbEhMTERYWhr1799rkd3FxMR599FGvtAdoGNMqGlY9celn+/btzT5mXFwc3nzzTbs/lp5ff/3rX/Hmm2+iXbt2Xnst1DK80krUDEmSsHDhQtxxxx02EwtcbsyYMXjmmWewbNky3H333XjmmWeQlJSEI0eOoLKyEq1bt8batWu9FigWb731FoqLi/Hll1+iT58+SEtLQ3JyMqqqqnD8+HHrGc633noLAGA0GvHGG2/gjTfeQExMDDp06AAhBH755ReUlpZCp9PhH//4h81zjB8/HvPmzcP777+Pb775BmlpadBoNF6bFKFv3754++23MX36dCxduhQrVqxAly5dUF1djRMnTqCmpgarVq3C4MGDATT8PSZOnIi3334bffr0Qffu3a0TJDUXUikpKfjXv/6FiRMn4uWXX0Z2djYyMzNx6tQp5OfnQ6PR4JVXXkHPnj09fl0XL17EggULsGDBAqSmpiIlJQXV1dX4+eefYTQakZqaiiVLlnj8PEREgWTr1q146qmncO2116JLly6Ii4vDL7/8gk8++QRhYWF45JFHADR027z99tuxbt069O3bFyNGjMCFCxfw2Wef4frrr8cvv/zi87YmJyejpKQEvXv3xujRo1FaWoo1a9agpqYGK1eubHZuBL1ej48++gg333wzhg4dihEjRqB79+4AgNOnT2Pnzp2Ii4uzTnr017/+FV9++SWGDx+ODh06wGAwYO/evdi2bRsyMzMxfvx4r7yuhx56CN9++y2ys7Oxa9cujBw5EikpKbhw4QKOHj2KnJwcvPfee8jIyIBGo8HDDz+Mv/71r+jVqxduvfVWlJWVYcuWLUhPT0dKSopX2kTEopXIBRMmTEDv3r2xf/9+h/ssXboU1157Lf7+97/j+++/x4ULF5CcnIx7770Xf/zjH31yli4iIgKff/453n//fbzzzjv44YcfsHfvXsTHx6Nnz54YNmwYbr/9dutSNldccQVWrlyJL774Avv377cuAZOWlobJkyfjD3/4Q5OuRR07dsSnn36KP//5z9i3bx9Onz4NIQSGDRvmtddxzz33oE+fPli+fDm2bduGgwcPIioqCldeeSVuvfVWjBo1ymb/FStWIDIyEhs3bsSPP/7o8oQhAHDbbbfhhx9+wLJly/Cf//wH+/fvR0xMDMaPH4/Zs2fbHevaErfffjuMRiO2bt2KY8eO4cCBA2jVqhW6d++OCRMm4Pe//73fZk0mIlKLm266yTpJ4Pr161FRUYHU1FRMmjQJc+bMsVlaLSsrCxkZGVi3bh3+7//+D2lpaXjyySfx9NNP2yzB4ys6nQ5ffvklnn76aWRnZ6O0tBQ9evTA/Pnzcdttt7n0GP369cOPP/6IF198EZs3b8bXX38NvV6P1NRUjBs3DpMnT7buO3PmTERHRyMnJ8fa+yktLQ3PPvssHn/8ca9N9ihJErKysnDLLbdg5cqV+Oyzz1BRUYHExERcccUVWL58OUaOHGndf+nSpYiNjUVWVhZee+01JCUlYdKkSVi8eLG1CCfylCR80d+PiIiIiChAWZYDajwEhIh8g2NaiYiIiIiISLFUWbSWl5djzpw5uPHGG5GQkABJkuwuymxPVlYWJEmy+3P+/HnfNpyIiEhmzFAiIlIbVY5pLSwsxBtvvIFevXph3Lhx1uVE3LFq1Sp06dLFZhunsyYiokDHDCV/2759u0uzufbu3Rvjxo3zeXsCWVZWlktdlseNG8d1R0lVVFm0pqeno7i4GJIkoaCgoEWB2717d/Tt29cHrSMiIlIuZij52/bt211aY/O+++5TTdGq1LGsWVlZ+Oqrr5rdLyMjg0UrqYoqi1ZJkuRuAhERkSoxQ8nfFi1a5HIXdPKMK1e0idRIlWNavWHMmDHQarWIjY3FhAkTcPDgQbmbREREpArMUCIi8idVXmn1RJs2bTBv3jwMGDAAUVFROHDgAJYtW4YBAwZg165d6NWrl9371dbWora21vq72WxGUVER4uLieNaaiCiICSFQXl6OlJQUaDSBfS6YGUpERN7kcoYKlbt48aIAIBYuXNjixzhx4oSIiIgQt912m8N9Fi5cKADwhz/84Q9/+GP359dff21xDsmFGcof/vCHP/xRwk9zGRp0V1rtycjIwODBg/Htt9863Gfu3Ll48sknrb+XlpYiLS0Np07tRVRUhD+aSTLbsWMrvvlmO/73vzaoji6BJq4Y2hAN6o2A+dcUJEfUITW1Grff/jukp7eXu7mKceJELjZsWI0zZ8JwvjIEmnZnEd5Kj6l3TEVGuwxUVFTgpayXUF5aCfOFREQZ9ejQoRAjR45Bnz795W6+T73zzus4fToPx461hWh/EprwOvTq2hOTx06Wu2nkhoqyCvRP74/IyEi5myILZigRyYEZGhhczVAWrb8RQji9JK3X66HX65tsj4qKQFRUcB6oBJtWrcJgMIQiNFSPep0OGn0otKEaSBJgDtVDp5NgMJgQGdmKn4nLREa2gsGgg06nQ2hdKDT6UIQaQtEqshUioyIBDaAz6BBaY4RZp4MOehgMOkREhAf8+xgWpoder0NoqB5CHwqNHjCEGxreF1KdYO7mygwlIn9jhgaW5jI0sAffuOjEiRPYtWsXBgwYIHdTiIiIVIUZSkREvqbaK61btmxBZWUlysvLAQCHDx/GRx99BAC45ZZbEB4ejhkzZiA7Oxu5ublIT08HAIwcORJDhgxBz549rZNIvPDCC5AkCUuWLJHt9RAREfkLM5SIiNREtUXrzJkzcerUKevvH374IT788EMADWd9MzIyYDKZYDKZIISw7tejRw988MEHWL58Oaqrq5GYmIjrr78e8+fPR6dOnfz+OoiIiPyNGUpERGqi2qL15MmTze6TlZWFrKwsm20vvfSSbxpERESkEsxQIiJSE45pJSIiIiIiIsVi0UpERERERESKxaKViIiIiIiIFItFKxERERERESkWi1YiIiIiIiJSLBatREREREREpFgsWomIiIiIiEixWLQSERERERGRYrFoJSIiIiIiIsVi0UpERERERESKxaKViIiIiIiIFItFKxERERERESkWi1YiIiIiIiJSLBatREREREREpFghcjeAApcQJpSW5sBovACdLgnR0f0hSVq5m0VERKR4zFAioktYtJJPFBRswvHj82E0nrNu0+mSkZm5BPHxo2VsGRERkbIxQ4mIbLF7MHldQcEmHD78gE3YAoDReB6HDz+AgoJNMrWMiIhI2ZihRERNsWglrxLChOPH5wMQ9m4FAOTmLoAQJr+2i4iISOmYoURE9rFoJa9qGH9zzskeArW1Z1FamuO3NhEREakBM5SIyD4WreRVRuMFr+5HREQULJihRET2sWglr9Lpkry6HxERUbBghhIR2ceilbwqOro/dLpkAJKDPSTo9SmIju7vz2YREREpHjOUiMg+Fq3kVZKkRWbmEstvjW8FAHTs+CeuNechIUwoKdmN/PwNKCnZzUk5iIgCADPUP5ihROrDdVrJ6+LjR6Nbt5VN1pjT65PRseOfuMach7h+HxFR4GKG+hYzlEidWLSST8THj0Zc3KjfZkK8AJ0uCdHR/Xl22EOW9fsaL4dgWb+vW7eVDF0iIpVjhvoGM5RIvVi0ks9IkhYxMYPkbkbAaH79Pgm5uQsQFzeKBzZERCrHDPUuZiiRunFMKwW8QBm7wvX7iIjI35ihRKQEvNJKAS2Qxq5w/T4iIvInZigRKQWvtFLAsoxdaXxm1TJ2paBgk0wtaxm1rd9nOTtfVbUVUVHnIElmuZtEREQuYobKK1CucBN5C6+0UkAKxLErlvX7jMbzsP+6JOj1yYpYv6/x2fnu3YEOHVph2+5h+EUYZG4dERE5wwyVVyBd4SbyFl5ppYAUiGNX1LJ+n6Oz82FhlRgzYhM6JubJ1DIiInIFM1Q+gXaFm8hbWLRSQGrJ2BU1dMWxrN+n07Wx2a7XJytiqn5nZ+el344Rhnb6ERLYVZiISKmYofJo/go3kJu7QJHvLZGvsXswBSR3x66oqSuOktfva+7svCQBkWHVaBN10Y+tIiIidzBD5eHOFW4uh0TBhkUrBSR3xq6ocbFxpa7f5+rZ+fDQah+3hIiIWooZKg/OcEzkGLsHU0BydewKAHbF8SJXz85X1YX5uCVERNRSzFB5qG2GYyJ/YtFKAcuVsSuBONmEnCxn55se5DQQAiivDsP5sgT/NoyIiNzCDPW/5jK04Qp3iiJmOCbyN3YPpoDW3NgV97ri8Opgcyxn5xu6ikm4/Oy7+O2fX/3cC4Lny4iIFM+7GUrNcZahSprhmEgOLFop4Dkbu+JeV5wyL7YqcFnOzjeelKOqKgL/+WYofhEGhEfI2EAiInKZ9zKUXOEoQ/X6ZHTs+CfFjQ8m8hcWrRTU3Fts/Es/t069Lj87f+bMj9ix4zscOpSBsxV6aNLOyN08IiLyAvcylFyl5BmOieTCPnoU1NSy2LgaWc7Oh4ePRFlZMoTg1w0RUSBhhvqOJUMTE8cjJmYQ30MKejyKpKCn9MXGiYiIlIoZSkT+wO7BRGBXHCIiopZihhKRr7FoJfqNUhcbJyIiUjpmKBH5ErsHExERERERkWKxaCUiIiIiIiLFYtFKREREREREisWilYiIiIiIiBSLEzGRbIQwcaZBIiKiFmCGElEwYdFKsigo2ITjx+fDaDxn3abTJSMzc0lQr+nGgxAiImoOM9Q+ZihR4FJl9+Dy8nLMmTMHN954IxISEiBJEhYtWuTy/fPz8zF16lTEx8cjPDwcAwcOxLZt23zXYLJRULAJhw8/YBO2AGA0nsfhww+goGCTTC2TV0HBJuTk9MNPP92Oo0cfxk8/3Y6cnH5B+34QkW8wQ9WNGWofM5QosKmyaC0sLMQbb7yB2tpajBs3zq371tbWYsSIEdi2bRtWrFiBjRs3IikpCaNGjcJXX33lmwaTlRAmHD8+H4CwdysAIDd3AYQw+bVdcuNBCBH5CzNUvZih9jFDiQKfKrsHp6eno7i4GJIkoaCgAG+++abL933rrbdw8OBB7N69GwMHDgQADB8+HL169cKcOXOQk5Pjq2YT8Fu3nXNO9hCorT2L0tKcoFmkvPmDEAm5uQsQFzeK3ZyIyGPMUPVihjbFDCUKDqq80ipJEiRJatF9N2zYgM6dO1vDFgBCQkJwzz334LvvvkNeXp63mkl2GI0XvLpfIHDnIMQZIUwoKdmN/PwNKCnZHXRn2onINcxQ9WKGNsUMJQoOqrzS6omDBw/iuuuua7K9Z8+eAIBDhw4hNTW1ye21tbWora21/l5WVua7RgYwnS7Jq/sFAm8chHBSDiLyB2aovJihTTFDiYKDKq+0eqKwsBCxsbFNtlu2FRYW2r3f0qVLER0dbf1p166dT9sZqKKj+0OnSwbg6Cy/BL0+BdHR/f3ZLFl5ehDSkrE8PKNMRC3BDJUXM7QpZihRcAi6ohWA025Rjm6bO3cuSktLrT+//vqrr5oX0CRJi8zMJZbfGt8KAOjY8U9BNe7Ek4OQlkzKwRkWicgTzFD5MEObYoYSBYegK1rj4uLsngkuKioCALtnkAFAr9cjKirK5ifQ+epMYnz8aHTrthI6XRub7Xp9Mrp1Wxl0XXE8OQhxdywPZ1gkIk8wQ13HDPUPZihRcAi6Ma09evTAgQMHmmy3bOvevbu/m6RIvh7fER8/GnFxo7gI+G8sByGN33O9PhkdO/7J4XvuzlgezrBIRJ5ihrqGGepfzFCiwBd0Rev48ePx8MMPIycnB/37N3QVqa+vx+rVq9G/f3+kpKTI3EL5Wc4kNv5itpxJ9NaZXEnSBs2U/K5oyUGIO2N5uFQCEXmKGdo8Zqg8mKFEgU21ReuWLVtQWVmJ8vJyAMDhw4fx0UcfAQBuueUWhIeHY8aMGcjOzkZubi7S09MBANOnT8err76KiRMnYtmyZUhMTMRrr72GY8eOYevWrbK9HqUItDOJQphUdSba3YMQy1geo/E87P/NJOj1yYiO7o+LFz9x6TGDaakEomDFDPUNZqi8mKFEgUu1RevMmTNx6tQp6+8ffvghPvzwQwDAiRMnkJGRAZPJBJPJBCEufRHp9Xps27YNc+bMwaOPPoqqqir07t0bW7ZswdChQ/3+OvzF1eAJpDOJ3u6edeFCGMrKIhEeboS5PgwXz7WHJkQDUx1gLkpCJIoBVHvxFTTPMpan4ay+BNvQtR3Lw6USiMiCGeoeZmgDTzL01Cng5MnDqKsrRGhoHCIiukOSLk2tEh9vRlqa2SttdxUzlEg9VFu0njx5stl9srKykJWV1WR7UlISsrOzvd8ohXIneAJl4XJvd8/av387pk0bB6PxLof7aLV1ePLJuS1tcou5OpbHnTPKRBTYmKGuY4Ze4kmGDhw4Dkbj9Q73MRgEjhy56PfClRlKpA6qLVrJNe4GTyCcSfR296yCgk34/vvXYDROcrqfyRSKysqIFrXZU66M5XHnjDIRETFD7dwKX2VoTY2EggKN34tWgBlKpAZBt+RNMGnJ+mOBsHC5u1PYO+P8PWwqIqJAtkXGLWN5EhPHIyZmkN3g5FIJRESuYYY64rsMLS//iRlKRHbxSmsAa8nYmkA4k+jN7lmX3sM2ze4LAB077sbZs2sRGblUseHFpRKIiJrHDPV8P3cz9H//+wP0+vNeWxrIF5ihRPLgldYA1tLgUfuZRG92z2rJuCOT6SIOH75f0YuMu3JGmYgomDFDPd+vJRlqNJ5jhhJRE7zSGsA8CZ6WnElUytT43pwswZNxRz//PNtnyxoo5b0mIgpUzFBmKBEpB4vWAOZp8Liz3pm3p8b3hDe7ZzU/Psmx+vpilJTsRuvW17l9X2eU9F4TEQUqZigzlIiUg92DA5gleH77rfGtALwztsYyu2LjsT+W2RXl6OLjre5Zl95D1yaRaKykZHeL7ueIEt9rIqJAxAxlhhKRcvBKa4Bzdf2xlvL21Pje5M3JEuLi6qDTVcNoDHO4j05XjejoAk+a7JSS32siokDEDGWGEpEysGgNAr6c6a4lsyv6kzvds+yxnJWNixN4553OKC2NBwAIAUiNTrxHRxcgKelXm23efM1Kf6+JiAIRM9T7GWoPM5SInGHRGiQ8DR5HvDk1vtI0PiublPSrTaCK307WNi5eLUJCWnv1PQ/k95qISMmYoe5rLkObwwwlostxTCt5xJtT4ytNc2dlJanhRzgYqtOp04te7WIUyO81EVEwCuTv9eavbDrHDCWiy7FoJY80PzOgBL0+xaWp8ZXG1bOtNXW2HRY0mgR06/am12chDOT32hEhTCgp2Y38/A0oKdkNIUxyN4mIyGsC+Xvd1QzVaKJtftfpkpmhXsIMpUDC7sHkEedT4wOAQJs2U2RomedcPdu6+adBMF9IQNvYMkRGanHzzXMRH9/J6+3x5jIEalBf/y1ych7hsgREFLCYocCVV66EJGl9vmZqsGUol/ahQMMrreQxR1PjW5w6tRw5Of1UN5V8c2dlhQDKa8KQV5yAM+fa4fTpK1BWluzTwPPWMgRKFxd3Gkbji1yWgIgCXrBmqOXKZkzMIMTEDEJi4njExAxihnoBl/ahQMQrreQVltkVT59egVOnXmxyu+WLUk2h4OysrGUc69e5vSFasGi6J3w5k6U7hDD5pA2SZEZm5h5HzwouS0BEgSbYMlTOK5uBnqFc2ocCFYtW8qpz51Y7uEWdX5SO1uirqGqFHbndcbIkVZZ2+WomS1e50+1ICBOios4hLc0EbXEUzjWzyHxSUh70+ione3BZAiIKTMGSod5a57al1Jah7hS3XNqHAhWLVvIaNXxRVlSUo6qq0s17XY327T/Fjz+uxi+/7MHx421xoqYVpLgSaEOb7l1aWoz8/PNeaa+SREVFw2AIs3Y7anwW196VgIKCTTh/fi66d79o3a+8Jgzfnurr8HnCw137+3BZAiIKJIGeoVVV+2AyXYRWm4Dw8KtgNmsDMisdaWmGujsulUv7UKBi0Upeo+QvSrPZjJycHdi5cxtMpvoWPopAWVkmTp5JhGiXd6lTsGSGFFmOsvJo1NSUYfPmdV5qtbLodHrcfPM4lJW51u2osPBzu8Ecoa/GyE47ISp3AOjQ5FGqqlq52B4uS0BEgSPwM9TiZwC7vNEsVfFWhjbXVZxL+1CgYtFKXuONL0pfjPEwGmvxySdrsW/fIeTlxaKuruWPV4N6iIxTkHT10Gg1iGoVheL6EojYYlTqanHoaDJ0WufdX9VKrzciJORlXHVV81cCSkp2OxxTY13btugVCHFvk9svXEhFbW24ky7CEvT65IBaloCIKBgyNJh5K0Ob6ypumQDLaDzv4P7MUFInFq3kNZ5+UfpievaiokKsXZuF48eLcOJcLETSRUDrwTplOiMkrUCoLgQ3DrkB1159LVZvWI2jx4/BHFkJk+EkqusD8b+VQLVRj/xC1w5WSkp2O+3mJkkATPmoKf0OCOlu+0xCg+PH++HKK7+CkibvICLypaDI0KDl3Qx11lVcqRNgEXkqEI+uSSaefFG6M8bDVXV1Rrz//ps4fboYJ061geh4ApKuvqFgavGEvxLCw8Nxz/i7ceUVVwIAHpj8ADZv34zt33yFek09oA/AQBeACKtFuaHWqw9bb8y3+y1UWJgGnW42gNWKmryDiMhXgiNDg5SPMtRRV3GlToBF5AkWreRVLfmi9NX07GVlpaiqqkRNjQ5CVw9Ja0ZIqBYJcfFIS0lz/8UBCDOE4bprrkNCbIJ1m1arxa0jbkVmeib2H94Ps9ncosdWspNnTuJiYQHOVrRGeXkkIiLKGw5cmmi4EhATMwi//vpys48bokuEo9FRISEDcPXVj8m+LAERkb8EeoYGK19lqLOu4kpZ2ofIW1i0kte5+0XpnxkTJUCSoNFocON1N+LqHle38HEc65rZFV0zu3r9cZXgi51fYMt/P4cZGny18waMvnk9hECj0L10JSAmZpDTbm5CAFJIIgzR16Ci0vHyNnIvS0BE5G/BmqGBzNsZ6uq4VGYoBRKN3A2gwGT5okxMHI+YmEFOz+wpecZEair3l8744YfhqKuzneVXr0+2dkGzdHOzR1jyN/YRnvElIrKDGRq43M/QxpdkOS6VghOvtJLsOD27+pw/nw6NpjN+97vrUV9fYPdKgKWb27Fjc2EyXVqntaImDN+e7osb2w+Ro+lERAGFGao+7mQox6USNWDRSrLj9OzKlndai1M/x6H4XHuYazVAcQouhOlgNhvwyy9DkZgIJCbaH8cbHz8apaUd8e9//wVlZSbkFUfhnE4gLMLg51dBRBSYmKHK5mmGclwqUQMWrSQ7Ts+uXHmntRjWNRm1NeMAjGty+0svAQaDwJEjF5GWZj90JUmLsrJknD4dhnOVodCknfFpm4mIggkzVLm8laEcl0rEMa2kEJZuMDpdG5vtl4/xIP8rKtCgtsb52gY1NRIKCvhVQkQkF2aoMjFDibyHV1pJMdgNhoiIqGWYoUQUyFi0BgkhTKoIMnaDISIipWGGEhHJi0VrECgo2NRk9jmdLhmZmUvYZYiIiMgJZigRkfxYtAa4goJNv03OYDujoNF4HocPP8CxLgqTd1qLIidjW2LjzUhNM/mxRUREwYsZqi7MUKLAxaI1gAlhwvHj82F/CnwBQEJu7gLExY1SZDenYHNplkHHkzboDQLbj5xj6BIR+RgzVF2YoUSBjdOVBbCG8TfnnOwhUFt7FqWlOX5rEznmyiyDtTWS07PIRETkHcxQdWGGEgU2/s8NYEbjBa/uR8EnNt4MvcHeVYZLDAaB+Hj768sREakVM5Q8xQwl8h52Dw5gOl2SV/ej4JOaZsL2I+ew+cvvsOv73TDXaoBf26JtSgESEgyYNGk6EhPhcFF0IiK1YoaSp5ihRN7DojWARUf3h06XDKPxPOyPyZGg1ycjOrq/v5tGKpKaZkJ6p0IczjsBU40GqNAgKekcUlLCcdVVddBqfT+WSy3LTRBR4GCGkjcwQ4m8g0VrAJMkLTIzl/w286EE29BtGPfRseOf+MVFisblJohIDsxQCgTMUAoUHNMa4OLjR6Nbt5XQ6drYbNfrkzlVPymeZbmJxpOhWJabKCjYJFPLiCgYMENJzZihFEh4pTUIxMePRlzcKHYNIVXhchNEpATMUFIjZigFGhatQUKStIiJGSR3M8gJyyyDza0xFxskswyazUdcXm6Cn23P5Z3WOl0KIjbezLUNKWgxQ5WPGWrLnSWb+Nn2HDPU91i0EimEZZZBfuk1EKLYpf243ITn8k5rMaxrcrMHe9uPnAuazx8RqQsz1BaXbPIfZqh/sGglUpDUNBO/0H4jSa1d2o/LTXiuqEDjNGwBoLZGQlGBhp9PIlIsZuglXLLJf5ih/sGJmIhIkTSartDpkmGZpbMpCXp9CpebICIiasSyZBMzlAIFi1YiUiTLchO//db4VgBcboKIiMgeZigFGhatRKRY/lhuQggTSkp2Iz9/A0pKdkMIdt0hIiL1Y4ZSIOGYViJSNF8uN+HPRdeFMDV5DURERL7EDKVAwaKViBTPF8tNWBZdb7yGnWXRdW+dhbY8l71gb9VqIIBWXnkOIiIie5ihFAjYPZiIgk7zi64DubkLvNLNyRLsjdfLMxrPIzl5PRITT3v8HERERP7CDCU5qLJoraiowOOPP46UlBQYDAb07t0b77//frP3y8rKgiRJdn/Onz/vh5YTkRK4s+i6J1wJ9k6d9kCS5F3sPjbeDL3BXhsv0RsEYuPlbSd5BzOUiDzBDLXFDPUPVXYPnjBhAvbs2YNly5ahU6dOeO+99zB58mSYzWZMmTKl2fuvWrUKXbp0sdkWFxfnq+Z6xF4ffs70RuQZfy263lywSxIQFlaFlJRfccajZ/JMapoJ24+cQ1GB4/OYsfFmri8XIJihzFAiTzBDbTFD/UN1RevmzZvx5ZdfWkMWAIYPH45Tp05h9uzZuOuuu6DVOg+k7t27o2/fvv5orkf8OcCdKJj4a9F1VwO7VasKwBTm0XN5KjXNZBOoeae1NgFcVKCx+d3dAG78eI0x0P2DGcoMJfIUM7QpZqjvqa5o3bBhAyIiIjBx4kSb7dOmTcOUKVOQk5ODQYO8O9hcDv4c4E4UbCyLrhuN52G/25EEvT7Z49kJXQ3sysoIwKCcsMk7rcWwrsmorXG0KH1DV6ftR865FJLefjxqOWYoM5TIU8xQ55ihvqG6Ma0HDx5E165dERJiW2/37NnTentzxowZA61Wi9jYWEyYMMGl+9TW1qKsrMzmx1f8OcCdKBj5a9F1S7A3fY4GQgDV1eE4e7adR8/jbUUFGqfhCAC1NZLTs76+fDxfyTutxYG9oQ5/8k6rv1spM5QZSuQpZqhzzFDfZKjqrrQWFhaiQ4cOTbbHxsZab3ekTZs2mDdvHgYMGICoqCgcOHAAy5Ytw4ABA7Br1y706tXL4X2XLl2KxYsXe/4CXODOAHdvT2FOFCwsi6437j6o1yejY8c/eeUqjCXYG674SLA9iG74/eef+0EI1Z0/DDjBciabGQowQ4k8xwyly/kjQ1VXtAKAJDl+Q5zdNmrUKIwaNcr6+5AhQzB69Gj06NEDCxYswMaNGx3ed+7cuXjyySetv5eVlaFdO9+c2fHXAHeilpAkM+LizqF1azNKS3ejdetBqp3YxJeLrl/+HI6C/cSJAcjP5xpzrvD1eB53zmSruWgFmKHu7kfkTcxQ95+DGeq5QMhQ1RWtcXFxds8EFxUVAbh0tthVGRkZGDx4ML799lun++n1euj1erceu6X8NcCdyF0dk85g6LVbEBlZDgA4ePBL1U9s4otF1xtzFOwHD74KyDrnoToEy1VQf2CGur8fkbcwQ1uGGeqZQMlQ1RWtPXr0wJo1a1BfX28zJufAgQMAGmY1dJcQAhqNcroW+GuAO5E7OsTn4eYrv2my3dWJTcrLW6OkOAYaXShqwnT4+WAEKgtCUVVlQOGZdNSZLsDgyxcgM38Ee6AKpqugvsYMBZihJAdPM/T0aQ0KnFwpi483Iy0tcNcBZYa2XKBkqOqK1vHjx2PlypVYt24d7rrrLuv27OxspKSkoH9/90LoxIkT2LVrF0aOHOntprZY8334vTPAnchlwozrMvcDaFgXrdGNACTk5i5AXNwou5/LkpJYfPDBQphModZtn796+R5/gkZrxPV3LEa0rtrLjSciC2YoM5Rk4GGGnj6tQdeuCahxUngYDAJHjlwM6MKVgpvqitabb74ZN9xwA2bOnImysjJkZmZizZo1+Pzzz7F69Wrr+nIzZsxAdnY2cnNzkZ6eDgAYOXIkhgwZgp49e1onkXjhhRcgSRKWLFni7Gn9zh8D3IlcZcDPiDQ4KyadT2xSWRlhU7DaYzbpYKyJAFi0EvkMM5QZSv7naYYWFGicFqwAUFMjoaBAw6KVApbqilYAWL9+PebNm4cFCxagqKgIXbp0wZo1azBp0iTrPiaTCSaTCUJcOsPao0cPfPDBB1i+fDmqq6uRmJiI66+/HvPnz0enTp3keClO+WOAO5ErQlDq0n5G4wUIYbL5zArh3hg5kl9svBl6g2h2/EtsvGsHR95+PPIMM5QZSv7lSYY2dGNX5eF60GKG+oYq/xdERERgxYoVWLFihcN9srKykJWVZbPtpZde8nHLvI99+EkJ6hHt0n7V1SeQk9PP5sqGVpuA6Ojxvmoa+UBqmgnbj5zz2kyD3n488gwzlMi/PMlQnS4ZVVWvARjnm8aR1zFDfUOVRSsR+VcNOqG8JgwR+mo743EAQEJISAxOnVqOxhOfmEwXkZ6+xx/NJC9KTTN5NQC9/XjexjPZROQrnmSo0Xgev/yyBCxa1YUZ2pSnGcqilYiaJ2mw83hv3HzlNxCi8UQSl090Ym+mTqIGvl4nzhM8k01EPuNRhjJXqUGwZ2iLitZdu3Zh8ODBAIC1a9di4sSJTfbJycnBiBEjUFlZidmzZ+OFF15ocSOJSBlqjDqE6Y0220JCYpCaOuO3M8T22T+zTMHEk3Xi/HUV1F9nspmhRMGppRnKwpWYoS0sWq+99lrcdttt+OSTT7BgwQJMmDDBOuMgABw7dgxjxoxBZWUl7rvvPvzlL3/xWoPVyN6gekcTQbizL/mXks9w+Vor8YPd9eUAoL6+GPX1rk0yQcHLk3XiAu0qKDPUPczQwMAMZYZSyzFDPegevGzZMmzatAlHjx7F6tWrcd999wEAzp49i5tuugkFBQUYM2YM3nzzTUhBfJmloGBTkyn3dbpkZGYuaTLlvjv7kn95coZLqVw9gBDChHi8D8DRFVMJ+fnrnT5XdHQBdLpqGI1hDvfRaI3QGSpcaToFIaWP53EXM9Q1zNDAwAz1fYYaDALxHHNPDgRChra4aO3atSumTp2Kt956C4sXL8aUKVNQWVmJUaNG4dSpUxg8eDDWrl2LkJDgHTZbULDpt8XNmw6qP3z4AXTrttIapO7sS/7nyRkuJXLnACI26huEoLhh2I1dAnV1hQgNjUNdXRHsdWNKTPwVr7/eB9kfTYPU5iIMYTpMGDUBqW1SUVVVhaz1WagzXYChWgsYDV55jURKxgxtHjM0cDBDPcvQpKQzeP/9IWjbdhMkyX6hHB9v5hqtFNAcnyJyweLFixEWFoYTJ07g1VdfxdixY3HgwAH06NEDn376KcLCHJ8RCnRCmHD8+Hw4G1Sfm7sAQpjc2tfbbSwp2Y38/A0oKdnt9ccn5XLnAKLemO/SYyYmTvjtX/YfNy8vHdGxZxHT5gRiU0+iU/cK9OhTh269axDX9hTCowvceQlEqscMdYwZSkrm3wxt+P3aa/8frr7ajD596u3+sGClQOdR0ZqamopZs2YBAJ544gns2LEDGRkZ+PzzzxETE9Nk/7179+LJJ59Er169EBUVhYiICAwYMADvvvuuJ81QpIYxNeec7CFQW3sWpaU5bu3rLQUFm5CT0w8//XQ7jh59GD/9dDtycvqhoGCT156DAkOILtGl/eLiRqFbt5XQ6drYbNdqE3Hs2HCcOdPRF80jUi1mqGPMUAoUnmaoXp/MngJE8MKSN4899hhefPFFmM1mxMbG4osvvkBKSordfV944QVs27YNt99+O37/+9+joqICq1atwj333IPjx49j4cKFnjZHMYzGC17dz919nWE3KnKHIfoa1KM1tKLY4XgcvT7ZOuFJXNwom4lQCgtjsXPnO/5uNpEqMEPtY4ZSoPA0QzmZGFEDj4rW+vp6PPjggzCbG7okVFVVOe3ONGvWLGRlZcFguDRmbebMmejduzeef/55zJo1C61bt/akSYqh0yV5dT9393Wk+W5UEnJzFyAubhS/JAkAIElaFGASkvAPB+vLAR07/sn6eZEkLWJiBln3KCr6nx9bS6QezFDHmKEUKDzNUCJq0OLuwUII3H///fjss8+QkJCA9u3bo6amxumZ3kGDBtmELQCEhYVhzJgxqKurw7Fjx1raHMWJju4PnS4ZjkfeS9DrUxAd3d+tfT0lRzcqUo6801oc2BuK40fdO19VKV2NLYcGoqLG9oBap2O3JXKNZZ04Z7yxTpxaMEOdY4aSEjFDSS7MUA+utM6ZMwfZ2dmIiIjApk2bcPz4cUyZMgXZ2dl46qmn0K1bN5cf6+zZswCAhISEljZHcSRJi8zMJb91IZJge1a26Zk1d/b1hC+6XJE6uDLboTO/FKTi+JlUpFTr0CH9DCIiWmPq1L8jJETn8mNIkhmprS8iNqoeonofhEhvUVtIfQJlnThvYYY6xwwlpVFChnId4uDFDG1h0bp8+XIsX74coaGhWLduHfr164e+ffti2bJl+OmnnzB37lxs3LjRpcc6fPgw1q9fjwEDBqBjx8CaqCU+fjS6dVvZZN04vT4ZHTv+yebMmjv7esIXXa6CgeUMV3PT2yv5DJcrsx02R0CDvLx0GEJ1SEkJdyss27bNxejeuxAZ8dtarBd241TxC2iV+rRHbQpkrq4DqBaBsE6cNzBDXcMMDRzM0AaeZCjXIXYfMzSwuF20vvPOO5gzZw4kSUJWVhZuvPFGAIAkSViyZAnGjh2LTz75BLt27cK1117r9LHKysowceJEaDQa/POf/2zZK1C4+PjRLg+qd2fflrJ0ozIaz8P+mJxLEwLQJcF4hsubBxCxsSfRufN/m2w3Gc+j7MQTSI8ZggMlcV55rkDhzjqAgfS5C3TMUPcwQwMDM9QznPzLfczQwONW0bp582bMmDEDQgi89NJLmDJlis3tt912G/r374+cnBw8/fTT+Prrrx0+VnV1NW699Vb8/PPP+Oijj9CzZ8+WvQIVcGdQva8H4LvS5apDh0XsfmKHWs5wOTqz6OoYnBX/KkBml3qvHUAIYUL79g3ju5rOnNgwcck17fbg4MmbPH6uQOLOOoBq+FwSM7SlmKGBgRnaMpz8q2WYoYHH5aL1m2++wcSJE1FfX4+nn34ajz/+uN39nn/+eYwcORK7du3Cxo0bMXbs2Cb7GI1GjB8/Hl9//TXeffddu/uQ7zjrRpWQMBa5uQvZ/USlPB1zAwCZXerRo09dM3uZERGRh4sXP4bBkOz0oKy29ifo9VVOHksgQl+FlNYF+PV8Gyf7KRvHGpEzzNDAwQwNXErMUHcm/1LzrMPMUGqOy0XrwIEDUVlZ2ex+I0aMgBCOZ7eqr6/HnXfeiS+++AJvvfUWJk2a5GoTyIvsdaOqqyvEkSMPgd1P1MsbY26a07HDMYwY/jnCwqrw888N4+6cHZSZzYUuPW4rXY1X2+kLjkKVY42oOczQwMIMDUxKzNBAmvyLGUqe8GidVneZzWbcc8892LhxI1577TVMmzbNn09PjVzejUoIE3Jy+oHdT8iZjklnMLr37ibbnR2UaTSujVWtNBqa30lGjkI1MXEczpx5HTxQJV9jhioLM5Tc1ZIMDZTJv5ih5Cm/Fq1/+MMf8MEHH2DIkCGIjIzE6tWrbW4fNGgQOnTo4M8m0W+CpfsJtZwEgaFd9jX828HYVHsHZXp9T9TWhkOnq7Jzv4ZHrqgNw9nieB+13HOOJ8E4hzNn/uHgXjxQJe9ihioXM5Sa09IMDYTJv5ih5A1+LVr37t0LANixYwd27NjR5PZVq1YxcGVSW+ssbC9RQ/cTajlnsx2mxFxEZFi1k3vbPyiTJC1OnOiPzp3/CyEah3XDL9/92g8Cvu2S1VLOJ8Fo9t48UCWvYYYqFzOUAN9lqL/WIfYFZih5i1+L1u3bt/vz6chFBQWbkJu7wKV9ld79hFxjmd2wMWezHYa7OObU3kFZUVEGdu26Cb0uX6cVgFbfBq1Snsap7/cCqGhyPyVo/gpK83igSt7ADFUmZmjw8XeG+msdYl9ghpK3+LVoJeVx1GWjKeV3PwFsB/nX1OgBmAE4XhcuWLk2u6GtKhfHnDo6KDtzpiO+/7kT2vb8EbFR9bj+uolI7zQOFZVVAPa61RZ/8kZYtuRANTbeDL1BNLvGnLfWASQi9zFDg5McGeqPdYh9gRlK3sKiNYi53mVD+d1PAPuD/Hv1agWzeSBOX+wtX8MCxNmSBJRXhyHCUO1wbGpzB2VCaJBXnIDiOj1GhF2l6M+ThWdXRlp+oJqaZsL2I+fsrhdo4a11AInIfcxQcoc3MtTX6xD7AjOUvIVFaxBztctGaGgsrrjiL4rufuLobLdOV4n+/bfiYlk4foFensb5kS/PLApI+OroVRjde7fDsalKPyhrieYnwbDw/lij1DQTA5VIoZihgYcZ6n3MUPIWFq1BzNUuGx06LFZ02Do72y1JgBDAsEH/xYndN/m/cX7m6zOLuRfaYtOWCdY15izUMK6mpVyZBKNt2/+H/PyPVTfWiIhajhkaeJih3scMJW9h0RrEXO2yodcn+7glnmnubLckAZER5UhpfREXa9r4sWW+lXdaK0u3l9xfOgPmCHTqVIoxY26AwZCsinE1nnBlEoz27eepbqwREbUcM1TdmKH+wwwlb2DRGsQCYe0vwPWz3a30Nbjo2uR9zZIr7C5//mFdk5vtwrT9yDkftUODiopUJCSMg1YbHKHS3CQYahxrREQtxwxtOWYoM5QZSu5i0RrE1L72l4WrZ7sra12bua858ocdUFSgcfr8AFBbI6GoQMPxHF7EUCUiC2ZoyzBDgxczlDzBecyDnKXLhk5n2+VHr09Gt24rVTGWwHK223KQ0JgQQHlFJM4WJ3jl+dwJOyIiClzMUPcxQ4moJXillVS79peFs7Pd4rd/bt89HMJBIBMREbUUM5SIyPd4GosAXOqykZg4HjExg1QTthaOznYbja2QkzMSuSc6ydQyIiIKdMxQIiLf4pXWACGESbVneb2l8dnumho91q7djbNneW6GiIgcY4YyQ4lI2Vi0BoCCgk1NphHX6ZKRmblEFeNpvOnyQf6FhRcBfCtvg4hkIPfMnERqwgy9hBlKxAxVKhatKldQsOm3cSi20+0bjedx+PADqpkIgoi8QwkzcxKpBTOUiC7HDFUu9vlQMSFMOH58PuyvD9ewLTd3AYSQ5z+VECaUlOxGfv4GlJTslq0dgSg23gy9wd7f/RK9QSA23uynFpEz/vy/wJk5iVzDDA1ezFB1YYYSwCutqtYw7uSckz0EamvPorQ0x+/rYimlu1VxcSzy8yNQUhwBKUyDUL2E3CPR0NWFAmhZFw9L2DV3Fs6XYZeaZsL2I+fYfcXLfDGuzdn/BSKSDzO0ecxQZqg7mKHkSyxaVcxovODV/bxFKd2tzpwJxfLlS1BfH2qz/cvXL/27JV08lBJ2qWkmBqoX+eIgsbn/C61ajQfQyoNWE1FLMUOdY4aSO5ih5GssWlVMp0vy6n7e0Hx3Kwm5uQsQFzfK5zMzFhVpm4RtY5YuHu4GF8MusPjiINGV/wsJCV8CuK2FrfaNxhNQ5J/XoKzk0u/RMQIJbS599nk1gtSKGeocM5RcxQy9hBnqOyxaVSw6uj90umQYjedh/z+1BL0+GdHR/f3WJiV3tyJ5CGFCVNQ5pKWZoC2Owjm7n1X5+Oog0ZX/C6Gh5WjdOh9AunuN9hFXJqBojBNSkFoxQ0kNlL4cEzP0Emaob7FoVTFJ0iIzc8lvZ7ck2H5hNPyH6djxT379clNqdyuSR0HBJpw/Pxfdu1+0biuvCcO3p/rK2CpbvjpIdPUzrtdXu/yYvubKBBSNtfRKC5HcmKGkdEoZ2+wMM/QSZqhvceorlYuPH41u3VZCp2tjs12vT5Zlqn4ldrcieVi6C5lMF222R+irMbLTTojKHTK1zJavDhJd/YzX1oa59bhE5D3MUFIqS4Y2LggtXW4LCjbJ1DJbzFDyF15pDQDx8aMRFzdKEd1HlNjdivzPWXchSQKEAFD0CoS41+9ta8xXB4mu/F+oq4tAcXGiW4/bHCXMzEmkJsxQUholjW1uDjOU/IVFa4CQJK0ixrcosbsV+V9z3YUkCYApHzWl3wEh3f3XMDt8dZDoyv+FixdvgLc7vChlZk4iNWGGkpKoaWwzM5T8hUUreZ2lu1XjcRh6fTI6dvyTYsZhkO+42g2o3pgv+7eQLw8Sm/u/8L//5QI441H77eHMnETqxQwlNY1tZoaSv7BoJZ9QQner2FgTQkLqnE7Zzy4evuFqN6AQXSLqfdwWV/jyINH5/4W/e6H1RBRomKHBTW1jm5mh5A8sWmWk9GnMPSV3d6u2bevwhz/Mx4kTEThfHAEp9RxC9RJuGnoTumZ2BcAuHm6TBBBihNEYgqqqSqxY8ZyDHc3o2bMVQkMrG7oCNyIEIIUkwhB9DSoqqy49vM6IuqpwmEwCX331BXbs+NI3r8OhWxEZeQ6hoVWoqwtHeXkydu36HsD3Xn6ehtdlNNaitlYLoTEBGh74OdJ43bvG+P84ODFDfYsZKh81jm325YkWuf8vqF2gZCiLVpmoYRrzQNC6dREqK4tQI0VDanMKujANOnYtRY8edXI3TVVSElMQEhoCU70RIuM0Tp9pg/LycGicFFoVFUMwdOiWhgL1ssJV/Ja/Uel/hCRpER4WjqjoKJSXVUK0Lka1th5HjiUhslWtj1+VI87Xe6uoaI2amlYObzcYKhERUezic4WiqDoEosMJSKH10Gi0SE+Vb705VyagaMzXV1pcWfeO69wFH2aofzBD5aHWsc2uFJenT2tQ4KSAio83Iy1NnSdxmaG+xaJVBpZpzBufPbNMYy7HNPtEzlzZ6UpMuGk81v97A2qrjRBpZ1FcFgGYHQdPYX4blO8ejmFX5SAy/NLV1Kq6VohJfxYJbScAALRaLR668yGsWpuFE7+ehDm6DEZ9LQqrlDeNfVV5LLatexZmk87hPhqtESMm/xHhkUXNP6AkgMQKSFozQnUhGDl4BK675jovttg99iagyD+vQVnJpd+jYwQS2lwKNl+foXVl3TuucxdcmKEUDAJxbPPp0xp07ZqAGiff6QaDwJEjF1VZuDJDfUuVRWtFRQWeffZZrF27FkVFRejSpQueeeYZTJo0qdn75ufnY86cOfjss89QVVWFXr164bnnnsOIESP80HLlTGMe6N2qyLskScLAPgORkpSCt9a+jdKSUoiY8mbv90t1a5zYfRNSWhcgwlCL+PgrMPqWuYhoFWWzX3RkNH5/38NYv2U9cvZ9h3qDETAYffVyWqyuNtZpwQoAZpMOdTpAii117UElILxVGO6+bQp6dOnhhVZ6hhNQBD5mqHfawQwlX1PC2GZvKijQOC1YAaCmRkJBgUaVRSvADPUlVRatEyZMwJ49e7Bs2TJ06tQJ7733HiZPngyz2YwpU6Y4vF9tbS1GjBiBkpISrFixAomJiXj11VcxatQobN26FUOHDvV525UwjTm7VVFLpaemY/YDf8C6LetwvuC863eUUtCxSy/ccN0N0Grth21oSCjuHHMn0tum4+s9X6PepIQpmmyF1se7tF9CQjwSkqtd2jcmMgYTbp6AxDjvrjVH5