Morten Hjorth-Jensen
2161 lines
437 KiB
Plaintext
2161 lines
437 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: -1.1183132530120519\n",
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"first power: 0.007326686369839082\n",
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"second power: 0.00023870096207253609\n"
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]
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"%matplotlib inline\n",
|
||
"\n",
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.preprocessing import PolynomialFeatures\n",
|
||
"from sklearn.linear_model import LinearRegression\n",
|
||
"\n",
|
||
"steps=250\n",
|
||
"\n",
|
||
"distance=0\n",
|
||
"x=0\n",
|
||
"distance_list=[]\n",
|
||
"steps_list=[]\n",
|
||
"while x<steps:\n",
|
||
" distance+=np.random.randint(-1,2)\n",
|
||
" distance_list.append(distance)\n",
|
||
" x+=1\n",
|
||
" steps_list.append(x)\n",
|
||
"plt.plot(steps_list,distance_list, color='green', label=\"Random Walk Data\")\n",
|
||
"\n",
|
||
"steps_list=np.asarray(steps_list)\n",
|
||
"distance_list=np.asarray(distance_list)\n",
|
||
"\n",
|
||
"X=steps_list[:,np.newaxis]\n",
|
||
"\n",
|
||
"#Polynomial fits\n",
|
||
"\n",
|
||
"#Degree 2\n",
|
||
"poly_features=PolynomialFeatures(degree=2, include_bias=False)\n",
|
||
"X_poly=poly_features.fit_transform(X)\n",
|
||
"\n",
|
||
"lin_reg=LinearRegression()\n",
|
||
"poly_fit=lin_reg.fit(X_poly,distance_list)\n",
|
||
"b=lin_reg.coef_\n",
|
||
"c=lin_reg.intercept_\n",
|
||
"print (\"2nd degree coefficients:\")\n",
|
||
"print (\"zero power: \",c)\n",
|
||
"print (\"first power: \", b[0])\n",
|
||
"print (\"second power: \",b[1])\n",
|
||
"\n",
|
||
"z = np.arange(0, steps, .01)\n",
|
||
"z_mod=b[1]*z**2+b[0]*z+c\n",
|
||
"\n",
|
||
"fit_mod=b[1]*X**2+b[0]*X+c\n",
|
||
"plt.plot(z, z_mod, color='r', label=\"2nd Degree Fit\")\n",
|
||
"plt.title(\"Polynomial Regression\")\n",
|
||
"\n",
|
||
"plt.xlabel(\"Steps\")\n",
|
||
"plt.ylabel(\"Distance\")\n",
|
||
"\n",
|
||
"#Degree 10\n",
|
||
"poly_features10=PolynomialFeatures(degree=10, include_bias=False)\n",
|
||
"X_poly10=poly_features10.fit_transform(X)\n",
|
||
"\n",
|
||
"poly_fit10=lin_reg.fit(X_poly10,distance_list)\n",
|
||
"\n",
|
||
"y_plot=poly_fit10.predict(X_poly10)\n",
|
||
"plt.plot(X, y_plot, color='black', label=\"10th Degree Fit\")\n",
|
||
"\n",
|
||
"plt.legend()\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"\n",
|
||
"#Decision Tree Regression\n",
|
||
"from sklearn.tree import DecisionTreeRegressor\n",
|
||
"regr_1=DecisionTreeRegressor(max_depth=2)\n",
|
||
"regr_2=DecisionTreeRegressor(max_depth=5)\n",
|
||
"regr_3=DecisionTreeRegressor(max_depth=7)\n",
|
||
"regr_1.fit(X, distance_list)\n",
|
||
"regr_2.fit(X, distance_list)\n",
|
||
"regr_3.fit(X, distance_list)\n",
|
||
"\n",
|
||
"X_test = np.arange(0.0, steps, 0.01)[:, np.newaxis]\n",
|
||
"y_1 = regr_1.predict(X_test)\n",
|
||
"y_2 = regr_2.predict(X_test)\n",
|
||
"y_3=regr_3.predict(X_test)\n",
|
||
"\n",
|
||
"# Plot the results\n",
|
||
"plt.figure()\n",
|
||
"plt.scatter(X, distance_list, s=2.5, c=\"black\", label=\"data\")\n",
|
||
"plt.plot(X_test, y_1, color=\"red\",\n",
|
||
" label=\"max_depth=2\", linewidth=2)\n",
|
||
"plt.plot(X_test, y_2, color=\"green\", label=\"max_depth=5\", linewidth=2)\n",
|
||
"plt.plot(X_test, y_3, color=\"m\", label=\"max_depth=7\", linewidth=2)\n",
|
||
"\n",
|
||
"plt.xlabel(\"Data\")\n",
|
||
"plt.ylabel(\"Darget\")\n",
|
||
"plt.title(\"Decision Tree Regression\")\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Building a tree, regression\n",
|
||
"\n",
|
||
"There are mainly two steps\n",
|
||
"1. We split the predictor space (the set of possible values $x_1,x_2,\\dots, x_p$) into $J$ distinct and non-non-overlapping regions, $R_1,R_2,\\dots,R_J$. \n",
|
||
"\n",
|
||
"2. For every observation that falls into the region $R_j$ , we make the same prediction, which is simply the mean of the response values for the training observations in $R_j$.\n",
|
||
"\n",
|
||
"How do we construct the regions $R_1,\\dots,R_J$? In theory, the\n",
|
||
"regions could have any shape. However, we choose to divide the\n",
|
||
"predictor space into high-dimensional rectangles, or boxes, for\n",
|
||
"simplicity and for ease of interpretation of the resulting predictive\n",
|
||
"model. The goal is to find boxes $R_1,\\dots,R_J$ that minimize the\n",
|
||
"MSE, given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sum_{j=1}^J\\sum_{i\\in R_j}(y_i-\\overline{y}_{R_j})^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $\\overline{y}_{R_j}$ is the mean response for the training observations \n",
|
||
"within box $j$. \n",
|
||
"\n",
|
||
"\n",
|
||
"Unfortunately, it is computationally infeasible to consider every\n",
|
||
"possible partition of the feature space into $J$ boxes. The common\n",
|
||
"strategy is to take a top-down approach\n",
|
||
"\n",
|
||
"The approach is top-down because it begins at the top of the tree (all\n",
|
||
"observations belong to a single region) and then successively splits\n",
|
||
"the predictor space; each split is indicated via two new branches\n",
|
||
"further down on the tree. It is greedy because at each step of the\n",
|
||
"tree-building process, the best split is made at that particular step,\n",
|
||
"rather than looking ahead and picking a split that will lead to a\n",
|
||
"better tree in some future step.\n",
|
||
"\n",
|
||
"\n",
|
||
"### Making a tree\n",
|
||
"\n",
|
||
"In order to implement the recursive binary splitting we start by selecting\n",
|
||
"the predictor $x_j$ and a cutpoint $s$ that splits the predictor space into two regions $R_1$ and $R_2$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\left\\{X\\vert x_j < s\\right\\},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\left\\{X\\vert x_j \\geq s\\right\\},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"so that we obtain the lowest MSE, that is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sum_{i:x_i\\in R_j}(y_i-\\overline{y}_{R_1})^2+\\sum_{i:x_i\\in R_2}(y_i-\\overline{y}_{R_2})^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"which we want to minimize by considering all predictors\n",
|
||
"$x_1,x_2,\\dots,x_p$. We consider also all possible values of $s$ for\n",
|
||
"each predictor. These values could be determined by randomly assigned\n",
|
||
"numbers or by starting at the midpoint and then proceed till we find\n",
|
||
"an optimal value.\n",
|
||
"\n",
|
||
"For any $j$ and $s$, we define the pair of half-planes where\n",
|
||
"$\\overline{y}_{R_1}$ is the mean response for the training\n",
|
||
"observations in $R_1(j,s)$, and $\\overline{y}_{R_2}$ is the mean\n",
|
||
"response for the training observations in $R_2(j,s)$.\n",
|
||
"\n",
|
||
"Finding the values of $j$ and $s$ that minimize the above equation can be\n",
|
||
"done quite quickly, especially when the number of features $p$ is not\n",
|
||
"too large.\n",
|
||
"\n",
|
||
"Next, we repeat the process, looking\n",
|
||
"for the best predictor and best cutpoint in order to split the data\n",
|
||
"further so as to minimize the MSE within each of the resulting\n",
|
||
"regions. However, this time, instead of splitting the entire predictor\n",
|
||
"space, we split one of the two previously identified regions. We now\n",
|
||
"have three regions. Again, we look to split one of these three regions\n",
|
||
"further, so as to minimize the MSE. The process continues until a\n",
|
||
"stopping criterion is reached; for instance, we may continue until no\n",
|
||
"region contains more than five observations.\n",
|
||
"\n",
|
||
"\n",
|
||
"The above procedure is rather straightforward, but leads often to\n",
|
||
"overfitting and unnecessarily large and complicated trees. The basic\n",
|
||
"idea is to grow a large tree $T_0$ and then prune it back in order to\n",
|
||
"obtain a subtree. A smaller tree with fewer splits (fewer regions) can\n",
|
||
"lead to smaller variance and better interpretation at the cost of a\n",
|
||
"little more bias.\n",
|
||
"\n",
|
||
"The so-called Cost complexity pruning algorithm gives us a\n",
|
||
"way to do just this. Rather than considering every possible subtree,\n",
|
||
"we consider a sequence of trees indexed by a nonnegative tuning\n",
|
||
"parameter $\\alpha$.\n",
|
||
"\n",
|
||
