Morten Hjorth-Jensen
3501 lines
654 KiB
Plaintext
3501 lines
654 KiB
Plaintext
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"<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
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"doconce format html week46.do.txt --no_mako -->\n",
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"<!-- dom:TITLE: Week 46: Decision Trees, Ensemble methods and Random Forests -->"
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"# Week 46: Decision Trees, Ensemble methods and Random Forests\n",
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"**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
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"\n",
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"Date: **Week 46, November 13-17**"
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"source": [
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"## Plan for week 46\n",
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"\n",
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"**Active learning sessions on Tuesday and Wednesday.**\n",
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"\n",
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" * Work and Discussion of project 2\n",
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"\n",
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" * Discussion of project 3 as well\n",
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"\n",
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" \n",
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"\n",
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"**Material for the lecture on Thursday November 16, 2023.**\n",
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"\n",
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" * Thursday: Basics of decision trees, classification and regression algorithms and ensemble models \n",
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"\n",
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" * Readings and Videos:\n",
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"\n",
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" * These lecture notes\n",
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"\n",
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" * [Video of lecture to be added](https://youtu.be/)\n",
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"\n",
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" * [Video on Decision trees](https://www.youtube.com/watch?v=RmajweUFKvM&ab_channel=Simplilearn)\n",
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"\n",
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" * Decision Trees: Geron's chapter 6 covers decision trees while ensemble models, voting and bagging are discussed in chapter 7. See also lecture from [STK-IN4300, lecture 7](https://www.uio.no/studier/emner/matnat/math/STK-IN4300/h20/slides/lecture_7.pdf). Chapter 9.2 of Hastie et al contains also a good discussion."
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"source": [
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"## Decision trees, overarching aims\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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"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**."
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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."
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"## A typical Decision Tree with its pertinent Jargon, Classification Problem\n",
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"\n",
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"<!-- dom:FIGURE: [DataFiles/cancer.png, width=600 frac=0.8] -->\n",
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"<!-- begin figure -->\n",
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"\n",
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"<img src=\"DataFiles/cancer.png\" width=\"600\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
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"<!-- end figure -->\n",
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"\n",
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"This tree was produced using the Wisconsin cancer data (discussed here as well, see code examples below) using **Scikit-Learn**'s decision tree classifier. Here we have used the so-called **gini** index (see below) to split the various branches."
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"source": [
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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."
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"source": [
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"## How do we set it up?\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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"metadata": {},
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"source": [
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"## Decision trees and Regression"
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]
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"text": [
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"2nd degree coefficients:\n",
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"zero power: 0.7163225806451621\n",
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"first power: 0.17047319577389736\n",
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"second power: -0.0006648714674365666\n"
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]
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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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14sSJalZWlrbe8ePH1dtuu01t3ry52rhxY/WSSy5RV61apQLq22+/raWz9WY6cuSIw/3/73//U8877zy1SZMmanh4uNqhQwd17NixWi+r7du3qzfddJPaoUMHNTw8XI2MjFTPPfdcNTU1VdvGjz/+qA4bNkxt1aqVdr5efvnl6h9//KGlcdSbSVVV9Y8//lAvuugibf99+/ZVf/jhB7s0VX2Gts976dKlVRx5IVxPRgAWQgg3+vzzz7nllltYsWIF/fv393R2hPBLEswIIYSLfPHFFxw8eJDu3btjMBhYtWoVr7/+Or17927wxyMIEUikzYwQQrhIREQEc+bM4ZVXXiE/Px+TycS4ceN45ZVXPJ01IfyalMwIIYQQwqfJoHlCCCGE8GkSzAghhBDCp0kwI4QQQgif5vcNgK1WK4cOHSIiIkIGexJCCCF8hKqqnDx5kvj4+BoHnfT7YObQoUO0adPG09kQQgghRB3s37+/xofx+n0wExERAZQdjGbNmnk4N0IIIYRwRm5uLm3atNHu49Xx+2DGVrXUrFkzCWaEEEIIH+NMExFpACyEEEIInybBjBBCCCF8mgQzQgghhPBpEswIIYQQwqdJMCOEEEIInybBjBBCCCF8mgQzQgghhPBpEswIIYQQwqdJMCOEEEIInybBjBBCCCF8mgQzQgghhPBpEswIIYQQwqdJMCOEEMIhi8XC4sWL2b17N4sXL8ZisVSaP3/+fObPn19pWVXTNe2rpnRCOOL3T80WQghRexaLhaSkJMxmMwaDAavVislkYsWKFQwYMACz2YyiKKiqCkBcXBx//fWXtqxiWpPJREZGBkajsdp9VZdOiKpIyYwQQohK0tLSMJvNAFitVgDMZjPz5s3T5tsCGYCsrCy7ZRXTms1m0tPTa9xXdemEqIoEM0IIISpJSUnBZDIBYDCU3Sri4+MZNWqUNl9RFC19XFyc3bKKaePj40lOTq5xX9WlE6IqiqoPrf1Qbm4ukZGRnDhxgmbNmnk6O0II4TMsFgvp6ekkJiaya9cukpOTMRqNdvM3btwIwMCBA+2WVUxrm65pXzWlE4GjNvdvCWaEEEII4XVqc/+WaiYhhBBC+DQJZoQQQgjh0ySYEUIIIYRPk2BGCCGEED5NghkhhBBC+DQJZoQQQgjh0ySYEUIIIYRPk2BGCCGEED5NghkhhBBC+DQJZoQQQgjh0xp5OgNCCCE8rzS/lC0jtpC7OtfTWalRcItgOk3tRPRl0Z7OivASEswIIYTg2M/HsCy2eDobTik9WcqBNw9IMCM0EswIIYSgNK9Uex0SF0KjKC+8PahwatspoKwkSQgbj56tv//+O6+//jppaWmYzWbmz5/PiBEjHKa95557+Oijj/jvf//LhAkTGjSfQgjh96zlL9u/1J74u+I9l5cqqKrKcsNyT2dDeCGPNgDOz8+nZ8+evPfee9Wm+/bbb1m9ejXx8d735RJCCH+gWlXttWJQPJgTJ6k1JxGBw6MlM8OGDWPYsGHVpjl48CAPPPAAv/zyC1dccUUD5UwIIbyHxWIhLS2NlJQUANLS0ujQoQOZmZmkpKRgNBqdXt9oNGKxWFi2bBkAgwYNKltfVzKzddtWCnYXVNp+xe3UtI+q8lwx786ktf3f6MxtS1UlmhHlvLBStJzVamXMmDE89thjJCUlObVOYWEhhYWF2nRurve3zBdCiKpYLBaSkpIwm83ExsaiKApZWVkYDAasVismk4mMjIwqA5rjx49z9rlnk30km5iYGL6Z/w0jrh7B0aNHAWjZsiW/LfkNJb+8NOb1919n0SeLUK0qMTExLP5tMQAXD7mY7OxsbV7zyOYA5JzIsVv2zfxvGHnNSLKzs2nRogWKonDkyBEUg4JqVbX/a5PW9v9SlgJQVFrE/hP7ATBFmGhk8OrbmXAzr/70/+///o9GjRrx0EMPOb3OpEmTePHFF92YKyGEaDi2NoUAhw8f1uZbrWVFKWazmfT0dIYMGVJpXatq5YLUC8gekw1ANtmc//X5MLY8zRGO0OPTHoxYM4J/8a+y9YZZUXuq2jo9Pu1Rlng0lefZ6Jad//X52vRRjmpJ1DN1Q7b/a5PW9j8vlP23wbyB/lP6A9C6WWvS706nZZOWlY6BCAxeO2heWloab7/9NqmpqSiK8/W3Tz31FCdOnND+9u/f78ZcCiGEe6WkpGAymQCIi4sjLi4OAIOh7PIdHx9PcnKyw3UzsjPYenKrU/tR1PLrrKp4bxWO1VYfpsvigdwD/JL5i2cyJLyC15bM/PHHH2RnZ9O2bVttXmlpKY888ghTpkxhz549DtcLDQ0lNDS0gXIphBDuZTQaycjIID09XQta0tPTSUxMZNeuXSQnJ1dZxVRsLdZex4fFc07rcwgJCaGoqIgjR44AZdVMISEh9NhTXtJyVrOzCGkXQl5+HsbmRkJCQgAoKirCkmOxm2dTcZl+GsCSY6Fpk6bk5edp/9cmre1/FECFqPAokk3JpJvTASixlrjgaAtf5bXBzJgxY7j44ovt5g0dOpQxY8Zw2223eShXQgjR8IxGo101ku11QkJCtetZ1fJWvdd0v4b3Lq+65+j+A/vJJBOA5y97npgbYuqTZbdZ9tAyUKGjsSP3pNzDPT/e4+ksCS/g0WAmLy+Pf/75R5vevXs3GzZsICoqirZt2xIdbT+6Y3BwMHFxcXTu3LmhsyqEED5H3+PHoNTQqkBfs+S1DRAoK5mhcm8m6d0U2DwazKxbt47Bgwdr0w8//DAAt956K6mpqR7KlRBC+Ad9yYxC9W0PfWWcGUVRyhsDC3GGR4OZQYMG1SqarqqdjBBCiMr0N/0aO1Loxpnx6pIZG9U+QJMAJ7D5wikrhBCiDmpTzeQrJTNa/CKxi9CRYEYIIfxUbaqZfKZkxovjLOE5XtubSQghApWqqmy9cSvHfjjmdAlE1LAokr5KsitVsapWnvrmKS7YdgEhSgi/G36vcn1rsS7wCfKBiEG1rzqTBsCBTYIZIYTwMnkb8jgy90it1jk6/ygn156k2XnNtHnqPyqXbrpUm7baFb9UrVGUF98aqujNJAKbF5+xQggRmKynyoOO4BbBhLQKqTJt0aEiio+UDY5XeqrUfjv55dspalaEMaH6B1ICGC822gVE3kbfm6nGqjMRMCSYEUIIL6MvdYgbF0eH1ztUmXbX07vYN2nfmRUrLNTFNuaLzFw6/1L8hlpxUkpqApk3N/MSQojApL8v16PwQS0t35Aa5Cc3e+nNJByQYEYIIbxNbYIZ/fIKN3hrqa6NjL9c7XXvtzYPIRb+zV9ObyGE8B91DGYqNYrVN6EJqmeevE3FaiZpEBzQJJgRQggvo78x11T6YLe8YslMia5kxl+CGenNJByQYEYIIbyNi6qZ9G1m/OVqrw/e5HEGwsZPTm8hhPAjLgpmAqmaSQQ2CWaE8BMWi4XFixdjsViqnSd8gO5GvWfPHu3zc/R5FhQUlK+mq3opOFAAH+s2GaRWe47s3r27wc+V2p6fFouFEmtJ2YQEM0JHxpkRwg9YLBaSkpIwm82YTCYyMjIAKs0zGmseNE14nv6hj7M+n8XopaNZsWIFAwYMqPQZT506lWu5FoC8k3lEEw3AhqEbCNlaPtje6aLT1Z4jBoMBq9XaYOeKo3O2un3a0n906iOa0pTS0lJ5nIHQSMmMEH4gLS0Ns9kMgNlsJj093eE84SMq3JfNZjPz5s1z+Bnn5uVq6f755x/tdcHWArttpIVXf45YrVa7Ze5W2/NTnx7sS6SEkGBGCD+QkpKCyWQCID4+nuTkZIfzhI9Q9S9V4uPjGTVqlMPPuGnTplrajh06lq1ToZRi9IOjMV5hrPYcMRgMdsvcrbbnpz49QFhomDzOQGikmkkIP2A0GsnIyCA9PZ3k5GStuN7RPOHdlu9ZzqIVi7iESwBof3l7+o3ux7/T/03/N/tz3HKcKGMU9y+5H4Ael/WAr8rWnbphKvuD9oMV7uZuALa03sLB6INEG6OrPUcSExPZtWtXg50rVZ2zNaXf0HYD5JUHXzbSmymwSTAjhJ8wGo0MGTKkxnnCe5VaS7n+q+tpv6u9FszsOrWLr//+2j6h7oHaQceC6EtfAH7f8zurQldhsBq0YMZWeBEcFFzjOZKQkOD6N1WN2p6fRqOR4EbBlFAiDYCFHalmEkIIL1FsLSY7PxtFdb76RFV0A+xpI8rplqMSFR7FlWdd6apsepbu2UzyOANhIyUzQgjhJWxtXfRtQSb0m8ALD71Q5Tonik+QsyQHgI+v/JjGlzVGLVbZ93LZk7T7tOrDwYcPEtYozG35blBVxC/SmymwSTAjhBDeRndfNjY20t7YvsqkexvvJYccAGKbxNLC2AJrkZV9lAUzYSFh/hPI6EnsInSkmkkIIbyMvmSmxqoURyMA12YEYV+jezaTPM5A2EgwI4QQXsJ2Q7ZrM1OHp2brB93zt3Yl/vZ+hGtIMCOEEF7GbvyUmgpmHD01259LZmykIEboSDAjhBBeQmvEWt8HTfpzMFNFbyZpABzYJJgRQggvU6s2Mw7Y3dj9NZgRQkeCGSGE8BL1bTPjqGTGb9uYSEGM0JFgRgghvExt2sw4agBsd6P3t6u89GYSDvjbaS6EED6rLm1mAq0BsPZ+JXYROhLMCCGEl6nvODP+3DXbrtDK396bqDMJZoQQwku4o82Mv5XMaCqUzEhvpsDm0WDm999/58orryQ+Ph5FUfj222+1ZcXFxTzxxBN0796dJk2aEB8fz9ixYzl06JDnMiyEEA2gVm1mHPHnYEbXNVsIG48GM/n5+fTs2ZP33nuv0rJTp06Rnp7Os88+S3p6Ot988w1///03V111lQdyKoQQ7ueozYxicL6aSRsBOEC6ZksDYGHj0QdNDhs2jGHDhjlcFhkZya+//mo379133+Xcc89l3759tG3btiGyKGrBYrGQlpZGSkoKRqPR09nxGRaLhWXLlgEwaNCgWh+7isfd0facSVNdvnr16kVmZqZ8tg0gNieWUStHlc+oRQPgLZu2EDI0hBJLicPl/qTwQCF8D0GlQZQGlXo6O8LDfOqp2SdOnEBRFJo3b15lmsLCQgoLC7Xp3NzcBsiZsFgsJCUlYTabMZlMZGRkyE3PCRaLhbPPPpvDhw8DEBcXx9atW50+dhWP+4oVK+jXr5/d9v766y8GDBhQbZqK+6yYL4PBgNVqlc/Wzayqlddnvk6b4220eadOn6p+JV2sMmnSJLb8bwuR1kimMQ2A4tJid2TVY/SlTqZnTAwbPowf+/zowRwJb+AzDYALCgp48sknufnmm2nWrFmV6SZNmkRkZKT216ZNmyrTCtdJS0vDbDYDYDabSU9P93COfENaWpoWMABkZWXV6thVPO7z5s2rtL158+bVmKbiPivmy2q1auvLZ+s+aoFqF8hYsbI/cn/1K1Wodjl8+DBHjhzR5p04ccLV2fSowrML7aYTDycC0gA40PlEyUxxcTE33ngjVquVqVOnVpv2qaee4uGHH9amc3NzJaBpACkpKZhMJsxmM/Hx8SQnJ3s6Sz4hJSWF2NhYu1KS2hy79hnt+U/YfzhdcJrwsHAGLRvEpNBJFBQWABAWGsagZYNqTBP1ThQZH2Zo240uirZLo6CgonIk4gi9uvVy0bsXFem7VAM8HPMwS29YWv1KFWqR4uLiiCyNhDPxTKQx0oU59LxeX/TiyQ5PcvPJm4EKjaVFwPL6YKa4uJjrr7+e3bt3s2TJkmpLZQBCQ0MJDQ1toNwJG6PRSEZGBunp6SQnJ0s1hJOMRiPbtm1j+fLlAAwcONDpY5e/NZ8DEw5wHueVzSiAUwtO0Ze+5YkKy+bVlObE95V/vdulsTkJpctL4XqnsihqSV+68E+nf1i6emmtvktPPfkUvR/vTbG5mK1JWwEICQlxeT49KaplFM//8Dw7B+0EKnRjFwHLq4MZWyCzc+dOli5dSnR0tKezJKphNBoZMmSIp7Phc4xGIyNGjKj1eoUHCmtO5Aae2m9A0BXMNApp5FQgo2/g27VrV4xGI4WndJ+RH97rI5uXlzbZghnpzRTYPBrM5OXl8c8//2jTu3fvZsOGDURFRREfH891111Heno6P/74I6WlpWRlZQEQFRXld782hKgtfZVE64mtaf1wa7ft6/hPx/l7/N9nduy23QS8OnWpdjQCsD93zQa792RQfabpp3AjjwYz69atY/Dgwdq0ra3LrbfeygsvvMD3338PlHUL1Vu6dCmDBg1qqGwK4Z2s5S8bNW9EWOswt+0quEWw9loaWrpRXQ6t7sZ+7MdjFJmLKDnh512zJX4RFXg0mBk0aFC1F0a5aApRNbvGou6+uDsaMl+4nP4zVRUnD7Tuszky7whH5h2pcrm/0AdotpIZuV8ENolvhfBVupKZGkeJrS8JZhpGHR5D0PyC5tWmbT6oeT0y5KV0dy5pACzAyxsACyGqJiUz/qcupQtNkppw3q7zyNuQV2lZaOtQIlIiXJE176IfW0caAAskmBHCdzVgyYy+WL/iWCjCdfTBjNPVTEB4+3DC24e7I0teSX++yzgzAqSaSQifJSUz/sfuM5V7dNUclMyIwCYlM0I0EMtpC6dLTrtseydPnSx/XXySQycPuWzbFeUVlFdh5BbkOrUvU1OTf/akcac6tJkJRHYlM7ZqJmkAHNAkmBGiATy/9Hle/v1ll9brD94ymOd4rmz7y5/n66KvXbbtivru6MskJgEw+c/JzAqaVeM63WK6se6udYQ2khG5nWVXzSRFYFWTcWZEBXIWCNEApq+f7vKbk754vTbtK+q2M/1L54oMtmRvYeWBlW7KkJ+SkhnnyJ1LVCAlM0I0gBJr2SBmjYMbc1nHy1yyzbOOnqW97mHqAWe7ZLMOtStop73u2qIrI88eWWXajOwMdhzbAUBxabH7MuWH/H7kXhdxOM6MlGQFNAlmhGgAtptUXNM4vr7eNdVBWYVZbGc7AHf2uZNW17dyyXYdOdbsGJv/sxmAG5Nu5Mnrn6wy7XNLn+Pl318G5AZTa1Iy4xwZZ0ZUIIV1QvgqXddsd3+Ta9M1W18NJY0ya0fazDjHUQNgEdikZEaIhqBC++z2JJxIIHd1rks2efqf8p5RMgKwf5BqJic5GjRPAueAJsGMEA3grm/u4pLVlwCQ/t901+/Ai8aZsSvFkcindqSayTn6aiY5UAIJZkQ9WSwWli1bBpQ9ONRoNGKxWEhLS6NDhw5kZmZq/6ekpGA0Gj2bYQ/ps7WPW7ffuFNjp9LZPhv9Z+HU56W7X+zetZvmluZ2n3X3uO6c+OEE+zP307KoJTeab2R9wnrt17Kj/dY2r47OtfpytI/a5tOVTpw4ob2uayDo6ffQEPQB8wXbL6D3rt4SOAc4CWZEnVksFs4++2wOHz4MQFxcHH/99RcDBgzAbDZjMBiwWq3a/yaTiYyMDL+9wFbHVhR+KuwUyw3LyT+Vj4KCikqTxk0YM2YMAJ999pndsor/A5XmHW5+mGndp9WYB4vFQlJSEmazWfssAG1edZ+X/ubx+eefM3rpaFasWKF91jMazaBtSVuCCCLpzL9SpRTLSAuWFpX3W9M5UDGvK1asoF+/fnbn2tatW+t1Ljnah+39eOJctVgsXD/qeqYyFQCraq1hDcfbqO2x9kkVSiLfmvkWaeemwQDPZEd4ngQzos7S0tK0mwtAVlYW8+bNw2w2A2C1Wu3+N5vNpKenM2TIkIbPrIfZgpmTjU8y+fhk+4Wn4NJRl6KqKpOnTXawdg1yYPz68TUe17S0NO2zsX0Wqqo693lVGGfGbDZrn7WCQtuStpX2F6QGkbUii7RGlfdb27zOmzev0rlW33PJ0T5qm09XSktL49jRY9p0cUntu7U7+oz98fsW3CIYtb2Ksqf8xCxeL8MABDIJZoRTVFXln3/9g+VXizavSWkTZgXNoqS0bAyVRkGNaPdRO7t5Nic5ybfR35KcnNyg+fY2iqJgMpnsSkLi4+O141Jxme1/RVG0KpuKy/TrVyclJUXbvjP7tNtuhWYJ8fHxjBo1iilTppBtztbm72EPu1vuZvCRwQC0im1V5X5rk9dRo0bx1ltv2ZXM1PdccrSPKVOm1CqfrpSSkkKL6BaQXzYdHBJcp23U9lj7IkVR6P5Hdz7p8QnnWc4DoHlkc89mSniUBDPCKSfXnuTguwcrzW+FbmyTUijJLLGfp3Nel/P8s8i7NhTIyMggPT2dxMREdu3aRXJysnZcKi7T/79x40YAevbsabdMv351jEajtn1n9mm3XV0wc9MNNzH5g8nl21uVDpeXLWvXox2FXQthTtl0WGhYlfutbV63bdvG8uXLARg4cGC9zyVH+6htPl3JaDTyxRdfcHzAcaBuPdQ8/R4aUovWLeh0Xyd4tWw6pFGIZzMkPEqCGeGUkpzykhYlRMEQ7nz3mdITpWUvTlafLlAYjUat6D8hIaHGZRX/r2pebfftzD5t9G1m2rVtp90kjUYjgy4cxB/8UTbdwkhY4zAtra00ydF+a5tXo9HIiBEjarWNuuzDk9UyzZo24zhlwUxdO+l4+j00pLDw8nNN2v8GNglmhHN0F4q2T7Yl4UXnb6K/N/kd6ylrQF9stLEw3P0MJXfRx64V3oJaWj5DCVLs09a+DWtAk3FmaknGPxJnyAjAwin1GpDKdsGRi43v0t00Kp4L1QUzNY0WLCqQcWZqRz/ejFUOWCCTYEbUXi2vGbYqikAeodPXB/bSVzNVVzJDUIW2HlIyUyvyOIPacfvI18JnSDAjnKMv/VZqG82c+V9ubL6ruuL8Ul2yIMW+Kk0+81qRaqZa0h+j0ipTiQAgwYxwTn1+JEo1k++/92qCGalmch0JZmrHZ9ugCZeTBsCi9mp7kT2TPpCrmTS+eoPS5fvAOwc49OEhbVr/uUoD4NrLXZvLtlu2Ubi/UBuwEKSayRl2pcRyrgU0CWZEZVlZ8NZbcKj8hsXBNsDQstdffwV/b3B6c8rpMUAoHDLD6NGuzKnvUK8v+7+kxCePQXBuM+DMe7CCtcDxnSN44+8oWduBdgCoP/8M6XMaJpM+yrzqfE5ndqk0vzBvr0+eKw0qKxIYVfZ6/YbaHy+jEf71L+jY0dU5Ew1MghlR2aRJ8M47drNU+qIFM5s2wabZtdjg9UAonDwJs2uznv9QQm8AQLWW+uQxaAy0J5+jnI9aRfFSKEdovXMqlJxTPnP73/Dbbw2TSR9VSjugLJgJNuxlW8tiDjc/zO6YGTDb7NnMeTvToPLXB83w57zab2P/fvj2W1flSHiIBDOisn37akhQ2+JvW3pfrWMRAO2ZSXtmOpGy/Anhqiqfec3Kj1FMk6c5/96yEtEbtngqP75EX0JYx3Otxuud8AUSzIjqrVgBMTHw22kYf+YheBMmwv3PO7+Ncw+BxYrath38ttM9+fR23beX/R8SDDv9+xioby6CD89MjB4Ld33g0fx4vYnH4MfTZa9nz4b0sudaccUVMGmKx7LlEz5fA2cuRcoFF8KiV51ft2tXKJaHU/oLCWZE9RITIS4Oth0FyoIZpUU0dGzn9CaURocBKzQKDuC66TPBjKL4/TFQmv1VPtEs0u/fb71FFAFngpk2rSC97KUSESHHribRuh8G4U1qd7xqO8SE8GoSzAjn1GdkUhlnxvcfZ1AbuvMj4oUIfn/ld7ftKrxzON3mdyM8Idxt+3A73SkhPf5qp7rBHEVgkWBGVOboguqCcWbkQh0YSpuXj16mlChYS9wXxeZvzOfw7MO0f6a92/bRoKSwoHb0xyuAfywJDwczv//+O6+//jppaWmYzWbmz59v91RcVVV58cUX+eijj7BYLJx33nm8//77JCUleS7Tos6PMwjkX06+/jiD2jjZ/yQ/Jv9Il4NdaNe8Hc3Dmrt8H6V5pRRkFgBgzfftu1hVA+UF0jlTZ0Eu2Ib8yPILHg1m8vPz6dmzJ7fddhvXXnttpeWTJ0/mrbfeIjU1lbPOOotXXnmFSy65hB07dhAREeGBHAeueo1MKiMABxQ1ROXNq94E4PORn3NJ90tcvo+c33PYMHBD2f5KffzE8vHsew3fjmlFPXk0mBk2bBjDhg1zuExVVaZMmcK///1vRo4cCcCMGTOIjY3l888/55577mnIrAaU00opX/WAQxHAhvegaQTGrUbO4iwAvkn7hqwfsjh27BitW7UmPLz69gq9i3sTQgjH847zwq8vEB4eTq+4Xlza4dLaP+fJAywWC2lpaaSkpGA0Guu2kTM3rFK1FIvFUvfteAn9MQHsjo/+M928ZTN9m/YlMzPTYVrbdjp06MCGDRsA6NWrl5Zen0Z//PPy87R91PTIBP0+asqHfnrZsmV2+bGtX/H/ep0XFaxdt1Z77QvfDY/TjTYdsiqEDU9s4NjJY3S/vzsxSTHVryvH1694bZuZ3bt3k5WVxaWXXqrNCw0NZeDAgfz1119VBjOFhYUUFhZq07m5uW7Pq7/5T+xOXup1ZmJ1WVfH87edz8u8DMCanDXMsY3qurfm7c0tnEtLWnKq5BQv/vWiNn/ZrcsY2H6gC3PuehaLhaSkJMxmMyaTiYyMjHrduIqLiklKSqr3djxJf0xiY2NRFIWsrCzt+OirRyZNmsT/ZfwfVqu1UtoVK1YwYMAAzGYziqJopX8GgwGr1VopjW37ADePuZmXeAmAgvwCp/Jq2251+bBN9+vXj8OHD9vlp6r/631e6GKxhx95GCbWbTOBSP/U7Pit8eRszSGIIH7++Geuzr7aZ79jova89kGTWVlZAMTGxtrNj42N1ZY5MmnSJCIjI7W/Nm3auDWf/mhT+IlK85R6DH5WVQ+ezdmb67zNhmJrzwVgNptJT0+v03b0N/j6bMcb6I/J4cOHte+j7X3ZlSgoaM8bqph23rx52nb01Zi29BXT2LaflpbGkWNHtPTZWdlO5dWZfNimbYGMfr2q/q/351lFwZK0mamZtZuV08GnK81vU9LGp79jova8tmTGpmJRq6qq1Ra/PvXUUzz88MPadG5urgQ09fC/Qf/FGNue4EXBMPfMzI2gHCz7JW00GnnnnXdo2rRpldto+kFTyAXltEKTzU3I754P+EbvppSUFEwmE2azmfj4eJKTk+u1PVVRXbIdT9Ifk7i4OKDsx4ftfW3fud0uva0Eo2LaUaNGMWXKlCpLZiqm0R+3qBZRcLRs+y2jWzqVV2fyYZt+6623nC6ZceXnKQ+XrCUj3Pyvm0nanwRbYHzGeFrTGgWF3sm9nduGD1yHRM28NpjRX3BMJpM2Pzs7u1JpjV5oaCihoaFuz58/03+1h7UdQlxCd45kHCGDsiL+u0bcxWtPvcauXbtITk6usSh3ZehKCikkOiKatx55