Agz1DPMUPInjuckaqC6onXz5s348ssvrSELAMOHD8epU6cwe/Zs3HXXXQ4Pit966y0cPHgQu3fvxsCBA6337dWrF+bMmYOcnByft1/uaczZrYo8FRkRiakTp/rksSVJwoCrBmDAVQN88vieOrA3FB/+pfn9pt4xFT36cMwXKQ8z1DPMUCIieXh3RV4/2LBhAyIiIjBx4kSb7dOmTcPZs2edhuaGDRvQuXNna9gCQEhICO655x589913yMvL81m7LeScxrz5blVAbu4CCMFuDUREgYgZ2nLMUCIi+aiuaD148CC6du2KkBDbi8Q9e/a03u7svpb97N330KFDXmypfZZpzC2zvzUlQa9P8ck05u50qyIiosDDDG05ZigRkXxUV7QWFhYiNja2yXbLtsLCQp/ct7a2FmVlZTY/LWGZxvy33xrfCsB305jL3a2KiIjkxQxtOWYoEZF8VFe0Ag3j3lpymyf3Xbp0KaKjo60/7dq1a76hDlimMdfp2ths1+uTfToeRs5uVURELWFZ984ZX69zF2iYoS3DDCUitQmkDFXdRExxcXF2z+YWFTWsiWjvLLA37jt37lw8+eST1t/Lyso8Dl1/T2Nu6VZlNJ6H/TE5EvT6ZJ90qyIKBK4sHK6WL3+1sLfuXWO+XucukDBDW44ZSuSZ+HgzDAbR7Dqt8cxQrwmkDFVd0dqjRw+sWbMG9fX1NmNyDhw4AADo3r270/ta9rucK/fV6/XQ6/UtbbZd/p7G3NKtqmHmQwm2oevbblVEgSCQvvzVhOveeQ8z1LPnY4YStVxamhlHjlxEgZMMjY83q3aNVqUKlAxVXffg8ePHo6KiAuvWrbPZnp2djZSUFPTv7/gM5/jx43H06FGb2RHr6+uxevVq9O/fHykpKT5rt1LI1a2KKFCkppnQo0+dw59ACAYKXMxQzzBDiTyTlmZGnz71Dn9YsJIjqrvSevPNN+OGG27AzJkzUVZWhszMTKxZswaff/45Vq9ebV1fbsaMGcjOzkZubi7S09MBANOnT8err76KiRMnYtmyZUhMTMRrr72GY8eOYevWrXK+LL+So1sVERHJjxnqOWYoEZH/qa5oBYD169dj3rx5WLBgAYqKitClSxesWbMGkyZNsu5jMplgMpkgxKXuO3q9Htu2bcOcOXPw6KOPoqqqCr1798aWLVswdOhQOV6KbLzdrUoIEwOciEgFmKGeY4YSEfmXKovWiIgIrFixAitWrHC4T1ZWFrKysppsT0pKQnZ2tg9bF3wKCjbh+PH5NuvX6XTJyMxcwq5SREQKwwxVFmYoEVHzVFm0knIUFGz6bVIK25kUjcbzOHz4AY7xUai801pOJkREJDNmqDoxQ4n8j0UrtZgQJhw/Ph/2p/4XACTk5i5AXNwodnPykDcDMu+0FsO6Jje7bMv2I+cYukREPsIM9R9mKJH6sWj10IkTuYiMbCV3M2RRU7PPpjtTUwK1tWdx5Mg6GAxX+a1dFhUVZS26n9LOoHo7IIsKNE4fCwBqayQUFWgYuCqjtM8uUXOYocxQX1Nyhp48eRySpLqFPBTDZKr36uMp7bNLtli0eujDD7NgMOjkboYsEhJOoGvX5vfbufNDXLz4ve8bZEd9vUBhUQJEdDEkyQxIGmg0jr+QlHgGlUUmuUKJn12i5jBDm9+PGeoZJWSoxlKYakwQ0SUoKIxAq1bFWLPmLZ88X7Awm80oLIyEuVUFpJCGAtbZ59MZJX52yRaLVg8dPpyC0FDvLpiuFikp9S4F7tGj7XD2bKrvG2SHSTLDnHwWUkQVJA2QGJuATu07OdxfCeFG1BL87JIaMUOb348Zqn49uvTAV3t2oLSkDGhzASUl0Sg/3BYaOH+vyDmzEKiPLYbULg/QCBgMBvS/yvFa087ws6t8LFo9VNf+BKAPlbsZsjgNgfLqMEQYqiHZ+X8uBFBRE4bTYXUQHXP938CGVkAKMUGj0aDrFV1w74R7ER4WLlNbiIjocsxQZmgwSIpPwuNTH8Pba1fhzLkzMLcugSmyHCYWrR6TtCZIGiC+dRym3TkV7VLayd0k8hEWrR7S6MzQ6MxyN0M2O473wi3dv4UQsAldy9J+O473gqQTkOxONOEfIaGhuH7gcNw87OYWdxshIiLvY4YyQ4NFXOs4PDZtFj749APsO7wfJo0Z9ifhIndIGg0y0zvivjt+h8hWkXI3h3yIRauHRg6+HmGtwuRuhqzOiV5IkNYiFMXWbfVojYviTlxxZR9cIWPbAKBT+07omN5R5lYQEVFjzFBmaDDR6XS4Z8I96NmtJ85eOCt3cwJCbEws+vboC62WM2wHOhatHrrhuhsQGRXsZ3ZuhhDPoKb0O9Qb8xGiS4Qh+hp04RT95AWczc81F8/z/xupDzMUYIYGF0mS0KtrL/Tq2ssvz8cMdQ0zVPlYtJJXSJIWYTED5W4GuSA23gy9QTQ7Q15svPxd9jibn2vyTmvxwO3xcjeDiFqIGaoezNDAwwxVBxatRArn7YBMTTNh+5Fzqjjzytn8XFNUoEGdkRN6EBE1xgxlhjaHGaoOLFqJLqPEM6i+CMjUNFNQB1SwCtUp4+w/EQUmZigFMmaovFi0El1GqWdQGZDkDW+su8jPERH5DDOUAhkzVF4sWokaUWK4cSIF8obENjxDTES+xQylQMUMlReLViKFC9SJFFw5iCAiIvIEM5QoMLBoJVK4QJxIwdWDiNc/vOjHVhERUaBhhhIFBsenaIiIfMTVg4iyEn5FERERXY4ZSsGIn2YiUqzoGAG9QTjdRynr4cnJMmOnM3yfiIiCCzPUNcxQdWD3YCJSrIQ2ypyJUmkun7Ez/7zG7tn16BhhfR+V+n5xshQiIu9hhrqGGaoOLFqJSNGUOBOlElneownXJalywpFAnSyFiEhOzFDXMEOVj92DiYgChDsTjiiNmttORETqp+YcUnPbXcUrrUQUtAK9Kw0REZGvMEPJn1i0EimcZYKA5rp8+HKCgEAMpmDoSkNEFOyYob7BDCV/Y9FKpHCXTxDgiC8DzxfBpISDiEBcu4+IiGwxQ32DGUr+xqKVSAXknEjBF8Ek90EEEREFD2YokfqxaCUiWXBGQyIiopZhhlKwUe8UUkRERERERBTwWLQSEQUIyzgnZ3w9zqml1Nx2IiJSPzXnkJrb7ip2DyYirzh+1PbrxJ/jaQJxZsaWUPM4JzW3nYjIU8xQ+ak5h9TcdlexaCUir3js3nib3/011T2n3bclxzgnbx3wcIwWEQUrZqgyMEOVi0UrEfmEv6a6b+nMjEpYMiAQ8ICHiMj7mKHBgRnqOhatROSUK8HkSP555Q6bD4auNP7o8sW1+oiIHGOGqvd7nxmqLCxaicgpe8H038/1WD6/dbP3LStRbuACgd2VhmdviYjkxwxVJ2ao8rBoJaJmNQ6mxhNGkPLw7C0RkTIwQ9WHGao8yj6FQ0REREREREGNRSsREREREREpFotWIiIiIiIiUiwWrUTktugY4dX9PGGZmdEZTrtPRERKwQwlch9HghOR2xLauDbpgKv7eSIYpt1XMq7VR0TkHmYoWTBDXceilYjcprQv2UCedl/peMBDROQeZihZMENdx6KViNzGL1nla+lBUUsWU+cBDxGR65ihyscMVR4WrUTUIvySbZ4QJtSUfod6Yz5CdIkwRF8DSdL65blbclDExdSJiPyDGdo8ZihdjkUrEZEPVBRsQcHxRTAZz1m3aXXJiM9chIj4m/3SBncPiriYOhERKQEzlBpj0UpE5CWFxYXYd2gf9PU5SJb+CQCQLsuv+tpzOH/oIZwTD6ECfWRqpWOnf44DcHuz++3+fhfOlBX6vkEq0UrXSu4mEBEFjIqCLbhw+P8BsJ3V2GQ837C92+t+K1xJOVi0EhF5waGfD2H1xndRXVWFqQO3AHrbghVo+F0IINL4DtbtvggB52dk/a3kXHu4VLT+8C0Onz3h+wapRKgUJncTiIgCghAmFBxfhMYF62