"Read more at the following [Scikit-Learn link on pruning](https://scikit-learn.org/stable/auto_examples/tree/plot_cost_complexity_pruning.html#sphx-glr-auto-examples-tree-plot-cost-complexity-pruning-py).\n",
|
||
"\n",
|
||
"\n",
|
||
"For each value of $\\alpha$ there corresponds a subtree $T \\in T_0$ such that"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sum_{m=1}^{\\overline{T}}\\sum_{i:x_i\\in R_m}(y_i-\\overline{y}_{R_m})^2+\\alpha\\overline{T},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"is as small as possible. Here $\\overline{T}$ is \n",
|
||
"the number of terminal nodes of the tree $T$ , $R_m$ is the\n",
|
||
"rectangle (i.e. the subset of predictor space) corresponding to the $m$-th terminal node.\n",
|
||
"\n",
|
||
"The tuning parameter $\\alpha$ controls a trade-off between the subtree’s\n",
|
||
"complexity and its fit to the training data. When $\\alpha = 0$, then the\n",
|
||
"subtree $T$ will simply equal $T_0$, \n",
|
||
"because then the above equation just measures the\n",
|
||
"training error. \n",
|
||
"However, as $\\alpha$ increases, there is a price to pay for\n",
|
||
"having a tree with many terminal nodes. The above equation will\n",
|
||
"tend to be minimized for a smaller subtree. \n",
|
||
"\n",
|
||
"\n",
|
||
"It turns out that as we increase $\\alpha$ from zero\n",
|
||
"branches get pruned from the tree in a nested and predictable fashion,\n",
|
||
"so obtaining the whole sequence of subtrees as a function of $\\alpha$ is\n",
|
||
"easy. We can select a value of $\\alpha$ using a validation set or using\n",
|
||
"cross-validation. We then return to the full data set and obtain the\n",
|
||
"subtree corresponding to $\\alpha$. \n",
|
||
"\n",
|
||
"\n",
|
||
"### Schematic Regression Procedure\n",
|
||
"\n",
|
||
"Building a Regression Tree\n",
|
||
"\n",
|
||
"1. Use recursive binary splitting to grow a large tree on the training data, stopping only when each terminal node has fewer than some minimum number of observations.\n",
|
||
"\n",
|
||
"2. Apply cost complexity pruning to the large tree in order to obtain a sequence of best subtrees, as a function of $\\alpha$.\n",
|
||
"\n",
|
||
"3. Use for example $K$-fold cross-validation to choose $\\alpha$. Divide the training observations into $K$ folds. For each $k=1,2,\\dots,K$ we: \n",
|
||
"\n",
|
||
" * repeat steps 1 and 2 on all but the $k$-th fold of the training data. \n",
|
||
"\n",
|
||
" * Then we valuate the mean squared prediction error on the data in the left-out $k$-th fold, as a function of $\\alpha$.\n",
|
||
"\n",
|
||
" * Finally we average the results for each value of $\\alpha$, and pick $\\alpha$ to minimize the average error.\n",
|
||
"\n",
|
||
"\n",
|
||
"4. Return the subtree from Step 2 that corresponds to the chosen value of $\\alpha$. \n",
|
||
"\n",
|
||
"!eblock\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"## A Classification Tree\n",
|
||
"\n",
|
||
"A classification tree is very similar to a regression tree, except\n",
|
||
"that it is used to predict a qualitative response rather than a\n",
|
||
"quantitative one. Recall that for a regression tree, the predicted\n",
|
||
"response for an observation is given by the mean response of the\n",
|
||
"training observations that belong to the same terminal node. In\n",
|
||
"contrast, for a classification tree, we predict that each observation\n",
|
||
"belongs to the most commonly occurring class of training observations\n",
|
||
"in the region to which it belongs. In interpreting the results of a\n",
|
||
"classification tree, we are often interested not only in the class\n",
|
||
"prediction corresponding to a particular terminal node region, but\n",
|
||
"also in the class proportions among the training observations that\n",
|
||
"fall into that region. \n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"The task of growing a\n",
|
||
"classification tree is quite similar to the task of growing a\n",
|
||
"regression tree. Just as in the regression setting, we use recursive\n",
|
||
"binary splitting to grow a classification tree. However, in the\n",
|
||
"classification setting, the MSE cannot be used as a criterion for making\n",
|
||
"the binary splits. A natural alternative to MSE is the **classification\n",
|
||
"error rate**. Since we plan to assign an observation in a given region\n",
|
||
"to the most commonly occurring error rate class of training\n",
|
||
"observations in that region, the classification error rate is simply\n",
|
||
"the fraction of the training observations in that region that do not\n",
|
||
"belong to the most common class. \n",
|
||
"\n",
|
||
"When building a classification tree, either the Gini index or the\n",
|
||
"entropy are typically used to evaluate the quality of a particular\n",
|
||
"split, since these two approaches are more sensitive to node purity\n",
|
||
"than is the classification error rate. \n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"If our targets are the outcome of a classification process that takes\n",
|
||
"for example $k=1,2,\\dots,K$ values, the only thing we need to think of\n",
|
||
"is to set up the splitting criteria for each node.\n",
|
||
"\n",
|
||
"We define a PDF $p_{mk}$ that represents the number of observations of\n",
|
||
"a class $k$ in a region $R_m$ with $N_m$ observations. We represent\n",
|
||
"this likelihood function in terms of the proportion $I(y_i=k)$ of\n",
|
||
"observations of this class in the region $R_m$ as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i=k).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We let $p_{mk}$ represent the majority class of observations in region\n",
|
||
"$m$. The three most common ways of splitting a node are given by\n",
|
||
"\n",
|
||
"* Misclassification error"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i\\ne k) = 1-p_{mk}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* Gini index $g$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"g = \\sum_{k=1}^K p_{mk}(1-p_{mk}).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* Information entropy or just entropy $s$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"s = -\\sum_{k=1}^K p_{mk}\\log{p_{mk}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Visualizing the Tree, Classification"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
" mean radius mean texture mean perimeter mean area mean smoothness \\\n",
|
||
"0 17.99 10.38 122.80 1001.0 0.11840 \n",
|
||
"1 20.57 17.77 132.90 1326.0 0.08474 \n",
|
||
"2 19.69 21.25 130.00 1203.0 0.10960 \n",
|
||
"3 11.42 20.38 77.58 386.1 0.14250 \n",
|
||
"4 20.29 14.34 135.10 1297.0 0.10030 \n",
|
||
".. ... ... ... ... ... \n",
|
||
"564 21.56 22.39 142.00 1479.0 0.11100 \n",
|
||
"565 20.13 28.25 131.20 1261.0 0.09780 \n",
|
||
"566 16.60 28.08 108.30 858.1 0.08455 \n",
|
||
"567 20.60 29.33 140.10 1265.0 0.11780 \n",
|
||
"568 7.76 24.54 47.92 181.0 0.05263 \n",
|
||
"\n",
|
||
" mean compactness mean concavity mean concave points mean symmetry \\\n",
|
||
"0 0.27760 0.30010 0.14710 0.2419 \n",
|
||
"1 0.07864 0.08690 0.07017 0.1812 \n",
|
||
"2 0.15990 0.19740 0.12790 0.2069 \n",
|
||
"3 0.28390 0.24140 0.10520 0.2597 \n",
|
||
"4 0.13280 0.19800 0.10430 0.1809 \n",
|
||
".. ... ... ... ... \n",
|
||
"564 0.11590 0.24390 0.13890 0.1726 \n",
|
||
"565 0.10340 0.14400 0.09791 0.1752 \n",
|
||
"566 0.10230 0.09251 0.05302 0.1590 \n",
|
||
"567 0.27700 0.35140 0.15200 0.2397 \n",
|
||
"568 0.04362 0.00000 0.00000 0.1587 \n",
|
||
"\n",
|
||
" mean fractal dimension ... worst radius worst texture \\\n",
|
||
"0 0.07871 ... 25.380 17.33 \n",
|
||
"1 0.05667 ... 24.990 23.41 \n",
|
||
"2 0.05999 ... 23.570 25.53 \n",
|
||
"3 0.09744 ... 14.910 26.50 \n",
|
||
"4 0.05883 ... 22.540 16.67 \n",
|
||
".. ... ... ... ... \n",
|
||
"564 0.05623 ... 25.450 26.40 \n",
|
||
"565 0.05533 ... 23.690 38.25 \n",
|
||
"566 0.05648 ... 18.980 34.12 \n",
|
||
"567 0.07016 ... 25.740 39.42 \n",
|
||
"568 0.05884 ... 9.456 30.37 \n",
|
||
"\n",
|
||
" worst perimeter worst area worst smoothness worst compactness \\\n",
|
||
"0 184.60 2019.0 0.16220 0.66560 \n",
|
||
"1 158.80 1956.0 0.12380 0.18660 \n",
|
||
"2 152.50 1709.0 0.14440 0.42450 \n",
|
||
"3 98.87 567.7 0.20980 0.86630 \n",
|
||
"4 152.20 1575.0 0.13740 0.20500 \n",
|
||
".. ... ... ... ... \n",
|
||
"564 166.10 2027.0 0.14100 0.21130 \n",
