Morten Hjorth-Jensen
3523 lines
824 KiB
Plaintext
3523 lines
824 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 week47.do.txt --no_mako -->\n",
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"<!-- dom:TITLE: Week 47: From Decision Trees to Ensemble Methods, Random Forests and Boosting Methods and Summary of Course -->"
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"# Week 47: From Decision Trees to Ensemble Methods, Random Forests and Boosting Methods and Summary of Course\n",
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"**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Ion Beams, Michigan State University\n",
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"\n",
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"Date: **November 20-24, 2023**"
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"source": [
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"## Plan for week 47\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 3\n",
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"\n",
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" * Last weekly exercise, course feedback, to be completed by Sunday November 26\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 23, 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](https://youtu.be/SpWXsvn5I9E)\n",
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"\n",
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" * [Whiteboard notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesNov23.pdf)\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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" * [Video on boosting methods by Hastie](https://www.youtube.com/watch?v=wPqtzj5VZus&ab_channel=H2O.ai)\n",
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"\n",
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" * [Video on AdaBoost](https://www.youtube.com/watch?v=LsK-xG1cLYA)\n",
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"\n",
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" * [Video on Gradient boost, part 1, parts 2-4 follow thereafter](https://www.youtube.com/watch?v=3CC4N4z3GJc)\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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"## Bagging\n",
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"\n",
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"The **plain** decision trees suffer from high\n",
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"variance. This means that if we split the training data into two parts\n",
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"at random, and fit a decision tree to both halves, the results that we\n",
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"get could be quite different. In contrast, a procedure with low\n",
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"variance will yield similar results if applied repeatedly to distinct\n",
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"data sets; linear regression tends to have low variance, if the ratio\n",
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"of $n$ to $p$ is moderately large. \n",
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"\n",
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"**Bootstrap aggregation**, or just **bagging**, is a\n",
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"general-purpose procedure for reducing the variance of a statistical\n",
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"learning method."
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"## More bagging\n",
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"\n",
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"Bagging typically results in improved accuracy\n",
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"over prediction using a single tree. Unfortunately, however, it can be\n",
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"difficult to interpret the resulting model. Recall that one of the\n",
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"advantages of decision trees is the attractive and easily interpreted\n",
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"diagram that results.\n",
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"\n",
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"However, when we bag a large number of trees, it is no longer\n",
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"possible to represent the resulting statistical learning procedure\n",
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"using a single tree, and it is no longer clear which variables are\n",
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"most important to the procedure. Thus, bagging improves prediction\n",
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"accuracy at the expense of interpretability. Although the collection\n",
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"of bagged trees is much more difficult to interpret than a single\n",
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"tree, one can obtain an overall summary of the importance of each\n",
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"predictor using the MSE (for bagging regression trees) or the Gini\n",
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"index (for bagging classification trees). In the case of bagging\n",
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"regression trees, we can record the total amount that the MSE is\n",
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"decreased due to splits over a given predictor, averaged over all $B$ possible\n",
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"trees. A large value indicates an important predictor. Similarly, in\n",
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"the context of bagging classification trees, we can add up the total\n",
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"amount that the Gini index is decreased by splits over a given\n",
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"predictor, averaged over all $B$ trees."
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"source": [
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"## Making your own Bootstrap: Changing the Level of the Decision Tree\n",
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"\n",
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"Let us bring up our good old boostrap example from the linear regression lectures. We change the linerar regression algorithm with\n",
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"a decision tree wth different depths and perform a bootstrap aggregate (in this case we perform as many bootstraps as data points $n$)."
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"text": [
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"Polynomial degree: 1\n",
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"Error: 0.05485044745873867\n",
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"Bias^2: 0.05363014989229746\n",
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"Var: 0.0012202975664411882\n",
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"0.05485044745873867 >= 0.05363014989229746 + 0.0012202975664411882 = 0.05485044745873865\n",
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"Polynomial degree: 2\n",
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"Error: 0.04754825003279861\n",
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"Bias^2: 0.0362312015777108\n",
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"Var: 0.01131704845508782\n",
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"0.04754825003279861 >= 0.0362312015777108 + 0.01131704845508782 = 0.04754825003279862\n",
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"Polynomial degree: 3\n",
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"Error: 0.028256917047283964\n",
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"Bias^2: 0.019709199043491926\n",
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"Var: 0.008547718003792035\n",
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"0.028256917047283964 >= 0.019709199043491926 + 0.008547718003792035 = 0.02825691704728396\n",
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"Polynomial degree: 4\n",
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"Error: 0.02417252675174287\n",
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"Bias^2: 0.016541517177965183\n",
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"Var: 0.007631009573777696\n",
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"0.02417252675174287 >= 0.016541517177965183 + 0.007631009573777696 = 0.02417252675174288\n",
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"Polynomial degree: 5\n",
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"Error: 0.020350773309798075\n",
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"Bias^2: 0.013742894355267554\n",
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"Var: 0.006607878954530523\n",
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"0.020350773309798075 >= 0.013742894355267554 + 0.006607878954530523 = 0.02035077330979808\n",
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"Polynomial degree: 6\n",
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"Error: 0.019509108923639135\n",
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"Bias^2: 0.01312013610582818\n",
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"Var: 0.006388972817810939\n",
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"0.019509108923639135 >= 0.01312013610582818 + 0.006388972817810939 = 0.01950910892363912\n",
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"Polynomial degree: 7\n",
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"Error: 0.020056743323946562\n",
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"Bias^2: 0.012815095479733507\n",
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"Var: 0.007241647844213045\n",
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"0.020056743323946562 >= 0.012815095479733507 + 0.007241647844213045 = 0.020056743323946552\n",