+3ApBQkLsIreJu9FtXYVIGFq1ERB4wm834YucX+HLnVtQZ65EaXYBIQ7XD/SUJiDRUIzmiEGeKEv3Y0uaZ61xbuttcp4HZyGW+LWrKfb+WIhFRMKgp/c6mS3BTAqbac6gp/Q5hMQP91i6SH4tWIqIWEkLg/U/fx54fv4ep3gRhDEWrUte6ikaVRCM0t6OPW+iekOIU1/Y70xahlSxaLfR6xycpiIjIdfXGfK/uR4GDRSsRUQuVV5TjcO5hmOrNEJXh0J5NRmyfAy7dNympGgZDno9b6J6zZ0OwbVvz+2Vm5iMlRVltl1N4eBTefVfuVhARqV+IzrUeSK7uR4GDRSsRUQuZxaX12URZNCIM9TAaEyBEa0hSscP7abWJuOWWPypuPM6hQ63wz382v9/NN4/HlVdW+r5BKmEyCcye/arczSAiUj1D9DXQ6pJhMp6H/XGtErT6NjBEX+PvppHMVFm0VlRU4Nlnn8XatWtRVFSELl264JlnnsGkSZOavW9WVhamTZtm97Zz586hTZs23m4uEQUVDcLCHkRNzQu//X556DZMvNS5858RH9/F7y1rTkiIBgaDQI2TKfsNBoFevdoiLc3scJ9gU1ZWLncT3MIMJSKlkiQt4jMX/TZ7sAR7GRrfcZHiTvoCDeu26g2i2XVaY+OZny2hyqJ1woQJ2LNnD5YtW4ZOnTrhvffew+TJk2E2mzFlyhSXHmPVqlXo0sX2oDEuLs4XzSWiIBMaOhAdOqzE8ePzYbxsQgm9PhkdO/4J8fGjZWydY2lpZhw5chEFThZTj483s2BVOWYoESlZRPzNQLfXm67Tqm+D+I7+W6fVXalpJmw/cg5FTjI0Nt7MNVpbSHVF6+bNm/Hll19aQxYAhg8fjlOnTmH27Nm46667oNU2f/ale/fu6Nu3r6+bS6Q6eae1/ML1gvj40YiLG4XS0hwYjReg0yUhOrq/Is8OXy4tjUVpIGOGEvkWM9Q7IuJvRqu4G1FT+h3qjfkI0SXCEH2N4jM0Nc3Ev6+PqK5o3bBhAyIiIjBx4kSb7dOmTcOUKVOQk5ODQYMGydQ6InXLO63FsK7JTru2hOoE3lh3EYltGgobBrBjkqRFTAy/j0g5mKFEvsMM9S5J0nJZG7JS3ZoFBw8eRNeuXRESYltv9+zZ03q7K8aMGQOtVovY2FhMmDCh2fvV1tairKzM5oco0BQVaJyGLQDUGSVMuzURo/u1weh+bTCsazLyTiv7zCcRNWCGEvkOM5TId1R3pbWwsBAdOnRosj02NtZ6uzNt2rTBvHnzMGDAAERFReHAgQNYtmwZBgwYgF27dqFXr15277d06VIsXrzY8xdAFGBqayQUFWgC7kyxK128WsX4rz1E3sAMJVKWYM7QQHvN5FuyFq3bt2/H8OHDXdp337596N27NwBAkhyfxXJ2GwCMGjUKo0aNsv4+ZMgQjB49Gj169MCCBQuwceNGu/ebO3cunnzySevvZWVlaNeunUttJyJ1caWLl94g8Ml3vFpE8mGGEpESuZqh24+cY+FKLpO1aO3cuTNWrlzp0r5paWkAGmYntHcmuKioCMCls8XuyMjIwODBg/Htt9863Eev10Ov17v92ETB4PhRx18lajyb6koXr9oaCcVF7NJF8mGGEgWGYM3QQLzCTL4ja9GanJyM+++/36379OjRA2vWrEF9fb3NmJwDBw4AaJjRsCWEENBoVDfEl0gRHrs33uFtPJtK5BvMUKLAwAwlap7qEmb8+PGoqKjAunXrbLZnZ2cjJSUF/fv3d/sxT5w4gV27dmHAgAHeaiYR/cZyNpWI5McMJVIXZihRA9VNxHTzzTfjhhtuwMyZM1FWVobMzEysWbMGn3/+OVavXm2zvtyMGTOQnZ2N3NxcpKenAwBGjhyJIUOGoGfPntZJJF544QVIkoQlS5bI9bKIiIh8jhlKRERqpLqiFQDWr1+PefPmYcGCBSgqKkKXLl2wZs0aTJo0yWY/k8kEk8kEIYR1W48ePfDBBx9g+fLlqK6uRmJiIq6//nrMnz8fnTp18vdLIVKU2Hgz9AbR7FgUIlIvZiiRbzBDiXxHEpenEbmsrKwM0dHROFR8CJFRkXI3h8hrLp+mfs/Xeix6orXHj7lpz3n06FPn8eP4y4G9oRjdr02z+72//X/YvOc5lJVUwHyuDWLqdcjMLMItt0zAVVe5382S1KmsrBytW3dCaWkpoqKi5G6OKjBDKVAxQ13PULW9LvKN8rJyXNn6ymYzVJVXWonId1LTTJzwgYiIqAWYoUS+wZHdRESNWLp4OaM3CLSO5YEJERHR5VzN0Nh4s59aRIGAV1qJiBpJTTNh+5FzTmdsjI03o1UMuzURERFdztUM5RVpcgeLViLyKbWeTXWli1dJmZ8aQ0REQSmQM5TIHSxaicghV2ZC1OkF3vioAAlt7IcTz6YSEVEwYoYSeQ+LViJyKJi7+Fw+AyQAXDyvRWnJpQOPqBgzwiINKDyTjsryKoRUGBBjqJSjqUREpEDMUOcZmtjm0hXkQH0fyHtYtBKRU8HYxSfvtBbDuia7sNZeIoA/AQA02jqMG/tnAEW+bh4REakEM9Q1eoPA9iPngu69Itdx9mAiokaKCjRuLw5vNoWitjbCRy0iIiJSh5ZkaG2N5PSKNBE/HURERERERKRYLFqJiIiIiIhIsVi0EhERERERkWKxaCUiIiIiIiLFYtFKREREREREisWilYiIiIiIiBSLRSsRUSOx8WboDcKt+2i0ddDrK3zUIiIiInVoSYbqDQKx8WYftYgCQYjcDSAiUprUNBO2Hzlns2bcxfNalJZcWncuKsaMsMhS/GvDv1BZXoWQCgMiDJVyNJeIiEgxXM3QxDaXitTYeDNS00x+bSepC4tWIiI7UtNMjQK0rsk+JWU1iNtzCqElFTCfawPU6/zXQCIiIoVyJUOJ3MHuwURERERERKRYLFqJiIiIiIhIsVi0EhERERERkWKxaCUiIiIiIiLFYtFKREREREREisWilYiIiIiIiBSLRSsREREREREpFotWIiIiIiIiUiwWrURERERERKRYLFqJiIiIiIhIsVi0EhERERERkWKxaCUiIiIiIiLFCpG7AUTkf3mntSgqcHzOKjbejNQ0kx9bREREpA7MUCL/Y9FKFGTyTmsxrGsyamskh/voDQLbj5xj6BIREV2GGUokD3YPJgoyRQUap2ELALU1ktOzyERERMGIGUokD/6PIiIiIiIiIsVi0UpERERERESKxaKViIiIiIiIFItFKxERERERESkWi1YiIiIiIiJSLBatREREREREpFgsWomCTGy8GXqDcLqP3iAQG2/2U4uIiIjUgRlKJI8QuRtARP6VmmbC9iPnnK4hFxtv5qLoREREjTBDieTBopUoCKWmmRioRERELcAMJfI/dg8mIiIiIiIixWLRSkRERERERIrFopWIiIiIiIgUi0UrERERERERKRaLViIiIiIiIlIsFq1ERERERESkWCxaiYiIiIiISLFUV7SWl5djzpw5uPHGG5GQkABJkrBo0SK3HiM/Px9Tp05FfHw8wsPDMXDgQGzbts03DSYiIlIIZigREamR6orWwsJCvPHGG6itrcW4cePcvn9tbS1GjBiBbdu2YcWKFdi4cSOSkpIwatQofPXVV95vMBERkUIwQ4mISI1C5G6Au9LT01FcXAxJklBQUIA333zTrfu/9dZbOHjwIHbv3o2BAwcCAIYPH45evXphzpw5yMnJ8UWziYiIZMcMJSIiNVLdlVZJkiBJUovvv2HDBnTu3NkatgAQEhKCe+65B9999x3y8vK80UwiIiLFYYYSEZEaqa5o9dTBgwfRs2fPJtst2w4dOuTvJhEREakCM5SIiOSguu7BniosLERsbGyT7ZZthYWFdu9XW1uL2tpa6++lpaUAgIqyCh+0kojUoKayBlGRUai4WAepXgu93gi9PhySFIKysnK5m0d+UvZbDgghZG6J7zFDiYjImypczFBZi9bt27dj+PDhLu27b98+9O7d2yvP66xrlKPbli5disWLFzfZ3j+9v1faRESB5HW5G0AyKC8vR3R0tN+ejxlKRESBorkMlbVo7dy5M1auXOnSvmlpaV55zri4OLtngouKigDA7hlkAJg7dy6efPJJ6+9msxlFRUWIi4vzaHyQnMrKytCuXTv8+uuviIqKkrs5QYfvv/z4N5BfIPwNhBAoLy9HSkqKX5+XGSqvQPjsqhnff/nxbyC/QPgbuJqhshatycnJuP/++/36nD169MCBAweabLds6969u9376fV66PV6m20xMTFeb58coqKiVPtBDwR8/+XHv4H81P438OcVVgtmqDKo/bOrdnz/5ce/gfzU/jdwJUODbiKm8ePH4+jRozbT8tfX12P16tXo37+/38+UExERqQUzlIiI5KDKiZi2bNmCyspKlJc3THRy+PBhfPTRRwCAW265BeHh4QCAGTNmIDs7G7m5uUhPTwcATJ8+Ha+++iomTpyIZcuWITExEa+99hqOHTuGrVu3yvOCiIiI/IQZSkREaqPKonXmzJk4deqU9fcPP/wQH374IQDgxIkTyMjIAACYTCaYTCab2aj0ej22bduGOXPm4NFHH0VVVRV69+6NLVu2YOjQoX59HXLT6/VYuHBhky5b5B98/+XHv4H8+DfwP2aod/CzKy++//Lj30B+wfQ3kEQwzNFPREREREREqhR0Y1qJiIiIiIhIPVi0EhERERERkWKxaCUiIiIiIiLFYtFKAIDy8nLMmTMHN954IxISEiBJEhYtWiR3swJSRUUFHn/8caSkpMBgMKB37954//335W5WUOHnXV7/+c9/MH36dHTp0gWtWrVCamoqxo4dix9++EHuphG1CL9T/IcZKj9+3uUVrBnKopUAAIWFhXjjjTdQW1uLcePGyd2cgDZhwgRkZ2dj4cKF2LJlC/r164fJkyfjvffek7tpQYOfd3n94x//wMmTJ/HYY49h8+bNWLFiBfLz8zFgwAD85z//kbt5RG7jd4r/MEPlx8+7vII1Qzl7MAGAdUkDSZJQUFCAhIQELFy4kGfOvGzz5s0YPXo03nvvPUyePNm6/cYbb8ShQ4dw+vRpaLVaGVsYHPh5l1d+fj4SExNttlVUVCAzMxPdu3fnep+kOvxO8Q9mqDLw8y6vYM1QXmklAA1fPJIkyd2MgLdhwwZERERg4sSJNtunTZuGs2fPIicnR6aWBRd+3uXVOGwBICIiAt26dcOvv/4qQ4uIPMPvFP9ghioDP+/yCtYMZdFK5EcHDx5E165dERISYrO9Z8+e1tuJglFpaSn27t2LK6+8Uu6mEJFCMUOJ7AuGDGXRSuRHhYWFiI2NbbLdsq2wsNDfTSJShN///veorKzEvHnz5G4KESkUM5TIvmDIUBatAWj79u3WrhvN/ezfv1/u5gYdZ11q2N2GgtH8+fPx7rvv4qWXXsLVV18td3MoyDFDlY0ZSmQrWDI0pPldSG06d+6MlStXurRvWlqaj1tDl4uLi7N7JrioqAgA7J5BJgpkixcvxnPPPYfnn38ejzzyiNzNIWKGKhgzlMhWMGUoi9YAlJycjPvvv1/uZpAdPXr0wJo1a1BfX28zJufAgQMAgO7du8vVNCK/W7x4MRYtWoRFixbhj3/8o9zNIQLADFUyZijRJcGWoeweTORH48ePR0VFBdatW2ezPTs7GykpKejfv79MLSPyryVLlmDRokV49tlnsXDhQrmbQ0QqwAwlahCMGcorrWS1ZcsWVFZWory8HABw+PBhfPTRRwCAW265BeHh4XI2LyDcfPPNuOGGGzBz5kyUlZUhMzMTa9asweeff47Vq1dzfTk/4uddPn/961+xYMECjBo1CqNHj8a3335rc/uAAQNkahlRy/E7xfeYocrBz7t8gjVDJWFZIZiCXkZGBk6dOmX3thMnTiAjI8O/DQpQFRUVmDdvHtauXYuioiJ06dIFc+fOxaRJk+RuWlDh510+w4YNw1dffeXwdsYSqRG/U/yDGaoM/LzLJ1gzlEUrERERERERKRbHtBIREREREZFisWglIiIiIiIixWLRSkRERERERIrFopWIiIiIiIgUi0UrERERERERKRaLViIiIiIiIlIsFq1ERERERESkWCxaiYiIiIiISLFYtBIREREREZFisWglIiIiIiIixWLRSkRERERERIrFopWImti1axckSYIkSfjwww/t7pOTk4OIiAhIkoQ5c+b4uYVERETKxAwl8j5JCCHkbgQRKc/YsWPxySefoEuXLjh48CC0Wq31tmPHjmHw4MEoKCjAfffdh1WrVkGSJBlbS0REpBzMUCLv4pVWIrJr2bJl0Gq1OHr0KFavXm3dfvbsWdx0000oKCjAmDFj8OabbzJsiYiILsMMJfIuXmklIofuv/9+vPXWW2jfvj2OHTuGyspKDBkyBAcOHMDgwYPxxRdfICwsTO5mEhERKQ4zlMh7WLQSkUN5eXm44oorUF1djZdeegkbNmzAjh070KNHD+zYsQMxMTFyN5GIiEiRmKFE3sPuwUTkUGpqKmbNmgUAeOKJJ7Bjxw5kZGTg888/txu2FRUVWLRoEcaMGYM2bdpAkiRMnTrVv40mIiJSAGYokfewaCUipx577DFoNA1fFbGxsfjiiy+QkpJid9+CggIsXrwYe/fuRd++ff3ZTCIiIsVhhhJ5R4jcDSAi5aqvr8eDDz4Is9kMAKiqqnI6/iY5ORlnzpxBamoqampqOFaHiIiCFjOUyHt4pZWI7BJC4P7778dnn32GhIQEtG/fHjU1NVi4cKHD++j1eqSmpvqxlURERMrDDCXyLhatRGTXnDlzkJ2djYiICGzatAnPP/88ACA7OxuHDx+WuXVERETKxQwl8i4WrUTUxPLly7F8+XKEhoZi3bp16NevHyZNmoSePXvCZDJh7ty5cjeRiIhIkZihRN7HopWIbLzzzjuYM2cOJElCVlYWbrzxRgCAJElYsmQJAOCTTz7Brl275GwmERGR4jBDiXyDRSsRWW3evBkzZsyAEAJ/+9vfMGXKFJvbb7vtNvTv3x8A8PTTT8vRRCIiIkVihhL5DotWIgIAfPPNN5g4cSLq6+vx9NNP4/HHH7e7n2Vczq5du7Bx40Y/tpCIiEiZmKFEvsUlb4gIADBw4EBUVlY2u9+IESMghPBDi4iIiNSBGUrkW7zSSkRERERERIrFK61E5FWvvPIKSkpKUF9fDwD46aef8NxzzwEAhgwZgiFDhsjZPCIiIsVihhLZJwn2USAiL8rIyMCpU6fs3rZw4UIsWrTIvw0iIiJSCWYokX0sWomIiIiIiEixOKaViIiIiIiIFItFKxERERERESkWi1YiIiIiIiJSLBatREREREREpFgsWomIiIiIiEixWLQSERERERGRYrFoJSIiIiIiIsVi0UpERERERESKxaKViIiIiIiIFItFKxERERERESkWi1YiIiIiIiJSrP8P4ghUm+uwyNwAAAAASUVORK5CYII=",
|
||
"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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",
|
||
"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/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": {
|
||
"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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",
|
||
"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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