i3sW+U57J6PRSEZGBunp6U6916rYSrZCQkLYsmWLTxd/VzwmgN3x0f/YePyJxxnfb7x2rlRMa9tOYmIiGzduBKBnz55255aj4z/v63n8PfBvAEKDq/6+V9xHTfmwTW/bto3ly5fb5ce2fsX/63NegH1Q/9aUtxizdwwgbWacoSgKOU1zWHH2CsYOHUviO4kUbSjCgMGnv2Oi9rw2mElISCAuLo5ff/2V3r3LIuyioiKWL1/O//3f/3k4dwHkzAVVf8HteFZH2ia0JSEhwcltlP0XEhxiV4LjK79CjUYjQ4YMccm2DEH+cZGteEyqOj5JSUkkJCTYnSv6tPrt6NPoXzs6/s2MzbTXNfVmqmofVeXDNq0fJsK2XlX/u0qflD5OtUMTlSUmJBIWHkYRRUDNpfjCv3g0mMnLy+Off/7Rpnfv3s2GDRuIioqibdu2TJgwgddee41OnTrRqVMnXnvtNRo3bszNN9/swVwHFldcCrRGehXuOb5QzSRqT9/Ww12fsb7hpz91zda3L5M2M3VQcRC96sahkUDHr3g0mFm3bh2DBw/Wpm1tXW699VZSU1N5/PHHOX36NPfdd582aN6iRYtkjBk3c3hr0A8zU9uLgG6cmUC/QPtKaVR96M8Pt71f3U0qb0Me+/7PM08+NoQZaHldS0Jb1aNq2/9PCbfRX0/+2PcHvfN604yyUrvp66ZzQ68baBbarKrVhR/xaDAzaNCgan+5KYrCCy+8wAsvvNBwmRI4vLq64NlMFT/rQLixB6IGKZkJKt9HXnoeeel51aR2r6wZWfRJ7+OSbcl3ou5+2/0bV+ZcSU96AnDfj/exKmsVn1z9iYdzJhqC13bNFp5jH7fUvyRF/ziDQK3D1rq2B8Dbb4iSmbCEMELbekdD//zN+fXbQFVdswP0u1IbfeL70Di4sTZdsZrOqeEfpLrbL3htA2DhJRw9V6kejzNoiF/twrMaoirR0MjAOZvPIWd5jsfazGQ+mklBZoGcxx4U3Tia3f/azV/7/wKgyc9NtAbUiqpISVcAkWBGOMUVz2YqsZQQ0yeGhaUL+SfuH0rOK3FZ/ryd7QZf1QCC/uqeH+/h/p/v93Q23OLtgrc5i7MotZYS/mr1j/SozrM7nqU//QG46LOL4ExBQ6C3L3NWTJMYRnQZAcCGphvIIQdwYqBPKfnyKxLMiErsCmFc8IUPjg7mNGWjdCqFCqGEknQgib2/74XL6r154WWiG0drr0usJZRY/TNoLVVLgbKbZkFJ1Y9UqIn+2VJF1iLttTHM97vwNzj94NOqIqVmAUSCGeFA9Q2AaxvgJLyWwJ4X9lCSU0Judi5B5rKuKMrpAPplFEDX1Ms7Xc6dve9k7aG1NSf2YY1DyopQDBjoGduzztvR97bp2rIrec3yaNe8HQ+e92C98xho9F32pWQrsEgwI6qlXRDq0WbGOMiIcVnZr8zvJ39Psyekq6Q/C2sUxsdXfezpbLhdWmoaJ/ecBGDD+A113s7mnzdzbNMxAJaMW0JITIgrsheYdNcmg2pwrs2MlN74BenNJCqx+2q7ul5Zv7kAuoYEapsZf2bXa0tuiF5BXzKDKp9LIJFgRjinPr2Z9Ksq9hcbIXyWqwJzF323BJVKZkTgkE9bVOKoAXC9ejPpBWrJzJmeFVKP70dcdC677Lsl7O5oCjV0zZbeTH5FghnhgPuijEAvmZFxL/yI/lSW6gyvoL++1Ng1W/gVCWZEtRw1AK5Pd219m5FAugFIiYz/cVlg7qLvlsDujmZQDQF1jQl0EsyISmpsACxtZupO7lX+yVXnspwf9VKxAbBTJODxCxLMCKfk59Xz+TNnFBYVlk948BpisVhYvHgxFoulyvkV01S1Tk3bt1gsgRm4VaM2x7I226nu83P1vvWBh+V47c8Rm+Ki4vrlQ5TTfSZXpl1JyGnp5h4oZJwZUS0FBYvFwtNPPc293AvAqdOn6rQti8XC9E+m8wRPAFBS7JmRYS0WC0lJSZjNZkwmExkZGRiNRrv5sbGxKIpCVlYWJpOJFStWMGDAgErr1LR923ZmMQuQNjNQ9fGv73b0n1HFz8/RZ1yffQOUlJafv71792b5X8udPkf07+GPP/6gF70AyDmRQ8uolnXKj4DikvLA8LZlt/FX4V8wsYrEUqXnV6RkRlRS8XablpbGiRMntOn9+/fXabtpaWnk5eVp0ydyTlST2n3S0tIwm80AmM1m0tPTK80/fPgwWVlZWpp58+Y5XKem7eu3A2C1Wl3/hnxMVce/vtvRf0YVPz9Hn3F99g3YnctZWVm1Okf076GwsLy0ctPGTXXOj4DjbY/bTZv2mzyUE9HQJJgR1VIUhZSUFJpHNtfmtWnbpk7bSklJoUnTJtp0s2aeGQk4JSUFk6nsIhcfH09ycnKl+XFxccTFxWlpRo0a5XCdmrZv247WNTtIfg1Wdfzrux39Z1Tx83P0Gddn3wBNmzXVXsebaneO6N9DWGiYNt2zV90fiyCg90u9eSb6GW3aoMgtLlBINZOoRLXvXoHRaOTVV15l/4NlJTJNmjSpYs3qGY1G7r77bni0bDq4UXB9s1rnfGRkZJCenk5ycrJWFVBxPmCXxtE6zmwfYH3UekB6q0DVx98V26nu83PlvgGCg8vP37S1aUS3iq71to1GI+cPOJ+TS8oei9Dc2LzO+REQFRXFDzt/YF3LdQSXBmNw5ve6NAD2CxLMCKc0btK4fKIe9+OwxuW/QvFgjYvRaGTIkCE1zte/rmodZ7bv1EU1gNTmWNZmO9V9fq7et/570Lx58zpvu1EjuQy7ktFoLB8CQuKUgCFXWFEthw+arM/29M+zkSuN8GWuGjRPHmfgcrZrS7UD50kpqV+RYEZU4vCy7KoLrm7dQByhUx406T/cMmZS4H0l3ML2PQvEa0ygkvJNUXsuGjSvIUfnVK0qJSdc0xW8UfNG0vZFuOdBk8IlJJgJPBLMiGrZ7tkuCzw8UDJTfLyY9L7pnN552iXba9K9CckrkwlqEuRUenmQoJ+SB016LWkzE3ikmklUYl8VUvnqWq9SCQ88nO/4guMuC2QA8jfnY1lSz9Fjhe+TB016LafazGiJ5bPzB1IyI6o0dP1QNnXbizV/L2qJa349euLZTNai8m5TjZMaE9Y2rJrUVTu96zSnd5QFRWqR85lXrXKx9EfyoEnvpVUzSVFXwJBgRlRi+6Fy8583U3Kscv/pRsZ6nDauamdQG7r9tH6oNfF3x9dpM/vf3E/mo5llm5Rfc0JPGgB7FS2YsUpvpkAhwYyoUmhxaNmLIGjSrWygvGbnNCP68ug6b9PjT82uz/VLXylbmzFyJO7xT9IA2GtJyUzgkWBGVMl2IQiJDeGcDee4aqMNzw2/mmtTdaQfT0e6ZvsRV53LMs6My0lvpsAjDYBFJbbvv3YhcOX1QL+tBhoB2FW9RRSDbmV5XqRwRwNgufe6RK16M0mVsV+QYEbUyJWNEu0CgobiqgaWum9LrUpmrK4JpoR3cVWVqbS/cr1a9WYSfkGCGVElt5fM+FibGbtATO4/wg3nsvRmcg2nqpnkWPsVCWZEJdqvGlwfzNg1yPNAb6Z6qWMDYBkUzU9JA2CvJW1mAo9XBzMlJSU888wzJCQkEB4eTmJiIi+99BJWqzRYaAjuKJnxSOmGixpY6vNe1wbAwo/Igya9lgQzgcerezP93//9Hx9++CEzZswgKSmJdevWcdtttxEZGcm//vUvT2fPb1W8LLuy6Fs16LbeQPd4l5WM1LXxst1blsDGX8iDJr1XrYIZabPkF7w6mFm5ciVXX301V1xxBQDt27fniy++YN26dR7OWWCwXQhOF5zGYrFgNBrrv03dDSBkfQgbntjAsdxjdLu3G7E9Yuu9fYd016qtW7dSsLuAzMxMUlJSAEhLS6NDhw7aPKPRiMViIS0tTZsG+5KZrRlbCbOEVTomFdezWCys/ms1YZSNOizjXriH/rgDlT47t9B9lJlvZGI+YaZ169aEh4dz+vRpDhw4oE3r2ZZFR0dz7NgxwveGI1zLFsw0z23O7v/tpt2YdhiCvboiQtSTVwcz559/Ph9++CF///03Z511Fhs3buTPP/9kypQpVa5TWFhIYWGhNp2bm9sAOfVPthvvoaxD3JJ0CxkZGfW+OeiDmfi/48mZnEMQQfz28W9cln0ZUVFR9dp+TV5//XV+ffNXrFYrsbGxKIpCVlYWBoMBq9WKyWRixYoVDBgwALPZjMlkKn/fumvhlP9OIW1Omt0xsVgsJCUlaevZtnM06yiLWATIODPuoD/u+s/U7rNzB10wk/1WNkEEYcaszas4rRdEEDmUnftFFDncpqg7/fds7x17KTlWQqfHOnkwR8Ld6hSqzpw50y5gsCkqKmLmzJn1zpTNE088wU033USXLl0IDg6md+/eTJgwgZtuuqnKdSZNmkRkZKT216ZNG5flJ1A46tZoNptJT0+v/8bPhrzQvEqz40vjWb96ff2370iFah5bm6vDhw+TlZUFoM0zm83MmzcPs9msTdvet75kRkGpdEzS0tLs1tO2Izcot9Ifd/1n6rJztgrNBzV36faa9W+GoZGUHrjClvZb7Kb3/76/ciLpzeRX6lQyc9ttt3HZZZcRExNjN//kyZPcdtttjB071iWZ+/LLL5k1axaff/45SUlJbNiwgQkTJhAfH8+tt97qcJ2nnnqKhx9+WJvOzc2VgKaeVFTi4+NJTk6u97aUpgq3/OsWuu/rDlvhjk13kEACAL169qr39h2qEMzYSmHi4uIA7Epm4uPjGTVqFFOmTMFsNtu/b919xoCh0jFJSUnBZDJp69m2c/TwUd0BcM9bDGT6467/TF11zlal1QOtaNa3Gcd3HOehhx7iuOU4UcYoJk2axFNPPaVNv/POOzRpWvY4kPy8fC2tQTFgVa1EGaN498N3aX1Va7flNdB8NOojtrXcxgO/PABAi+gWHs6RcLc6BTOqqjpsFHrgwAEiIyPrnSmbxx57jCeffJIbb7wRgO7du7N3714mTZpUZTATGhpKaGioy/IQyGwlM61atWLL5i0uazOT2ziXFV1WcOPFN9JlehcKV5WV8jVv3rze23dE3wD4ySefZNrd09i1a5d2o0tPTycxMVGbZzQaycjIID09XZsG+5KZhx58iN4v9rY7Jo7Wy8jIYPVfq2G4W96aoPJxByp9du6gKArNzmlGs3OaMeOKGXb7nHH9DId5aElLLW3Fc064UCNYn1Be0hsaIvcEf1erYKZ3794oioKiKAwZMoRGjcpXLy0tZffu3Vx22WUuy9ypU6cwGOyLXYOCgqRrtpvZbv22NjONmzR2y8W2Xbt2hIeHU0ih/Y7dKKlbErEJsSQkJGjzhgwZAmA3z2g0avM1uvi9bXBbgv4OIhf7NllBBHFO03Pgb8gllyCCSGmcQgYZrn8zQlPx86r02TXw/h2ePw6W6c854ToKin37tOquLdKbyS/UKpgZMWIEABs2bGDo0KE0bdpUWxYSEkL79u259tprXZa5K6+8kldffZW2bduSlJTE+vXreeutt7j99ttdtg9RNbeMM1NxY+54vk1Fbhg078BbBzjw1gEXbVgI4UqKotg/4FUCFr9Xq2Dm+eefB8q6SN9www2EhYW5JVM27777Ls8++yz33Xcf2dnZxMfHc8899/Dcc8+5db+BruJYKO4aYl1V1YYZRM9Fg5I17tS43lk5Hnu83tsQQjihphGapQGwX6lTm5lbb72VnJwcZs2aRWZmJo899hhRUVGkp6cTGxtLq1atXJK5iIgIpkyZUm1XbOE+bimZ0V1AVNSGeVaTi4KZiJQIus7ryok/T9RqvVJrKe+teY+cJjlYRlh4hEfqngkhRI0U7EtmZKxK/1enYGbTpk1cfPHFREZGsmfPHu666y6ioqKYP38+e/fudWn3bOE5bn82U8Vtu6uWyYXPRoq5LoaY62JqTqhTUFLA+6++D8CgZoPqlwEhhFOcbjMj/EKdgpmJEycybtw4Jk+eTEREhDZ/2LBh3HzzzS7LnPAMrQGwO56arbMocxG9j/bGhAmARxY+QnHTYpfvp9PWTvSmNwD/S/8f+yMcjDnhRiXWEu21jAAshPvVqs2MtKfxC3UKZtatW8dHH31UaX6rVq20AauE/3Blm5kgQ5D2euPhjezL3acFM/9b/z/ywisPqFdf1+27Tgtmft39K0ubLHX5PpxlUGRQNCHcTUFpmCps4TXqdGUNCwtz+JiAHTt20LJly3pnSngHd5TMJJuSaRfZTpvW/3py1xNu9dv19IMer+lyjUf3L0SgkDYzgaVOJTNXX301L730EnPnzgXKfrnv27ePJ5980qVds4VnVBxnxpXBTFijMP5+8G8ysjNQUTn1xylK/imrhlkyZgmGaNeXXBRaCylcVDaWzX8u+Q/BVwa7fB/OaNG4BW0j23pk30IEEkVxYpwZ6c3kV+oUzLzxxhtcfvnlxMTEcPr0aQYOHEhWVhb9+vXj1VdfdXUehYe4q81MSFAIvU1l1T6bwjZxnLLuyj1iexDSMsS1OwP2N9tPJpkAJEQlEGOqXQNeIYTvkXFmAkudgplmzZrx559/smTJEtLT07FarSQnJ3PxxRe7On/CAxpqnJlK226I3kxCCL8nbWYCT52CGZuLLrqIiy66yFV5EV7G3b2ZKm27AcaZcWdgJoTwHk63mZEfO36hTsHMO++843C+oiiEhYXRsWNHLrzwQoKCghymE77BHW1mHOxE0yCPM5BYRgi/51SbGeFX6hTM/Pe//+XIkSOcOnUKo9GIqqrk5OTQuHFjmjZtSnZ2NomJiSxdupQ2bdq4Os/CzRpqnJlK2/byEYCFEL6h4gjADn8oSSmtX6lT15HXXnuNc845h507d3Ls2DGOHz/O33//zXnnncfbb7/Nvn37iIuLY+LEia7Or2hAtmDGrW1mGuLZTEKIwCNtZgJKnUpmnnnmGb7++ms6dOigzevYsSNvvPEG1157Lbt27WLy5MnSTdvHGWyxrjvHefOxxxkIIbxfxRGAJZjxf3UKZsxmMyUlJZXml5SUaCMAx8fHc/LkyfrlTnhEUEkIl2y8pHxGA1UzLfh5AWoLlUGDBmE0GrFYLKSlpdGhQwcyMzPp0KEDGzZsAKBXr15kZmaSkpKC0Wh0uGnb+i2OtSjfnQtLmWzbT0lJAdBeV5UfEXj057Dt3LWd38K9rIpVe71u9zrm/TKPuE1xBO8I5sSJE0RHXUFYUwsXqZkEylCvaqnK0R+OcnzDcTIzy4ariI+P59ixYyRemEi7m9thaOSbo5TXKZgZPHgw99xzD9OnT6d377LxQtavX8+9996r9W7avHkzCQkJrsupaDAD11zLkNU3aNOlpaVu25c+uLj77rs5whHi4uL466+/GDBgAGazGYPBgNVqLfu1daaUxTbPZDKRkZFR6eZgsVhISkrCbDYzWhnNHdwBQF5+Hi1oQX3ptx8bG4uiKGRlZVWZHxF49OeI/tyNi4tj69atco64UcWu2Xvy9/DzZz8zefZkXapkAL5q8ws3WiwB8Xlkf5nNtlu2AdCYxgDkkEMQQez9ZC/WU1Y6jO9Q3Sa8Vp1CsE8++YSoqChSUlIIDQ0lNDSUPn36EBUVxSeffAJA06ZNefPNN12aWdEwYo/Yj1Kb18H1z0vSKPqXZRNZWVnMmzcPs9kMgNVa9gtLX11km2c2m0lPT6+02bS0NG19/XqZuzJdkm399g8fPqyVSFaVHxF4qjoHs7Ky5Bxxs4HtB9o/KgWFDocd36SbnkoMmM8jb1P11/K9S/Y2UE5cr9YlM6qqUlhYyHfffcf+/fvZsWMHqqrSpUsXOnfurKUbPHiwSzMqGo5BF+NObf4WH05Ndd/OHAQzcXFxjBo1iilTptRYMhMfH09ycnKlzaakpGAymbRfxbbrmr6dV33otx8XFweU3aSqyo8IPBXPQX3JjJwj7jX9yuksj1sOb52ZsR+a5jXVls+Ons31lusJtgYDSuB8Hrq2Q9OZzh720F5pz53qnQDExsR6KGP1V6dgplOnTmRkZNC5c2e7AEb4B0UXYby//F2ioqLcuTPNRx9+hDXWysCBAzEajWRkZJCenk5iYiK7du0iMTGRjRs3AtCzZ0927dpFcnKyw+Jh/fpRP0dx4q0TADSNaFopbV3ot2+7ENpeB0JxtahZxXPYdu7azm/hPkGGIAa0G8BKVgJwQc8LMF1oImtSWQnqjRNvpPiFYoKtwRgwBM7nUd6MiBtevYHSrqV0LunM4VGHAQgNCfVQxuqv1sGMwWCgU6dOHDt2jE6dOrkjT8LTdE+Zbm5s7tZd6dvMXHLJJYQnhmvTRqORIUOGAGjtr/TtsGpqk2Vbf89fezjBiUr7qy99/gC710KA43NYNAz9d71FixZ2N+peKb1Yo6wpSxdAXRz11Z3RZ0cT1CeInPQcbZ4510xsYSwRoREeyF391KnNzOTJk3nsscfYsmWLq/MjvICi6ut+3PxFl0HzhBDuUPHaouvHoASVjxBsd73zcwdzDmqv7/7xbvp+0pc7frhDmzd3y1xa/7c1WXlZnshevdQpmBk9ejRr1qyhZ8+ehIeHExUVZfcnfJvdLxV399JriMcZCCECT4VgRi3VNQgOUlC1rtuBE8zssezRXtu6ruu7sCuqQm5hLsv3LG/orNVbnbpmT5kyxcXZEN5E/0vF7SN+S8mMEMIdaghmtNeqb46rUheqtfwYDE4YzKUpl9L87+baPNu136paK67q9eoUzNx6662uzofwKrqrQJB7v+j6eu1D0w4R0jLE5fs48ecJ3Q5dvnkhhBfSX1tUVbULZgiyL5EIFPrS7xu638CFl13IyZiTpJEGgOFMYKf64JDJdQpm9E6fPk1xcbHdvGbNmtV3s8KD7NvMuHlnuljpwJsH3Lwz9z5nSgjhRWpoM2Mrsg2kkhl9byaDoerH1fhilX+dPsX8/HweeOABYmJiaNq0KUaj0e5P+Dh9NZObv+fNBzV37w50DOEGIvr4Xit9IUQd6IKZ4wuOc+Cd8h9L9g2AGzpjHqR7r4Yzpe76H3gGHw7s6lQy8/jjj7N06VKmTp3K2LFjef/99zl48CDTpk3jP//5j6vzKBqYoQF7M5luM9G0Z1MK9hW4dT8Akf0jCY4Odvt+hBCeZwg3YAgzYC2wlt3EdTfy4Ojg8mDG7b0cvIe+zYyjkhlbqXzAVDP98MMPzJw5k0GDBnH77bdzwQUX0LFjR9q1a8fs2bO55ZZbXJ1P0aAarmQGICI5gohkKTERQrhOUFgQHd/tiHmaGWtxWf2KYlBoMbIF4R3Cy2/Yvnffrjvde1UMZ67z+t+utmDGB6uZ6hTMHD9+XBsAqlmzZhw/fhyA888/n3vvvdd1uRMeYVeHbJA2JkII3xR/Zzzxd8Y7XFZezRQ4JTOO2swoumu8bVgOXyyZqdOnmJiYyJ49ewDo2rUrc+fOBcpKbJo3b+6qvAkPsWsALMGMEMIPlVczBdA1Th/MBFVdzeSL6hTM3HbbbdpzRp566immTp1KaGgoEydO5LHHHnNpBoVnSecfIYR/CrwRgPXVR7aGv44aAAdMNdPEiRO114MHD2b79u2sW7eODh060LNnT5dlTniGfTWT5/IhhBDuYhsBOJCCGWdLZnyxmqnWwYzVaiU1NZVvvvmGPXv2oCgKCQkJXHfddfTo0cMdeRQNTP/VlnFZhBD+SFdG4cFcNDB912xbbyY/aQBcq9/dqqpy1VVXceedd3Lw4EG6d+9OUlISe/fuZdy4cVxzzTUuz+DBgwcZPXo00dHRNG7cmF69epGWluby/YhytpIZK1apZxJC+KXykpkAKn52NM6MnzQArlXJTGpqKr///ju//fYbgwcPtlu2ZMkSRowYwcyZMxk7dqxLMmexWBgwYACDBw9mwYIFxMTEkJmZKY2M3c0WnQfUaFJCiEBS3gA4cOhLXKormfFFtQpmvvjiC55++ulKgQzARRddxJNPPsns2bNdFsz83//9H23atOHTTz/V5rVv394l2xb2Vv6wkq3fbeXEiRO0z28LeC6YsVgspKWlkZKSUuOI0ra0HTp0IDMzk5SUFACn12/IvAohPKfyd7Xs+hZaFM60cdPIz8+n40UdGX7P8PIbvQ87uOsgv075lePm4zRp0oT8/Hxa/tNSW+6oa/aQLUP4vs/31VYznVh1gqyFWRw4dICu47pi6m9y35uohVoFM5s2bWLy5MlVLh82bBjvvPNOvTNl8/333zN06FBGjRrF8uXLadWqFffddx933XVXlesUFhZSWFioTefm5rosP/5q56adnL7qNB3oYDdfRcVisWCMi2uwvFgsFpKSkjCbzZhMJjIyMqoMEvRpDQYDVquV2NhYFEUhKyurxvUbMq9CCM9x9F21/VgLKwmj84zOZQm/gkWNF3HZrZd5MLeusWjoIhL+SaA97R0uz8/PL3tRIW57O/VtdgzaAcmV1zm95zTr+68HFYIIYv309QTvDaZFmxauzXwd1Cr8PH78OLGxsVUuj42NxWKx1DtTNrt27eKDDz6gU6dO/PLLL4wfP56HHnqImTNnVrnOpEmTiIyM1P7atGnjsvz4q8xVmRgcnAr7Yzewfv36Bs1LWloaZrMZALPZTHp6ulNprday+u/Dhw+TlZXl1PoNmVchhOc4+q7mNt/kMO32JdsbMmtuE7M/pspl5mZmjp0+BkBofChqvH1JTN6aPIfr5W/Jt2t301htzMZFG+ufWReoVclMaWkpjRpVvUpQUBAlJSX1zpSN1WqlT58+vPbaawD07t2bjIwMPvjggyqrsp566ikefvhhbTo3N1cCmhroixQXt1lMvHUZHa1F3HR4PQXJ7n+StV5KSgomkwmz2Ux8fDzJyQ5+HjhIayuZiTtTipSVlVXj+g2ZVyGE5zj6rl6QfzMrYn/lUKMm/NWoJ6P2jgLwmzaZtsa82U2zebf5u6iqiqIolFpLMQeZST+37MeXEqTQfWV3Puv1Gb0tvQGIjo52vFEHtU9ndznbLfmvrVoFM6qqMm7cOEJDQx0u11fvuILJZKJr1652884++2y+/vrrKtcJDQ2tMn/CMf3Dx6LPjea2/cWEr1kLQHgDV5sYjUYyMjJIT08nOTm52mobfdrExER27dqlBRTOrN+QeRVCeI7D76pBYfDhDZyOi6N47J0wqSxtcJB/PIzW1pi3qEkRM3+fya5du+yuk/rrVYu2LYi9NRamlE2HBldxD7VWntUsopmLc143tQpmbr311hrTuKrxL8CAAQPYsWOH3by///6bdu3auWwfokIw0yKa8CNhHsxN2YVnyJAhtU5re14Y4PT69VWbvAohPKeq72p4WBjNjc3LZ/hJJ05bMKMElY0FZ7s+6q+TeiFhIeUTVRwDhw2DveR41SqY0fcqaggTJ06kf//+vPbaa1x//fWsWbOGjz76iI8++qhB8+Hv9MEMCuCDAyYJIUSd6Xok210PfZjWzdrJ3tb6AVKrPAYOSma85Xh5df+zc845h/nz5/PFF1/QrVs3Xn75ZaZMmcItt9zi6az5FbvndciDJYUQgURV7a973nFvrjdtADyDk29IHw1UtYqj+V5yvOr0bKaGNHz4cIYPH+7pbPg1tbRCyYyejAAshPBzTpVK+JhaD4CnT+6gBAYcHxtvOV5eXTIjGoaUzAghAo4ugFGC/LBkprYjude1ZKaKwKehSTAjKreZEUKIAOLXJTN1aDNTm5IZbwn+vL6aSTQAfSxjUKQBsBAioPhNm5m0NPj7bwAUtWyAW9VaDF98UfO6uw8AUWXr7NnjcJ3SFSGA/Rg0l04fzKh1Z/NIuxvBg01CJJgR1beZEUIIf1ahAbDPlszMnw8jR2qTBpaWvSgogJvvqHF1pfVQ4JyyiZWr4It/V0qzveXFGLCfn2ct5JX9s3nk7TUeDWakmknYt5kJkmhGCBFY/KJk5q+/tJf6WiJVca5Ri6p/41U0Hi4MqjxPURVOecE4g1IyI+x+iSgVi2akN5MQws/5W5sZ64MPwrtnJsJC4e23a1xHWWmBOWcmevWGhysPMKj+lQdfVlgPBbVREDzzTP0yXU8SzAj7XyJSVieECAT63kz+UDKjK2FXrxmpBTNqaDA8dFfN65+aXx7MdOgED1Uez03N+6lSMGNQDagGBVw4+n9dyK1L2JfMSANgIUSAsQtmvKSrcX3om0HWaQTgKu4BjuYrqlJl+oYkwYyoHMwIIUQAsWsA7AU35jrRl8zo5zt7SddFA4rV8UrW0sqRnqIq9u1tPESCGSHjzAghApeqOjXGii+x6q7pTg+ap69pk5IZ4YuqLZmRBsBCCD/nF12zdQFFqf49OHmXd6aqzdGxUZCSGeEtKg6aJ4QQ/k73Q80QpLsVev6+XG/6khJXPs7AUTBjUL0jjPCOXAiXsVgsLF68GIvF4nC6ou3rtqN+7D8NgGt6v0IIUZH+R1y7Oe1Y/t1yD+amjs5ct08EhzF/xsby+XVoAGz4w8CGJzbw2/2/cejPQ+x8fSe/3fkbtnH49EauGkl0brTHq5qka7YfsVgsJCUlYTabMZlMrFixggEDBmjTGRkZGI1GLX1hQSHbhmwjLjeufF5RoSey7hIV33/F9yuEEI4ohvKqkiA1iMJrC/l7w9+c1e0sD+es9ubF30nHL5K1aaeDDF3RRvymeHI25RBEEH9PLXs8QhBBGKl8Pe37T19emfMKx/99nOio6ErLG4qUzPiRtLQ0zGYzAGazmXnz5tlNp6en26XP3p+NMbf85CxVSlHa+W41U8X3X/H9CiFEJapKj8E9yA/N12aFlIbw+4+/ezBTdRdUmGg3ndsl16n1SnqUUBRUVKd9Jh5OJC09rU7ruooEM34kJSUFk8kEQHx8PKNGjbKbTk5Otkuvj9hLlVIeavcQw64bZr9RH2oAXPH9V3y/QgjhiLGlkY7rOnIo8pA2r23bth7MUR2cuZ4rukcRPH/W84yd5uRgdjFw44QbeeaGZ3imyzNkkWW3+DjHebbDszxzwzOMmjiKjZ+UV2UpqkLv3r3r/x7qQYIZP2I0GsnIyGDx4sVs2bKFhIQEu+mKVS76MQO299zOn+l/+nS1TMX378vvRQjRsDp368zJQSe16fDQcA/mpj7Kg5kvfvuC6Gjnqn4UFCwRFlacvYJm/2pGVMcou+WNYxvT8bWOrDh7BUcjjxKZHMmBdgeAskbAzZs3d9k7qAsJZvyM0WhkyJAh2o284rSevmV6aFioX9z8q3u/QgihcVDq3CjYh5uRaiXt5e8ruoXzbVj0DYAXHF7Anrw9dsuPFh8ldVuqNm1QDHYRhKe7Z0swE8BKS0vLJ/Tfax/uzSSEEHWmH2rFwWi3vkDRdZU2GJy/xXdp0aXChuwnKwYrXVt21dIEqUHSm0l4jt3JKWGtECLA+fTgeQ6CCbvxc2rQpUUXfh3zK8v3lHVLj/siDszly6OaRPHMBWVPxu7bui994vuwTdmmLbeqng3+JJgJYKr+aWRVtfP1oQbAQghRa6rjH3U+F8ycoS+ZUWp5/b448WIuTrwYgLRmaZykvA1RyyYtefmilyvsrPylp4+X/B4PYGodhrwWQgi/5cvVTA7azNSmmqmSiqs62JR+dGFPVzPJLSyA2X1ZpQBGCBFIHJRa+MPjXGxds0uV0hpS1rCdisfH0aHxouBPqpn8iGWJhe23b6f4cLHjBAaIHR1L52mdgQqRtDQAFkIEOi+6OddaxZKZ+sZlFYo6HAV6UjIj3OLguwcp3FuItcDq+O+UFfNHZgr2FQBgtUrJjBBC2Ng1APbRH3XKmYu5ValnMFbxnlBDyYxdG0wPkJIZP1KaV16s2KRbEwgqX1a4r5ASS0lZulNl6ZxqMyMNgIUQ/qyKEmpP35zr7Ew1U33HfalYEuPtJTMSzPgR/ZcveXUyQY3Lo5ntt20nK/XM8NRnkvlcMaoQQriTvjeTr5XM2B5ncOZN6AONOqllyYyn7ydSzeRH9MGMElRN4y1bMKOvZpIzQQgRSGpoAOzprsZ1dibb9Q1mKpXESG8m0VDsikWDKix0EMxIA2AhhNDxonFTas3NJTMOx6zxomo5CWb8if7pBNWUzNiCGBlnRgghyvlDyYyta3a9gxkZZ0Z4ilpy5mRSKkfRdtO2kplSCWaEEELjByUztjdR7wbAzowzo7tvSJuZWpg0aRKKojBhwgRPZ8Ur2YKTSqUyUHObGem0JIQIRLoSBb/omu2mkhmHAwpKA+DaW7t2LR999BE9evTwdFa8lhbMNHIumKmyzYwQQgQiL2oDUmtamxnXBDO+1gDYJ7pm5+Xlccstt/Dxxx/zyiuveDo7DSbn9xwOLznMAfMBut7RlbBOYaSlpZGSkoLRaMRisZCWlkbPHj1ZM3cNTTY1AaCYYl749QUOHDxA61atCQ8Pp83BNsQTD8Cn6Z9StK+I5v9tTgc6lO1Mf6L66C8SIYRwWg29mY6+fZQNfTfQq1+vBsxU7eRvy+fAvAMc2HeApEPNWNvqAmIPtgEavgHwz8//zJ2pd9Zvn/XgE8HM/fffzxVXXMHFF19cYzBTWFhIYWGhNp2bm+vu7LlFfkY+GwZuACCIINZ8vIYHYh7gwOEDmEwmVqxYwYABAzCbzQzvPJxHdjyirXtaPc2Lf71YNrG37L8JhydwNVcD8M7qd7h78d10yOygrVNaWr/neAghhK/TBzOJexPZdMUm2uxsQ3R0tAdz5VhpfilpfdOw5loJIojtXE4El2vLraoVi8WC0Wis0/aLS+0fi1NSWlIpjZXyqqWYL2Ow/Lfu+6svr69mmjNnDunp6UyaNMmp9JMmTSIyMlL7a9OmjZtz6B55m/LspiPVSIoOFwFgNpuZN28eZrMZgLiCOLu0G9tvrHbbiqqQeDjRbl5xZwfPc5LRf4UQAeSsYWfZ3aDbWtqybvU6D+aoagX7C7DmVt1OZUP0BtLT0+u8/Zz2OXbTJzucrJQmr0v5fepE2Il67a++vDqY2b9/P//617+YNWsWYWFhTq3z1FNPceLECe1v//79bs6lmzgoIYxtEQtAfHw8o0aNwmQyARAWUn5sZraZyX8j/0vzhc1hDhh/MfLhoA8J2R+ipXn5/JdpHtJcm36kwyPc8swtbnkbQgjh1XTV6ucMPYfI5ZF2i3v09NJ2mtXUIs1t9ymfWD8hOTm5zpvvPak3z0Y/yzM8w4vRL9Lr7V6V0ox9ZyxPdnySZ1o9w/9i/lev/dWXV1czpaWlkZ2dTUpKijavtLSU33//nffee4/CwkKCguxHhwsNDSU0NLShs+pyjroFLvplERmWDJKTkzEajWRkZJCens4/7/0DO8vS9BvfjzfvfROA9PR0Le3mKzdzbPoxAIadPYzNQZspphg1TmXx2sUeKxoUQghvknJhCv87638k/l1Weh3ZLLKGNTykms5DA65N4tVnptTruh4VFcX3O7+3u49UFB0dzYI1C6pN01C8OpgZMmQImzdvtpt322230aVLF5544olKgYxfcRB1N2vajCHJQ7Rpo9HIkCFD2PPeHm1e165dtRNqyJDytHYlW2r59sObhFc+AaUBsBDC31VXja6/tXjp5bC63kOdOnVwSWBhu8fUN01D8OpgJiIigm7dutnNa9KkCdHR0ZXm+x0HUXdVXQX1pTiGRlXUHOq/t9bydRy2UBdCiEDmC4PnVVMyE2Tw6lu7W3h1m5lA5jDqrurk1XVEqrK0quLjDGyblzNACCHs2HVr9tJYprp8BQUF3oXd58K3ZcuWeToLDaMWJTP6tIaqTuIKg+ZpvzaqK5iRUhshhL9z8MNRH8x4emTbqlRXYhSIwUzgvWNf4eA8rerkdaaaqdKzmWyxjKMhqoUQIpD5QjVTNdkyKIF3aw+8d+wjHH6BqhjXTikt/+Y5U82ESnlpjqNYRhoACyECmC9UM0nJjL3Ae8e+wlHJjDPVTE40AFZVVWuTIyUzQoiAVE01ui9UM1XbZsbgxz19q+BzbWYCwbYj21izcw3taGc3/7P1n5FXlFcpveFUeQDjkpIZIYQIZBU7THihrNysKpc1CQlvwJx4BwlmvMyp4lP0/19/Ltx2IROZaLcs9tFYjI0qjx1gzC+fV9s2M9WWzUkDYCFEIKowlIU3Ol10usplkSHNGjAn3kGCGS+z/8R+cgpyMKiVo4wWeS1qXL9tfFvHC6rozSTjzAghAloNvZm8tQFwtQ8HDsAGJBLMeBnVVmRS4ftjja7h54EBTLeaaBzf2PHyisWmts05Oum9tFhVCCEahO56abV6Z9FMdflSggLvR6oEM17GVj+rL5k5e/bZxN4cW78NVyyZsQUsgXfOCyGE0w2AvbWaqdqSmQAUgIVR3s1WMqPoowwXfEqV2syc+YJKbyYhhLDnC9VM1ZYYBWDJjAQzXkbrMq2Wn4wuCTgq9maSBsBCCOGY7rrorcFMdSUzgXjplmDGy2glM7pgxiVVQVV0NZQGwEKIgOaoAbCu0aLqpaPmVTv+TQCWuEsw42XcVTJjtw19QC9ngBBC2NOXzFQ1WKmHVVvNFHixjNzKvI2KStsjbblxxY3lMxWwWCwsXrwYi8Vi9xqoNO2Q7uReO3mtw/nlmfDOL68QQjQI3XVx/XPrObrnqOfy4sD+nfv5581/qlwegI9mkt5M3saab+W9T94joiBCm5ednc0lSZdgNpuJjY1FURSysrIwmUysWLGCAQMGYDabMZlMZGRkYDRWHlhP/+UMXRKqvZYW8UKIgORkb6bwr8OZ9tM07jt0n+NrqwcsuXQJHfd0rHL5ybw8whowP94gAOM371Z6qNQukCmiiEUHFmE2mwE4fPgwWVllw1ibzWbmzZunLTObzaSnpzvcbvOBzR3OP9nhZNWZkfY0QogAtL/rfrvp+IL4Kq+tnhB7sOqhOsI5wN9HtjVgbryDBDNeRt9y/mSjk0yIncCIO0ZgMpkAiIuLIy4uDoD4+HhGjRqlLYuPjyc5Odnhdo0XGem8qjNvRL7BM2f+PR/1PL3e6eXeNySEED5my6At3H333dp0cKPgKq+tnqBvUzkhcQKt/mpFbsjLdOMpUriLbj26eTB3niHVTF5G39No77l7WfHjCoxGIxkZGaSnp2tfKNvrisuqKwY1nWfis92fsXz5cgAGDhzoNcWmQgjhEVW0EdwZv5NTIadoXNSYDh06eNW10