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"Simple tree: 0.5601973572808581\n"
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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week47_6_1.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"%matplotlib inline\n",
|
||
"\n",
|
||
"# Common imports\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",
|
||
"import pandas as pd\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.preprocessing import StandardScaler, OneHotEncoder\n",
|
||
"from sklearn.compose import ColumnTransformer\n",
|
||
"from IPython.display import Image \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",
|
||
"\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": "ec697394",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "2f8e4054",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"m\\approx \\sqrt{p}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5476fc65",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "024d17cc",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "adbab589",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Random Forests Compared with other Methods on the Cancer Data"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"id": "44d47f87",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"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"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[0.93333333 0.73333333 0.93333333 1. 1. 0.92857143\n",
|
||
" 1. 0.92857143 0.92857143 1. ]\n",
|
||
"Test set accuracy with Random Forests and scaled data: 0.98\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week47_12_2.png"
|
||
}
|
||
},
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||
"output_type": "display_data"
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||
},
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||
{
|
||
"data": {
|
||
"image/png": 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\n",
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||
"text/plain": [
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||
"<Figure size 640x480 with 1 Axes>"
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]
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||
},
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"metadata": {
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"filenames": {
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"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week47_12_3.png"
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}
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},
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"output_type": "display_data"
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},
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{
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"data": {
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"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week47_12_4.png"
|
||
}
|
||
},
|
||
"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": "2670f5de",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "622c79ae",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Compare Bagging on Trees with Random Forests"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"id": "eceba36c",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"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": 4,
|
||