|
||
"565 155.00 1731.0 0.11660 0.19220 \n",
|
||
"566 126.70 1124.0 0.11390 0.30940 \n",
|
||
"567 184.60 1821.0 0.16500 0.86810 \n",
|
||
"568 59.16 268.6 0.08996 0.06444 \n",
|
||
"\n",
|
||
" worst concavity worst concave points worst symmetry \\\n",
|
||
"0 0.7119 0.2654 0.4601 \n",
|
||
"1 0.2416 0.1860 0.2750 \n",
|
||
"2 0.4504 0.2430 0.3613 \n",
|
||
"3 0.6869 0.2575 0.6638 \n",
|
||
"4 0.4000 0.1625 0.2364 \n",
|
||
".. ... ... ... \n",
|
||
"564 0.4107 0.2216 0.2060 \n",
|
||
"565 0.3215 0.1628 0.2572 \n",
|
||
"566 0.3403 0.1418 0.2218 \n",
|
||
"567 0.9387 0.2650 0.4087 \n",
|
||
"568 0.0000 0.0000 0.2871 \n",
|
||
"\n",
|
||
" worst fractal dimension \n",
|
||
"0 0.11890 \n",
|
||
"1 0.08902 \n",
|
||
"2 0.08758 \n",
|
||
"3 0.17300 \n",
|
||
"4 0.07678 \n",
|
||
".. ... \n",
|
||
"564 0.07115 \n",
|
||
"565 0.06637 \n",
|
||
"566 0.07820 \n",
|
||
"567 0.12400 \n",
|
||
"568 0.07039 \n",
|
||
"\n",
|
||
"[569 rows x 30 columns]\n",
|
||
" malignant benign\n",
|
||
"0 True False\n",
|
||
"1 True False\n",
|
||
"2 True False\n",
|
||
"3 True False\n",
|
||
"4 True False\n",
|
||
".. ... ...\n",
|
||
"564 True False\n",
|
||
"565 True False\n",
|
||
"566 True False\n",
|
||
"567 True False\n",
|
||
"568 False True\n",
|
||
"\n",
|
||
"[569 rows x 2 columns]\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0"
|
||
]
|
||
},
|
||
"execution_count": 2,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"import os\n",
|
||
"from sklearn.datasets import load_breast_cancer\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.metrics import confusion_matrix\n",
|
||
"from sklearn.tree import export_graphviz\n",
|
||
"\n",
|
||
"from IPython.display import Image \n",
|
||
"from pydot import graph_from_dot_data\n",
|
||
"import pandas as pd\n",
|
||
"import numpy as np\n",
|
||
"\n",
|
||
"\n",
|
||
"cancer = load_breast_cancer()\n",
|
||
"X = pd.DataFrame(cancer.data, columns=cancer.feature_names)\n",
|
||
"print(X)\n",
|
||
"y = pd.Categorical.from_codes(cancer.target, cancer.target_names)\n",
|
||
"y = pd.get_dummies(y)\n",
|
||
"print(y)\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)\n",
|
||
"tree_clf = DecisionTreeClassifier(max_depth=5)\n",
|
||
"tree_clf.fit(X_train, y_train)\n",
|
||
"\n",
|
||
"export_graphviz(\n",
|
||
" tree_clf,\n",
|
||
" out_file=\"DataFiles/cancer.dot\",\n",
|
||
" feature_names=cancer.feature_names,\n",
|
||
" class_names=cancer.target_names,\n",
|
||
" rounded=True,\n",
|
||
" filled=True\n",
|
||
")\n",
|
||
"cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'\n",
|
||
"os.system(cmd)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0"
|
||
]
|
||
},
|
||
"execution_count": 3,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Common imports\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.model_selection import train_test_split \n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.datasets import make_moons\n",
|
||
"from sklearn.tree import export_graphviz\n",
|
||
"from pydot import graph_from_dot_data\n",
|
||
"import pandas as pd\n",
|
||
"import os\n",
|
||
"\n",
|
||
"np.random.seed(42)\n",
|
||
"X, y = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X,y,random_state=0)\n",
|
||
"tree_clf = DecisionTreeClassifier(max_depth=5)\n",
|
||
"tree_clf.fit(X_train, y_train)\n",
|
||
"\n",
|
||
"export_graphviz(\n",
|
||
" tree_clf,\n",
|
||
" out_file=\"DataFiles/moons.dot\",\n",
|
||
" rounded=True,\n",
|
||
" filled=True\n",
|
||
")\n",
|
||
"cmd = 'dot -Tpng DataFiles/moons.dot -o DataFiles/moons.png'\n",
|
||
"os.system(cmd)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Other ways of visualizing the trees\n",
|
||
"\n",
|
||
"**Scikit-Learn** has also another way to visualize the trees which is very useful, here with the Iris data."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"[Text(0.5, 0.9166666666666666, 'x[2] <= 2.45\\ngini = 0.667\\nsamples = 150\\nvalue = [50, 50, 50]'),\n",
|
||
" Text(0.4230769230769231, 0.75, 'gini = 0.0\\nsamples = 50\\nvalue = [50, 0, 0]'),\n",
|
||
" Text(0.46153846153846156, 0.8333333333333333, 'True '),\n",
|
||
" Text(0.5769230769230769, 0.75, 'x[3] <= 1.75\\ngini = 0.5\\nsamples = 100\\nvalue = [0, 50, 50]'),\n",
|
||
" Text(0.5384615384615384, 0.8333333333333333, ' False'),\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",
|
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" 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",
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" Text(0.6923076923076923, 0.25, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 0, 2]'),\n",
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||
" 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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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.datasets import load_iris\n",
|
||
"from sklearn import tree\n",
|
||
"X, y = load_iris(return_X_y=True)\n",
|
||
"tree_clf = tree.DecisionTreeClassifier()\n",
|
||
"tree_clf = tree_clf.fit(X, y)\n",
|
||
"# and then plot the tree\n",
|
||
"tree.plot_tree(tree_clf)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Alternatively, the tree can also be exported in textual format with the function exporttext.\n",
|
||
"This method doesn’t require the installation of external libraries and is more compact:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"|--- petal width (cm) <= 0.80\n",
|
||
"| |--- class: 0\n",
|
||
"|--- petal width (cm) > 0.80\n",
|
||
"| |--- petal width (cm) <= 1.75\n",
|
||
"| | |--- class: 1\n",
|
||
"| |--- petal width (cm) > 1.75\n",
|
||
"| | |--- class: 2\n",
|
||
"\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.datasets import load_iris\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.tree import export_text\n",
|
||
"iris = load_iris()\n",
|
||
"decision_tree = DecisionTreeClassifier(random_state=0, max_depth=2)\n",
|
||
"decision_tree = decision_tree.fit(iris.data, iris.target)\n",
|
||
"r = export_text(decision_tree, feature_names=iris['feature_names'])\n",
|
||
"print(r)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Algorithms for Setting up Decision Trees\n",
|
||
"\n",
|
||
"Two algorithms stand out in the set up of decision trees:\n",
|
||
"1. The CART (Classification And Regression Tree) algorithm for both classification and regression\n",
|
||
"\n",
|
||
"2. The ID3 algorithm based on the computation of the information gain for classification\n",
|
||
"\n",
|
||
"We discuss both algorithms with applications here. The popular library\n",
|
||
"**Scikit-Learn** uses the CART algorithm. For classification problems\n",
|
||
"you can use either the **gini** index or the **entropy** to split a tree\n",
|
||
"in two branches.\n",
|
||
"\n",
|
||
"### The CART algorithm for Classification\n",
|
||
"\n",
|
||
"For classification, the CART algorithm splits the data set in two subsets using a single feature $k$ and a threshold $t_k$.\n",
|
||
"This could be for example a threshold set by a number below a certain circumference of a malign tumor.\n",
|
||
"\n",
|
||
"How do we find these two quantities?\n",
|
||
"We search for the pair $(k,t_k)$ that produces the purest subset using for example the **gini** factor $G$.\n",
|
||
"The cost function it tries to minimize is then"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"C(k,t_k) = \\frac{m_{\\mathrm{left}}}{m}G_{\\mathrm{left}}+ \\frac{m_{\\mathrm{right}}}{m}G_{\\mathrm{right}},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $G_{\\mathrm{left/right}}$ measures the impurity of the left/right subset and $m_{\\mathrm{left/right}}$\n",
|
||
" is the number of instances in the left/right subset\n",
|
||
"\n",
|
||
"Once it has successfully split the training set in two, it splits the subsets using the same logic, then the subsubsets\n",
|
||
"and so on, recursively. It stops recursing once it reaches the maximum depth (defined by the\n",
|
||
"$max\\_depth$ hyperparameter), or if it cannot find a split that will reduce impurity. A few other\n",
|
||
"hyperparameters control additional stopping conditions such as the $min\\_samples\\_split$,\n",
|
||
"$min\\_samples\\_leaf$, $min\\_weight\\_fraction\\_leaf$, and $max\\_leaf\\_nodes$.\n",
|
||
"\n",
|
||
"\n",
|
||
"### The CART algorithm for Regression\n",
|
||
"\n",
|
||
"The CART algorithm for regression works is similar to the one for classification except that instead of trying to split the\n",