jao6j7TPpauW4rRaKTtiBaEzp0LQGRkpCez5xESzHgZfclM46aNtS+Q0WhkyJAh2jL964rLqmM0GhkxYkQNmZAGwEKIwGUbssLWLTvIEOTJ7FRJaaRo94jQ4GDdgsBrIiDBjJexG6Ap8M5H4UBpaSnFxcWezobwYSEhIRgM0qrAjhM3fK0hsJf9vnP0IOJAJ8GMl/GqYCYAo3tvoqoqWVlZ5OTkeDorwscZDAYSEhIICQnxdFZ8glLh4qt6W2m1LcYy6PKlz2MAXrslmPEyXhXMCI+yBTIxMTE0btxYRmsWdWK1Wjl06BBms5m2bdvKeeQErZrJS0tmgtSyai+7B2IGOAlmvIzdLwApSQxYpaWlWiATHR3t6ewIH9eyZUsOHTpESUkJwfq2FaLaNoLaowy8KGbQ3yPsghkpmRF18uijsHevyzerngoB7gJA2bcXRo1y+T5qtGtXw+9T2LG1kWncuLGHcyL8ga16qbS0VIIZJ9iqmbyyZEYfv0jJjEaCmbr69VfYtMnlm1Vjz8IWzKgnLPDVVy7fh9MayenhaVIlIFxBzqPaqXi8vKrNTFVZ8aY8eoBUZHgZ1Ztaqd95p6dzIIQQ7uGjvZn07SrtGgDrBWDwKj+962rRInBHd9nFaXDbmdfdk2DF/mqTu01oKLRs6Zl9C78zaNAgevXqxZQpUzydFSFqpFUzeWGbGa/KixeRYKauYqt+NkZ9qM12AWce7R4SDK1bu2U/QnirZcuWMXjwYCwWC82bN/d0dkQA8ubeTFWWzAR4A2AvqtMQoPslAPLpCCGEuznR1sRb28xIA+Bycrv0MmqpjDMjfFt+fj5jx46ladOmmEwm3nzzTbvls2bNok+fPkRERBAXF8fNN99MdnY2AHv27GHw4MFA2aM3FEVh3LhxACxcuJDzzz+f5s2bEx0dzfDhw8nMzGzQ9yYCg1f3ZrKWv5Su2eUkmPE2+i+NfDrCBz322GMsXbqU+fPns2jRIpYtW0ZaWpq2vKioiJdffpmNGzfy7bffsnv3bi1gadOmDV9//TUAO3bswGw28/bbbwNlQdLDDz/M2rVr+e233zAYDFxzzTVYrdZKeRCiRs40APbCNjNVjjMT4KTNjJdRrWr5UNqBF1wLN7BYLKSlpZGSkuL2J//m5eXxySefMHPmTC655BIAZsyYQWtd26/bb79de52YmMg777zDueeeS15eHk2bNiUqKgqAmJgYuzYz1157rd2+PvnkE2JiYti6dSvdunVz47sSgcab28zoS2bs7hFSMuO9Jk2axDnnnENERAQxMTGMGDGCHTt2eDpbbiWPMxCuZLFYSEpK4pJLLiEpKQmLxeLW/WVmZlJUVES/fv20eVFRUXTu3FmbXr9+PVdffTXt2rUjIiKCQYMGAbBv374at33zzTeTmJhIs2bNSEhIcGo9IWrLm5/NZNcAWEpmNF5dMrN8+XLuv/9+zjnnHEpKSvj3v//NpZdeytatW2nSpImns+cWdsGMV4eawhekpaVhNpsBMJvNpKenM2TIELftr6aLfn5+PpdeeimXXnops2bNomXLluzbt4+hQ4dSVFRU7bpXXnklbdq04eOPPyY+Ph6r1Uq3bt1qXE+IahUXw/r19vPOPNxVCxaKHKTxlFzdd8xaWp4v/Q+VACyZ8epgZuHChXbTn376KTExMaSlpXHhhRd6KFfus3/nfna9tYtOdAJk1E5RfykpKZhMJsxmM/Hx8SQnJ7t1fx07diQ4OJhVq1bRtm1boKx06O+//2bgwIFs376do0eP8p///Ic2bdoAsG7dOrtt6Ifetzl27Bjbtm1j2rRpXHDBBQD8+eefbn0vIkCcPAkVvhfKdUA3XZuZI0cgeZDLdplHAsc5F1vxu0IpLVhBOIeqXa+EcMxcBYwHQD2ZWynvgcqrg5mKTpw4AaDVqTtSWFhIYWGhNp2bm+v2fLnKkqFL6LS7kzZdXOqGQflEQDEajWRkZJCenk5ycrLb28w0bdqUO+64g8cee4zo6GhiY2P597//jcFQVszYtm1bQkJCePfddxk/fjxbtmzh5ZdftttGu3btUBSFH3/8kcsvv5zw8HCMRiPR0dF89NFHmEwm9u3bx5NPPunW9yL8XGIi7NzpcJHtZ2R5NY7rfliW0IR03sdKuN38A1zHedyEgaobtO/ibg4xQpdRByWhzZpBNfdIf+UzwYyqqjz88MOcf/751Tb2mzRpEi+++GID5sx1Yg/YD8RnPUt6aYj6MxqNbq1aquj1118nLy+Pq666ioiICB555BHth0jLli1JTU3l6aef5p133iE5OZk33niDq666Slu/VatWvPjiizz55JPcdtttjB07ltTUVObMmcNDDz1Et27d6Ny5M++8847W3kaIWvvwQ5g2Dc6cm3YifwX+0SZPoTAV6Ne3LytXrdLmX3XllajADz/8oM2rmEaftnXr1pw+0hzrV+GVlhcSw/5Lr6VdhxZVZvn4l33gePn0zsS/Yfi95TMaNSp7OHEAPqBWUb2pZVM17r//fn766Sf+/PNPu54RFTkqmWnTpg0nTpygWbNmDZHVOlsYspCw4jAAJiROYOm6pW7/JS28U0FBAbt37yYhIYGwsDBPZ0f4ODmfauemr29izpY5fD7lc0w5Jo5znAfjH+TPP/9kwIABWrXtli1bAEhKStLm6dMYDAasVquW1mg0krsul/Rz0gFYxSqa05wudCnbzt9JtOxU9WNk1vRdw6nVpwB44PYHaHJuE1bfs9rNR8NzcnNziYyMdOr+7RMlMw8++CDff/89v//+e7WBDEBoaCihoaENlDPXMpx5yOR+034JZIQQwsNsbWaMzY1aMOKo2rbiPNt0YmIiu3btsq/iLW8KxrnXnEuTk004vfg0AJHNIqvNTyND+S17a+ut9AvuV03qwOLVwYyqqjz44IPMnz+fZcuWaV0x/daZMjKlkSKBjBBCeEjFEYBDGoVo12RH1bYV5+mnK9639D1W27ZvS8HuAk5TFszUWFFS4VEGFbuQBzKvDmbuv/9+Pv/8c7777jsiIiLIysoCIDIykvDwynWOvs5WMiOEEMJzKvYkdWVrDLtH1hiwb1tcQzPJiuOQSY/Xcl599/zggw84ceIEgwYNwmQyaX9ffvmlp7PmFpWeByKEEMJj3DICsK6aSQlS7O/CNe3nzPJSpbT6dAHIq0tmfKRtssso1jPBjCGw3rcQQngT7YflmehBVVUsp10zenbe6TztdaG1kGJr+RAcdiUvDlRcLtVM5bw6mAk0BluILuenEEJ4TMVnM+WcziFqsmvGbknOTOZNyp4k/+bqN2l9vDWDKXtSfI0lM2eqoayK1S6fwsurmQKJ3ZN/5fwUQgiPMTU12U0rqusuykFqkPbaarCWjzIMnDjtYMwbPVutlzRFqERKZryEPNZdCCG8w8S+E8ktzKVJSNkzAIMNwQzrOMwl207IL+/d1CG6A+jil5KSkmrXtVUz2e4RUs1UToIZL2EtlZIZIYTwBqYIEx8O/5A1kWs4ZT5FuBLOnI5zXLLtE4dPkEkmAKN7j2ZB1gJtWU1tZrSSmTMvpJqpnAQzXkJfzSQlM0K4T2pqKhMmTCDnzJOR3WncuHHk5OTw7bffun1fwg3OxArWU1bS+6a7fvMG+95MzjYAlntEZdJmxkvYlczIpyKET9mzZw+KorBhwwa37+eOO+4gISGB8PBwOnTowPPPP09RUZFb9xuows9y73hm4WeF25XE290HHKnQZkaqmcpJyYyXkDYzQoiabN++HavVyrRp0+jYsSNbtmzhrrvuIj8/nzfeeMPT2fM7nd7rRNNeTSnJqb4tS1007d6UFiNawHvl82ocjkR6M1VJghkvUVqqH0nJc/kQoj4GDRpE9+7dCQoKYsaMGYSEhPDyyy9zyy238MADD/DVV18RExPDe++9x7BhwygtLeXuu+9myZIlZGVl0bZtW+677z7+9a9/AWUPSExJSWHAgAF89NFHAOzevZtevXrxxhtvcNddd9WYp9TUVJ577jmOHj3K0KFDOf/88yul+eGHH3jhhRfIyMggPj6eW2+9lX//+980alR2iVQUhalTp/L999+zbNky4uLimDx5MqNGjQLKh6zv3bs3AAMHDmTZsmXa9t944w3efPNNioqKuPHGG5kyZQrBwcG1Pr6XXXYZl112mTadmJjIjh07+OCDDySYcYOw1mEkvNBwj9Gx69XqQI1tagKYVGh4iYrDVAvhq2bMmEGLFi1Ys2YNDz74IPfeey+jRo2if//+pKenM3ToUMaMGcOpU6ewWq20bt2auXPnsnXrVp577jmefvpp5s6dC0BYWBizZ89mxowZfPvtt5SWljJmzBgGDx7sVCCzevVqbr/9du677z42bNjA4MGDeeWVV+zS/PLLL4wePZqHHnqIrVu3Mm3aNFJTU3n11Vft0j377LNce+21bNy4kdGjR3PTTTexbds2ANasWQPA4sWLMZvNfPPNN9p6S5cuJTMzk6VLlzJjxgxSU1NJTU3Vlo8fP56mTZtW+7dv374q3+OJEyeIinLNGCjCA/RtZkqdawCslczIzUKjqH4+zG5tHiHuSTlHc9jQcgMAu5J2cfuW2z2bIeFRBQUF7N69m4SEBMLCwspm9ukDZ55P1qDi4mDdOqeSDho0iNLSUv744w+grMQxMjKSkSNHMnPmTACysrIwmUysXLmSvn37VtrG/fffz+HDh/nqq6+0ea+//jqTJ0/mpptuYt68eWzevJkWLVrUmJ+bb74Zi8XCggXlPUZuvPFGFi5cqDUAvvDCCxk2bBhPPfWUlmbWrFk8/vjjHDp0CCgrmRk/fjwffPCBlqZv374kJyczdepU9uzZQ0JCAuvXr6dXr15amnHjxrFs2TIyMzMJCiobX+T666/HYDAwZ05Z75js7Gxyc3OrfR/t27fXSon0MjMzSU5O5s033+TOO++scn2H55PwCh8M+YCzl5wNQKsVrejUv1OVaVd1XEVBZgEnwk8w4okRDEkYwuKxixsqqw2uNvdvqWbyEtIAWNQoKwsOHvR0LmrUo0cP7XVQUBDR0dF0795dmxcbGwuU3cQBPvzwQ6ZPn87evXs5ffo0RUVFdgEBwCOPPMJ3333Hu+++y4IFC5wKZAC2bdvGNddcYzevX79+LFy4UJtOS0tj7dq1diUxpaWlFBQUcOrUKRo3bqytV3E7zjT4TUpK0gIZAJPJxObNm7XpmJgYYmJinHo/eocOHeKyyy5j1KhR1QYywsvVojdTpQbA0mZGI8GMl7CqNbRiFyIuzif2W7EtiKIodvNsF2Cr1crcuXOZOHEib775Jv369SMiIoLXX3+d1atX220jOzubHTt2EBQUxM6dO+3ajVTHmYJnq9XKiy++yMiRIystq6kUw5mbiaPjoW8bMX78eGbNmlXtNrZu3Urbtm216UOHDjF48GD69euntSUSvknf4aPG+0DFBsBSzaSRYKaOzP8zU3ykmNOnT3PgwAGio6M5duwYHS/pSNtRbcvGDwAsFgtpaWmkpKRgNBodbivnWA7fP/89iSQC8qBJUQUnq3p8yR9//EH//v257777tHmZmZmV0t1+++1069aNu+66izvuuIMhQ4bQtWvXGrfftWtXVq1aZTev4nRycjI7duygY8eO1W5r1apVjB071m7a1uA3JCQEqNCQ30kvvfQSjz76aLVp4uPjtdcHDx5k8ODBpKSk8Omnn2IwSFFuQ6h4LbdNd+jQgczMTFJSUgAcXu8tFovWILxXr15aeqPRaBcQb31tK7ta7KLzgM60v7U9QeFlJXrWEivHvjtGwZ6ChnvDPkaCmTo68PYB8jflAxBEEDnkEEQQuz/ZDSq0u7EdFouFpKQkzGYzJpOJjIwMhwHNl2O+pPOCztq0nzdjEkLTsWNHZs6cyS+//EJCQgKfffYZa9eu1XoHAbz//vusXLmSTZs20aZNGxYsWMAtt9zC6tWrtSCiKg899BD9+/dn8uTJjBgxgkWLFtlVMQE899xzDB8+nDZt2jBq1CgMBgObNm1i8+bNdo2F582bR58+fTj//POZPXs2a9as4ZNPPgHKqorCw8NZuHAhrVu3JiwsjMjISKeOQW2qmQ4dOsSgQYNo27Ytb7zxBkeOHNGWxXmq5C4AVLyWr1ixggEDBmA2mzEYDFitVmJjY1EURWsTZrveWywWzj77bA4fPgygpbel0f94jVpY1pB7/6z9FGUWcfbrZW1pDs84zI47d2jppJqpMgnp3SDz17JflmlpaZjNZgDMZjPp6Y5HkAzaEWQ3fbLLSfdmUAgvMX78eEaOHMkNN9zAeeedx7Fjx+xKabZv385jjz3G1KlTadOmDVAW3OTk5PDss8/WuP2+ffsyffp03n33XXr16sWiRYt45pln7NIMHTqUH3/8kV9//ZVzzjmHvn378tZbb9GuXTu7dC+++CJz5syhR48ezJgxg9mzZ2ulQ40aNeKdd95h2rRpxMfHc/XVV9f30Di0aNEi/vnnH5YsWULr1q0xmUzan3CfitfyefPmadO2KsPDhw+TdaaBvv56n5aWpgUy+vS2NIe7lS/Ty/qrvLF/3qY8u2Ub2m8ApJpJT3oz1ZFliYUTh07w0EMPcdxynC50YTSjAYj7dxxdXuliF83Hx8ezZcsWhyUzqZ1Saf9PewCeOesZvvvrO6Kjo12WV+F7pPeJd1EUhfnz5zNixAhPZ6VO5Hyqn4rX8j///LNSyYytZCwrK8vuel9VyYwtzcTlE/njlz8wWUw0/akpT+Y9CUCzYc1I/jkZgJ0P7eTgu2WN/z9u9DFznpqDNcjK0A5DWTh6oYMc+wfpzdQAjBcZMWJkxhUzSE9PJ25PHEfuLCvyDQstu1gYjUYyMjJIT08nOTm5yjYz+uj669+/lkBGCCG8iKNruW06MTGRXbt2kZxcFnhUvN4bjUa2bdvG8uXLAejZs6eW3mg0YlAM7Irbxa64XUwdNBXuLdtncCNdw3FdkcONb97I55bPAalm0pNgpp6MRiNDhgzh2IJjHOFM/bVaeXl1FLX8hIxqIYNfCeGsYcOGaWPaVPT000/z9NNPN3COhL+qeC3XT+vbeDm63huNRrtSPX16/Y/Z8y88n2McK5vQ3Uf0FSjJycnwW+V1A50EM66iO6dqPeS0LrlBkWZMQjhr+vTpnD592uEyV46K6+e18cKD9Nd8fTdtu3NO/1Ke3eeQBDMuYuuKDdideE6te6ZkxopVig2FqIVWrVp5OgtC1Iv+mm9FN86M/j5SxT1F7hflpBjAVfTnVC3Hv7MFM6qiSrGhEEIEELuSGaoojdGX9uvu2nK/KCclMy6iL5mpdZH0meBHVVSJtIUQIoDoA5LZm2cznOEA7Dq+iwV/lj1TrL25PbGUPQbk84zPGz6TPkBKZlylPiUzZ1a2DVEthBAiMOhLZj5M/1B7vfPoTp787Ume/O1J1h5Yq82fljZNey0/fstJyUwdnfvxuWzOLn9YXPdd3ZnMZABeX/E6Sx5awtNfPk3c8fJROXMjc4n9IJYLR11oty3FKiekEEIEokHtBzF13VSgQuPeKgr49WkGthvozqz5FAlm6qiwtJCCkvLnZBRZi7TX1lIrg9MG0y7bfgTRlsda8vfbf1cKZrT1DFIyI4QQgWRU0ig2ttjILssuyAf+Uza/V2wv5t8wH4DwzeFwZgD5KZdNwXqWFVNTE+e2OtczmfZCEszUUefoznZ1nYm5idrrmMYxhBWUj7J5NPooLY61AEApqFwKYyuZUWvbDUoIUWupqalMmDCBnJwct+9r3Lhx5OTk8O2337p9X8J39YjtQY/YHpTklfAnfwLQsnFLLulyCQDbI7eTRdnjDYZ0GEKTLk08lldvJW1m6mjuqLlsGL9B+/vfNf/Tlt3a41au63KdNp2cmly+ooN4xRYUyfgBQvimPXv2oCgKGzZscPu+2rdvj6Iodn9PPvmk2/cr3M+uDYz+dqAvtJdWCQ5JyYyL2I0zYwW1tPxMNDTSxYyO4pUz8ySYEUI446WXXuKuu+7Spps2berB3AiX0QcqVYwALEUQjslhcZUKJ6FaUn7yKcHVD6inVTNJMCN83KBBg3jwwQeZMGECRqOR2NhYPvroI/Lz87ntttuIiIigQ4cOLFhQ1uW0tLSUO+64g4SEBMLDw+ncuTNvv/22tr2CggKSkpK4++67tXm7d+8mMjKSjz/+2Kk8paam0rZtWxo3bsw111zDsWPHKqX54YcfSElJISwsjMTERF588UVKSkq05Yqi8MEHHzBs2DDCw8NJSEhg3rx52nLb8PS9e/dGURQGDRpkt/033ngDk8lEdHQ0999/P8XFxU7lvSoRERHExcVpfxLM+Ikqghn9a+nB5JgEMy5iN86MVbUrmQlqFFSeUKqZhJ+bMWMGLVq0YM2aNTz44IPce++9jBo1iv79+5Oens7QoUMZM2YMp06dwmq10rp1a+bOncvWrVt57rnnePrpp5k7dy4AYWFhzJ49mxkzZvDtt99SWlrKmDFjGDx4sF3JRFVWr17N7bffzn333ceGDRsYPHgwr7zyil2aX375hdGjR/PQQw+xdetWpk2bRmpqKq+++qpdumeffZZrr72WjRs3Mnr0aG666Sa2bdsGwJo1awBYvHgxZrOZb775Rltv6dKlZGZmsnTpUmbMmEFqaiqpqana8vHjx9O0adNq//bt22eXl//7v/8jOjqaXr168eqrr1JUVITwfRXvI+UT+kQNlx9foqh+/tCR2jxCvF77WZNL+nllzc1bPdiK4iPFZM/JBqDTn53Yef5OADJ7ZnLHhjvs1p0XM4+WR1qSG57LVaeuclsehe8oKChg9+7dJCQkEBZW1pi8z0d9yMrLavC8xDWNY93d65xKO2jQIEpLS7WHP5aWlhIZGcnIkSOZOXMmAFlZWZhMJlauXEnfvn0rbeP+++/n8OHDfPXVV9q8119/ncmTJ3PTTTcxb948Nm/eTIsWLWrMz80334zFYtFKggBuvPFGFi5cqDUAvvDCCxk2bBhPPfWUlmbWrFk8/vjjHDp0CCj7NTx+/Hg++OADLU3fvn1JTk5m6tSp7Nmzh4SEBNavX0+vXr20NOPGjWPZsmVkZmYSFFT2o+b666/HYDAwZ84cALKzs8nNza32fbRv355GjcpaBfz3v//Vnri8Zs0annrqKa6++mqmT59e5fqOzifhfaxFVn4P/R2AyAsi6f17bwC2jdnG4VmHATj373Np3Kmxx/LYkGpz//aJNjNTp07l9ddfx2w2k5SUxJQpU7jgggs8nS17+mYxFUpmDME1tJmxLZKSGVGNrLwsDp486Ols1KhHjx7a66CgIKKjo+nevbs2Lza2bCTT7OyyYP/DDz9k+vTp7N27l9OnT1NUVGQXEAA88sgjfPfdd7z77rssWLDAqUAGYNu2bVxzzTV28/r168fChQu16bS0NNauXWtXElNaWkpBQQGnTp2icePG2noVt+NMg9+kpCQtkAEwmUxs3lw+RlVMTAwxMTFOvR+AiRMnaq979OiB0Wjkuuuu00prhA9zps2MlMw45PXBzJdffsmECROYOnUqAwYMYNq0aQwbNoytW7fStm1bT2dPU/FBk/pgRmkkbWZE/cU1jas5kRfsNzg42G5aURS7ebY6f6vVyty5c5k4cSJvvvkm/fr1IyIigtdff53Vq1fbbSM7O5sdO3YQFBTEzp07ueyyy5zKizMFz1arlRdffJGRI0dWWlZTKYYz7RccHQ+rtbx7yvjx45k1a1a126juemcr3frnn38kmPF1+luF/tzV9WaSNjOOeX0w89Zbb3HHHXdw5513AjBlyhR++eUXPvjgAyZNmuTh3Onozq+DSw4SUhqiTecV5JUv1J+fJVaOfXdMG4NGghlRHWerenzJH3/8Qf/+/bnvvvu0eZmZmZXS3X777XTr1o277rqLO+64gyFDhtC1a9cat9+1a1dWrVplN6/idHJyMjt27KBjx47VbmvVqlWMHTvWbrp377JqgJCQsu97aWlpjXmq6KWXXuLRRx+tNk18fHyVy9avXw+UlfgI36YPVE5YTmCxWDAajRQV6tpESSzjkFcHM0VFRaSlpVUaQ+HSSy/lr7/+crhOYWEhhYWF2nRNddGuoi+ZUbYrFFPeW2HktSN5h3fKJnQR9uGZh9lxxw5t2qpatZNXiEDQsWNHZs6cyS+//EJCQgKfffYZa9eu1XoHAbz//vusXLmSTZs20aZNGxYsWMAtt9zC6tWrtSCiKg899BD9+/dn8uTJjBgxgkWLFtlVMQE899xzDB8+nDZt2jBq1CgMBgObNm1i8+bNdo2F582bR58+fTj//POZPXs2a9as4ZNPPgHKqorCw8NZuHAhrVu3JiwsjMjISKeOQW2qmVauXMmqVasYPHgwkZGRrF27lokTJ3LVVVd5VUm1qCNdoJKxNYNbkm5hxYoVLPh5Af0oq+bMPZlLOOEeyqD38ureTEePHqW0tFSrY7eJjY0lK8txQ8hJkyYRGRmp/bVp06Yhskp453BUY+WSld3sJvNo+S9NfXfPvE15dmk3tNtAenq6+zIphJcZP348I0eO5IYbbuC8887j2LFjdqU027dv57HHHmPq1Knad/n9998nJyeHZ599tsbt9+3bl+nTp/Puu+/Sq1cvFi1axDPPPGOXZujQofz444/8+uuvnHPOOfTt25e33nqLdu3sH0fy4osvMmfOHHr06MGMGTOYPXu2VjrUqFEj3nnnHaZNm0Z8fDxXX311fQ+NQ6GhoXz55ZcMGjSIrl278txzz3HXXXfxxRdfuGV/ooEp+pcKZrOZefPmUVBQ/uicLRlbPJAx7+fVvZkOHTpEq1at+Ouvv+wa37366qt89tlnbN++vdI6jkpm2rRp4/beTABH9xxlXPI4ciw5GBQDxWox5hgzaiOVGYdmAJB5diZ3bC3rzbTzXzs5+E5Zg87pF01nzrlzOPL4ESmZEdL7xMsoisL8+fMZMWKEp7NSJ3I++Y5lyjIAtrKVV+Nf5c8//+TLrl/St6CsbdTZm84mtntsNVvwH37Tm6lFixYEBQVVKoXJzs6uVFpjExoaSmhoaENkr5IW7VvwWeZnpKenk5iYyK5du0hOTubUiVPsTCjrmq1/npO+ymldh3WER4RLICOEEIFMAVQ4u/PZbFm5BaPRyNBLh3Li+xMARDZ3rvoy0Hh1NVNISAgpKSn8+uuvdvN//fVX+vfv76FcVc9oNDJkyBASEhIYMmQIRqMRY5QuQKmiu52qqBgMXv1xCOF1hg0bVuVAc6+99pqnsydE7Z35vdssopn24za4UXCl5cKeV5fMADz88MOMGTOGPn360K9fPz766CP27dvH+PHjPZ01p9k1Dq6iZEZFtV8mhKjR9OnTOX36tMNlUVFRLtuPF9fGC39z5jZgd87J4wxq5PXBzA033MCxY8d46aWXMJvNdOvWjZ9//rlS4zxvZlCqGDRP301bscpJKkQttWrVytNZEMKlFEVBRaXIXMS+/yt7jMWpHad0CTyUMS/n9cEMwH333WfXw8HX2FUf6YNtq/2ojlIyI4QQAe7M7aLoUBG7ntxVebncJhySRhoNoOLowI5eS8mMEEKI5oOaV7mscZfGhMRWP7ZSoPKJkhlfV1WQoi+ZkTYzQgghuv/QnZylOZSeth9NWmmkYBxstP9xLDQSzDQAuwbAquNSGlVRpWRGCCECnCHEQNRQ1zVeDxRSzdQA7IIUfTWTvjeTPJdJCCGEqBMJZhqCE491VxWpZhKiIaSmptK8efMG2de4ceN8dtRgIXyJBDMNoYpgptI4M1LNJIRP2rNnD4qisGHDBrfuZ9myZSiK4vBv7dq1bt23EN5M2sw0AH2Qoi990TcAtipWKZkRQlSrf//+mM1mu3nPPvssixcvpk+fPh7KlRCeJyUzDayguIBhs4cxbPYwlu5eWr5AkZEdhe8bNGgQDz74IBMmTMBoNBIbG8tHH31Efn4+t912GxEREXTo0IEFCxYAUFpayh133EFCQgLh4eF07tyZt99+W9teQUEBSUlJ3H333dq83bt3ExkZyccff+xUnlJTU2nbti2NGzfmmmuu4dixY5XS/PDDD6SkpBAWFkZiYiIvvvii3RPuFUXhgw8+YNiwYYSHh5OQkMC8efO05QkJCQD07t0bRVEYNGiQ3fbfeOMNTCYT0dHR3H///RQXFzuV94pCQkKIi4vT/qKjo/n++++5/fbb5fohApoEMw3EqpTVKVmtVhb+s5CF/ywkKzfLbnlIkIwfIHzfjBkzaNGiBWvWrOHBBx/k3nvvZdSoUfTv35/09HSGDh3KmDFjOHXqFFarldatWzN37ly2bt3Kc889x9NPP83cuXMBCAsLY/bs2cyYMYNvv/2W0tJSxowZw+DBg7nrrrtqzMvq1au5/fbbue+++9iwYQODBw/mlVdesUvzyy+/MHr0aB566CG2bt3KtGnTSE1N5dVXX7VL9+yzz3LttdeyceNGRo8ezU033cS2bdsAWLNmDQCLFy/GbDbzzTffaOstXbqUzMxMli5dyowZM0hNTSU1NVVbPn78+CqfL2X727dvn8P39/3333P06FHGjRtX47EQwp8pqp8/dKQ2jxB3p6VBS1GsCtvjt3Pv3fcC8Oy8Z7ko4yIARj88mgeveZAnzn/CY3kU3qOgoIDdu3eTkJBAWFgYAOv6rKMoq6jB8xISF0Kfdc5VYQwaNIjS0lL++OMPoKzkJTIykpEjRzJz5kwAsrKyMJlMrFy5kr59+1baxv3338/hw4f56quvtHmvv/46kydP5qabbmLevHls3ryZFi1a1Jifm2++GYvFopUEAdx4440sXLiQnJwcAC688EKGDRvGU089paWZNWsWjz/+OIcOHQLKSmbGjx/PBx98oKXp27cvycnJTJ06lT179pCQkMD69evp1auXlmbcuHEsW7aMzMxMgoKCALj++usxGAzMmTMHgOzsbHJzc6t9H+3bt6dRo8qtAi6//HIAfv7552rXd3Q+CeHtanP/ljYzDcRWBNw7rjeWJywA7Nm0h5yMHAA237cZYwdjVasLQVFWEUUHGz6Yqa0ePXpor4OCgoiOjqZ79+7avNjYWKDsJg7w4YcfMn36dPbu3cvp06cpKiqyCwgAHnnkEb777jveffddFixY4FQgA7Bt2zauueYau3n9+vVj4cKF2nRaWhpr1661K4kpLS2loKCAU6dO0bhxY229ittxpsFvUlKSFsgAmEwmNm/erE3HxMQQExPj1PvRO3DgAL/88otWiiVEIJNgpoEoBgW1VCWIIJqHNQcg2FD+WPfw0HAP5Uz4ipA4z1RD1na/wcHBdtOKotjNswX2VquVuXPnMnHiRN5880369etHREQEr7/+OqtXr7bbRnZ2Njt27CAoKIidO3dy2WWXOZUXZwqerVYrL774IiNHjqy0rKZSDGfaqTg6HlZreVfG8ePHM2vWrGq3sXXrVtq2bWs379NPPyU6OpqrrrqqxjwI4e8kmGkoZ655J/eeZMMTGzh27Bhhm8ovlNJ4T9TE2aoeX/LHH3/Qv39/uwfJZmZmVkp3++23061bN+666y7uuOMOhgwZQteuXWvcfteuXVm1apXdvIrTycnJ7Nixg44dO1a7rVWrVjF27Fi76d69ewNlDXOhrESntl566SUeffTRatPEx8fbTauqyqeffsrYsWMrBUvCf1gsFtLS0khJScFolJL76kgw01DOxCrKMYWcyTkEEUQx5T0aTpw4QUyr2hc1C+HLOnbsyMyZM/nll19ISEjgs88+Y+3atVrvIID333+flStXsmnTJtq0acOCBQu45ZZbWL16tRZEVOWhhx6if//+TJ48mREjRrBo0SK7KiaA5557juHDh9OmTRtGjRqFwWBg06ZNbN682a6x8Lx58+jTpw/nn38+s2fPZs2aNXzyySdAWVVReHg4CxcupHXr1oSFhREZGenUMahLNdOSJUvYvXs3d9xxR63WE77DYrGQlJSE2WzGZDKRkZEhAU01pDdTAyntVvUvtn3sY/PBzVUuF8JfjR8/npEjR3LDDTdw3nnncezYMbtSmu3bt/PYY48xdepU2rRpA5QFNzk5OTz77LM1br9v375Mnz6dd999l169erFo0SKeeeYZuzRDhw7lxx9/5Ndff+Wcc86hb9++vPXWW7Rr184u3YsvvsicOXPo0aMHM2bMYPbs2VrpUKNGjXjnnXeYNm0a8fHxXH311fU9NNX65JNP6N+/P2effbZb9yM8Jy0tTRtTyGw2k56e7uEceTfpzdRAjh0+xi1dbyHveB4GxYBVtWJQDBSrxRyOO0za1jSJuoVGep94F0VRmD9/vs8+mkDOJ9+jL5mJj49ny5YtAXePkN5MXig6Npov/vmC9PR0EhMT2bVrl/Z/cnJywJ2kQgghqmY0GsnIyCA9PV3uEU6QYKYBGY1GhgwZApSPGKpvGyCEqJ1hw4ZpY9pU9PTTT/P00083cI6EcB39PUNUT4IZIYTPmj59OqdPn3a4LCoqymX78fPaeCF8ngQzQgif1apVK09nQQjhBaQ3kxBCCCF8mgQzQngxqd4QriDnkfB3EswI4YVso7qeOnXKwzkR/qCoqOyZXvpnRAnhT6TNjBBeKCgoiObNm2sPY2zcuLE88kLUidVq5ciRIzRu3Njhk7eF8AdyZgvhpeLi4oDyp0sLUVcGg4G2bdtKQCz8lgQzQngpRVEwmUzExMRQXFxc8wpCVCEkJASDQVoVCP8lwYwQXi4oKEjaOgghRDUkVBdCCCGET5NgRgghhBA+TYIZIYQQQvg0v28zYxssKjc318M5EUIIIYSzbPdtZwZ99Ptg5uTJkwC0adPGwzkRQgghRG2dPHmSyMjIatMoqp+Pc221Wjl06BAREREuH2MhNzeXNm3asH//fpo1a+bSbYtycpwbhhznhiHHuWHIcW4Y7jzOqqpy8uRJ4uPjaxxawO9LZgwGA61bt3brPpo1ayZflgYgx7lhyHFuGHKcG4Yc54bhruNcU4mMjTQAFkIIIYRPk2BGCCGEED5Ngpl6CA0N5fnnnyc0NNTTWfFrcpwbhhznhiHHuWHIcW4Y3nKc/b4BsBBCCCH8m5TMCCGEEMKnSTAjhBBCCJ8mwYwQQgghfJoEM0IIIYTwaRLM1NHUqVNJSEggLCyMlJQU/vjjD09nyae98MILKIpi9xcXF6ctV1WVF154gfj4eMLDwxk0aBAZGRkezLFv+P3337nyyiuJj49HURS+/fZbu+XOHNfCwkIefPBBWrRoQZMmTbjqqqs4cOBAA74L71fTcR43blyl87tv3752aeQ412zSpEmcc845REREEBMTw4gRI9ixY4ddGjmn68+Z4+xt57QEM3Xw5ZdfMmHCBP7973+zfv16LrjgAoYNG8a+ffs8nTWflpSUhNls1v42b96sLZs8eTJvvfUW7733HmvXriUuLo5LLrlEe/aWcCw/P5+ePXvy3nvvOVzuzHGdMGEC8+fPZ86cOfz555/k5eUxfPhwSktLG+pteL2ajjPAZZddZnd+//zzz3bL5TjXbPny5dx///2sWrWKX3/9lZKSEi699FLy8/O1NHJO158zxxm87JxWRa2de+656vjx4+3mdenSRX3yySc9lCPf9/zzz6s9e/Z0uMxqtapxcXHqf/7zH21eQUGBGhkZqX744YcNlEPfB6jz58/Xpp05rjk5OWpwcLA6Z84cLc3BgwdVg8GgLly4sMHy7ksqHmdVVdVbb71Vvfrqq6tcR45z3WRnZ6uAunz5clVV5Zx2l4rHWVW975yWkplaKioqIi0tjUsvvdRu/qWXXspff/3loVz5h507dxIfH09CQgI33ngju3btAmD37t1kZWXZHfPQ0FAGDhwox7wenDmuaWlpFBcX26WJj4+nW7ducuxradmyZcTExHDWWWdx1113kZ2drS2T41w3J06cACAqKgqQc9pdKh5nG286pyWYqaWjR49SWlpKbGys3fzY2FiysrI8lCvfd9555zFz5kx++eUXPv74Y7Kysujfvz/Hjh3Tjqscc9dy5rhmZWUREhKC0WisMo2o2bBhw5g9ezZLlizhzTffZO3atVx00UUUFhYCcpzrQlVVHn74Yc4//3y6desGyDntDo6OM3jfOe33T812F0VR7KZVVa00Tzhv2LBh2uvu3bvTr18/OnTowIwZM7RGZXLM3aMux1WOfe3ccMMN2utu3brRp08f2rVrx08//cTIkSOrXE+Oc9UeeOABNm3axJ9//llpmZzTrlPVcfa2c1pKZmqpRYsWBAUFVYoss7OzK/0aEHXXpEkTunfvzs6dO7VeTXLMXcuZ4xoXF0dRUREWi6XKNKL2TCYT7dq1Y+fOnYAc59p68MEH+f7771m6dCmtW7fW5ss57VpVHWdHPH1OSzBTSyEhIaSkpPDrr7/azf/111/p37+/h3LlfwoLC9m2bRsmk4mEhATi4uLsjnlRURHLly+XY14PzhzXlJQUgoOD7dKYzWa2bNkix74ejh07xv79+zGZTIAcZ2epqsoDDzzAN998w5IlS0hISLBbLue0a9R0nB3x+Dnt8ibFAWDOnDlqcHCw+sknn6hbt25VJ0yYoDZp0kTds2ePp7Pmsx555BF12bJl6q5du9RVq1apw4cPVyMiIrRj+p///EeNjIxUv/nmG3Xz5s3qTTfdpJpMJjU3N9fDOfduJ0+eVNevX6+uX79eBdS33npLXb9+vbp3715VVZ07ruPHj1dbt26tLl68WE1PT1cvuugitWfPnmpJSYmn3pbXqe44nzx5Un3kkUfUv/76S929e7e6dOlStV+/fmqrVq3kONfSvffeq0ZGRqrLli1TzWaz9nfq1CktjZzT9VfTcfbGc1qCmTp6//331Xbt2qkhISFqcnKyXZc1UXs33HCDajKZ1ODgYDU+Pl4dOXKkmpGRoS23Wq3q888/r8bFxamhoaHqhRdeqG7evNmDOfYNS5cuVYFKf7feequqqs4d19OnT6sPPPCAGhUVpYaHh6vDhw9X9+3b54F3472qO86nTp1SL730UrVly5ZqcHCw2rZtW/XWW2+tdAzlONfM0TEG1E8//VRLI+d0/dV0nL3xnFbOZFwIIYQQwidJmxkhhBBC+DQJZoQQQgjh0ySYEUIIIYRPk2BGCCGEED5NghkhhBBC+DQJZoQQQgjh0ySYEUIIIYRPk2BGCCGEED5NghkhhMeNGzcORVFQFIXg4GBiY2O55JJL+N///ofVanV6O6mpqTRv3tx9GRVCeCUJZoQQXuGyyy7DbDazZ88eFixYwODBg/nXv/7F8OHDKSkp8XT2hBBeTIIZIYRXCA0NJS4ujlatWpGcnMzTTz/Nd999x4IFC0hNTQXgrbfeonv37jRp0oQ2bdpw3333kZeXB8CyZcu47bbbOHHihFbK88ILLwAwa9Ys+vTpQ0REBHFxcdx8881kZ2d76J0KIVxNghkhhNe66KKL6NmzJ9988w0ABoOBd955hy1btjBjxgyWLFnC448/DkD//v2ZMmUKzZo1w2w2YzabefTRRwEoKiri5ZdfZuPGjXz77bfs3r2bcePGeeptCSFcrJGnMyCEENXp0qULmzZtAmDChAna/ISEBF5++WXuvfdepk6dSkhICJGRkSiKQlxcnN02bv//9uzQpbUoAMD4N4WlLS6IqFPbWDAZTBZFRFi0LZis/g2Cm6KGiWAU1KKIaLLo/gCnCwZNgoJg2NomiJP7giAsvBcebO7A90uXyz2Hc9p3z1la+nkeGxujVCoxOTlJo9EgkUh0ZR+SOseTGUk9LYoiYrEYAOVymZmZGQYHB0kmk+Tzeer1Os1m859zVKtVcrkcIyMjJJNJpqenAXh5een08iV1gTEjqac9PDwwOjrK8/Mz8/PzZLNZTk9Pub29ZXd3F4DPz8+/jm82m8zOzpJIJDg8POTm5oazszPg+/pJUvi8ZpLUs66vr7m/v2dlZYVKpUKr1WJra4u+vu//sOPj47bv4/E4X19fbe8eHx+p1WoUi0WGhoYAqFQq3dmApK7wZEZST/j4+ODt7Y3X11fu7u5YW1sjl8uxsLBAPp9nfHycVqvFzs4OT09PHBwcsLe31zZHOp2m0WhwdXVFrVbj/f2d4eFh4vH4z7iLiwtWV1d/aZeSOsGYkdQTLi8vGRgYIJ1OMzc3R7lcplQqcX5+Tn9/PxMTE2xvb7O+vk42m+Xo6IhCodA2x9TUFMvLyywuLpJKpdjY2CCVSrG/v8/JyQmZTIZiscjm5uYv7VJSJ8SiKIp+exGSJEn/y5MZSZIUNGNGkiQFzZiRJElBM2YkSVLQjBlJkhQ0Y0aSJAXNmJEkSUEzZiRJUtCMGUmSFDRjRpIkBc2YkSRJQTNmJElS0P4AeP73qfP7zvwAAAAASUVORK5CYII=\n",