"id": "40d42e1a",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0.9790209790209791"
|
||
]
|
||
},
|
||
"execution_count": 4,
|
||
"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": "bee77377",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "4ea2d5e4",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "c69bf1b6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f_M(x) = \\sum_{i=1}^M \\beta_m b(x;\\gamma_m),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d53b6cb2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "57ee288e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sigma(t) = \\frac{1}{1+\\exp{(-t)}},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d03b9aa0",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "3caace0f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "99c4d861",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "15e7309c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\boldsymbol{\\beta}=\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "78f883b0",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "95d67f7e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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 ${\\cal C}(\\boldsymbol{y},\\boldsymbol{f}) = \\frac{1}{n} \\sum_{i=0}^{n-1}(y_i-f_M(x_i))^2$ 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": "571085d4",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "6c23e842",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "6a3315ef",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "c377e717",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "0effec3c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5104bdd4",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "07255d2b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "e597dcd5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\gamma \\boldsymbol{w}^T(\\boldsymbol{y}-\\beta\\gamma \\boldsymbol{w})=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5044ba81",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which gives us $\\beta = \\boldsymbol{w}^T\\boldsymbol{y}/(\\boldsymbol{w}^T\\boldsymbol{w})$. Similarly we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6ec9b996",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\beta\\gamma \\boldsymbol{x}^T(\\boldsymbol{y}-\\beta(1+\\gamma \\boldsymbol{x}))=0,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f6835c6d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "ec4ec69c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "ee339678",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "e8eaad5d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "b401d599",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f_M(x) = \\sum_{i=1}^M \\beta_m b(x;\\gamma_m),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a9e7822e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"will be a function of"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "715194ce",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"G_M(x) = \\mathrm{sign} \\sum_{i=1}^M \\alpha_m G_m(x).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "195fc1da",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Adaptive Boosting, AdaBoost\n",
|
||
"\n",
|
||