|
||
"training set in a way that minimizes say the **gini** or **entropy** impurity, it now tries to split the training set in a way that minimizes our well-known mean-squared error (MSE). The cost function is now"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"C(k,t_k) = \\frac{m_{\\mathrm{left}}}{m}\\mathrm{MSE}_{\\mathrm{left}}+ \\frac{m_{\\mathrm{right}}}{m}\\mathrm{MSE}_{\\mathrm{right}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Here the MSE for a specific node is defined as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathrm{MSE}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}(\\overline{y}_{\\mathrm{node}}-y_i)^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"with"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\overline{y}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}y_i,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"the mean value of all observations in a specific node.\n",
|
||
"\n",
|
||
"Without any regularization, the regression task for decision trees, \n",
|
||
"just like for classification tasks, is prone to overfitting.\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"### Computing the Gini index\n",
|
||
"\n",
|
||
"The example we will look at is a classical one in many Machine\n",
|
||
"Learning applications. Based on various meteorological features, we\n",
|
||
"have several so-called attributes which decide whether we at the end\n",
|
||
"will do some outdoor activity like skiing, going for a bike ride etc\n",
|
||
"etc. The table here contains the feautures **outlook**, **temperature**,\n",
|
||
"**humidity** and **wind**. The target or output is whether we ride\n",
|
||
"(True=1) or whether we do something else that day (False=0). The\n",
|
||
"attributes for each feature are then sunny, overcast and rain for the\n",
|
||
"outlook, hot, cold and mild for temperature, high and normal for\n",
|
||
"humidity and weak and strong for wind.\n",
|
||
"\n",
|
||
"The table here summarizes the various attributes and\n",
|
||
"<table border=\"1\">\n",
|
||
"<thead>\n",
|
||
"<tr><th align=\"center\">Day</th> <th align=\"center\">Outlook </th> <th align=\"center\">Temperature</th> <th align=\"center\">Humidity</th> <th align=\"center\"> Wind </th> <th align=\"center\">Ride</th> </tr>\n",
|
||
"</thead>\n",
|
||
"<tbody>\n",
|
||
"<tr><td align=\"center\"> 1 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Hot </td> <td align=\"center\"> High </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 0 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 2 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Hot </td> <td align=\"center\"> High </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 3 </td> <td align=\"center\"> Overcast </td> <td align=\"center\"> Hot </td> <td align=\"center\"> High </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 4 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Mild </td> <td align=\"center\"> High </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 5 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Cool </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 6 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Cool </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 0 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 7 </td> <td align=\"center\"> Overcast </td> <td align=\"center\"> Cool </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 8 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Mild </td> <td align=\"center\"> High </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 0 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 9 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Cool </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 10 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Mild </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 11 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Mild </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 12 </td> <td align=\"center\"> Overcast </td> <td align=\"center\"> Mild </td> <td align=\"center\"> High </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 13 </td> <td align=\"center\"> Overcast </td> <td align=\"center\"> Hot </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 14 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Mild </td> <td align=\"center\"> High </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 0 </td> </tr>\n",
|
||
"</tbody>\n",
|
||
"</table>\n",
|
||
"\n",
|
||
"### Simple Python Code to read in Data and perform Classification"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
" (0, 0)\t1.0\n",
|
||
" (0, 7)\t1.0\n",
|
||
" (0, 9)\t1.0\n",
|
||
" (0, 13)\t1.0\n",
|
||
" (1, 3)\t1.0\n",
|
||
" (1, 5)\t1.0\n",
|
||
" (1, 8)\t1.0\n",
|
||
" (1, 12)\t1.0\n",
|
||
" (2, 3)\t1.0\n",
|
||
" (2, 5)\t1.0\n",
|
||
" (2, 8)\t1.0\n",
|
||
" (2, 11)\t1.0\n",
|
||
" (3, 1)\t1.0\n",
|
||
" (3, 5)\t1.0\n",
|
||
" (3, 8)\t1.0\n",
|
||
" (3, 12)\t1.0\n",
|
||
" (4, 2)\t1.0\n",
|
||
" (4, 6)\t1.0\n",
|
||
" (4, 8)\t1.0\n",
|
||
" (4, 12)\t1.0\n",
|
||
" (5, 2)\t1.0\n",
|
||
" (5, 4)\t1.0\n",
|
||
" (5, 10)\t1.0\n",
|
||
" (5, 12)\t1.0\n",
|
||
" (6, 2)\t1.0\n",
|
||
" :\t:\n",
|
||
" (8, 12)\t1.0\n",
|
||
" (9, 3)\t1.0\n",
|
||
" (9, 4)\t1.0\n",
|
||
" (9, 10)\t1.0\n",
|
||
" (9, 12)\t1.0\n",
|
||
" (10, 2)\t1.0\n",
|
||
" (10, 6)\t1.0\n",
|
||
" (10, 10)\t1.0\n",
|
||
" (10, 12)\t1.0\n",
|
||
" (11, 3)\t1.0\n",
|
||
" (11, 6)\t1.0\n",
|
||
" (11, 10)\t1.0\n",
|
||
" (11, 11)\t1.0\n",
|
||
" (12, 1)\t1.0\n",
|
||
" (12, 6)\t1.0\n",
|
||
" (12, 8)\t1.0\n",
|
||
" (12, 11)\t1.0\n",
|
||
" (13, 1)\t1.0\n",
|
||
" (13, 5)\t1.0\n",
|
||
" (13, 10)\t1.0\n",
|
||
" (13, 12)\t1.0\n",
|
||
" (14, 2)\t1.0\n",
|
||
" (14, 6)\t1.0\n",
|
||
" (14, 8)\t1.0\n",
|
||
" (14, 11)\t1.0\n",
|
||
"Train set accuracy with Decision Tree: 0.73\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0"
|
||
]
|
||
},
|
||
"execution_count": 6,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Common imports\n",
|
||
"import numpy as np\n",
|
||
"import pandas as pd\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.tree import export_graphviz\n",
|
||
"from sklearn.preprocessing import StandardScaler, OneHotEncoder\n",
|
||
"from sklearn.compose import ColumnTransformer\n",
|
||
"from IPython.display import Image \n",
|
||
"from pydot import graph_from_dot_data\n",
|
||
"import os\n",
|
||
"\n",
|
||
"# Where to save the figures and data files\n",
|
||
"PROJECT_ROOT_DIR = \"Results\"\n",
|
||
"FIGURE_ID = \"Results/FigureFiles\"\n",
|
||
"DATA_ID = \"DataFiles/\"\n",
|
||
"\n",
|
||
"if not os.path.exists(PROJECT_ROOT_DIR):\n",
|
||
" os.mkdir(PROJECT_ROOT_DIR)\n",
|
||
"\n",
|
||
"if not os.path.exists(FIGURE_ID):\n",
|
||
" os.makedirs(FIGURE_ID)\n",
|
||
"\n",
|
||
"if not os.path.exists(DATA_ID):\n",
|
||
" os.makedirs(DATA_ID)\n",
|
||
"\n",
|
||
"def image_path(fig_id):\n",
|
||
" return os.path.join(FIGURE_ID, fig_id)\n",
|
||
"\n",
|
||
"def data_path(dat_id):\n",
|
||
" return os.path.join(DATA_ID, dat_id)\n",
|
||
"\n",
|
||
"def save_fig(fig_id):\n",
|
||
" plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
|
||
"\n",
|
||
"infile = open(data_path(\"rideclass.csv\"),'r')\n",
|
||
"\n",
|
||
"# Read the experimental data with Pandas\n",
|
||
"from IPython.display import display\n",
|
||
"ridedata = pd.read_csv(infile,names = ('Outlook','Temperature','Humidity','Wind','Ride'))\n",
|
||
"ridedata = pd.DataFrame(ridedata)\n",
|
||
"\n",
|
||
"# Features and targets\n",
|
||
"X = ridedata.loc[:, ridedata.columns != 'Ride'].values\n",
|
||
"y = ridedata.loc[:, ridedata.columns == 'Ride'].values\n",
|
||
"\n",
|
||
"# Create the encoder.\n",
|
||
"encoder = OneHotEncoder(handle_unknown=\"ignore\")\n",
|
||
"# Assume for simplicity all features are categorical.\n",
|
||
"encoder.fit(X) \n",
|
||
"# Apply the encoder.\n",
|
||
"X = encoder.transform(X)\n",
|
||
"print(X)\n",
|
||
"# Then do a Classification tree\n",
|
||
"tree_clf = DecisionTreeClassifier(max_depth=2)\n",
|
||
"tree_clf.fit(X, y)\n",
|
||
"print(\"Train set accuracy with Decision Tree: {:.2f}\".format(tree_clf.score(X,y)))\n",
|
||
"#transfer to a decision tree graph\n",
|
||
"export_graphviz(\n",
|
||
" tree_clf,\n",
|
||
" out_file=\"DataFiles/ride.dot\",\n",
|
||