|
||
"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",
|
||
"id": "967f86f4",
|
||
"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",
|
||
"id": "58c89f85",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sum_{j=1}^J\\sum_{i\\in R_j}(y_i-\\overline{y}_{R_j})^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8d28defb",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $\\overline{y}_{R_j}$ is the mean response for the training observations \n",
|
||
"within box $j$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3f6c36d6",
|
||
"metadata": {},
|
||
"source": [
|
||
"## A top-down approach, recursive binary splitting\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."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a89a52db",
|
||
"metadata": {},
|
||
"source": [
|
||
"## 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",
|
||
"id": "5feb6c75",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\left\\{X\\vert x_j < s\\right\\},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8de30cae",
|
||
"metadata": {},
|
||
"source": [
|
||
"and"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "95d5c167",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\left\\{X\\vert x_j \\geq s\\right\\},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c5f10599",
|
||
"metadata": {},
|
||
"source": [
|
||
"so that we obtain the lowest MSE, that is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ff6f03cb",
|
||
"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",
|
||
"id": "9f031abb",
|
||
"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."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "83f9c272",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Pruning the tree\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)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9f23f5ac",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Cost complexity pruning\n",
|
||
"\n",
|
||
"For each value of $\\alpha$ there corresponds a subtree $T \\in T_0$ such that"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a9b2646e",
|
||
"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",
|
||
"id": "8c9f1038",
|
||
"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",
|
||
"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 $\\alpha$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1e4cf9ca",
|
||
"metadata": {},
|
||
"source": [
|
||
"## 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",
|
||
"4. Return the subtree from Step 2 that corresponds to the chosen value of $\\alpha$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "328198af",
|
||
"metadata": {},
|
||
"source": [
|
||
"## 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."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "338052bc",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Growing a classification tree\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."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c96ca06b",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Classification tree, how to split nodes\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",
|
||
"id": "970d1672",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i=k).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e5a9ac3c",
|
||
"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",
|
||
"id": "a0e10726",
|
||
"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",
|
||
"id": "f73a5a66",
|
||
"metadata": {},
|
||
"source": [
|
||
"* Gini index $g$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c6e5ec5f",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"g = \\sum_{k=1}^K p_{mk}(1-p_{mk}).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c50e4c55",
|
||
"metadata": {},
|
||
"source": [
|
||
"* Information entropy or just entropy $s$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "34f4deed",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"s = -\\sum_{k=1}^K p_{mk}\\log{p_{mk}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b2f791b8",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Visualizing the Tree, Classification"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"id": "b373a31c",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
" mean radius mean texture mean perimeter mean area mean smoothness \\\n",
|
||
"0 17.99 10.38 122.80 1001.0 0.11840 \n",
|
||
"1 20.57 17.77 132.90 1326.0 0.08474 \n",
|
||
"2 19.69 21.25 130.00 1203.0 0.10960 \n",
|
||
"3 11.42 20.38 77.58 386.1 0.14250 \n",
|
||
"4 20.29 14.34 135.10 1297.0 0.10030 \n",
|
||
".. ... ... ... ... ... \n",
|
||
"564 21.56 22.39 142.00 1479.0 0.11100 \n",
|
||
"565 20.13 28.25 131.20 1261.0 0.09780 \n",
|
||
"566 16.60 28.08 108.30 858.1 0.08455 \n",
|
||
"567 20.60 29.33 140.10 1265.0 0.11780 \n",
|
||
"568 7.76 24.54 47.92 181.0 0.05263 \n",
|
||
"\n",
|
||
" mean compactness mean concavity mean concave points mean symmetry \\\n",
|
||
"0 0.27760 0.30010 0.14710 0.2419 \n",
|
||
"1 0.07864 0.08690 0.07017 0.1812 \n",
|
||
"2 0.15990 0.19740 0.12790 0.2069 \n",
|
||
"3 0.28390 0.24140 0.10520 0.2597 \n",
|
||
"4 0.13280 0.19800 0.10430 0.1809 \n",
|
||
".. ... ... ... ... \n",
|
||
"564 0.11590 0.24390 0.13890 0.1726 \n",
|
||
"565 0.10340 0.14400 0.09791 0.1752 \n",
|
||
"566 0.10230 0.09251 0.05302 0.1590 \n",
|
||
"567 0.27700 0.35140 0.15200 0.2397 \n",
|
||
"568 0.04362 0.00000 0.00000 0.1587 \n",
|
||
"\n",
|
||
" mean fractal dimension ... worst radius worst texture \\\n",
|
||
"0 0.07871 ... 25.380 17.33 \n",
|
||
"1 0.05667 ... 24.990 23.41 \n",
|
||
"2 0.05999 ... 23.570 25.53 \n",
|
||
"3 0.09744 ... 14.910 26.50 \n",
|
||
"4 0.05883 ... 22.540 16.67 \n",
|
||
".. ... ... ... ... \n",
|
||
"564 0.05623 ... 25.450 26.40 \n",
|
||
"565 0.05533 ... 23.690 38.25 \n",
|
||
"566 0.05648 ... 18.980 34.12 \n",
|
||
"567 0.07016 ... 25.740 39.42 \n",
|
||
"568 0.05884 ... 9.456 30.37 \n",
|
||
"\n",
|
||
" worst perimeter worst area worst smoothness worst compactness \\\n",
|
||
"0 184.60 2019.0 0.16220 0.66560 \n",
|
||
"1 158.80 1956.0 0.12380 0.18660 \n",
|
||
"2 152.50 1709.0 0.14440 0.42450 \n",
|
||
"3 98.87 567.7 0.20980 0.86630 \n",
|
||
"4 152.20 1575.0 0.13740 0.20500 \n",
|
||
".. ... ... ... ... \n",
|
||
"564 166.10 2027.0 0.14100 0.21130 \n",
|
||
"565 155.00 1731.0 0.11660 0.19220 \n",
|
||
"566 126.70 1124.0 0.11390 0.30940 \n",
|
||
"567 184.60 1821.0 0.16500 0.86810 \n",
|
||
"568 59.16 268.6 0.08996 0.06444 \n",
|
||
"\n",
|
||
" worst concavity worst concave points worst symmetry \\\n",
|
||
"0 0.7119 0.2654 0.4601 \n",
|
||
"1 0.2416 0.1860 0.2750 \n",
|
||
"2 0.4504 0.2430 0.3613 \n",
|
||
"3 0.6869 0.2575 0.6638 \n",
|
||
"4 0.4000 0.1625 0.2364 \n",
|
||
".. ... ... ... \n",
|
||
"564 0.4107 0.2216 0.2060 \n",
|
||
"565 0.3215 0.1628 0.2572 \n",
|
||
"566 0.3403 0.1418 0.2218 \n",
|
||
"567 0.9387 0.2650 0.4087 \n",
|
||
"568 0.0000 0.0000 0.2871 \n",
|
||
"\n",
|
||
" worst fractal dimension \n",
|
||
"0 0.11890 \n",
|
||
"1 0.08902 \n",
|
||
"2 0.08758 \n",
|
||
"3 0.17300 \n",
|
||
"4 0.07678 \n",
|
||
".. ... \n",
|
||
"564 0.07115 \n",
|
||
"565 0.06637 \n",
|
||
"566 0.07820 \n",
|
||
"567 0.12400 \n",
|
||
"568 0.07039 \n",
|
||
"\n",
|
||
"[569 rows x 30 columns]\n",
|
||
" malignant benign\n",
|
||
"0 1 0\n",
|
||
"1 1 0\n",
|
||
"2 1 0\n",
|
||
"3 1 0\n",
|
||
"4 1 0\n",
|
||
".. ... ...\n",
|
||
"564 1 0\n",
|
||
"565 1 0\n",
|
||
"566 1 0\n",
|
||
"567 1 0\n",
|
||
"568 0 1\n",
|
||
"\n",
|
||
"[569 rows x 2 columns]\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0"
|
||
]
|
||
},
|
||
"execution_count": 2,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"import os\n",
|
||
"from sklearn.datasets import load_breast_cancer\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.metrics import confusion_matrix\n",
|
||
"from sklearn.tree import export_graphviz\n",
|
||
"\n",
|
||
"from IPython.display import Image \n",
|
||
"from pydot import graph_from_dot_data\n",
|
||
"import pandas as pd\n",
|
||
"import numpy as np\n",
|
||
"\n",
|
||
"\n",
|
||
"cancer = load_breast_cancer()\n",
|
||
"X = pd.DataFrame(cancer.data, columns=cancer.feature_names)\n",
|
||
"print(X)\n",
|
||
"y = pd.Categorical.from_codes(cancer.target, cancer.target_names)\n",
|
||
"y = pd.get_dummies(y)\n",
|
||
"print(y)\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)\n",
|
||
"tree_clf = DecisionTreeClassifier(max_depth=5)\n",
|
||
"tree_clf.fit(X_train, y_train)\n",
|
||
"\n",
|
||
"export_graphviz(\n",
|
||
" tree_clf,\n",
|
||
" out_file=\"DataFiles/cancer.dot\",\n",
|
||
" feature_names=cancer.feature_names,\n",
|
||
" class_names=cancer.target_names,\n",
|
||
" rounded=True,\n",
|
||
" filled=True\n",
|
||
")\n",
|
||
"cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'\n",
|
||
"os.system(cmd)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f1649fd9",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Visualizing the Tree, The Moons"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"id": "63e625c0",
|
||
"metadata": {},
|
||
"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",
|
||
"id": "119ea0ae",
|
||
"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,
|
||
"id": "711bdf8d",
|
||
"metadata": {},
|
||
"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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\n",
|
||
"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",
|
||
"id": "a80a7f27",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Printing out as text\n",
|
||
"\n",
|
||
"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,
|
||
"id": "3aa4b27b",
|
||
"metadata": {},
|
||
"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",
|
||
"id": "e155d65a",
|
||
"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."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9f64d255",
|
||
"metadata": {},
|
||
"source": [
|
||
"## 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",
|
||
"id": "c67ea6bd",
|
||
"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",
|
||
"id": "60be0c2f",
|
||
"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 $max\\_leaf\\_nodes$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "68adc691",
|
||
"metadata": {},
|
||
"source": [
|
||
"## 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",
|
||
"id": "3aa84faa",
|
||
"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",
|
||
"id": "05821fe6",
|
||
"metadata": {},
|
||
"source": [
|
||
"Here the MSE for a specific node is defined as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "321fb878",
|
||
"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",
|
||
"id": "5703ea44",
|
||
"metadata": {},
|
||
"source": [
|
||
"with"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6b6cf145",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\overline{y}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}y_i,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "57f159ee",
|
||
"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."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8dba6c9f",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Why binary splits?\n",
|
||
"\n",
|
||
"It is custom to split to a tree uising binary splits. The reason is\n",
|
||
"that multiway splits fragment the data too quickly, leaving\n",
|
||
"insufficient data at the next level down. Multiway splits can be\n",
|
||
"achieved by a series of binary split and this is normally preferred."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "54686dd2",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Computing a Tree using the Gini Index\n",
|
||
"\n",
|
||
"Consider the following example with attributes/features and two\n",
|
||
"possible outcomes (classes) for each attribute. Assume we wish to find some\n",
|
||
"correlations between the average grade of a student as function of the\n",
|
||
"number of hours studied and hours slept. We want also to correlate the\n",
|
||
"grade in a given course with the general trend, whether the students\n",
|
||
"recently has gotten grades below average or above.\n",
|
||
"\n",
|
||
"We have three features/attributes\n",
|
||
"1. Trend of average grades before present course, classified as either below or above the average grade of the whole class \n",
|
||
"\n",
|
||
"2. The number of hours studies, classified again as either higher (more than 3 hours per day) or lower . Here we have used a standard for one $ECTS$ which is scaled to 25-30 hours of work for a semester which lasts 18 weeks, with 15 weeks of lectures and 3 weeks for exams, assuming a total of 30 ECTS per semester. \n",
|
||
"\n",
|
||
"3. The number of hours slept as high for more than $8$ hours and below for less than 8 hours of sleep, classified again as either high or low\n",
|
||
"\n",
|
||
"4. The final grade whether it is above or below average"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "226714bc",
|
||
"metadata": {},
|
||
"source": [
|
||
"## The Table\n",
|
||
"\n",
|
||
"<table class=\"dotable\" border=\"1\">\n",
|
||
"<thead>\n",
|
||
"<tr><th align=\"center\">Grade Trend</th> <th align=\"center\">Hours slept</th> <th align=\"center\">Hours Studied</th> <th align=\"center\">Grade</th> </tr>\n",
|
||
"</thead>\n",
|
||
"<tbody>\n",
|
||
"<tr><td align=\"center\"> Above </td> <td align=\"center\"> Low </td> <td align=\"center\"> High </td> <td align=\"center\"> Above </td> </tr>\n",
|
||
"<tr><td align=\"center\"> Below </td> <td align=\"center\"> High </td> <td align=\"center\"> Low </td> <td align=\"center\"> Below </td> </tr>\n",
|
||
"<tr><td align=\"center\"> Above </td> <td align=\"center\"> Low </td> <td align=\"center\"> High </td> <td align=\"center\"> Above </td> </tr>\n",
|
||
"<tr><td align=\"center\"> Above </td> <td align=\"center\"> High </td> <td align=\"center\"> High </td> <td align=\"center\"> Above </td> </tr>\n",
|
||
"<tr><td align=\"center\"> Below </td> <td align=\"center\"> Low </td> <td align=\"center\"> High </td> <td align=\"center\"> Below </td> </tr>\n",
|
||
"<tr><td align=\"center\"> Above </td> <td align=\"center\"> Low </td> <td align=\"center\"> Low </td> <td align=\"center\"> Below </td> </tr>\n",
|
||
"<tr><td align=\"center\"> Below </td> <td align=\"center\"> High </td> <td align=\"center\"> High </td> <td align=\"center\"> Below </td> </tr>\n",
|
||
"<tr><td align=\"center\"> Below </td> <td align=\"center\"> Low </td> <td align=\"center\"> High </td> <td align=\"center\"> Below </td> </tr>\n",
|
||
"<tr><td align=\"center\"> Above </td> <td align=\"center\"> Low </td> <td align=\"center\"> Low </td> <td align=\"center\"> Below </td> </tr>\n",
|
||
"<tr><td align=\"center\"> Above </td> <td align=\"center\"> High </td> <td align=\"center\"> High </td> <td align=\"center\"> Above </td> </tr>\n",
|
||
"</tbody>\n",
|
||
"</table>"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "132a6df7",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Computing the various Gini Indices\n",
|
||
"\n",
|
||
"In computations we will translate all classes into numbers. Being\n",
|
||
"these binary classes, they can easily be split into ones and zeros.\n",
|
||
"\n",
|
||
"**Gini index for Average trend.**\n",
|
||
"\n",
|
||
"[See handwritten notes November 3](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2022/NotesNov32022.pdf)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "75ab3e53",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Computing the various Gini Indices, Hours slept\n",
|
||
"\n",
|
||
"**Gini index for hour slept.**\n",
|
||
"\n",
|
||
"[See handwritten notes November 3](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2022/NotesNov32022.pdf)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "be9d82ec",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Computing the various Gini Indices, Hours studied\n",
|
||
"\n",
|
||
"**Gini index for hour studied.**\n",