"In our iterative procedure we define thus"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9436883a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f_m(x) = f_{m-1}(x)+\\beta_mG_m(x).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4ebf9f1e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "603422c9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "da3e2e12",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "851833f0",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "4bbf5443",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where we have defined $w_i^m= \\exp{(-y_if_{m-1}(x_i))}$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b63b18c5",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Building up AdaBoost\n",
|
||
"\n",
|
||
"First, for any $\\beta > 0$, we optimize $G$ by setting"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f3f75de8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "998b02e8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "98b1751b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "4b030d99",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which can be rewritten as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e286c8e8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "7328b345",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which leads to"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b10d1b97",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\beta_m = \\frac{1}{2}\\log{\\frac{1-\\mathrm{\\overline{err}}}{\\mathrm{\\overline{err}}}},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6601235f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where we have redefined the error as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2d7d9eb9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "41a404a6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"which leads to an update of"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "65f30690",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f_m(x) = f_{m-1}(x) +\\beta_m G_m(x).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "aea33aa2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"This leads to the new weights"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "225e3f3e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"w_i^{m+1} = w_i^m \\exp{(-y_i\\beta_m G_m(x_i))}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "eb9cd9ea",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "09491585",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathrm{err}=\\frac{1}{n}\\sum_{i=0}^{n-1}I(y_i\\ne G(x_i)),\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "60b25717",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where the function $I()$ is one if we misclassify and zero if we classify correctly."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "af1b7fce",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "e207bb04",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "50ea5302",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": "e6b2e841",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"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": 5,
|
||
"id": "f3473567",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
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"text/plain": [
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"<Figure size 640x480 with 2 Axes>"
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]
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},
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"metadata": {
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"filenames": {