" rounded=True,\n",
|
||
" filled=True\n",
|
||
")\n",
|
||
"cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'\n",
|
||
"os.system(cmd)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"The above functions (gini, entropy and misclassification error) are\n",
|
||
"important components of the so-called CART algorithm. We will discuss\n",
|
||
"this algorithm below after we have discussed the information gain\n",
|
||
"algorithm ID3.\n",
|
||
"\n",
|
||
"In the example here we have converted all our attributes into numerical values $0,1,2$ etc."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 1.000 Gini=0.394\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X1 < 1.000 Gini=0.394\n",
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 1.000 Gini=0.394\n",
|
||
"X1 < 1.000 Gini=0.394\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X2 < 0.000 Gini=0.408\n",
|
||
"X2 < 0.000 Gini=0.408\n",
|
||
"X2 < 0.000 Gini=0.408\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 2.000 Gini=0.407\n",
|
||
"X2 < 2.000 Gini=0.407\n",
|
||
"X2 < 2.000 Gini=0.407\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 2.000 Gini=0.407\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 0.000 Gini=0.408\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"Split: [X3 < 1.000]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"# Split a dataset based on an attribute and an attribute value\n",
|
||
"def test_split(index, value, dataset):\n",
|
||
"\tleft, right = list(), list()\n",
|
||
"\tfor row in dataset:\n",
|
||
"\t\tif row[index] < value:\n",
|
||
"\t\t\tleft.append(row)\n",
|
||
"\t\telse:\n",
|
||
"\t\t\tright.append(row)\n",
|
||
"\treturn left, right\n",
|
||
" \n",
|
||
"# Calculate the Gini index for a split dataset\n",
|
||
"def gini_index(groups, classes):\n",
|
||
"\t# count all samples at split point\n",
|
||
"\tn_instances = float(sum([len(group) for group in groups]))\n",
|
||
"\t# sum weighted Gini index for each group\n",
|
||
"\tgini = 0.0\n",
|
||
"\tfor group in groups:\n",
|
||
"\t\tsize = float(len(group))\n",
|
||
"\t\t# avoid divide by zero\n",
|
||
"\t\tif size == 0:\n",
|
||
"\t\t\tcontinue\n",
|
||
"\t\tscore = 0.0\n",
|
||
"\t\t# score the group based on the score for each class\n",
|
||
"\t\tfor class_val in classes:\n",
|
||
"\t\t\tp = [row[-1] for row in group].count(class_val) / size\n",
|
||
"\t\t\tscore += p * p\n",
|
||
"\t\t# weight the group score by its relative size\n",
|
||
"\t\tgini += (1.0 - score) * (size / n_instances)\n",
|
||
"\treturn gini\n",
|
||
"\n",
|
||
"# Select the best split point for a dataset\n",
|
||
"def get_split(dataset):\n",
|
||
"\tclass_values = list(set(row[-1] for row in dataset))\n",
|
||
"\tb_index, b_value, b_score, b_groups = 999, 999, 999, None\n",
|
||
"\tfor index in range(len(dataset[0])-1):\n",
|
||
"\t\tfor row in dataset:\n",
|
||
"\t\t\tgroups = test_split(index, row[index], dataset)\n",
|
||
"\t\t\tgini = gini_index(groups, class_values)\n",
|
||
"\t\t\tprint('X%d < %.3f Gini=%.3f' % ((index+1), row[index], gini))\n",
|
||
"\t\t\tif gini < b_score:\n",
|
||
"\t\t\t\tb_index, b_value, b_score, b_groups = index, row[index], gini, groups\n",
|
||
"\treturn {'index':b_index, 'value':b_value, 'groups':b_groups}\n",
|
||
" \n",
|
||
"dataset = [[0,0,0,0,0],\n",
|
||
" [0,0,0,1,1],\n",
|
||
" [1,0,0,0,1],\n",
|
||
" [2,1,0,0,1],\n",
|
||
" [2,2,1,0,1],\n",
|
||
" [2,2,1,1,0],\n",
|
||
" [1,2,1,1,1],\n",
|
||
" [0,1,0,0,0],\n",
|
||
" [0,2,1,0,1],\n",
|
||
" [2,1,1,0,1],\n",
|
||
" [0,1,1,1,1],\n",
|
||
" [1,1,0,1,1],\n",
|
||
" [1,0,1,0,1],\n",
|
||
" [2,1,0,1,0]]\n",
|
||
"\n",
|
||
"split = get_split(dataset)\n",
|
||
"print('Split: [X%d < %.3f]' % ((split['index']+1), split['value']))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Entropy and the ID3 algorithm\n",
|
||
"\n",
|
||
"The ID3 algorithm learns decision trees by constructing\n",
|
||
"them in a top down way, beginning with the question **which attribute should be tested at the root of the tree**?\n",
|
||
"\n",
|
||
"1. Each instance attribute is evaluated using a statistical test to determine how well it alone classifies the training examples.\n",
|
||
"\n",
|
||
"2. The best attribute is selected and used as the test at the root node of the tree.\n",
|
||
"\n",
|
||
"3. A descendant of the root node is then created for each possible value of this attribute.\n",
|
||
"\n",
|
||
"4. Training examples are sorted to the appropriate descendant node.\n",
|
||
"\n",
|
||
"5. The entire process is then repeated using the training examples associated with each descendant node to select the best attribute to test at that point in the tree.\n",
|
||
"\n",
|
||
"6. This forms a greedy search for an acceptable decision tree, in which the algorithm never backtracks to reconsider earlier choices. \n",
|
||
"\n",
|
||
"The ID3 algorithm selects which attribute to test at each node in the\n",
|
||
"tree.\n",
|
||
"\n",
|
||
"We would like to select the attribute that is most useful for classifying\n",
|
||
"examples.\n",
|
||
"\n",
|
||
"What is a good quantitative measure of the worth of an attribute?\n",
|
||
"\n",
|
||
"Information gain measures how well a given attribute separates the\n",
|
||
"training examples according to their target classification.\n",
|
||
"\n",
|
||
"The ID3 algorithm uses this information gain measure to select among the candidate\n",
|
||
"attributes at each step while growing the tree.\n",
|
||
"\n",
|
||
"\n",
|
||
"### Cancer Data again now with Decision Trees and other Methods"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"(426, 30)\n",
|
||
"(143, 30)\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Test set accuracy with Logistic Regression: 0.95\n",
|
||
"Test set accuracy with SVM: 0.63\n",
|
||
"Test set accuracy with Decision Trees: 0.90\n",
|
||
"Test set accuracy Logistic Regression with scaled data: 0.96\n",
|
||
"Test set accuracy SVM with scaled data: 0.96\n",
|
||
"Test set accuracy with Decision Trees and scaled data: 0.89\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:465: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
|
||
"STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
|
||
"\n",
|
||
"Increase the number of iterations (max_iter) or scale the data as shown in:\n",
|
||
" https://scikit-learn.org/stable/modules/preprocessing.html\n",
|
||
"Please also refer to the documentation for alternative solver options:\n",
|
||
" https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
|
||
" n_iter_i = _check_optimize_result(\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.model_selection import train_test_split \n",
|
||
"from sklearn.datasets import load_breast_cancer\n",
|
||
"from sklearn.svm import SVC\n",
|
||
"from sklearn.linear_model import LogisticRegression\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"\n",
|
||
"# Load the data\n",
|
||
"cancer = load_breast_cancer()\n",
|
||
"\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
|
||
"print(X_train.shape)\n",
|
||
"print(X_test.shape)\n",
|
||
"# Logistic Regression\n",
|
||
"logreg = LogisticRegression(solver='lbfgs')\n",
|
||
"logreg.fit(X_train, y_train)\n",
|
||
"print(\"Test set accuracy with Logistic Regression: {:.2f}\".format(logreg.score(X_test,y_test)))\n",
|
||
"# Support vector machine\n",
|
||
"svm = SVC(gamma='auto', C=100)\n",
|
||
"svm.fit(X_train, y_train)\n",
|
||
"print(\"Test set accuracy with SVM: {:.2f}\".format(svm.score(X_test,y_test)))\n",
|
||
"# Decision Trees\n",
|
||
"deep_tree_clf = DecisionTreeClassifier(max_depth=None)\n",
|
||
"deep_tree_clf.fit(X_train, y_train)\n",
|
||
"print(\"Test set accuracy with Decision Trees: {:.2f}\".format(deep_tree_clf.score(X_test,y_test)))\n",
|
||
"#now scale the data\n",
|
||
"from sklearn.preprocessing import StandardScaler\n",
|
||
"scaler = StandardScaler()\n",
|
||
"scaler.fit(X_train)\n",
|
||
"X_train_scaled = scaler.transform(X_train)\n",
|
||
"X_test_scaled = scaler.transform(X_test)\n",
|
||
"# Logistic Regression\n",
|
||
"logreg.fit(X_train_scaled, y_train)\n",
|
||
"print(\"Test set accuracy Logistic Regression with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
|
||
"# Support Vector Machine\n",
|
||
"svm.fit(X_train_scaled, y_train)\n",
|
||
"print(\"Test set accuracy SVM with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
|
||
"# Decision Trees\n",