|
||
"\n",
|
||
"[See handwritten notes November 3](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2022/NotesNov32022.pdf)\n",
|
||
"\n",
|
||
"For final tree, see the above handwritten notes"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b502bb89",
|
||
"metadata": {},
|
||
"source": [
|
||
"## A possible code using Scikit-Learn"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"id": "2e5fc857",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/html": [
|
||
"<div>\n",
|
||
"<style scoped>\n",
|
||
" .dataframe tbody tr th:only-of-type {\n",
|
||
" vertical-align: middle;\n",
|
||
" }\n",
|
||
"\n",
|
||
" .dataframe tbody tr th {\n",
|
||
" vertical-align: top;\n",
|
||
" }\n",
|
||
"\n",
|
||
" .dataframe thead th {\n",
|
||
" text-align: right;\n",
|
||
" }\n",
|
||
"</style>\n",
|
||
"<table border=\"1\" class=\"dataframe\">\n",
|
||
" <thead>\n",
|
||
" <tr style=\"text-align: right;\">\n",
|
||
" <th></th>\n",
|
||
" <th>Grade Trend</th>\n",
|
||
" <th>Hours slept</th>\n",
|
||
" <th>Hours Studied</th>\n",
|
||
" <th>Grade</th>\n",
|
||
" </tr>\n",
|
||
" </thead>\n",
|
||
" <tbody>\n",
|
||
" <tr>\n",
|
||
" <th>0</th>\n",
|
||
" <td>1</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>1</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>1</th>\n",
|
||
" <td>0</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>0</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>2</th>\n",
|
||
" <td>1</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>1</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>3</th>\n",
|
||
" <td>1</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>1</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>4</th>\n",
|
||
" <td>0</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>0</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>5</th>\n",
|
||
" <td>1</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>0</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>6</th>\n",
|
||
" <td>0</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>0</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>7</th>\n",
|
||
" <td>0</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>0</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>8</th>\n",
|
||
" <td>1</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>0</td>\n",
|
||
" <td>0</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>9</th>\n",
|
||
" <td>1</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>1</td>\n",
|
||
" <td>1</td>\n",
|
||
" </tr>\n",
|
||
" </tbody>\n",
|
||
"</table>\n",
|
||
"</div>"
|
||
],
|
||
"text/plain": [
|
||
" Grade Trend Hours slept Hours Studied Grade\n",
|
||
"0 1 0 1 1\n",
|
||
"1 0 1 0 0\n",
|
||
"2 1 0 1 1\n",
|
||
"3 1 1 1 1\n",
|
||
"4 0 0 1 0\n",
|
||
"5 1 0 0 0\n",
|
||
"6 0 1 1 0\n",
|
||
"7 0 0 1 0\n",
|
||
"8 1 0 0 0\n",
|
||
"9 1 1 1 1"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[[1 0 1]\n",
|
||
" [0 1 0]\n",
|
||
" [1 0 1]\n",
|
||
" [1 1 1]\n",
|
||
" [0 0 1]\n",
|
||
" [1 0 0]\n",
|
||
" [0 1 1]\n",
|
||
" [0 0 1]\n",
|
||
" [1 0 0]\n",
|
||
" [1 1 1]]\n",
|
||
"Train set accuracy with Decision Tree: 1.00\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0"
|
||
]
|
||
},
|
||
"execution_count": 7,
|
||
"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(\"grades.csv\"),'r')\n",
|
||
"\n",
|
||
"# Read the experimental data with Pandas\n",
|
||
"from IPython.display import display\n",
|
||
"grades = pd.read_csv(infile)\n",
|
||
"grades = pd.DataFrame(grades)\n",
|
||
"display(grades)\n",
|
||
"# Features and targets\n",
|
||
"X = grades.loc[:, grades.columns != 'Grade'].values\n",
|
||
"y = grades.loc[:, grades.columns == 'Grade'].values\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/grade.dot\",\n",
|
||
" rounded=True,\n",
|
||
" filled=True\n",
|
||
")\n",
|
||
"cmd = 'dot -Tpng DataFiles/grade.dot -o DataFiles/grades.png'\n",
|
||
"os.system(cmd)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fe2aa246",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Further example: Computing the Gini index\n",
|
||
"\n",
|
||
"The next 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 class=\"dotable\" 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>"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "46f289da",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Simple Python Code to read in Data and perform Classification"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"id": "38aedbca",
|
||
"metadata": {},
|
||
"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": 8,
|
||
"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",
|
||
"id": "a6f5da59",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Computing the Gini Factor\n",
|
||
"\n",
|
||
"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": 9,
|
||
"id": "e51855f9",
|
||
"metadata": {},
|
||
"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",
|
||
"id": "f6add3e5",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Regression trees"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"id": "74ecc649",
|
||
"metadata": {},
|
||
"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": 11,
|
||
"id": "04024d89",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"DecisionTreeRegressor(max_depth=2, random_state=42)"
|
||
]
|
||
},
|
||
"execution_count": 11,
|
||
"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": "markdown",
|
||
"id": "878b4d23",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Final regressor code"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"id": "3c96bff5",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"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": 13,
|
||
"id": "527b27ca",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"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",
|
||
"id": "f2a0dd48",
|
||
"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)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9f896560",
|
||
"metadata": {},
|
||
"source": [
|
||
"## 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."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3f6f50e2",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods\n",
|
||
"\n",
|
||
"As stated above and seen in many of the examples discussed here about\n",
|
||
"a single decision tree, we often end up overfitting our training\n",
|
||
"data. This normally means that we have a high variance. Can we reduce\n",
|
||
"the variance of a statistical learning method?\n",
|
||
"\n",
|
||
"This leads us to a set of different methods that can combine different\n",
|
||
"machine learning algorithms or just use one of them to construct\n",
|
||
"forests and jungles of trees, homogeneous ones or heterogenous\n",
|
||
"ones. These methods are recognized by different names which we will\n",
|
||
"try to explain here. These are\n",
|
||
"\n",
|
||
"1. Voting classifiers\n",
|
||
"\n",
|
||
"2. Bagging and Pasting\n",
|
||
"\n",
|
||
"3. Random forests\n",
|
||
"\n",
|
||
"4. Boosting methods, from adaptive to Extreme Gradient Boosting (XGBoost)\n",
|
||
"\n",
|
||
"We discuss these methods here."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "24509012",
|
||
"metadata": {},
|
||
"source": [
|
||
"## An Overview of Ensemble Methods\n",
|
||
"\n",
|
||
"<!-- dom:FIGURE: [DataFiles/ensembleoverview.png, width=600 frac=0.8] -->\n",
|
||
"<!-- begin figure -->\n",
|
||
"\n",
|
||
"<img src=\"DataFiles/ensembleoverview.png\" width=\"600\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
|
||
"<!-- end figure -->"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "15a871bc",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Why Voting?\n",
|
||
"\n",
|
||
"The idea behind boosting, and voting as well can be phrased as follows:\n",
|
||
"**Can a group of people somehow arrive at highly\n",
|
||
"reasoned decisions, despite the weak judgement of the individual\n",
|
||
"members?**\n",
|
||
"\n",
|
||
"The aim is to create a good classifier by combining several weak classifiers.\n",
|
||
"**A weak classifier is a classifier which is able to produce results that are only slightly better than guessing at random.**\n",
|
||
"\n",
|
||
"The basic approach is to apply repeatedly (in boosting this is done in an iterative way) a weak classifier to modifications of the data.\n",
|
||
"In voting we simply apply the law of large numbers while in boosting we give more weight to misclassified data in\n",
|
||
"each iteration. \n",
|
||
"\n",
|
||
"Decision trees play an important role as our weak classifier. They serve as the basic method."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e6d75533",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Tossing coins\n",
|
||
"\n",
|
||
"The simplest case is a so-called voting ensemble. To illustrate this,\n",
|
||
"think of yourself tossing coins with a biased outcome of 51 per cent\n",
|
||
"for heads and 49% for tails. With only few tosses,\n",
|
||
"you may not clearly see this distribution for heads and tails. However, after some\n",
|
||
"thousands of tosses, there will be a clear majority of heads. With 2000 tosses\n",
|
||
"you should see approximately 1020 heads and 980 tails.\n",
|
||
"\n",
|
||
"We can then state that the outcome is a clear majority of heads. If\n",
|
||
"you do this ten thousand times, it is easy to see that there is a 97%\n",
|
||
"likelihood of a majority of heads.\n",
|
||
"\n",
|
||
"Another example would be to collect all polls before an\n",
|
||
"election. Different polls may show different likelihoods for a\n",
|
||
"candidate winning with say a majority of the popular vote. The majority vote\n",
|
||
"would then consist in many polls indicating that this candidate will\n",
|
||
"actually win.\n",
|
||
"\n",
|
||
"The example here shows how we can implement the coin tossing case,\n",
|
||
"clealry demostrating that after some tosses we see the [law of large](https://en.wikipedia.org/wiki/Law_of_large_numbers)\n",
|
||
"numbers kicking in."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8ecb23d0",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Standard imports first"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"id": "b42d0a08",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Common imports\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",
|
||
"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')"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e3060cfd",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Simple Voting Example, head or tail"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 15,
|
||
"id": "59d25264",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 800x350 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"\n",
|
||
"# Common imports\n",
|
||
"import numpy as np\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",
|
||
"heads_proba = 0.51\n",
|
||
"coin_tosses = (np.random.rand(10000, 10) < heads_proba).astype(np.int32)\n",
|
||
"cumulative_heads_ratio = np.cumsum(coin_tosses, axis=0) / np.arange(1, 10001).reshape(-1, 1)\n",
|
||
"plt.figure(figsize=(8,3.5))\n",
|
||
"plt.plot(cumulative_heads_ratio)\n",
|
||
"plt.plot([0, 10000], [0.51, 0.51], \"k--\", linewidth=2, label=\"51%\")\n",
|
||
"plt.plot([0, 10000], [0.5, 0.5], \"k-\", label=\"50%\")\n",
|
||
"plt.xlabel(\"Number of coin tosses\")\n",
|
||
"plt.ylabel(\"Heads ratio\")\n",
|
||
"plt.legend(loc=\"lower right\")\n",
|
||
"plt.axis([0, 10000, 0.42, 0.58])\n",
|
||
"save_fig(\"votingsimple\")\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f8cf0e6e",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Using the Voting Classifier\n",
|
||
"\n",
|
||
"We can use the voting classifier on other data sets, here the exciting binary case of two distinct objects using the make moons functionality of **Scikit-Learn**."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 16,
|
||
"id": "76fd4c2d",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"LogisticRegression 0.864\n",
|
||
"RandomForestClassifier 0.872\n",
|
||
"SVC 0.888\n",
|
||
"VotingClassifier 0.896\n",
|
||
"LogisticRegression 0.864\n",
|
||
"RandomForestClassifier 0.872\n",
|
||
"SVC 0.888\n",
|
||
"VotingClassifier 0.912\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.datasets import make_moons\n",
|
||
"\n",
|
||
"X, y = make_moons(n_samples=500, noise=0.30, random_state=42)\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n",
|
||
"\n",
|
||
"from sklearn.ensemble import RandomForestClassifier\n",
|
||
"from sklearn.ensemble import VotingClassifier\n",
|
||
"from sklearn.linear_model import LogisticRegression\n",
|
||
"from sklearn.svm import SVC\n",
|
||
"\n",
|
||
"log_clf = LogisticRegression(solver=\"liblinear\", random_state=42)\n",
|
||
"rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)\n",
|
||
"svm_clf = SVC(gamma=\"auto\", random_state=42)\n",
|
||
"\n",
|
||
"voting_clf = VotingClassifier(\n",
|
||
" estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],\n",
|
||
" voting='hard')\n",
|
||
"\n",
|
||
"voting_clf.fit(X_train, y_train)\n",
|
||
"\n",
|
||
"from sklearn.metrics import accuracy_score\n",
|
||
"\n",
|
||
"for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n",
|
||
" clf.fit(X_train, y_train)\n",
|
||
" y_pred = clf.predict(X_test)\n",
|
||
" print(clf.__class__.__name__, accuracy_score(y_test, y_pred))\n",
|
||
"\n",
|
||
"log_clf = LogisticRegression(solver=\"liblinear\", random_state=42)\n",
|
||
"rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)\n",
|
||
"svm_clf = SVC(gamma=\"auto\", probability=True, random_state=42)\n",
|
||
"voting_clf = VotingClassifier(\n",
|
||
" estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],\n",
|
||
" voting='soft')\n",
|
||
"voting_clf.fit(X_train, y_train)\n",
|
||
"\n",
|
||
"from sklearn.metrics import accuracy_score\n",
|
||
"\n",
|
||
"for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n",
|
||
" clf.fit(X_train, y_train)\n",
|
||
" y_pred = clf.predict(X_test)\n",
|
||
" print(clf.__class__.__name__, accuracy_score(y_test, y_pred))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "eacefe6c",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Voting and Bagging"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 17,
|
||
"id": "796dfa6b",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"VotingClassifier(estimators=[('lr', LogisticRegression(random_state=42)),\n",
|
||
" ('rf', RandomForestClassifier(random_state=42)),\n",
|
||
" ('svc', SVC(random_state=42))])"
|
||
]
|
||
},
|
||
"execution_count": 17,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.datasets import make_moons\n",
|
||
"\n",
|
||
"X, y = make_moons(n_samples=500, noise=0.30, random_state=42)\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n",
|
||
"from sklearn.ensemble import RandomForestClassifier\n",
|
||
"from sklearn.ensemble import VotingClassifier\n",
|
||
"from sklearn.linear_model import LogisticRegression\n",
|
||
"from sklearn.svm import SVC\n",
|
||
"\n",
|
||
"log_clf = LogisticRegression(random_state=42)\n",
|
||
"rnd_clf = RandomForestClassifier(random_state=42)\n",
|
||
"svm_clf = SVC(random_state=42)\n",
|
||
"\n",
|
||
"voting_clf = VotingClassifier(\n",
|
||
" estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],\n",
|
||
" voting='hard')\n",
|
||
"voting_clf.fit(X_train, y_train)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 18,
|
||
"id": "90ec162f",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"LogisticRegression 0.864\n",
|
||
"RandomForestClassifier 0.896\n",
|
||
"SVC 0.896\n",
|
||
"VotingClassifier 0.912\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.metrics import accuracy_score\n",
|
||
"\n",
|
||
"for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n",
|
||
" clf.fit(X_train, y_train)\n",
|
||
" y_pred = clf.predict(X_test)\n",
|
||
" print(clf.__class__.__name__, accuracy_score(y_test, y_pred))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 19,
|
||
"id": "e46dcb77",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"VotingClassifier(estimators=[('lr', LogisticRegression(random_state=42)),\n",
|
||
" ('rf', RandomForestClassifier(random_state=42)),\n",
|
||
" ('svc', SVC(probability=True, random_state=42))],\n",
|
||
" voting='soft')"
|
||
]
|
||
},
|
||
"execution_count": 19,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"log_clf = LogisticRegression(random_state=42)\n",
|
||
"rnd_clf = RandomForestClassifier(random_state=42)\n",
|
||
"svm_clf = SVC(probability=True, random_state=42)\n",
|
||
"\n",
|
||
"voting_clf = VotingClassifier(\n",
|
||
" estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],\n",
|
||
" voting='soft')\n",
|
||
"voting_clf.fit(X_train, y_train)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 20,
|
||
"id": "67a3b080",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"LogisticRegression 0.864\n",
|
||
"RandomForestClassifier 0.896\n",
|
||
"SVC 0.896\n",
|
||
"VotingClassifier 0.92\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.metrics import accuracy_score\n",
|
||
"\n",
|
||
"for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n",
|
||
" clf.fit(X_train, y_train)\n",
|
||
" y_pred = clf.predict(X_test)\n",
|
||
" print(clf.__class__.__name__, accuracy_score(y_test, y_pred))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f0d51672",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Bagging\n",
|
||
"\n",
|
||
"The **plain** decision trees suffer from high\n",
|
||
"variance. This means that if we split the training data into two parts\n",
|
||
"at random, and fit a decision tree to both halves, the results that we\n",
|
||
"get could be quite different. In contrast, a procedure with low\n",
|
||
"variance will yield similar results if applied repeatedly to distinct\n",
|
||
"data sets; linear regression tends to have low variance, if the ratio\n",
|
||
"of $n$ to $p$ is moderately large. \n",
|
||
"\n",
|
||
"**Bootstrap aggregation**, or just **bagging**, is a\n",
|
||
"general-purpose procedure for reducing the variance of a statistical\n",
|
||
"learning method."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ab182ea8",
|
||
"metadata": {},
|
||
"source": [
|
||
"## More bagging\n",
|
||
"\n",
|
||
"Bagging typically results in improved accuracy\n",
|
||
"over prediction using a single tree. Unfortunately, however, it can be\n",
|
||
"difficult to interpret the resulting model. Recall that one of the\n",
|
||
"advantages of decision trees is the attractive and easily interpreted\n",
|
||
"diagram that results.\n",
|
||
"\n",
|
||
"However, when we bag a large number of trees, it is no longer\n",
|
||
"possible to represent the resulting statistical learning procedure\n",
|
||
"using a single tree, and it is no longer clear which variables are\n",
|
||
"most important to the procedure. Thus, bagging improves prediction\n",
|
||
"accuracy at the expense of interpretability. Although the collection\n",
|
||
"of bagged trees is much more difficult to interpret than a single\n",
|
||
"tree, one can obtain an overall summary of the importance of each\n",
|
||
"predictor using the MSE (for bagging regression trees) or the Gini\n",
|
||
"index (for bagging classification trees). In the case of bagging\n",
|
||
"regression trees, we can record the total amount that the MSE is\n",
|
||
"decreased due to splits over a given predictor, averaged over all $B$ possible\n",
|
||
"trees. A large value indicates an important predictor. Similarly, in\n",
|
||
"the context of bagging classification trees, we can add up the total\n",
|
||
"amount that the Gini index is decreased by splits over a given\n",
|
||
"predictor, averaged over all $B$ trees."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "998512be",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Making your own Bootstrap: Changing the Level of the Decision Tree\n",
|
||
"\n",
|
||
"Let us bring up our good old boostrap example from the linear regression lectures. We change the linerar regression algorithm with\n",
|
||
"a decision tree wth different depths and perform a bootstrap aggregate (in this case we perform as many bootstraps as data points $n$)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 21,
|
||
"id": "6ac20f8b",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Polynomial degree: 1\n",
|
||
"Error: 0.06380941468319971\n",
|
||
"Bias^2: 0.05160313473529168\n",
|
||
"Var: 0.01220627994790804\n",
|
||
"0.06380941468319971 >= 0.05160313473529168 + 0.01220627994790804 = 0.06380941468319971\n",
|
||
"Polynomial degree: 2\n",
|
||
"Error: 0.043464037468677004\n",
|
||
"Bias^2: 0.02659851591375224\n",
|
||
"Var: 0.01686552155492476\n",
|
||
"0.043464037468677004 >= 0.02659851591375224 + 0.01686552155492476 = 0.043464037468677\n",
|
||
"Polynomial degree: 3\n",
|
||
"Error: 0.020716391693769383\n",
|
||
"Bias^2: 0.01159033914386312\n",
|
||
"Var: 0.00912605254990626\n",
|
||
"0.020716391693769383 >= 0.01159033914386312 + 0.00912605254990626 = 0.02071639169376938\n",
|
||
"Polynomial degree: 4\n",
|
||
"Error: 0.02063627410934057\n",
|
||
"Bias^2: 0.0117496656370668\n",
|
||
"Var: 0.008886608472273775\n",
|
||
"0.02063627410934057 >= 0.0117496656370668 + 0.008886608472273775 = 0.020636274109340574\n",
|
||
"Polynomial degree: 5\n",
|
||
"Error: 0.02087627881701288\n",
|
||
"Bias^2: 0.01349183949256158\n",
|
||
"Var: 0.007384439324451296\n",
|
||
"0.02087627881701288 >= 0.01349183949256158 + 0.007384439324451296 = 0.020876278817012876\n",
|
||
"Polynomial degree: 6\n",
|
||
"Error: 0.02069601123831537\n",
|
||
"Bias^2: 0.013918526350129823\n",
|
||
"Var: 0.0067774848881855445\n",
|
||
"0.02069601123831537 >= 0.013918526350129823 + 0.0067774848881855445 = 0.020696011238315368\n",
|
||
"Polynomial degree: 7\n",
|
||
"Error: 0.022964339924731444\n",
|
||
"Bias^2: 0.01550381208433455\n",
|
||
"Var: 0.007460527840396904\n",
|
||
"0.022964339924731444 >= 0.01550381208433455 + 0.007460527840396904 = 0.022964339924731455\n",
|
||
"Simple tree: 0.5148389267750961\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.pipeline import make_pipeline\n",
|
||
"from sklearn.utils import resample\n",
|
||
"from sklearn.tree import DecisionTreeRegressor\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"n_boostraps = 100\n",
|
||
"maxdepth = 8\n",
|
||
"\n",
|
||
"# Make data set.\n",
|
||
"x = np.linspace(-3, 3, n).reshape(-1, 1)\n",
|
||
"y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)\n",
|
||
"error = np.zeros(maxdepth)\n",
|
||
"bias = np.zeros(maxdepth)\n",
|
||
"variance = np.zeros(maxdepth)\n",
|
||
"polydegree = np.zeros(maxdepth)\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n",
|
||
"\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",
|
||
"\n",
|
||
"# we produce a simple tree first as benchmark\n",
|
||
"simpletree = DecisionTreeRegressor(max_depth=3) \n",
|
||
"simpletree.fit(X_train_scaled, y_train)\n",
|
||
"simpleprediction = simpletree.predict(X_test_scaled)\n",
|
||
"for degree in range(1,maxdepth):\n",
|
||
" model = DecisionTreeRegressor(max_depth=degree) \n",
|
||
" y_pred = np.empty((y_test.shape[0], n_boostraps))\n",
|
||
" for i in range(n_boostraps):\n",
|
||
" x_, y_ = resample(X_train_scaled, y_train)\n",
|
||
" model.fit(x_, y_)\n",
|
||
" y_pred[:, i] = model.predict(X_test_scaled)#.ravel()\n",
|
||
"\n",
|
||
" polydegree[degree] = degree\n",
|
||
" error[degree] = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )\n",
|
||
" bias[degree] = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )\n",
|
||
" variance[degree] = np.mean( np.var(y_pred, axis=1, keepdims=True) )\n",
|
||
" print('Polynomial degree:', degree)\n",
|
||
" print('Error:', error[degree])\n",
|
||
" print('Bias^2:', bias[degree])\n",
|
||
" print('Var:', variance[degree])\n",
|
||
" print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))\n",
|
||
" \n",
|
||
"mse_simpletree= np.mean( np.mean((y_test - simpleprediction)**2))\n",
|
||
"print(\"Simple tree:\",mse_simpletree)\n",
|
||
"plt.xlim(1,maxdepth)\n",
|
||
"plt.plot(polydegree, error, label='MSE')\n",
|
||
"plt.plot(polydegree, bias, label='bias')\n",
|
||
"plt.plot(polydegree, variance, label='Variance')\n",
|
||
"plt.legend()\n",
|
||
"save_fig(\"baggingboot\")\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c9a44ff4",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Random forests\n",
|
||
"\n",
|
||
"Random forests provide an improvement over bagged trees by way of a\n",
|
||
"small tweak that decorrelates the trees. \n",
|
||
"\n",
|
||
"As in bagging, we build a\n",
|
||
"number of decision trees on bootstrapped training samples. But when\n",
|
||
"building these decision trees, each time a split in a tree is\n",
|
||
"considered, a random sample of $m$ predictors is chosen as split\n",
|
||
"candidates from the full set of $p$ predictors. The split is allowed to\n",
|
||
"use only one of those $m$ predictors. \n",
|
||
"\n",
|
||
"A fresh sample of $m$ predictors is\n",
|
||
"taken at each split, and typically we choose"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "74f9056f",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"m\\approx \\sqrt{p}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9a0166e1",
|
||
"metadata": {},
|
||
"source": [
|
||
"In building a random forest, at\n",
|
||
"each split in the tree, the algorithm is not even allowed to consider\n",
|
||
"a majority of the available predictors. \n",
|
||
"\n",
|
||
"The reason for this is rather clever. Suppose that there is one very\n",
|
||
"strong predictor in the data set, along with a number of other\n",
|
||
"moderately strong predictors. Then in the collection of bagged\n",
|
||
"variable importance random forest trees, most or all of the trees will\n",
|
||
"use this strong predictor in the top split. Consequently, all of the\n",
|
||
"bagged trees will look quite similar to each other. Hence the\n",
|
||
"predictions from the bagged trees will be highly correlated.\n",
|
||
"Unfortunately, averaging many highly correlated quantities does not\n",
|
||
"lead to as large of a reduction in variance as averaging many\n",
|
||
"uncorrelated quantities. In particular, this means that bagging will\n",
|
||
"not lead to a substantial reduction in variance over a single tree in\n",
|
||
"this setting."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7e5dd3c9",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Random Forest Algorithm\n",
|
||
"The algorithm described here can be applied to both classification and regression problems.\n",
|
||
"\n",
|
||
"We will grow of forest of say $B$ trees.\n",
|
||
"1. For $b=1:B$\n",
|
||
"\n",
|
||
" * Draw a bootstrap sample from the training data organized in our $\\boldsymbol{X}$ matrix.\n",
|
||
"\n",
|
||
" * We grow then a random forest tree $T_b$ based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached\n",
|
||
"\n",
|
||
"1. we select $m \\le p$ variables at random from the $p$ predictors/features\n",
|
||
"\n",
|
||
"2. pick the best split point among the $m$ features using for example the CART algorithm and create a new node\n",
|
||
"\n",
|
||
"3. split the node into daughter nodes\n",
|
||
"\n",
|
||
"4. Output then the ensemble of trees $\\{T_b\\}_1^{B}$ and make predictions for either a regression type of problem or a classification type of problem."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b2476d94",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Random Forests Compared with other Methods on the Cancer Data"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 22,
|
||
"id": "0a56d5de",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"(426, 30)\n",
|
||
"(143, 30)\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: 0.87\n",
|
||
"[0.93333333 0.73333333 0.93333333 1. 1. 0.92857143\n",
|
||
" 1. 0.92857143 0.92857143 0.92857143]\n",
|
||
"Test set accuracy with Random Forests and scaled data: 0.98\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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LHD16tPjgwQONfqXN6hZFzRnR2sQye/ZsEYB47949dduePXvE5s2bi3K5XKxdu7Y4efJk8bvvvtOYGS6K2s3GB1Dm6++zo+/duyeGh4eLXl5eoq2trejs7CwGBASIERERYk5OjrrfjRs3xDfffFN0cHAQq1SpIr755pvir7/+qtVs/GJXrlwRx4wZIzZs2FCUyWSivb292LhxY3HChAklZsSvW7dObNasmWhnZyc6OTmJffr0UV8d8PefQ+XKlUvsp/hn+/zPp7Tf2x9//CF269ZNdHR0FGvUqCF+/PHH4r59+zR+5r///rs4ePBgsUGDBqK9vb3o5OQktm7dWoyNjS2xj+eviLh+/boYEhIiuri4iLa2tmKjRo3Ezz77TCwqKlL3KZ61/tlnn5WID4A4e/bsEu1/V9Zn73mlzajX9jOXnZ0tvvXWW2LVqlVFQRDUP98Xxf78bPxz586J9vb2JX5GeXl5YkBAgFivXr0Sf29ExiCIoihW4HcLIiIiqmA8Z09ERGThmOyJiIgsHJM9ERGRhWOyJyIisnBM9kRERBaOyZ6IiMjCmfVNdVQqFW7duoUqVaoY5XauRERkXKIo4vHjx3B3d4eVlfHqz7y8PBQUFOi9HTs7uxLPpjAHZp3sb926BQ8PD1OHQUREesrIyECdOnWMsu28vDzYV3EBlE/03lbNmjWRlpZmdgnfrJN9lSpVAAB2jYdCsLYzcTRExpF+ZImpQyAymscKBRp6eaj/PTeGgoICQPkEssZDAX1yRVEBMi/FoaCggMm+IhUP3QvWdkz2ZLEcHR1NHQKR0VXIqVgbuV65QhTMd5qbWSd7IiIirQkA9PlSYcZTw5jsiYhIGgSrZy991jdT5hs5ERERaYWVPRERSYMg6DmMb77j+Ez2REQkDRzGJyIiIkvFyp6IiKSBw/hERESWTs9hfDMeDDffyImIiEgrrOyJiEgaOIxPRERk4Tgbn4iIiCwVK3siIpIGDuMTERFZOAkP4zPZExGRNEi4sjffrylERESkFVb2REQkDRzGJyIisnCCoGey5zA+ERER/UOxsiciImmwEp699FnfTDHZExGRNEj4nL35Rk5ERERaYWVPRETSIOHr7JnsiYhIGjiMT0RERJaKlT0REUkDh/GJiIgsnISH8ZnsiYhIGiRc2Zvv1xQiIiLSCit7IiKSBg7jExERWTgO4xMREZGlYmVPREQSoecwvhnXx0z2REQkDRzGJyIiIkvFyp6IiKRBEPScjW++lT2TPRERSYOEL70z38iJiIhIK6zsiYhIGiQ8QY/JnoiIpEHCw/hM9kREJA0SruzN92sKERERaYWVPRERSQOH8YmIiCwch/GJiIjIUrGyJyIiSRAEAYJEK3smeyIikgQpJ3sO4xMREVk4VvZERCQNwv9e+qxvppjsiYhIEjiMT0RERBaLlT0REUmClCt7JnsiIpIEJnsiIiILJ+Vkz3P2REREFo6VPRERSQMvvSMiIrJsHMYnIiIii8XKnoiIJOHZE271qewNF0tFY7InIiJJEKDnML4ZZ3sO4xMREVk4JnsiIpKE4gl6+rx0lZOTg3HjxsHd3R1yuRwtWrTA1q1btVo3MTERQUFBcHV1hYODA5o1a4bly5ejqKhI5zg4jE9ERNJggkvv+vfvjxMnTiAqKgre3t7YsmULBg8eDJVKhZCQkDLX+/HHH9G9e3e89tprWLt2LSpXrozdu3dj7NixuHLlCr744gud4mCyJyIiMoL9+/fj4MGD6gQPAJ06dcL169cxefJkDBw4ENbW1qWuGxsbC1tbW+zduxeVK1cGAHTt2hWXL19GbGyszsmew/hERCQN+g7h6ziMn5CQAAcHBwwYMECjPTQ0FLdu3cLx48fLXNfW1hZ2dnawt7fXaK9atSrkcrlOcQBM9kREJBGGOmevUCg0Xvn5+aXu78KFC/D19YWNjeYgerNmzdTLyzJq1CgUFBQgPDwct27dwsOHD7Fp0yYkJCRgypQpOh87kz0REUmCoZK9h4cHnJyc1K/IyMhS95eVlQVnZ+cS7cVtWVlZZcbapk0bHD58GAkJCahduzaqVauG0NBQLFy4EBMnTtT52HnOnoiISAcZGRlwdHRUv5fJZGX2fdEM/hctO3XqFPr164c2bdpg9erVqFy5Mg4fPowZM2YgLy8PM2fO1ClmJnsiIpIGA83Gd3R01Ej2ZXFxcSm1es/OzgaAUqv+Yh9++CHc3NyQkJCgnsTXqVMnWFlZYc6cOXjnnXdQv359rUPnMD4REUlCRV9n7+fnh9TUVCiVSo328+fPAwCaNm1a5rpnzpxBQEBAidn6rVq1gkqlQmpqqk6xMNkTEREZQb9+/ZCTk4MdO3ZotMfFxcHd3R1t2rQpc113d3ecPHmyxA10kpKSAAB16tTRKRYO4xMRkSTo+4hbXdcNDg5GUFAQRo8eDYVCgYYNGyI+Ph4HDhzA5s2b1VV7WFgY4uLicOXKFXh6egIAxo8fj/DwcPTu3RsffPABKlWqhEOHDuHzzz9H165d0bx5c51iYbInIiJJqOhkDwA7d+5EREQEZs2ahezsbPj4+CA+Ph6DBg1S9ykqKkJRURFEUVS3ffzxx6hduzaWLl2KESNG4OnTp6hXrx5mz56N8ePH6x67+PetmxmFQgEnJyfI/EZCsLYzdThERvHgxApTh0BkNAqFAm4uTnj06JFWk97Kuw8nJye4Dv0aVnaVyr0dVcET3I0bYtRYjYWVPRERSYIpKvt/CiZ7IiKSBhM8COefgrPxiYiILBwreyIikgQO4xMREVk4JnsiIiILJ+Vkz3P2REREFo6VPRERSYOEZ+Mz2RMRkSRwGJ+IiIgsFpO9xL0/oANS987Bg+Sl+OWbKXjVv8EL+3/w9mtI2TED2UnROJswEyG9Wpfo81FIR5xNmInspGj8+d18fDqxP2R2HEQi01i9MgY+r3ihqoMc7VsH4Oefj72w/7GjP6F96wBUdZDD17s+1q5epbF8w7q16NKxA2rVqIZaNaqhR/euOPHbb8Y8BDKQin7E7T+JyZN9TEwMvLy8IJfLERAQgGPHXvyHSIbzVreW+Gzym1i8/nu0HRyFX1OuYNeKMfCoWa3U/iMH/AvzPu6Nhav3o+VbC7Fg1X4s++Rt9Hjt/5/JPCg4EPPD+2DR6u/Qov8CjJr7Dd7qHoD5H79RUYdFpPaf7dsweeI4TP0kAsknUtD+Xx3Qt1cw0tPTS+1/LS0NfXv3QPt/dUDyiRRMmTodE8eHI2Hn/z+i9OhPR/D2wME4cDARR44lwcOjLnr36IabN29W1GFROQnQM9mb8Ul7kyb7bdu2Ydy4cYiIiEBKSgo6dOiA4OCy/xDJsMLf7YzYXUmITUjC5bQ7mLxkB25kPsDIAR1K7R/SszXW7/gF//3hNK7dzMJ/vj+FuF1JmDgsSN2nTTMvJJ25im0HTiL9djYOJf+O7QdOomXjuhV1WERqy5dFY1hoGELDRsDH1xdLopehjocH1q5eWWr/tWtWwaNuXSyJXgYfX1+Eho3A0GHDsSx6ibpP7KZv8MHoMWjeogUa+fggZvVaqFQqHDl8qKIOi0hnJk320dHRCAsLw4gRI+Dr64tly5bBw8MDK1eW/odIhmNrYw1/Xw8cSkrVaD+UnIq2zb1KXcfO1gZ5BYUabU/zCxHY1BM2Ns8+Sr+euQr/xh4IbPLsmcz1arug+6tNcODni0Y4CqKyFRQUIOX0KXQJ6qbR3qVrNyQn/VrqOseTk9Clq2b/rt264/SpkygsLCx1nSdPnqCwsBDVnJ0NEzgZjZSH8U12IrWgoACnTp3CJ598otHerVs3/Ppr6X+IZDjVqznAxsYad7Mfa7TfyXoMN5fSH934Y1IqhvVtjz2J55CSmoGWjetiSJ+2sLO1QfWqDsi8r8B/vj+F6tUccGjjeAgQYGtrjdXbj2LJxoMVcVhEavfv30dRURFcXd002t3c3HDnTmap69y5kwk3N83+rq5uUCqVuH//PmrVqlVinZnTP4F77dro3KWr4YIn4+CldxWv+A/x+T8sNzc3ZGaW/oeYn5+P/Px89XuFQmHUGKVAFDXfC4IA8fnG/4lcewBuLo74KW4SBAG4m/0Ym3cfx8TQIBQVqQAAHQJewZSw7hgbuQ0nzl9HA4/qWDL5LWTeVyBq7QFjHw5RCc9XY6IovrBCK61/ae0A8PmST7F9Wzy+//EI5HK5AaIlMg6TT5HW5Q8xMjISc+fOrYiwLN79BzlQKovg5lJFo93V2aFEtV8sL78Qo+Z+g48WxsPN2RG37z9C2JuvQpHzFPcf5gIAZo/pifh9vyE2IQkAcPGvW6hkL8NXMwZj8brvy/wiQWRo1atXh7W1dYkq/u7duyWq/WJubjVLFBv37t2FjY0NXFxcNNqXRi/BZ1GLsO/Aj/Br1sywwZNR8Dp7Eyj+Q3z+D+vu3bslqv1i06ZNw6NHj9SvjIyMigjVIhUqi5CSmoHObX002ju39UHy2bQXrqtUqnDz7kOoVCIGdA/Ad8cuqpO4vdwOKpVmQlepVBAEwIz/TsgM2dnZwb9lAA7/qHkK6fChg2jbrn2p67Rp2w6HD2n2P3TwB7QMCIStra26LfrzzxC1cD6+3XsAAYGBhg+ejILn7E3Azs4OAQEBOHjwIPr166duP3jwIPr06VPqOjKZDDKZrKJCtHjLNx/G+gVDcPpSOo6fS0NY/1fhUdMZ6/777PLHeR+/AXdXJ4yYuQkA0LCuKwKbeuLEhWuoVqUSwt/rjMYN3NXLAWD/0QsIf7cTzl6+gd/OX0MDjxqYNboX9v10vsSXACJjCx83AWHD3kPLgEC0adsO69etQUZ6Oka8PwoAMDNiGm7dvIn1sV8DAEa+PwqrYlZgyqQJGB42EseTkxC7cT3iNsert/n5kk8xb/ZMxG7aAs969dQFi4ODAxwcHCr+IElr+hYdZpzrTTuMP2HCBLz33nsIDAxEu3btsGbNGqSnp2PUqFGmDEsy/vvDaTg7Vcb094NRs7ojLv51G30/jkH67QcAgJrVHeFR8/9nGFtbCxj7Xmd4e7qhUFmEoyf/QKdhnyP9dra6T9S6AxBFEbPH9IK7qxPuP8jBvqMXMGfFngo/PqIBbw9EdlYWFi2ch8zbt9GkSVPs2rMfnp7PrhbJvH0bGRn/f6lvPS8v7NqzH1MmjsfqlV+hlrs7Pl+6HP36v6nus2ZVDAoKChAy8C2NfUXMnI0Zs+ZUyHER6UoQTXwSNSYmBp9++ilu376Npk2bYunSpXjttde0WlehUMDJyQkyv5EQrO2MHCmRaTw4scLUIRAZjUKhgJuLEx49egRHx9KvBDLEPpycnFD/4//CSla53NtR5efi6pdvGTVWYzH5BL0xY8ZgzJgxpg6DiIgsnb5zh8x4GN/kt8slIiIi4zJ5ZU9ERFQRpHzpHZM9ERFJgpRn43MYn4iIyMKxsiciIkmwshJgZVX+8lzUY11TY7InIiJJ4DA+ERERWSxW9kREJAmcjU9ERGThpDyMz2RPRESSIOXKnufsiYiILBwreyIikgQpV/ZM9kREJAlSPmfPYXwiIiILx8qeiIgkQYCew/hm/IxbJnsiIpIEDuMTERGRxWJlT0REksDZ+ERERBaOw/hERERksVjZExGRJHAYn4iIyMJJeRifyZ6IiCRBypU9z9kTERFZOFb2REQkDXoO45vxDfSY7ImISBo4jE9EREQWi5U9ERFJAmfjExERWTgO4xMREZHFYmVPRESSwGF8IiIiC8dhfCIiIrJYrOyJiEgSpFzZM9kTEZEk8Jw9ERGRhZNyZc9z9kRERBaOlT0REUkCh/GJiIgsHIfxiYiIyGKxsiciIkkQoOcwvsEiqXhM9kREJAlWggArPbK9PuuaGofxiYiIjCQnJwfjxo2Du7s75HI5WrRoga1bt2q9/rfffovXX38djo6OqFy5Mpo0aYI1a9boHAcreyIikgRTzMbv378/Tpw4gaioKHh7e2PLli0YPHgwVCoVQkJCXrhuVFQUIiIiMGrUKEybNg22trb4/fffUVBQoHMcTPZERCQJFT0bf//+/Th48KA6wQNAp06dcP36dUyePBkDBw6EtbV1qeueOnUKERERiIyMxJQpU9TtXbp0KVfsHMYnIiJJsBL0f+kiISEBDg4OGDBggEZ7aGgobt26hePHj5e57ooVKyCTyfDxxx+X51BLYLInIiLSgUKh0Hjl5+eX2u/ChQvw9fWFjY3mIHqzZs3Uy