|
||
"deep_tree_clf.fit(X_train_scaled, y_train)\n",
|
||
"print(\"Test set accuracy with Decision Trees and scaled data: {:.2f}\".format(deep_tree_clf.score(X_test_scaled,y_test)))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Another example, the moons again"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"from __future__ import division, print_function, unicode_literals\n",
|
||
"\n",
|
||
"# Common imports\n",
|
||
"import numpy as np\n",
|
||
"import os\n",
|
||
"\n",
|
||
"# to make this notebook's output stable across runs\n",
|
||
"np.random.seed(42)\n",
|
||
"\n",
|
||
"# To plot pretty figures\n",
|
||
"import matplotlib\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from matplotlib.colors import ListedColormap\n",
|
||
"plt.rcParams['axes.labelsize'] = 14\n",
|
||
"plt.rcParams['xtick.labelsize'] = 12\n",
|
||
"plt.rcParams['ytick.labelsize'] = 12\n",
|
||
"\n",
|
||
"\n",
|
||
"from sklearn.svm import SVC\n",
|
||
"from sklearn import datasets\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.datasets import make_moons\n",
|
||
"from sklearn.tree import export_graphviz\n",
|
||
"\n",
|
||
"Xm, ym = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
|
||
"\n",
|
||
"deep_tree_clf1 = DecisionTreeClassifier(random_state=42)\n",
|
||
"deep_tree_clf2 = DecisionTreeClassifier(min_samples_leaf=4, random_state=42)\n",
|
||
"deep_tree_clf1.fit(Xm, ym)\n",
|
||
"deep_tree_clf2.fit(Xm, ym)\n",
|
||
"\n",
|
||
"\n",
|
||
"def plot_decision_boundary(clf, X, y, axes=[0, 7.5, 0, 3], iris=True, legend=False, plot_training=True):\n",
|
||
" x1s = np.linspace(axes[0], axes[1], 100)\n",
|
||
" x2s = np.linspace(axes[2], axes[3], 100)\n",
|
||
" x1, x2 = np.meshgrid(x1s, x2s)\n",
|
||
" X_new = np.c_[x1.ravel(), x2.ravel()]\n",
|
||
" y_pred = clf.predict(X_new).reshape(x1.shape)\n",
|
||
" custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
|
||
" plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)\n",
|
||
" if not iris:\n",
|
||
" custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])\n",
|
||
" plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)\n",
|
||
" if plot_training:\n",
|
||
" plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", label=\"Iris-Setosa\")\n",
|
||
" plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", label=\"Iris-Versicolor\")\n",
|
||
" plt.plot(X[:, 0][y==2], X[:, 1][y==2], \"g^\", label=\"Iris-Virginica\")\n",
|
||
" plt.axis(axes)\n",
|
||
" if iris:\n",
|
||
" plt.xlabel(\"Petal length\", fontsize=14)\n",
|
||
" plt.ylabel(\"Petal width\", fontsize=14)\n",
|
||
" else:\n",
|
||
" plt.xlabel(r\"$x_1$\", fontsize=18)\n",
|
||
" plt.ylabel(r\"$x_2$\", fontsize=18, rotation=0)\n",
|
||
" if legend:\n",
|
||
" plt.legend(loc=\"lower right\", fontsize=14)\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"plt.subplot(121)\n",
|
||
"plot_decision_boundary(deep_tree_clf1, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
|
||
"plt.title(\"No restrictions\", fontsize=16)\n",
|
||
"plt.subplot(122)\n",
|
||
"plot_decision_boundary(deep_tree_clf2, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
|
||
"plt.title(\"min_samples_leaf = {}\".format(deep_tree_clf2.min_samples_leaf), fontsize=14)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"np.random.seed(6)\n",
|
||
"Xs = np.random.rand(100, 2) - 0.5\n",
|
||
"ys = (Xs[:, 0] > 0).astype(np.float32) * 2\n",
|
||
"\n",
|
||
"angle = np.pi/4\n",
|
||
"rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])\n",
|
||
"Xsr = Xs.dot(rotation_matrix)\n",
|
||
"\n",
|
||
"tree_clf_s = DecisionTreeClassifier(random_state=42)\n",
|
||
"tree_clf_s.fit(Xs, ys)\n",
|
||
"tree_clf_sr = DecisionTreeClassifier(random_state=42)\n",
|
||
"tree_clf_sr.fit(Xsr, ys)\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"plt.subplot(121)\n",
|
||
"plot_decision_boundary(tree_clf_s, Xs, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
|
||
"plt.subplot(122)\n",
|
||
"plot_decision_boundary(tree_clf_sr, Xsr, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Quadratic training set + noise\n",
|
||
"np.random.seed(42)\n",
|
||
"m = 200\n",
|
||
"X = np.random.rand(m, 1)\n",
|
||
"y = 4 * (X - 0.5) ** 2\n",
|
||
"y = y + np.random.randn(m, 1) / 10"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/html": [
|
||
"<style>#sk-container-id-1 {\n",
|
||
" /* Definition of color scheme common for light and dark mode */\n",
|
||
" --sklearn-color-text: #000;\n",
|
||
" --sklearn-color-text-muted: #666;\n",
|
||
" --sklearn-color-line: gray;\n",
|
||
" /* Definition of color scheme for unfitted estimators */\n",
|
||
" --sklearn-color-unfitted-level-0: #fff5e6;\n",
|
||
" --sklearn-color-unfitted-level-1: #f6e4d2;\n",
|
||
" --sklearn-color-unfitted-level-2: #ffe0b3;\n",
|
||
" --sklearn-color-unfitted-level-3: chocolate;\n",
|
||
" /* Definition of color scheme for fitted estimators */\n",
|
||
" --sklearn-color-fitted-level-0: #f0f8ff;\n",
|
||
" --sklearn-color-fitted-level-1: #d4ebff;\n",
|
||
" --sklearn-color-fitted-level-2: #b3dbfd;\n",
|
||
" --sklearn-color-fitted-level-3: cornflowerblue;\n",
|
||
"\n",
|
||
" /* Specific color for light theme */\n",
|
||
" --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
|
||
" --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
|
||
" --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
|
||
" --sklearn-color-icon: #696969;\n",
|
||
"\n",
|
||
" @media (prefers-color-scheme: dark) {\n",
|
||
" /* Redefinition of color scheme for dark theme */\n",
|
||
" --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
|
||
" --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
|
||
" --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
|
||
" --sklearn-color-icon: #878787;\n",
|
||
" }\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 {\n",
|
||
" color: var(--sklearn-color-text);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 pre {\n",
|
||
" padding: 0;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 input.sk-hidden--visually {\n",
|
||
" border: 0;\n",
|
||
" clip: rect(1px 1px 1px 1px);\n",
|
||
" clip: rect(1px, 1px, 1px, 1px);\n",
|
||
" height: 1px;\n",
|
||
" margin: -1px;\n",
|
||
" overflow: hidden;\n",
|
||
" padding: 0;\n",
|
||
" position: absolute;\n",
|
||
" width: 1px;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-dashed-wrapped {\n",
|
||
" border: 1px dashed var(--sklearn-color-line);\n",
|
||
" margin: 0 0.4em 0.5em 0.4em;\n",
|
||
" box-sizing: border-box;\n",
|
||
" padding-bottom: 0.4em;\n",
|
||
" background-color: var(--sklearn-color-background);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-container {\n",
|
||
" /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
|
||
" but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
|
||
" so we also need the `!important` here to be able to override the\n",
|
||
" default hidden behavior on the sphinx rendered scikit-learn.org.\n",
|
||
" See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
|
||
" display: inline-block !important;\n",
|
||
" position: relative;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-text-repr-fallback {\n",
|
||
" display: none;\n",
|
||
"}\n",
|
||
"\n",
|
||
"div.sk-parallel-item,\n",
|
||
"div.sk-serial,\n",
|
||
"div.sk-item {\n",
|
||
" /* draw centered vertical line to link estimators */\n",
|
||
" background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
|
||
" background-size: 2px 100%;\n",
|
||
" background-repeat: no-repeat;\n",
|
||
" background-position: center center;\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Parallel-specific style estimator block */\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-parallel-item::after {\n",
|
||
" content: \"\";\n",
|
||
" width: 100%;\n",
|
||
" border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
|
||
" flex-grow: 1;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-parallel {\n",
|
||
" display: flex;\n",
|
||
" align-items: stretch;\n",
|
||
" justify-content: center;\n",
|
||
" background-color: var(--sklearn-color-background);\n",
|
||
" position: relative;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-parallel-item {\n",
|
||
" display: flex;\n",
|
||
" flex-direction: column;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
|
||
" align-self: flex-end;\n",
|
||
" width: 50%;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
|