8ty9OhR+Pr6YseOHWjUqBGsra1Rp04dfPLJJ+UaxmeyJyIiaRD+fyi/PK/ia+88PDzg5OSkfkVGRpa6u6ysLDg7O5doL27LysoqM9SbN2/izz//RHh4OMLDw/Hjjz9i2LBhWLJkCUJDQ3U+dJ6zJyIiSTDUBL2MjAw4Ojqq22Uy2QvWKXuHL1qmUqnw+PFjxMfHY9CgQQCene/Pzc3FsmXLMHfuXDRs2FDr2FnZExER6cDR0VHjVVayd3FxKbV6z87OBoBSq/6/rwsA3bt312gPDg4GAJw+fVqnmJnsiYhIEgQD/KcLPz8/pKamQqlUarSfP38eANC0adMy1y0+r/88URQBAFZWuqVvJnsiIpKEip6N369fP+Tk5GDHjh0a7XFxcXB3d0ebNm3KXPfNN98EAHz33Xca7fv374eVlRVatWqlUyw8Z09ERGQEwcHBCAoKwujRo6FQKNCwYUPEx8fjwIED2Lx5s/oa+7CwMMTFxeHKlSvw9PQE8OzyvNWrV2PMmDG4f/8+GjdujB9//BFfffUVxowZo+6nLSZ7IiKSBFM84nbnzp2IiIjArFmzkJ2dDR8fH41JdwBQVFSEoqIi9RA9ANja2uLgwYOYPn06Fi1ahOzsbHh5eSEqKgoTJkzQPXbx71svw/Lly7XeYHh4uM5BlJdCoYCTkxNkfiMhWNtV2H6JKtKDEytMHQKR0SgUCri5OOHRo0caM9wNvQ8nJyf0WJ4IW3uHcm+n8GkO9od3MmqsxqJVZb906VKtNiYIQoUmeyIiIno5rZJ9WlqaseMgIiIyKj7ithwKCgpw+fLlEpcUEBER/RMV31RHn5e50jnZP3nyBGFhYahUqRKaNGmC9PR0AM/O1UdFRRk8QCIiIkPQ51a5+k7uMzWdk/20adNw9uxZHDlyBHK5XN3etWtXbNu2zaDBERERkf50vvRu165d2LZtG9q2bavxLadx48a4cuWKQYMjIiIyFEPdG98c6Zzs7927B1dX1xLtubm5Zj3EQURElo0T9HTQqlUr7Nu3T/2+OMGvXbsW7dq1M1xkREREZBA6V/aRkZH497//jUuXLkGpVOKLL77AxYsXkZSUhJ9++skYMRIREelNAHR8lE3J9c2VzpV9+/bt8csvv+DJkydo0KABfvjhB7i5uSEpKQkBAQHGiJGIiEhvUp6NX6574/v5+SEuLs7QsRAREZERlCvZFxUVISEhAampqRAEAb6+vujTpw9sbPhcHSIi+mcqz2Nqn1/fXOmcnS9cuIA+ffogMzMTjRo1AgD88ccfqFGjBnbv3g0/Pz+DB0lERKQvUzz17p9C53P2I0aMQJMmTXDjxg2cPn0ap0+fRkZGBpo1a4b333/fGDESERGRHnSu7M+ePYuTJ0+iWrVq6rZq1aph4cKFaNWqlUGDIyIiMiQzLs71onNl36hRI9y5c6dE+927d9GwYUODBEVERGRonI3/EgqFQv3/ixYtQnh4OObMmYO2bdsCAJKTkzFv3jwsXrzYOFESERHpiRP0XqJq1aoa32hEUcTbb7+tbhNFEQDQu3dvFBUVGSFMIiIiKi+tkn1iYqKx4yAiIjIqKc/G1yrZv/7668aOg4iIyKikfLvcct8F58mTJ0hPT0dBQYFGe7NmzfQOioiIiAynXI+4DQ0NxXfffVfqcp6zJyKifyI+4lYH48aNw4MHD5CcnAx7e3scOHAAcXFxeOWVV7B7925jxEhERKQ3QdD/Za50ruwPHz6Mb7/9Fq1atYKVlRU8PT0RFBQER0dHREZGomfPnsaIk4iIiMpJ58o+NzcXrq6uAABnZ2fcu3cPwLMn4Z0+fdqw0RERERmIlG+qU6476F2+fBkA0KJFC6xevRo3b97EqlWrUKtWLYMHSEREZAgcxtfBuHHjcPv2bQDA7Nmz0b17d3zzzTews7NDbGysoeMjIiIiPemc7N955x31//v7++PatWv4/fffUbduXVSvXt2gwRERERmKlGfjl/s6+2KVKlVCy5YtDRELERGR0eg7FG/GuV67ZD9hwgStNxgdHV3uYIiIiIyFt8t9iZSUFK02Zs4/CCIiIktlEQ/CST+yBI6OjqYOg8goqrX6yNQhEBmNWFTw8k4GYoVyXIL23PrmSu9z9kREROZAysP45vxFhYiIiLTAyp6IiCRBEAArzsYnIiKyXFZ6Jnt91jU1DuMTERFZuHIl+02bNuHVV1+Fu7s7rl+/DgBYtmwZvv32W4MGR0REZCh8EI4OVq5ciQkTJqBHjx54+PAhioqKAABVq1bFsmXLDB0fERGRQRQP4+vzMlc6J/svv/wSa9euRUREBKytrdXtgYGBOH/+vEGDIyIiIv3pPEEvLS0N/v7+JdplMhlyc3MNEhQREZGhSfne+DpX9l5eXjhz5kyJ9u+++w6NGzc2RExEREQGV/zUO31e5krnyn7y5Mn48MMPkZeXB1EU8dtvvyE+Ph6RkZFYt26dMWIkIiLSG2+Xq4PQ0FAolUpMmTIFT548QUhICGrXro0vvvgCgwYNMkaMREREpIdy3VRn5MiRGDlyJO7fvw+VSgVXV1dDx0VERGRQUj5nr9cd9KpXr26oOIiIiIzKCvqdd7eC+WZ7nZO9l5fXC28scPXqVb0CIiIiIsPSOdmPGzdO431hYSFSUlJw4MABTJ482VBxERERGRSH8XUwduzYUtu/+uornDx5Uu+AiIiIjIEPwjGA4OBg7Nixw1CbIyIiIgMx2CNu//vf/8LZ2dlQmyMiIjKoZ8+zL395LqlhfH9/f40JeqIoIjMzE/fu3UNMTIxBgyMiIjIUnrPXQd++fTXeW1lZoUaNGujYsSN8fHwMFRcREREZiE7JXqlUol69eujevTtq1qxprJiIiIgMjhP0tGRjY4PRo0cjPz/fWPEQEREZhWCA/8yVzrPx27Rpg5SUFGPEQkREZDTFlb0+L3Ol8zn7MWPGYOLEibhx4wYCAgJQuXJljeXNmjUzWHBERESkP62T/fDhw7Fs2TIMHDgQABAeHq5eJggCRFGEIAgoKioyfJRERER6kvI5e62TfVxcHKKiopCWlmbMeIiIiIxCEIQXPttFm/XNldbJXhRFAICnp6fRgiEiIiLD0+mcvTl/qyEiImnjML6WvL29X5rws7Oz9QqIiIjIGHgHPS3NnTsXTk5OxoqFiIiIjECnZD9o0CC4uroaKxYiIiKjsRIEvR6Eo8+6pqb1TXV4vp6IiMyZKW6qk5OTg3HjxsHd3R1yuRwtWrTA1q1bdd7OjBkzIAgCmjZtqnsQKMdsfCIiItJO//79ceLECURFRcHb2xtbtmzB4MGDoVKpEBISotU2zpw5gyVLlsDNza3ccWid7FUqVbl3QkREZHJ6TtDT9db4+/fvx8GDB9UJHgA6deqE69evY/LkyRg4cCCsra1fuA2lUonQ0FB88MEHOHv2LO7fv1+u0HW+Nz4REZE5soKg90sXCQkJcHBwwIABAzTaQ0NDcevWLRw/fvyl24iKikJ2djYWLlyo076fp/O98YmIiMyRoS69UygUGu0ymQwymaxE/wsXLsDX1xc2NpqptvgZMhcuXED79u3L3N+lS5ewYMEC7Ny5Ew4ODuUPHKzsiYiIdOLh4QEnJyf1KzIystR+WVlZcHZ2LtFe3JaVlVXmPlQqFYYPH47+/fujR48eesfMyp6IiCTBUHfQy8jIgKOjo7q9tKq+2IuuZHvRsujoaPz555/YvXu37oGWgsmeiIgkwVDX2Ts6Omok+7K4uLiUWr0X32m2tKofANLT0zFr1ixERUXBzs4ODx8+BPBssp5KpcLDhw8hk8lgb2+vfexa9yQiIiKt+fn5ITU1FUqlUqP9/PnzAFDmNfNXr17F06dPMXbsWFSrVk39+uWXX5Camopq1aph2rRpOsXCyp6IiCShou+N369fP6xduxY7duzAwIED1e1xcXFwd3dHmzZtSl2vRYsWSExMLNE+btw4PHr0CBs3bkSdOnV0ioXJnoiIJMEKeg7j63jpXXBwMIKCgjB69GgoFAo0bNgQ8fHxOHDgADZv3qy+xj4sLAxxcXG4cuUKPD09UbVqVXTs2LHE9qpWrQqlUlnqspdhsiciIjKSnTt3IiIiArNmzUJ2djZ8fHwQHx+PQYMGqfsUFRWhqKjIqHeqFUQzvg+uQqGAk5MT7mQ90mqyBJE5qtbqI1OHQGQ0YlEB8s+vxaNHxvt3vDhXrDh8AfYOVcq9nac5j/FR56ZGjdVYWNkTEZEkWEG/WenmPKPdnGMnIiIiLbCyJyIiSRAEQa/HtZvzo96Z7ImISBIE6PzguhLrmysmeyIikgRD3UHPHPGcPRERkYVjZU9ERJJhvrW5fpjsiYhIEir6drn/JBzGJyIisnCs7ImISBJ46R0REZGF4x30iIiIyGKxsiciIkngMD4REZGFk/Id9DiMT0REZOFY2RMRkSRwGJ+IiMjCSXk2PpM9ERFJgpQre3P+okJERERaYGVPRESSIOXZ+Ez2REQkCXwQDhEREVksVvZERCQJVhBgpcdgvD7rmhqTPRERSQKH8YmIiMhisbInIiJJEP73nz7rmysmeyIikgQO4xMREZHFYmVPRESSIOg5G5/D+ERERP9wUh7GZ7InIiJJkHKy5zl7IiIiC8fKnoiIJIGX3hEREVk4K+HZS5/1zRWH8YmIiCwcK3siIpIEDuMTERFZOM7GJyIiIovFyp6IiCRBgH5D8WZc2DPZExGRNHA2PhEREVksJnuJW70yBj6veKGqgxztWwfg55+PvbD/saM/oX3rAFR1kMPXuz7Wrl6lsXzDurXo0rEDatWohlo1qqFH96448dtvxjwEohd6f0AHpO6dgwfJS/HLN1Pwqn+DF/b/4O3XkLJjBrKTonE2YSZCerUu0eejkI44mzAT2UnR+PO7+fh0Yn/I7DhQ+k8nGOA/c2XSZH/06FH07t0b7u7uEAQBu3btMmU4kvOf7dsweeI4TP0kAsknUtD+Xx3Qt1cw0tPTS+1/LS0NfXv3QPt/dUDyiRRMmTodE8eHI2HnDnWfoz8dwdsDB+PAwUQcOZYED4+66N2jG27evFlRh0Wk9la3lvhs8ptYvP57tB0chV9TrmDXijHwqFmt1P4jB/wL8z7ujYWr96PlWwuxYNV+LPvkbfR4ram6z6DgQMwP74NFq79Di/4LMGruN3irewDmf/xGRR0WlVPxbHx9XubKpMk+NzcXzZs3x4oVK0wZhmQtXxaNYaFhCA0bAR9fXyyJXoY6Hh5Yu3plqf3XrlkFj7p1sSR6GXx8fREaNgJDhw3Hsugl6j6xm77BB6PHoHmLFmjk44OY1WuhUqlw5PChijosIrXwdzsjdlcSYhOScDntDiYv2YEbmQ8wckCHUvuH9GyN9Tt+wX9/OI1rN7Pwn+9PIW5XEiYOC1L3adPMC0lnrmLbgZNIv52NQ8m/Y/uBk2jZuG5FHRaVk2CAl7kyabIPDg7GggUL0L9/f1OGIUkFBQVIOX0KXYK6abR36doNyUm/lrrO8eQkdOmq2b9rt+44feokCgsLS13nyZMnKCwsRDVnZ8METqQlWxtr+Pt64FBSqkb7oeRUtG3uVeo6drY2yCvQ/Cw/zS9EYFNP2Ng8++fy1zNX4d/YA4FNPAEA9Wq7oPurTXDg54tGOAoiwzCrk0z5+fnIz89Xv1coFCaMxrzdv38fRUVFcHV102h3c3PDnTuZpa5z504m3Nw0+7u6ukGpVOL+/fuoVatWiXVmTv8E7rVro3OXroYLnkgL1as5wMbGGnezH2u038l6DDcXx1LX+TEpFcP6tseexHNISc1Ay8Z1MaRPW9jZ2qB6VQdk3lfgP9+fQvVqDji0cTwECLC1tcbq7UexZOPBijgs0oMVBFjpMRZvZca1vVkl+8jISMydO9fUYVgU4bkPviiKJdpe1r+0dgD4fMmn2L4tHt//eARyudwA0RLp7n8fUTVBENSf2+dFrj0ANxdH/BQ3CYIA3M1+jM27j2NiaBCKilQAgA4Br2BKWHeMjdyGE+evo4FHdSyZ/BYy7ysQtfaAsQ+H9KDvULz5pnozm40/bdo0PHr0SP3KyMgwdUhmq3r16rC2ti5Rxd+9e7dEtV/Mza0mMjM1+9+7dxc2NjZwcXHRaF8avQSfRS3Cnv0/wK9ZM8MGT6SF+w9yoFQWwc2lika7q7NDiWq/WF5+IUbN/QbO7cfDp+dsvBI8E9dvZ0GR8xT3H+YCAGaP6Yn4fb8hNiEJF/+6hd2J5zBrxR5MDu32wi/KRKZkVsleJpPB0dFR40XlY2dnB/+WATj8o+bQ4+FDB9G2XftS12nTth0OH9Lsf+jgD2gZEAhbW1t1W/TnnyFq4Xx8u/cAAgIDDR88kRYKlUVISc1A57Y+Gu2d2/og+WzaC9dVKlW4efchVCoRA7oH4LtjF9WjAfZyO6hUmiMDKpXK7GdrS4KEZ+iZ1TA+GVb4uAkIG/YeWgYEok3bdli/bg0y0tMx4v1RAICZEdNw6+ZNrI/9GgAw8v1RWBWzAlMmTcDwsJE4npyE2I3rEbc5Xr3Nz5d8inmzZyJ20xZ41qunHglwcHCAg4NDxR8kSdryzYexfsEQnL6UjuPn0hDW/1V41HTGuv8+u5/EvI/fgLurE0bM3AQAaFjXFYFNPXHiwjVUq1IJ4e91RuMG7urlALD/6AWEv9sJZy/fwG/nr6GBRw3MGt0L+346X+JLAP2z8Kl3JpKTk4O//vpL/T4tLQ1nzpyBs7Mz6tblZSzGNuDtgcjOysKihfOQefs2mjRpil179sPT89ks48zbt5GR8f/X3Nfz8sKuPfsxZeJ4rF75FWq5u+PzpcvRr/+b6j5rVsWgoKAAIQPf0thXxMzZmDFrToUcF1Gx//5wGs5OlTH9/WDUrO6Ii3/dRt+PY5B++wEAoGZ1R3jU/P8rRaytBYx9rzO8Pd1QqCzC0ZN/oNOwz5F+O1vdJ2rdAYiiiNljesHd1Qn3H+Rg39ELmLNiT4UfH5G2BLGsmSoV4MiRI+jUqVOJ9qFDhyI2Nval6ysUCjg5OeFO1iMO6ZPFqtbqI1OHQGQ0YlEB8s+vxaNHxvt3vDhXHDqTDocq5d9HzmMFurSoa9RYjcWklX3Hjh3LnBVLRERkSJyNT0RERBaLE/SIiEgaJFzaM9kTEZEkcDY+ERGRhdP3XgjmfB8FnrMnIiKycKzsiYhIEiR8yp7JnoiIJELC2Z7D+ERERBaOlT0REUkCZ+MTERFZOM7GJyIiIovFZE9ERJJgisfZ5+TkYNy4cXB3d4dcLkeLFi2wdevWl663c+dODB48GA0bNoS9vT3q1auHd955B3/++Wc5ouAwPhERSYUJZuP3798fJ06cQFRUFLy9vbFlyxYMHjwYKpUKISEhZa63ePFi1KxZExEREahfvz4yMjKwaNEitGzZEsnJyWjSpIlOcTDZExERGcH+/ftx8OBBdYIHgE6dOuH69euYPHkyBg4cCGtr61LX3bNnD1xdXTXaOnfujHr16mHp0qVYt26dTrFwGJ+IiCRBMMB/ukhISICDgwMGDBig0R4aGopbt27h+PHjZa77fKIHAHd3d9SpUwcZGRk6xQEw2RMRkUQUz8bX5wUACoVC45Wfn1/q/i5cuABfX1/Y2GgOojdr1ky9XBdXr17F9evXdR7CB5jsiYhIIgw1Qc/DwwNOTk7qV2RkZKn7y8rKgrOzc4n24rasrCytY1cqlQgLC4ODgwPGjx+v9XrFeM6eiIhIBxkZGXB0dFS/l8lkZfYVXnBx/ouW/Z0oiggLC8OxY8ewY8cOeHh4aB/s/zDZExGRNBhoNr6jo6NGsi+Li4tLqdV7dnY2AJRa9T9PFEWMGDECmzdvRlxcHPr06aNbzP/DYXwiIpKEip6g5+fnh9TUVCiVSo328+fPAwCaNm36wvWLE/3GjRuxbt06vPvuu7od8N8w2RMRERlBv379kJOTgx07dmi0x8XFwd3dHW3atClzXVEUMXLkSGzcuBGrV69GaGioXrFwGJ+IiCShou+NHxwcjKCgIIwePRoKhQINGzZEfHw8Dhw4gM2bN6uvsQ8LC0NcXByuXLkCT09PAEB4eDjWr1+P4cOHw8/PD8nJyertymQy+Pv76xQLkz0REUmCKR5nv3PnTkRERGDWrFnIzs6Gj48P4uPjMWjQIHWfoqIiFBUVQRRFdduePXsAABs2bMCGDRs0tunp6Ylr167pFrv4962bGYVCAScnJ9zJeqTVZAkic1St1UemDoHIaMSiAuSfX4tHj4z373hxrvjt91twqFL+feQ8VqC1j7tRYzUWVvZERCQNpijt/yGY7ImISBLKM6P++fXNFWfjExERWThW9kREJAkVPRv/n4TJnoiIJEHCp+yZ7ImISCIknO15zp6IiMjCsbInIiJJkPJsfCZ7IiKSBj0n6JlxrucwPhERkaVjZU9ERJIg4fl5TPZERCQREs72HMYnIiKycKzsiYhIEjgbn4iIyMJJ+Xa5HMYnIiKycKzsiYhIEiQ8P4/JnoiIJELC2Z7JnoiIJEHKE/R4zp6IiMjCsbInIiJJEKDnbHyDRVLxmOyJiEgSJHzKnsP4RERElo6VPRERSYKUb6rDZE9ERBIh3YF8DuMTERFZOFb2REQkCRzGJyIisnDSHcTnMD4REZHFY2VPRESSwGF8IiIiCyfle+Mz2RMRkTRI+KQ9z9kTERFZOFb2REQkCRIu7JnsiYhIGqQ8QY/D+ERERBaOlT0REUkCZ+MTERFZOgmftOcwPhERkYVjZU9ERJIg4cKeyZ6IiKSBs/GJiIjIYrGyJyIiidBvNr45D+Qz2RMRkSRwGJ+IiIgsFpM9ERGRheMwPhERSYKUh/GZ7ImISBKkfLtcDuMTERFZOFb2REQkCRzGJyIisnBSvl0uh/GJiIgsHCt7IiKSBgmX9kz2REQkCZyNT0RERBaLlT0REUkCZ+MTERFZOAmfsmeyJyIiiZBwtuc5eyIiIgvHyp6IiCRByrPxmeyJiEgSOEHPTImiCAB4rFCYOBIi4xGLCkwdApHRFH++i/89NyaFnrlC3/VNyayT/ePHjwEADb08TBwJERHp4/Hjx3BycjLKtu3s7FCzZk28YoBcUbNmTdjZ2RkgqooliBXxdcpIVCoVbt26hSpVqkAw5/EVM6JQKODh4YGMjAw4OjqaOhwig+Lnu+KJoojHjx/D3d0dVlbGmzOel5eHggL9R8ns7Owgl8sNEFHFMuvK3srKCnXq1DF1GJLk6OjIfwzJYvHzXbGMVdH/nVwuN8skbSi89I6IiMjCMdkTERFZOCZ70olMJsPs2bMhk8lMHQqRwfHzTZbKrCfoERER0cuxsiciIrJwTPZEREQWjsmeiIjIwjHZExERWTgme9JaTEwMvLy8IJfLERAQgGPHjpk6JCKDOHr0KHr37g13d3cIgoBdu3aZOiQig2KyJ61s27YN48aNQ0REBFJSUtChQwcEBwcjPT3d1KER6S03NxfNmzfHihUrTB0KkVHw0jvSSps2bdCyZUusXLlS3ebr64u+ffsiMjLShJERGZYgCEhISEDfvn1NHQqRwbCyp5cqKCjAqVOn0K1bN432bt264ddffzVRVEREpC0me3qp+/fvo6ioCG5ubhrtbm5uyMzMNFFURESkLSZ70trzjxEWRZGPFiYiMgNM9vRS1atXh7W1dYkq/u7duyWqfSIi+udhsqeXsrOzQ0BAAA4ePKjRfvDgQbRv395EURERkbZsTB0AmYcJEybgvffeQ2BgINq1a4c1a9YgPT0do0aNMnVoRHrLycnBX3/9pX6flpaGM2fOwNnZGXXr1jVhZESGwUvvSGsxMTH49NNPcfv2bTRt2hRLly7Fa6+9ZuqwiPR25MgRdOrUqUT70KFDERsbW/EBERkYkz0REZGF4zl7IiIiC8dkT0REZOGY7ImIiCwckz0REZGFY7InIiKycEz2REREFo7JnoiIyMIx2RPpac6cOWjRooX6/bBhw0zyLPRr165BEAScOXOmzD716tXDsmXLtN5mbGwsqlatqndsgiBg165dem+HiMqHyZ4s0rBhwyAIAgRBgK2tLerXr49JkyYhNzfX6Pv+4osvtL7rmjYJmohIX7w3Plmsf//739i4cSMKCwtx7NgxjBgxArm5uVi5cmWJvoWFhbC1tTXIfp2cnAyyHSIiQ2FlTxZLJpOhZs2a8PDwQEhICN555x31UHLx0PuGDRtQv359yGQyiKKIR48e4f3334erqyscHR3RuXNnnD17VmO7UVFRcHNzQ5UqVRAWFoa8vDyN5c8P46tUKixevBgNGzaETCZD3bp1sXDhQgCAl5cXAMDf3x+CIKBjx47q9TZu3AhfX1/I5XL4+PggJiZGYz+//fYb/P39IZfLERgYiJSUFJ1/RtHR0fDz80PlypXh4eGBMWPGICcnp0S/Xbt2wdvbG3K5HEFBQcjIyNBYvmfPHgQEBEAul6N+/fqYO3culEqlzvEQkXEw2ZNk2Nvbo7CwUP3+r7/+wvbt27Fjxw71MHrPnj2RmZmJ/fv349SpU2jZsiW6dOmC7OxsAMD27dsxe/ZsLFy4ECdPnkStWrVKJOHnTZs2DYsXL8bMmTNx6dIlbNmyBW5ubgCeJWwA+PHHH3H79m3s3LkTALB27VpERERg4cKFSE1NxaJFizBz5kzExcUBAHJzc9GrVy80atQIp06dwpw5czBp0iSdfyZWVlZYvnw5Lly4gLi4OBw+fBhTpkzR6PPkyRMsXLgQcXFx+OWXX6BQKDBo0CD18u+//x7vvvsuwsPDcenSJaxevRqxsbHqLzRE9A8gElmgoUOHin369FG/P378uOji4iK+/fbboiiK4uzZs0VbW1vx7t276j6HDh0SHR0dxby8PI1tNWjQQFy9erUoiqLYrl07cdSoURrL27RpIzZv3rzUfSsUClEmk4lr164tNc60tDQRgJiSkqLR7uHhIW7ZskWjbf78+WK7du1EURTF1atXi87OzmJubq56+cqVK0vd1t95enqKS5cuLXP59u3bRRcXF/X7jRs3igDE5ORkdVtqaqoIQDx+/LgoiqLYoUMHcdGiRRrb2bRpk1irVi31ewBiQkJCmfslIuPiOXuyWHv37oWDgwOUSiUKCwvRp08ffPnll+rlnp6eqFGjhvr9qVOnkJOTAxcXF43tPH36FFeuXAEApKamYtSoURrL27Vrh8TExFJjSE1NRX5+Prp06aJ13Pfu3UNGRgbCwsIwcuRIdbtSqVTPB0hNTUXz5s1RqVIljTh0lZiYiEWLFuHSpUtQKBRQKpXIy8tDbm4uKleuDACwsbFBYGCgeh0fHx9UrVoVqampaN26NU6dOoUTJ05oVPJFRUXIy8vDkydPNGIkItNgsieL1alTJ6xcuRK2trZwd3cvMQGvOJkVU6lUqFWrFo4cOVJiW+W9/Mze3l7ndVQqFYBnQ/lt2rTRWGZtbQ0AEA3wZOrr16+jR48eGDVqFObPnw9nZ2f8/PPPCAsL0zjdATy7dO55xW0qlQpz585F//79S/SRy+V6x0lE+mOyJ4tVuXJlNGzYUOv+LVu2RGZmJmxsbFCvXr1S+/j6+iI5ORlDhgxRtyUnJ5e5zVdeeQX29vY4dOgQRowYUWK5nZ0dgGeVcDE3NzfUrl0bV69exTvvvFPqdhs3boxNmzbh6dOn6i8UL4qjNCdPnoRSqcTnn38OK6tn03e2b99eop9SqcTJkyfRunVrAMDly5fx8OFD+Pj4AHj2c7t8+bJOP2siqlhM9kT/07VrV7Rr1w59+/bF4sWL0ahRI9y6dQv79+9H3759ERgYiLFjx2Lo0KEIDAzEv/71L3zzzTe4ePEi6tevX+o25XI5pk6diilTpsDOzg6vvvoq7t27h4sXLyIsLAyurq6wt7fHgQMHUKdOHcjlcjg5OWHOnDkIDw+Ho6MjgoODkZ+fj5MnT+LBgweYMGECQkJCEBERgbCwMMyYMQPXrl3DkiVLdDreBg0aQKlU4ssvv0Tv3r3xyy+/YNWqVSX62dra4uOPP8by5ctha2uLjz76CG3btlUn/1mzZqFXr17w8PDAgAEDYGVlhXPnzuH8+fNYsGCB7r8IIjI4zsYn+h9BELB//3689tprGD58OLy9vTFo0CBcu3ZNPXt+4MCBmDVrFqZOnYqAgABcv34do0ePfuF2Z86ciYkTJ2LWrFnw9fXFwIEDcffuXQDPzocvX74cq1evhru7O/r06QMAGDFiBNatW4fY2Fj4+fnh9ddfR2xsrPpSPQcHB+zZsweXLl2Cv78/IiIisHjxYp2Ot0WLFoiOjsbixYvRtGlTfPPNN4iMjCzRr1KlSpg6dSpCQkLQrl072NvbY+vWrerl3bt3x969e3Hw4EG0atUKbdu2RXR0NDw9PXWKh4iMRxANcfKPiIiI/rFY2RMREVk4JnsiIiILx2RPRERk4ZjsiYiILByTPRERkYVjsiciIrJwTPZEREQWjsmeiIjIwjHZExERWTgmeyIiIgvHZE9ERGThmOyJiIgs3P8BTPz5iJ5MwFQAAAAASUVORK5CYII=\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"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",
|
||
"from sklearn.ensemble import BaggingClassifier\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",
|
||
"#define methods\n",
|
||
"# Logistic Regression\n",
|
||
"logreg = LogisticRegression(solver='lbfgs')\n",
|
||
"# Support vector machine\n",
|
||
"svm = SVC(gamma='auto', C=100)\n",
|
||
"# Decision Trees\n",
|
||
"deep_tree_clf = DecisionTreeClassifier(max_depth=None)\n",
|
||
"#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)))\n",
|
||
"\n",
|
||
"\n",
|
||
"from sklearn.ensemble import RandomForestClassifier\n",
|
||
"from sklearn.preprocessing import LabelEncoder\n",
|
||
"from sklearn.model_selection import cross_validate\n",
|
||
"# Data set not specificied\n",
|
||
"#Instantiate the model with 500 trees and entropy as splitting criteria\n",
|
||
"Random_Forest_model = RandomForestClassifier(n_estimators=500,criterion=\"entropy\")\n",
|
||
"Random_Forest_model.fit(X_train_scaled, y_train)\n",
|
||
"#Cross validation\n",
|
||
"accuracy = cross_validate(Random_Forest_model,X_test_scaled,y_test,cv=10)['test_score']\n",
|
||
"print(accuracy)\n",
|
||
"print(\"Test set accuracy with Random Forests and scaled data: {:.2f}\".format(Random_Forest_model.score(X_test_scaled,y_test)))\n",
|
||
"\n",
|
||
"\n",
|
||
"import scikitplot as skplt\n",
|
||
"y_pred = Random_Forest_model.predict(X_test_scaled)\n",
|
||
"skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)\n",
|
||
"plt.show()\n",
|
||
"y_probas = Random_Forest_model.predict_proba(X_test_scaled)\n",
|
||
"skplt.metrics.plot_roc(y_test, y_probas)\n",
|
||
"plt.show()\n",
|
||
"skplt.metrics.plot_cumulative_gain(y_test, y_probas)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ef32420e",
|
||
"metadata": {},
|
||
"source": [
|
||
"Recall that the cumulative gains curve shows the percentage of the\n",
|
||
"overall number of cases in a given category *gained* by targeting a\n",
|
||
"percentage of the total number of cases.\n",
|
||
"\n",
|
||
"Similarly, the receiver operating characteristic curve, or ROC curve,\n",
|
||
"displays the diagnostic ability of a binary classifier system as its\n",
|
||
"discrimination threshold is varied. It plots the true positive rate against the false positive rate."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5820ebfd",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Compare Bagging on Trees with Random Forests"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 23,
|
||
"id": "bb5bea62",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"bag_clf = BaggingClassifier(\n",
|
||
" DecisionTreeClassifier(splitter=\"random\", max_leaf_nodes=16, random_state=42),\n",
|
||
" n_estimators=500, max_samples=1.0, bootstrap=True, n_jobs=-1, random_state=42)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 24,
|
||
"id": "b879f3ce",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0.9790209790209791"
|
||
]
|
||
},
|
||
"execution_count": 24,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"bag_clf.fit(X_train, y_train)\n",
|
||
"y_pred = bag_clf.predict(X_test)\n",
|
||
"from sklearn.ensemble import RandomForestClassifier\n",
|
||
"rnd_clf = RandomForestClassifier(n_estimators=500, max_leaf_nodes=16, n_jobs=-1, random_state=42)\n",
|
||
"rnd_clf.fit(X_train, y_train)\n",
|
||
"y_pred_rf = rnd_clf.predict(X_test)\n",
|
||
"np.sum(y_pred == y_pred_rf) / len(y_pred)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "60160f97",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Boosting, a Bird's Eye View\n",
|
||
"\n",
|
||
"The basic idea is to combine weak classifiers in order to create a good\n",
|
||
"classifier. With a weak classifier we often intend a classifier which\n",
|
||
"produces results which are only slightly better than we would get by\n",
|
||
"random guesses.\n",
|
||
"\n",
|
||
"This is done by applying in an iterative way a weak (or a standard\n",
|
||
"classifier like decision trees) to modify the data. In each iteration\n",
|
||
"we emphasize those observations which are misclassified by weighting\n",
|
||
"them with a factor."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b351b1bd",
|
||
"metadata": {},
|
||
"source": [
|
||
"## What is boosting? Additive Modelling/Iterative Fitting\n",
|
||
"\n",
|
||
"Boosting is a way of fitting an additive expansion in a set of\n",
|
||
"elementary basis functions like for example some simple polynomials.\n",
|
||