||
" align-self: flex-start;\n",
|
||
" width: 50%;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
|
||
" width: 0;\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Serial-specific style estimator block */\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-serial {\n",
|
||
" display: flex;\n",
|
||
" flex-direction: column;\n",
|
||
" align-items: center;\n",
|
||
" background-color: var(--sklearn-color-background);\n",
|
||
" padding-right: 1em;\n",
|
||
" padding-left: 1em;\n",
|
||
"}\n",
|
||
"\n",
|
||
"\n",
|
||
"/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
|
||
"clickable and can be expanded/collapsed.\n",
|
||
"- Pipeline and ColumnTransformer use this feature and define the default style\n",
|
||
"- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
|
||
"*/\n",
|
||
"\n",
|
||
"/* Pipeline and ColumnTransformer style (default) */\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-toggleable {\n",
|
||
" /* Default theme specific background. It is overwritten whether we have a\n",
|
||
" specific estimator or a Pipeline/ColumnTransformer */\n",
|
||
" background-color: var(--sklearn-color-background);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Toggleable label */\n",
|
||
"#sk-container-id-1 label.sk-toggleable__label {\n",
|
||
" cursor: pointer;\n",
|
||
" display: flex;\n",
|
||
" width: 100%;\n",
|
||
" margin-bottom: 0;\n",
|
||
" padding: 0.5em;\n",
|
||
" box-sizing: border-box;\n",
|
||
" text-align: center;\n",
|
||
" align-items: start;\n",
|
||
" justify-content: space-between;\n",
|
||
" gap: 0.5em;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 label.sk-toggleable__label .caption {\n",
|
||
" font-size: 0.6rem;\n",
|
||
" font-weight: lighter;\n",
|
||
" color: var(--sklearn-color-text-muted);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
|
||
" /* Arrow on the left of the label */\n",
|
||
" content: \"▸\";\n",
|
||
" float: left;\n",
|
||
" margin-right: 0.25em;\n",
|
||
" color: var(--sklearn-color-icon);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
|
||
" color: var(--sklearn-color-text);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Toggleable content - dropdown */\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-toggleable__content {\n",
|
||
" max-height: 0;\n",
|
||
" max-width: 0;\n",
|
||
" overflow: hidden;\n",
|
||
" text-align: left;\n",
|
||
" /* unfitted */\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-0);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
|
||
" /* fitted */\n",
|
||
" background-color: var(--sklearn-color-fitted-level-0);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-toggleable__content pre {\n",
|
||
" margin: 0.2em;\n",
|
||
" border-radius: 0.25em;\n",
|
||
" color: var(--sklearn-color-text);\n",
|
||
" /* unfitted */\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-0);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
|
||
" /* unfitted */\n",
|
||
" background-color: var(--sklearn-color-fitted-level-0);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
|
||
" /* Expand drop-down */\n",
|
||
" max-height: 200px;\n",
|
||
" max-width: 100%;\n",
|
||
" overflow: auto;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
|
||
" content: \"▾\";\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Pipeline/ColumnTransformer-specific style */\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
|
||
" color: var(--sklearn-color-text);\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-2);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
|
||
" background-color: var(--sklearn-color-fitted-level-2);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Estimator-specific style */\n",
|
||
"\n",
|
||
"/* Colorize estimator box */\n",
|
||
"#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
|
||
" /* unfitted */\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-2);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
|
||
" /* fitted */\n",
|
||
" background-color: var(--sklearn-color-fitted-level-2);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
|
||
"#sk-container-id-1 div.sk-label label {\n",
|
||
" /* The background is the default theme color */\n",
|
||
" color: var(--sklearn-color-text-on-default-background);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* On hover, darken the color of the background */\n",
|
||
"#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
|
||
" color: var(--sklearn-color-text);\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-2);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Label box, darken color on hover, fitted */\n",
|
||
"#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
|
||
" color: var(--sklearn-color-text);\n",
|
||
" background-color: var(--sklearn-color-fitted-level-2);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Estimator label */\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-label label {\n",
|
||
" font-family: monospace;\n",
|
||
" font-weight: bold;\n",
|
||
" display: inline-block;\n",
|
||
" line-height: 1.2em;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-label-container {\n",
|
||
" text-align: center;\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Estimator-specific */\n",
|
||
"#sk-container-id-1 div.sk-estimator {\n",
|
||
" font-family: monospace;\n",
|
||
" border: 1px dotted var(--sklearn-color-border-box);\n",
|
||
" border-radius: 0.25em;\n",
|
||
" box-sizing: border-box;\n",
|
||
" margin-bottom: 0.5em;\n",
|
||
" /* unfitted */\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-0);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-estimator.fitted {\n",
|
||
" /* fitted */\n",
|
||
" background-color: var(--sklearn-color-fitted-level-0);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* on hover */\n",
|
||
"#sk-container-id-1 div.sk-estimator:hover {\n",
|
||
" /* unfitted */\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-2);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
|
||
" /* fitted */\n",
|
||
" background-color: var(--sklearn-color-fitted-level-2);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
|
||
"\n",
|
||
"/* Common style for \"i\" and \"?\" */\n",
|
||
"\n",
|
||
".sk-estimator-doc-link,\n",
|
||
"a:link.sk-estimator-doc-link,\n",
|
||
"a:visited.sk-estimator-doc-link {\n",
|
||
" float: right;\n",
|
||
" font-size: smaller;\n",
|
||
" line-height: 1em;\n",
|
||
" font-family: monospace;\n",
|
||
" background-color: var(--sklearn-color-background);\n",
|
||
" border-radius: 1em;\n",
|
||
" height: 1em;\n",
|
||
" width: 1em;\n",
|
||
" text-decoration: none !important;\n",
|
||
" margin-left: 0.5em;\n",
|
||
" text-align: center;\n",
|
||
" /* unfitted */\n",
|
||
" border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
|
||
" color: var(--sklearn-color-unfitted-level-1);\n",
|
||
"}\n",
|
||
"\n",
|
||
".sk-estimator-doc-link.fitted,\n",
|
||
"a:link.sk-estimator-doc-link.fitted,\n",
|
||
"a:visited.sk-estimator-doc-link.fitted {\n",
|
||
" /* fitted */\n",
|
||
" border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
|
||
" color: var(--sklearn-color-fitted-level-1);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* On hover */\n",
|
||
"div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
|
||
".sk-estimator-doc-link:hover,\n",
|
||
"div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
|
||
".sk-estimator-doc-link:hover {\n",
|
||
" /* unfitted */\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-3);\n",
|
||
" color: var(--sklearn-color-background);\n",
|
||
" text-decoration: none;\n",
|
||
"}\n",
|
||
"\n",
|
||
"div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
|
||
".sk-estimator-doc-link.fitted:hover,\n",
|
||
"div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
|
||
".sk-estimator-doc-link.fitted:hover {\n",
|
||
" /* fitted */\n",
|
||
" background-color: var(--sklearn-color-fitted-level-3);\n",
|
||
" color: var(--sklearn-color-background);\n",
|
||
" text-decoration: none;\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Span, style for the box shown on hovering the info icon */\n",
|
||
".sk-estimator-doc-link span {\n",
|
||
" display: none;\n",
|
||
" z-index: 9999;\n",
|
||
" position: relative;\n",
|
||
" font-weight: normal;\n",
|
||
" right: .2ex;\n",
|
||
" padding: .5ex;\n",
|
||
" margin: .5ex;\n",
|
||
" width: min-content;\n",
|
||
" min-width: 20ex;\n",
|
||
" max-width: 50ex;\n",
|
||
" color: var(--sklearn-color-text);\n",
|
||
" box-shadow: 2pt 2pt 4pt #999;\n",
|
||
" /* unfitted */\n",
|
||
" background: var(--sklearn-color-unfitted-level-0);\n",
|
||
" border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
|
||
"}\n",
|
||
"\n",
|
||
".sk-estimator-doc-link.fitted span {\n",
|
||
" /* fitted */\n",
|
||
" background: var(--sklearn-color-fitted-level-0);\n",
|
||
" border: var(--sklearn-color-fitted-level-3);\n",
|
||
"}\n",
|
||
"\n",
|
||
".sk-estimator-doc-link:hover span {\n",
|
||
" display: block;\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* \"?\"-specific style due to the `<a>` HTML tag */\n",
|
||
"\n",
|
||
"#sk-container-id-1 a.estimator_doc_link {\n",
|
||
" float: right;\n",
|
||
" font-size: 1rem;\n",
|
||
" line-height: 1em;\n",
|
||
" font-family: monospace;\n",
|
||
" background-color: var(--sklearn-color-background);\n",
|
||
" border-radius: 1rem;\n",
|
||
" height: 1rem;\n",
|
||
" width: 1rem;\n",
|
||
" text-decoration: none;\n",
|
||
" /* unfitted */\n",
|
||
" color: var(--sklearn-color-unfitted-level-1);\n",
|
||
" border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 a.estimator_doc_link.fitted {\n",
|
||
" /* fitted */\n",
|
||
" border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
|
||
" color: var(--sklearn-color-fitted-level-1);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* On hover */\n",
|
||
"#sk-container-id-1 a.estimator_doc_link:hover {\n",
|
||
" /* unfitted */\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-3);\n",
|
||
" color: var(--sklearn-color-background);\n",
|
||
" text-decoration: none;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
|
||
" /* fitted */\n",
|
||
" background-color: var(--sklearn-color-fitted-level-3);\n",
|
||
"}\n",
|
||
"</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 fitted 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 fitted sk-toggleable__label-arrow\"><div><div>DecisionTreeRegressor</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.6/modules/generated/sklearn.tree.DecisionTreeRegressor.html\">?<span>Documentation for DecisionTreeRegressor</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\"><pre>DecisionTreeRegressor(max_depth=2, random_state=42)</pre></div> </div></div></div></div>"
|
||
],
|
||
"text/plain": [
|
||
"DecisionTreeRegressor(max_depth=2, random_state=42)"
|
||
]
|
||
},
|
||
"execution_count": 12,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.tree import DecisionTreeRegressor\n",
|
||
"\n",
|
||
"tree_reg = DecisionTreeRegressor(max_depth=2, random_state=42)\n",
|
||
"tree_reg.fit(X, y)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 13,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.tree import DecisionTreeRegressor\n",
|
||
"\n",
|
||
"tree_reg1 = DecisionTreeRegressor(random_state=42, max_depth=2)\n",
|
||
"tree_reg2 = DecisionTreeRegressor(random_state=42, max_depth=3)\n",
|
||
"tree_reg1.fit(X, y)\n",
|
||
"tree_reg2.fit(X, y)\n",
|
||
"\n",
|
||
"def plot_regression_predictions(tree_reg, X, y, axes=[0, 1, -0.2, 1], ylabel=\"$y$\"):\n",
|
||
" x1 = np.linspace(axes[0], axes[1], 500).reshape(-1, 1)\n",
|
||
" y_pred = tree_reg.predict(x1)\n",
|
||
" plt.axis(axes)\n",
|
||
" plt.xlabel(\"$x_1$\", fontsize=18)\n",
|
||
" if ylabel:\n",
|
||
" plt.ylabel(ylabel, fontsize=18, rotation=0)\n",
|
||
" plt.plot(X, y, \"b.\")\n",
|
||
" plt.plot(x1, y_pred, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"plt.subplot(121)\n",
|
||
"plot_regression_predictions(tree_reg1, X, y)\n",
|
||
"for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
|
||
" plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
|
||
"plt.text(0.21, 0.65, \"Depth=0\", fontsize=15)\n",
|
||
"plt.text(0.01, 0.2, \"Depth=1\", fontsize=13)\n",
|
||
"plt.text(0.65, 0.8, \"Depth=1\", fontsize=13)\n",
|
||
"plt.legend(loc=\"upper center\", fontsize=18)\n",
|
||
"plt.title(\"max_depth=2\", fontsize=14)\n",
|
||
"\n",
|
||
"plt.subplot(122)\n",
|
||
"plot_regression_predictions(tree_reg2, X, y, ylabel=None)\n",
|
||
"for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
|
||
" plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
|
||
"for split in (0.0458, 0.1298, 0.2873, 0.9040):\n",
|
||
" plt.plot([split, split], [-0.2, 1], \"k:\", linewidth=1)\n",
|
||
"plt.text(0.3, 0.5, \"Depth=2\", fontsize=13)\n",
|
||
"plt.title(\"max_depth=3\", fontsize=14)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"tree_reg1 = DecisionTreeRegressor(random_state=42)\n",
|
||
"tree_reg2 = DecisionTreeRegressor(random_state=42, min_samples_leaf=10)\n",
|
||
"tree_reg1.fit(X, y)\n",
|
||
"tree_reg2.fit(X, y)\n",
|
||
"\n",
|
||
"x1 = np.linspace(0, 1, 500).reshape(-1, 1)\n",
|
||
"y_pred1 = tree_reg1.predict(x1)\n",
|
||
"y_pred2 = tree_reg2.predict(x1)\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"\n",
|
||
"plt.subplot(121)\n",
|
||
"plt.plot(X, y, \"b.\")\n",
|
||
"plt.plot(x1, y_pred1, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
|
||
"plt.axis([0, 1, -0.2, 1.1])\n",
|
||
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
|
||
"plt.ylabel(\"$y$\", fontsize=18, rotation=0)\n",
|
||
"plt.legend(loc=\"upper center\", fontsize=18)\n",
|
||
"plt.title(\"No restrictions\", fontsize=14)\n",
|
||
"\n",
|
||
"plt.subplot(122)\n",
|
||
"plt.plot(X, y, \"b.\")\n",
|
||
"plt.plot(x1, y_pred2, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
|
||
"plt.axis([0, 1, -0.2, 1.1])\n",
|
||
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
|
||
"plt.title(\"min_samples_leaf={}\".format(tree_reg2.min_samples_leaf), fontsize=14)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Pros and cons of trees, pros\n",
|
||
"\n",
|
||
"* White box, easy to interpret model. Some people believe that decision trees more closely mirror human decision-making than do the regression and classification approaches discussed earlier (think of support vector machines)\n",
|
||
"\n",
|
||
"* Trees are very easy to explain to people. In fact, they are even easier to explain than linear regression!\n",
|
||
"\n",
|
||
"* No feature normalization needed\n",
|
||
"\n",
|
||
"* Tree models can handle both continuous and categorical data (Classification and Regression Trees)\n",
|
||
"\n",
|
||
"* Can model nonlinear relationships\n",
|
||
"\n",
|
||
"* Can model interactions between the different descriptive features\n",
|
||
"\n",
|
||
"* Trees can be displayed graphically, and are easily interpreted even by a non-expert (especially if they are small)\n",
|
||
"\n",
|
||
"### Disadvantages\n",
|
||
"\n",
|
||
"* Unfortunately, trees generally do not have the same level of predictive accuracy as some of the other regression and classification approaches\n",
|
||
"\n",
|
||
"* If continuous features are used the tree may become quite large and hence less interpretable\n",
|
||
"\n",
|
||
"* Decision trees are prone to overfit the training data and hence do not well generalize the data if no stopping criteria or improvements like pruning, boosting or bagging are implemented\n",
|
||
"\n",
|
||
"* Small changes in the data may lead to a completely different tree. This issue can be addressed by using ensemble methods like bagging, boosting or random forests\n",
|
||
"\n",
|
||
"* Unbalanced datasets where some target feature values occur much more frequently than others may lead to biased trees since the frequently occurring feature values are preferred over the less frequently occurring ones. \n",
|
||
"\n",
|
||
"* If the number of features is relatively large (high dimensional) and the number of instances is relatively low, the tree might overfit the data\n",
|
||
"\n",
|
||
"* Features with many levels may be preferred over features with less levels since for them it is *more easy* to split the dataset such that the sub datasets only contain pure target feature values. This issue can be addressed by preferring for instance the information gain ratio as splitting criteria over information gain\n",
|
||
"\n",
|
||
"However, by aggregating many decision trees, using methods like\n",
|
||
"bagging, random forests, and boosting, the predictive performance of\n",
|
||
"trees can be substantially improved."
|
||
]
|
||
}
|
||
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|
||
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