"Assume for example that we have a function"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6e9174ef",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"f_M(x) = \\sum_{i=1}^M \\beta_m b(x;\\gamma_m),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fc319721",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $\\beta_m$ are the expansion parameters to be determined in a\n",
|
||
"minimization process and $b(x;\\gamma_m)$ are some simple functions of\n",
|
||
"the multivariable parameter $x$ which is characterized by the\n",
|
||
"parameters $\\gamma_m$.\n",
|
||
"\n",
|
||
"As an example, consider the Sigmoid function we used in logistic\n",
|
||
"regression. In that case, we can translate the function\n",
|
||
"$b(x;\\gamma_m)$ into the Sigmoid function"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "da4ba861",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sigma(t) = \\frac{1}{1+\\exp{(-t)}},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f444a5a4",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $t=\\gamma_0+\\gamma_1 x$ and the parameters $\\gamma_0$ and\n",
|
||
"$\\gamma_1$ were determined by the Logistic Regression fitting\n",
|
||
"algorithm.\n",
|
||
"\n",
|
||
"As another example, consider the cost function we defined for linear regression"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8a4d8175",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\boldsymbol{y},\\boldsymbol{f}) = \\frac{1}{n} \\sum_{i=0}^{n-1}(y_i-f(x_i))^2.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "de12bc14",
|
||
"metadata": {},
|
||
"source": [
|
||
"In this case the function $f(x)$ was replaced by the design matrix\n",
|
||
"$\\boldsymbol{X}$ and the unknown linear regression parameters $\\boldsymbol{\\beta}$,\n",
|
||
"that is $\\boldsymbol{f}=\\boldsymbol{X}\\boldsymbol{\\beta}$. In linear regression we can \n",
|
||
"simply invert a matrix and obtain the parameters $\\beta$ by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "735bf417",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{\\beta}=\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "22b8d82f",
|
||
"metadata": {},
|
||
"source": [
|
||
"In iterative fitting or additive modeling, we minimize the cost function with respect to the parameters $\\beta_m$ and $\\gamma_m$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "661db2e1",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Iterative Fitting, Regression and Squared-error Cost Function\n",
|
||
"\n",
|
||
"The way we proceed is as follows (here we specialize to the squared-error cost function)\n",
|
||
"\n",
|
||
"1. Establish a cost function, here $C(\\boldsymbol{y},\\boldsymbol{f}) = \\frac{1}{n} \\sum_{i=0}^{n-1}(y_i-f_M(x_i))^2$ with $f_M(x) = \\sum_{i=1}^M \\beta_m b(x;\\gamma_m)$.\n",
|
||
"\n",
|
||
"2. Initialize with a guess $f_0(x)$. It could be one or even zero or some random numbers.\n",
|
||
"\n",
|
||
"3. For $m=1:M$\n",
|
||
"\n",
|
||
"a. minimize $\\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta b(x;\\gamma))^2$ wrt $\\gamma$ and $\\beta$\n",
|
||
"\n",
|
||
"b. This gives the optimal values $\\beta_m$ and $\\gamma_m$\n",
|
||
"\n",
|
||
"c. Determine then the new values $f_m(x)=f_{m-1}(x) +\\beta_m b(x;\\gamma_m)$\n",
|
||
"\n",
|
||
"We could use any of the algorithms we have discussed till now. If we\n",
|
||
"use trees, $\\gamma$ parameterizes the split variables and split points\n",
|
||
"at the internal nodes, and the predictions at the terminal nodes."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2b14c81e",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Squared-Error Example and Iterative Fitting\n",
|
||
"\n",
|
||
"To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.\n",
|
||
"\n",
|
||
"For simplicity we assume also that our functions $b(x;\\gamma)=1+\\gamma x$. \n",
|
||
"\n",
|
||
"This means that for every iteration $m$, we need to optimize"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "64c44231",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"(\\beta_m,\\gamma_m) = \\mathrm{argmin}_{\\beta,\\lambda}\\hspace{0.1cm} \\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta b(x;\\gamma))^2=\\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta(1+\\gamma x_i))^2.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1040bdaf",
|
||
"metadata": {},
|
||
"source": [
|
||
"We start our iteration by simply setting $f_0(x)=0$. \n",
|
||
"Taking the derivatives with respect to $\\beta$ and $\\gamma$ we obtain"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "de59d269",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial {\\cal C}}{\\partial \\beta} = -2\\sum_{i}(1+\\gamma x_i)(y_i-\\beta(1+\\gamma x_i))=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5f87e844",
|
||
"metadata": {},
|
||
"source": [
|
||
"and"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a2f9215c",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\frac{\\partial {\\cal C}}{\\partial \\gamma} =-2\\sum_{i}\\beta x_i(y_i-\\beta(1+\\gamma x_i))=0.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "67f71f90",
|
||
"metadata": {},
|
||
"source": [
|
||
"We can then rewrite these equations as (defining $\\boldsymbol{w}=\\boldsymbol{e}+\\gamma \\boldsymbol{x})$ with $\\boldsymbol{e}$ being the unit vector)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5410f260",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\gamma \\boldsymbol{w}^T(\\boldsymbol{y}-\\beta\\gamma \\boldsymbol{w})=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0485a1f5",
|
||
"metadata": {},
|
||
"source": [
|
||
"which gives us $\\beta = \\boldsymbol{w}^T\\boldsymbol{y}/(\\boldsymbol{w}^T\\boldsymbol{w})$. Similarly we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3a256711",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\beta\\gamma \\boldsymbol{x}^T(\\boldsymbol{y}-\\beta(1+\\gamma \\boldsymbol{x}))=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fc8cd2ae",
|
||
"metadata": {},
|
||
"source": [
|
||
"which leads to $\\gamma =(\\boldsymbol{x}^T\\boldsymbol{y}-\\beta\\boldsymbol{x}^T\\boldsymbol{e})/(\\beta\\boldsymbol{x}^T\\boldsymbol{x})$. Inserting\n",
|
||
"for $\\beta$ gives us an equation for $\\gamma$. This is a non-linear equation in the unknown $\\gamma$ and has to be solved numerically. \n",
|
||
"\n",
|
||
"The solution to these two equations gives us in turn $\\beta_1$ and $\\gamma_1$ leading to the new expression for $f_1(x)$ as\n",
|
||
"$f_1(x) = \\beta_1(1+\\gamma_1x)$. Doing this $M$ times results in our final estimate for the function $f$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0a9ecf4b",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Iterative Fitting, Classification and AdaBoost\n",
|
||
"\n",
|
||
"Let us consider a binary classification problem with two outcomes $y_i \\in \\{-1,1\\}$ and $i=0,1,2,\\dots,n-1$ as our set of\n",
|
||
"observations. We define a classification function $G(x)$ which produces a prediction taking one or the other of the two values \n",
|
||
"$\\{-1,1\\}$.\n",
|
||
"\n",
|
||
"The error rate of the training sample is then"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ac605ae7",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathrm{\\overline{err}}=\\frac{1}{n} \\sum_{i=0}^{n-1} I(y_i\\ne G(x_i)).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b4d530db",
|
||
"metadata": {},
|
||
"source": [
|
||
"The iterative procedure starts with defining a weak classifier whose\n",
|
||
"error rate is barely better than random guessing. The iterative\n",
|
||
"procedure in boosting is to sequentially apply a weak\n",
|
||
"classification algorithm to repeatedly modified versions of the data\n",
|
||
"producing a sequence of weak classifiers $G_m(x)$.\n",
|
||
"\n",
|
||
"Here we will express our function $f(x)$ in terms of $G(x)$. That is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0f9fce0f",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"f_M(x) = \\sum_{i=1}^M \\beta_m b(x;\\gamma_m),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "73471c17",
|
||
"metadata": {},
|
||
"source": [
|
||
"will be a function of"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d8244842",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"G_M(x) = \\mathrm{sign} \\sum_{i=1}^M \\alpha_m G_m(x).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "be09fe99",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Adaptive Boosting, AdaBoost\n",
|
||
"\n",
|
||
"In our iterative procedure we define thus"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a547cf77",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"f_m(x) = f_{m-1}(x)+\\beta_mG_m(x).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "67b1198a",
|
||
"metadata": {},
|
||
"source": [
|
||
"The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the\n",
|
||
"exponential cost/loss function defined as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f0a75e83",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\boldsymbol{y},\\boldsymbol{f}) = \\sum_{i=0}^{n-1}\\exp{(-y_i(f_{m-1}(x_i)+\\beta G(x_i))}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9d2d96dc",
|
||
"metadata": {},
|
||
"source": [
|
||
"We optimize $\\beta$ and $G$ for each value of $m=1:M$ as we did in the regression case.\n",
|
||
"This is normally done in two steps. Let us however first rewrite the cost function as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a6c2a558",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\boldsymbol{y},\\boldsymbol{f}) = \\sum_{i=0}^{n-1}w_i^{m}\\exp{(-y_i\\beta G(x_i))},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5a582df6",
|
||
"metadata": {},
|
||
"source": [
|
||
"where we have defined $w_i^m= \\exp{(-y_if_{m-1}(x_i))}$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "654c5f13",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Building up AdaBoost\n",
|
||
"\n",
|
||
"First, for any $\\beta > 0$, we optimize $G$ by setting"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "efecb2bc",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"G_m(x) = \\mathrm{sign} \\sum_{i=0}^{n-1} w_i^m I(y_i \\ne G_(x_i)),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "da78bb27",
|
||
"metadata": {},
|
||
"source": [
|
||
"which is the classifier that minimizes the weighted error rate in predicting $y$.\n",
|
||
"\n",
|
||
"We can do this by rewriting"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "dc1c118f",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\exp{-(\\beta)}\\sum_{y_i=G(x_i)}w_i^m+\\exp{(\\beta)}\\sum_{y_i\\ne G(x_i)}w_i^m,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1b77640d",
|
||
"metadata": {},
|
||
"source": [
|
||
"which can be rewritten as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d7944742",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"(\\exp{(\\beta)}-\\exp{-(\\beta)})\\sum_{i=0}^{n-1}w_i^mI(y_i\\ne G(x_i))+\\exp{(-\\beta)}\\sum_{i=0}^{n-1}w_i^m=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "94ffa0c4",
|
||
"metadata": {},
|
||
"source": [
|
||
"which leads to"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "eae46622",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\beta_m = \\frac{1}{2}\\log{\\frac{1-\\mathrm{\\overline{err}}}{\\mathrm{\\overline{err}}}},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "099f71b5",
|
||
"metadata": {},
|
||
"source": [
|
||
"where we have redefined the error as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "11e5f200",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathrm{\\overline{err}}_m=\\frac{1}{n}\\frac{\\sum_{i=0}^{n-1}w_i^mI(y_i\\ne G(x_i)}{\\sum_{i=0}^{n-1}w_i^m},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "77b52ed2",
|
||
"metadata": {},
|
||
"source": [
|
||
"which leads to an update of"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e8fe5df6",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"f_m(x) = f_{m-1}(x) +\\beta_m G_m(x).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4c1ea9b7",
|
||
"metadata": {},
|
||
"source": [
|
||
"This leads to the new weights"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a61b875a",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"w_i^{m+1} = w_i^m \\exp{(-y_i\\beta_m G_m(x_i))}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a0df6e36",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Adaptive boosting: AdaBoost, Basic Algorithm\n",
|
||
"\n",
|
||
"The algorithm here is rather straightforward. Assume that our weak\n",
|
||
"classifier is a decision tree and we consider a binary set of outputs\n",
|
||
"with $y_i \\in \\{-1,1\\}$ and $i=0,1,2,\\dots,n-1$ as our set of\n",
|
||
"observations. Our design matrix is given in terms of the\n",
|
||
"feature/predictor vectors\n",
|
||
"$\\boldsymbol{X}=[\\boldsymbol{x}_0\\boldsymbol{x}_1\\dots\\boldsymbol{x}_{p-1}]$. Finally, we define also a\n",
|
||
"classifier determined by our data via a function $G(x)$. This function tells us how well we are able to classify our outputs/targets $\\boldsymbol{y}$. \n",
|
||
"\n",
|
||
"We have already defined the misclassification error $\\mathrm{err}$ as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "862806de",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathrm{err}=\\frac{1}{n}\\sum_{i=0}^{n-1}I(y_i\\ne G(x_i)),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "60c6b96e",
|
||
"metadata": {},
|
||
"source": [
|
||
"where the function $I()$ is one if we misclassify and zero if we classify correctly."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d4cf16bb",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Basic Steps of AdaBoost\n",
|
||
"\n",
|
||
"With the above definitions we are now ready to set up the algorithm for AdaBoost.\n",
|
||
"The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.\n",
|
||
"1. We start by initializing all weights to $w_i = 1/n$, with $i=0,1,2,\\dots n-1$. It is easy to see that we must have $\\sum_{i=0}^{n-1}w_i = 1$.\n",
|
||
"\n",
|
||
"2. We rewrite the misclassification error as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "91e907b9",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathrm{\\overline{err}}_m=\\frac{\\sum_{i=0}^{n-1}w_i^m I(y_i\\ne G(x_i))}{\\sum_{i=0}^{n-1}w_i},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "cc913a38",
|
||
"metadata": {},
|
||
"source": [
|
||
"1. Then we start looping over all attempts at classifying, namely we start an iterative process for $m=1:M$, where $M$ is the final number of classifications. Our given classifier could for example be a plain decision tree.\n",
|
||
"\n",
|
||
"a. Fit then a given classifier to the training set using the weights $w_i$.\n",
|
||
"\n",
|
||
"b. Compute then $\\mathrm{err}$ and figure out which events are classified properly and which are classified wrongly.\n",
|
||
"\n",
|
||
"c. Define a quantity $\\alpha_{m} = \\log{(1-\\mathrm{\\overline{err}}_m)/\\mathrm{\\overline{err}}_m}$\n",
|
||
"\n",
|
||
"d. Set the new weights to $w_i = w_i\\times \\exp{(\\alpha_m I(y_i\\ne G(x_i)}$.\n",
|
||
"\n",
|
||
"5. Compute the new classifier $G(x)= \\sum_{i=0}^{n-1}\\alpha_m I(y_i\\ne G(x_i)$.\n",
|
||
"\n",
|
||
"For the iterations with $m \\le 2$ the weights are modified\n",
|
||
"individually at each steps. The observations which were misclassified\n",
|
||
"at iteration $m-1$ have a weight which is larger than those which were\n",
|
||
"classified properly. As this proceeds, the observations which were\n",
|
||
"difficult to classifiy correctly are given a larger influence. Each\n",
|
||
"new classification step $m$ is then forced to concentrate on those\n",
|
||
"observations that are missed in the previous iterations."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "87e49535",
|
||
"metadata": {},
|
||
"source": [
|
||
"## AdaBoost Examples\n",
|
||
"\n",
|
||
"Using **Scikit-Learn** it is easy to apply the adaptive boosting algorithm, as done here."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 24,
|
||
"id": "a48ac6a2",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"from sklearn.ensemble import AdaBoostClassifier\n",
|
||
"\n",
|
||
"ada_clf = AdaBoostClassifier(\n",
|
||
" DecisionTreeClassifier(max_depth=1), n_estimators=200,\n",
|
||
" algorithm=\"SAMME.R\", learning_rate=0.5, random_state=42)\n",
|
||
"ada_clf.fit(X_train, y_train)\n",
|
||
"\n",
|
||
"from sklearn.ensemble import AdaBoostClassifier\n",
|
||
"\n",
|
||
"ada_clf = AdaBoostClassifier(\n",
|
||
" DecisionTreeClassifier(max_depth=1), n_estimators=200,\n",
|
||
" algorithm=\"SAMME.R\", learning_rate=0.5, random_state=42)\n",
|
||
"ada_clf.fit(X_train_scaled, y_train)\n",
|
||
"y_pred = ada_clf.predict(X_test_scaled)\n",
|
||
"skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)\n",
|
||
"plt.show()\n",
|
||
"y_probas = ada_clf.predict_proba(X_test_scaled)\n",
|
||
"skplt.metrics.plot_roc(y_test, y_probas)\n",
|
||
"plt.show()\n",
|
||
"skplt.metrics.plot_cumulative_gain(y_test, y_probas)\n",
|
||
"plt.show()"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "Python 3 (ipykernel)",
|
||
"language": "python",
|
||
"name": "python3"
|
||
},
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.9.10"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
}
|