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"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week47_73_0.png"
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}
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},
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"output_type": "display_data"
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},
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{
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"data": {
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"image/png": 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\n",
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||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
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||
]
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||
},
|
||
"metadata": {
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||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week47_73_1.png"
|
||
}
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||
},
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||
"output_type": "display_data"
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||
},
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||
{
|
||
"data": {
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||
"image/png": 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bN2+qYrdv38bOzo4iRYpkeoyjo2OGjSMBPDw8HnuMyD16vR4XFxeKFCkihZCGkvQGVpyIxsbRxRSrW64IH75ZWcOs8q/U1FT27d9Hvbr1sLN7xl/TRgNeJ2bgfmkzNoakLJ3PNvk+dsn3gf/edO6Va8udF3tl6XXyIoPBwIm/TlCtajVsbW21TiffOHL8L0aO+4xRQ/vT+s03AIiJiYXv25h9WItVFUJ16tRR7bAMsHXrVmrWrClvokI8h5WHIrgTp97VfGSzSlTzLaRNQvmcXq/nWgGoWtL92X+3bf0Yjv1ongRK1aFw53kUtsv4R2R+o9frOXvjAeX9G8j7TC4wGo189dVXjB8/HoPBwIQp3/NWx65UqFCBqKioHDmnptPn4+LiCA8PJzw8HEibHh8eHk5ERASQdlurW7dupuf379+fK1euMGLECE6fPs2iRYtYuHAhH3zwgRbpC5EnJOkNzN51QRVrUMGTgNKFNcpIZNnRn2C/mYqgwmUgKASkCBK57Pbt27Ro0YKPPvoIg8EAQEBAAK6urjl6Xk07QkeOHKFx48amxw/H8nTv3p0lS5YQGRlpKooA/Pz82Lx5M8OHD2fmzJn4+Pgwffp02rdvn+u5C2FprkYn8H7ocU5ciyErq2KkbTuvjr3/RgXzJidyzsXdsGnE05/3LAp6Q/AqcJVhAyJ37dq1i+DgYCIjI4G0cb/jx4/nk08+yfFbkpoWQo0aNXriL+wlS5ZkiDVs2JBjx47lYFZCWB9FURi84hgnrsU892vVLedBzTIykcAq3D0Pq7qCMVUdb/wxFKuStdeycwLfV8DJ3Xz5CfEUBoOBzz//nEmTJmE0GoG02eAhISG88cYbuZKDVY0REkJkbue/t81SBAEMaVzOLK8jclhCNKzoCEnprnu996HhKG1yEiILbt26RXBwMDt27DDFmjRpwvLlyzMslZOTZNNVIaycoihM+/3cc7+OTgdNfIzUlLFBli81BVZ1g+h0yx1Ubg1vTNQkJSGySlEU/v77bwBsbGz47LPP2LJlS64WQSAdISGs3q5/7/BXum7Qx62qUK+8Z5Zex8PZloO7fzdnaiInKApsGg6X96rjxatCu3lgxhV3hchJxYsXJyQkhJ49e7J8+XIaNmyoSR5SCAlhxRRFYdp2dTeoTBEXetQtg51t1t4Q9Xq9OVMTOWX/dDi+XB0r6A3BYeCQs7NrhHge169fx9nZWbWYcZMmTTh37hxOTk6a5SV/OghhxXadvcOJq/dVscGvV8hyESSsxOlfYNsEdczOGTqvBDcfbXIS4hls2bIFf39/evbsmWGSlJZFEEghJITVUhSFH9KNDSpdxIW2/vKGmCdFnoC1fUlb8OAR7eaBT3VNUhLiafR6PWPHjqVFixbcvXuXDRs2MHfuXK3TUpFbY0JYqd1n7xCerhs0qHF56QblRbGRsKIT6BPU8TcmwAtttMlJiKe4evUqnTp1Yv/+/aZY69at6dixo4ZZZSS/MYWwQoqi8EO6sUGlPFx4p3oJjTISOSYlHlZ2ggc31HH/LlB/uDY5CfEUGzduxN/f31QE2dnZ8d1337FhwwaL2+dTOkJCWKG95+5yPOK+Kja4cXnspRuUtyhGWNcPIsPV8dL1oPW0tDUPhLAgKSkpjB07lqlTp5pipUuXJiwsjNq1a2uY2eNJISSElUlbN+isKubr4cw7NaQblNfY7PoCTqs3mqawHwQuAzsHbZIS4jFiY2Np2rQphw4dMsXatm3LokWLKFzYctcnkz8fhbAyf5y/yzHpBuV5vlF7sd0/TR10cpe9wITFKliwIGXKlAHAwcGB6dOns3btWosugkA6QkJYlcxmipUs7Ey7GiU1ykiYzZX9cPMkKAo2SbH4X12k/rjOFgKXQtGK2uQnxFPodDrmz59PTEwMn3/+OQEBAVqn9EykEBLCiuw7H8WRK/dUsUHSDbJ+O7+A3V+ZHma613ar76Bso9zKSIinunDhAlevXqVRo0ammJubG1u2bNEuqWyQ355CWIm0mWLqsUElCjnTXrpB1i18haoIytSrg6Bmz9zJR4hnsHr1amrUqEH79u25evWq1uk8FymEhLASBy5Ecfhyxm6Qg538GFuty/tgw9AnP6dCc2j2We7kI8RTJCUlMXDgQAIDA4mNjSU6OpqPPvpI67Sei9waE8IKZLbDfIlCznQIkG6Q1Yq6AGFdwJhuj7dSdTDa2HE3KpoiVZtj22g02GR6s0yIXHX27FkCAwM5ceKEKRYcHMysWbM0zOr5SSEkhBU4cDGKQ5ejVbGBjctJN8haJd6DFUFp/31UncHQ/HMMej0HNm+mZaOW2Nrba5OjEI9YsWIF/fr1Iy4uDkjbH2zGjBn06tULnZWvZyWFkBBWIP1MMR93JzoG+GqUjXguBj2s7gFR6mtKxRbQ9FNNUhLicRISEhg6dCgLFy40xapUqcKqVat46aWXNMzMfKQQEsLCHbgQxZ+X1N2gATI2yDopCmweBRd3qeNeL0P7BXILTFgURVF488032bt3rynWvXt3Zs6ciaurq4aZmZf8JhXCwqWfKebt7kRgTRkbZJUOzoaji9WxAl4QHAqOBbTJSYjH0Ol0jBgxAgAXFxeWLFnCkiVL8lQRBNIREsKiHbwYxcGL6cYGNSqHo510DqzOv1vgt3Sza+ycoNNKcJfCVlimtm3b8u2339KyZUuqVKmidTo5QjpCQliw9GODirs5EfiKjA2yOjf/hv/1BhR1vO1sKGkdq++KvO/vv//m448/RlHU36cjR47Ms0UQSEdICIt16FI0By5GqWIDG0s3yOo8uAUrO0FKnDre+GN4qZ02OQnxCEVRWLhwIUOGDCEpKQk/Pz969+6tdVq5RjpCQlio9GODvNwcCawp3SCrok+E0GCISbfybtUgeO0DbXIS4hEPHjzg3XffpW/fviQlJQGwcOFCjEajxpnlHimEhLBAhy9Hs+98um5Qo/I42Us3yGoYjbB+AFw/oo77vgptfgQrX3tFWL/w8HACAgJYsWKFKTZgwAB27NiBjU3+KQ/k1pgQFiI51UBMYtoqw9N+z9gNCpKxQdZl95fwzzp1rFBp6BQCdo7a5CQEabfC5syZw/Dhw0lOTgbSNkudP38+gYGBGmeX+6QQEsICLNh7ke+2niVRb8j04/0blpNukDX5a1XGjVQd3SB4Fbh6apOTEEBMTAx9+/Zl9erVplhAQABhYWGUK1dOw8y0k396X0JYqL+vxzB50+nHFkHFCjrSuVapXM5KZFvEn/DzIHVMZwsdF0OxytrkJMT/+/DDD1VF0NChQ9m3b1++LYJACiEhNJd+M9X0pBtkRe5dThscbUhRx1t8BeWbaJKSEI+aPHkyJUqUoFChQqxbt44ffvgBR8f8fatWbo0JoaG/r8fw++lbmX7MzkZHG38futUpnctZiWxJiknbSDXhrjpeqx/U6qtNTiLfUxRFtSmqp6cn69evx9PTkzJlymiXmAWRQkgIDf2wXd0NKuRiz6/vN8DJzhYne1ucHaQTZBUMqbCmF9w5o46XbwLNv9AmJ5Hv/fnnnwwfPpx169bh5eVlitesWVPDrCyP3BoTQiP/3Ihh2yl1N6hvg7J4uztT2NVBiiBr8ttHcP53daxoFeiwCGzl702RuxRF4bvvvqN+/focOHCArl275qt1gbJKfkKF0Mj0TLpB3euW0SYZkX2H5sOhueqYiycEh4GTuzY5iXwrKiqKHj168Msvv5hi8fHxxMTEULhwYQ0zs1zSERJCA6duxPLbP+puUJ/6fhRwlL9NrMq53+HX0eqYrSN0WgGFZWyXyF379u2jevXqqiJozJgx7Nq1S4qgJ5DfukJoIH03yN1ZukFW5/ZpWNMTlHS3HN6eCaVqa5OTyJeMRiNff/01H3/8MQZD2jIcnp6eLFu2jDfffFPj7CyfFEJC5LLTkbFs+eemKtanvh8Fnew1ykhkWfxdWBEIybHqeMMPoWpHbXIS+dKdO3fo1q0bW7ZsMcVee+01VqxYQYkSJTTMzHrIrTEhcln6bpCbkx3d65XRJhmRdfqktLWC7keo4y+2g0ZjtclJ5Fvbt283FUE6nY7x48ezfft2KYKyQDpCQuSiMzdj+fXvdN2gBmVxk26QdVAU2DgUrv6pjpeoCW1nyUaqItd16tSJrVu3snnzZpYvX06TJrJwZ1ZJISRELvpx+3nVYzcnO3pIN8h67PkW/gpTx9x90wZH2ztrk5PIVx48eEDBggVVsRkzZhAbG0vx4sU1ysq6ya0xIXLJvzcfsPnvSFWsV30/6QZZi7/Xws7J6phDAegcCgW9Mj9GCDPavn07FStWZNWqVaq4i4uLFEHPQQohIXLJ9B3nUJT/Hhd0sqNnPT/tEhLP7tpRWD9AHdPZpC2YWPwlbXIS+YbBYGDChAk0bdqUmzdv0qdPHy5cuKB1WnmG3BoTIhecu/WAzSfTdYPq+eHuLN0gi3f/KqzsBKlJ6njzL6Bic21yEvnGjRs3CA4OZvfu3aZYnTp1MtweE9knHSEhcsH0HefV3SBHO3pJN8jyJT9IK4Lib6vjNXtB7f7a5CTyjd9++w1/f39TEWRra8uUKVP49ddfKVasmMbZ5R3SERIih5279YBf/rqhivWs74e7i3SDLJrRAP/rA7f+VsfLNoIWX8sMMZFjUlNTGT9+PF9++aUpVrJkSVauXEn9+vU1zCxvkkJIiBz2YybdoN7SDbJ82z6Bs1vUMc+K0PEnsJUiVuSM69evExQUxL59+0yxVq1asWTJEjw9PTXMLO+SW2NC5KDzt+PYmK4b1KNeGekGWboji+HADHXM2SNtI1XnQpqkJPIHnU7H2bNnAbCzs+Pbb79lw4YNUgTlICmEhMhBP6abKVbA0Y7e9aUbZNEu7oLNH6hjNvbQKQQ8ymqSksg/fHx8WLZsGWXKlGHv3r2MHDkSGxt5q85JcmtMiBxy4U4cG0+k6wbVLUMhFweNMhJPdecshHUDY6o63mY6lK6rTU4iT7ty5Qru7u4UKlTIFGvevDlnzpzB0dFRu8TyESkzhcghM3acx/hIN8jVwVa6QZYsIfr/N1KNUcfrjwD/YG1yEnna+vXr8ff3p3fv3iiPto5BiqBcJIWQEDng4p04fg6/ror1qFeGwq7SDbJIqSkQ9i7cu6SOV2kDr4/XJieRZyUnJ/P+++/zzjvvcP/+fdauXcuiRYu0TivfkltjQuSAzLpBferL+BKLpCjwyzC4sk8d9/aHd+aCjM8QZnTx4kUCAwM5evSoKdahQwc6dOigYVb5m/yEC2Fml+7Gsz5dN6hbXekGWax90yA8RB0r6JO2h5iDiyYpibxpzZo1VK9e3VQEOTo6MmvWLFatWoW7u7vG2eVf0hESwsx+3HFO1Q1ycbClbwPpBlmkUxvg94nqmL0LBIeCm7cmKYm8JykpiZEjRzJr1ixTrEKFCqxatQp/f3/tEhOAFEJCmNXlu/H8HK6eKdatThk8pBtkeW4ch7XvpQvqoN188K6mSUoi77l37x6vv/464eHhpljnzp2ZO3eu7BdmIeTWmBBmNGPneQyPtIOc7W3p20Bmilmc2BuwsjOkJqrjTSdBldba5CTypEKFClG+fHkAnJycmDdvHiEhIVIEWRDpCAlhJlei4ll3PP3YoNIUKSDTYC1KSjysCIIHkep49a5Qd6g2OYk8S6fTsWDBAhISEpgyZQpVq1bVOiWRjhRCQpjJjB0Zu0Hvydggy2I0pt0Ou/mXOl6mAbSaKhupiud2+vRpbt26RaNGjUwxd3d3Nm3apF1S4onk1pgQZhARlcDadN2grnWkG2Rxtk+CM7+oYx7lIHAp2Mk4LvF8li5dSs2aNenYsSPXr19/+gHCIkghJIQZzNh5TtUNcrK34b3XpBtkUY4vT5sq/yinQhC8Clw8tMhI5BHx8fH07NmT7t27k5CQwN27d5kwYYLWaYlnJLfGhHhOV6MTWHssXTfo1dJ4SjfIclz+AzYOU8ds7CBoGXiW1yQlkTf8/fffBAYGcvr0aVOsT58+/PDDDxpmJbJCOkJCPKeZO8+TmqEbVE7DjIRK1IW07TOMenW81VTwe02bnITVUxSFhQsXUqtWLVMRVKBAAUJCQpg/fz4uLrIYp7WQjpAQz+FqdAJrjl5Txd6tXZqiBaUbZBES76VtpJp4Tx2vOwQCumuTk7B6Dx48YMCAAYSE/LciebVq1Vi1ahUVK1bUMDORHVIICfEcZu1Sd4Mc7Wx4r6GMDbIIBj2s6gZR59XxSi2hySRtchJWT1EUmjRpwqFDh0yxAQMGMHXqVJycnDTMTGSX5rfGZs2ahZ+fH05OTgQEBLB3794nPj8kJIRq1arh4uKCt7c3PXv2JCoqKpeyFeI/1+4lsPqIuhvUpXZpihWUX4aaUxTY/AFc2qOOF385beVoG1tt8hJWT6fTMWrUKAAKFixIWFgYs2bNkiLIimlaCIWFhTFs2DDGjRvH8ePHadCgAS1atCAiIiLT5//xxx9069aN3r17888//7B69WoOHz5Mnz59cjlzIWDmzgsZukH9pRtkGQ7MhKNL1LECxaFzGDgW0CQlkXd06NCB7777juPHjxMYGKh1OuI5aVoITZ06ld69e9OnTx+qVKnCtGnT8PX1Zfbs2Zk+/+DBg5QpU4ahQ4fi5+dH/fr16devH0eOHMnlzEV+d/1+ImuOXlXFgmuXopib/FWouX9/ha0fq2N2ztB5JbiX0CYnYbWOHTumGgv00IgRIyhXTiZF5AWajRFKSUnh6NGjjBkzRhVv1qwZ+/fvz/SYunXrMm7cODZv3kyLFi24ffs2a9asoVWrVo89T3JyMsnJyabHsbGxAOj1evR6/eMOE7nk4TWwtmsxY/tZ9Ib/ukEOdjb0rlvK6j6PR1nrtVC59Td2a3qjQ1GFU9vMRCn2MljJ55YnroWVUxSFWbNm8eGHH5KSkkKTJk3o2bOn1mnlazn186BZIXT37l0MBgNeXl6quJeXFzdv3sz0mLp16xISEkJQUBBJSUmkpqbSpk0bfvzxx8eeZ8qUKUyalHFg5M6dO2V6owXZtm2b1ik8s+hkWHXcFvhvO4ZXPVM5+scO7ZIyI2u6Fo9y1N/ntX8nYq+PV8VPeXfg3CU7uLRZo8yyz1qvhbWLi4tjxowZHDx40BSbMWMGxYoVQyfbsGgmISEhR15X81lj6b+pFEV57DfaqVOnGDp0KJ988gnNmzcnMjKSUaNG0b9/fxYuXJjpMWPHjmXEiBGmx7Gxsfj6+tK4cWOKFClivk9EZIter2fbtm00bdoUe3t7rdN5JhM2nsKg/DdI2sHOhi+6voaXld8Ws8ZrYaJPwHbZ29joo1Vh48tBVHhrBhWs7M3Lqq+FlTt06BDDhg3j8uXLplibNm346aefcHV11S4xkWMTozQrhDw9PbG1tc3Q/bl9+3aGLtFDU6ZMoV69eqYR+1WrVsXV1ZUGDRowefJkvL29Mxzj6OiIo2PGNV3s7e3lF4wFsZbrceN+ImuO3lDFOr/iS8kiBTXKyPys5VqYGI2wbghEHlfHS9XB5u0fsbHiPcSs7lpYMUVR+P777/nwww9JTU0FoHDhwixcuBAbGxtcXV3lWmgsp77+mg2WdnBwICAgIEPrd9u2bdStWzfTYxISErCxUadsa5s2DVZRlMwOEcKsZu+6QIrBaHrsYGvDgEayRYOmdn0Bp35WxwqXgaAQsJOFLcXTRUVF0aZNG0aOHGkqgurWrUt4eDitW7fWODuR0zSdNTZixAgWLFjAokWLOH36NMOHDyciIoL+/fsDabe1unXrZnr+W2+9xdq1a5k9ezYXL15k3759DB06lFq1auHj46PVpyHyiciYRMIOq2eKdarlS3F3674lZtVOhMGeb9QxR/e0jVRd5da3eDYffPABv/zyi+nxhx9+yK5duyhVqpSGWYncoukYoaCgIKKiovj000+JjIzkpZdeYvPmzZQuXRqAyMhI1ZpCPXr04MGDB8yYMYORI0dSqFAhXn/9db766iutPgWRj8zJtBsk02c1E3EQNgxWx3S2ELgEilbSJCVhnb766it+++039Ho9y5Yt480339Q6JZGLNB8sPXDgQAYOHJjpx5YsWZIhNmTIEIYMGZLDWQmhdjMmiZWH1N2goFd88XZ31iijfC76EoQGgyFFHW/5DZR7XZuchNVIPymnWLFi/Pzzz/j4+FCihKw1ld9ovsWGENZgzm51N8jeVifdIK0kxcCKIEhIN4Ok9gB4pbc2OQmrsWfPHl599VXu3Lmjir/yyitSBOVTUggJ8RS3YpNYcUi97UtgTV98Ckk3KNcZUmF1D7j7rzpeoRk0/1yTlIR1MBgMTJ48mcaNG3Po0CG6d++O0Wh8+oEiz9P81pgQlm72rgukpKq7QQMby0wxTWwZAxfSLVxZ7AVov1A2UhWPdevWLd59911+//13Uyw5OZm4uDjc3Nw0zExYAukICfEEt2OTWJmuG9Sxpi8lpBuU+/6cC4fnq2OuRSE4DJzkzUxkbseOHVSrVs1UBNnY2DBp0iS2bt0qRZAApCMkxBPN2X2R5PTdIBkblPvObUvrBj3K1hE6rYRCMsVZZGQwGPj000/57LPPTOvMeXt7s2LFCho1aqRtcsKiSCEkxGPcjk0i5M8rqliHAF9KFpY96nLVrVOwuico6cZztJ0Fvq9ok5OwaDdu3KBLly7s2rXLFGvWrBnLli2jWLFi2iUmLJLcGhPiMebuUXeD7GykG5Tr4u6kzRBLeaCONxoLL3fQJidh8bZv324qgmxtbfniiy/49ddfpQgSmZKOkBCZuP0gs25QSXw9pBuUa/RJaWsFxajHaPFSB2j4oTY5Cavw7rvvsm3bNnbs2EFoaCj169fXOiVhwaQQEiIT83ZfJEmv7gYNkpliuUdR4OdBcO2QOl6yFrw9E6xsN3mRs2JiYnB3dzc91ul0zJo1i6SkJDw9PTXMTFgDuTUmRDp3HiSzPF03qH0N6Qblqt1fw99r1DH3UtApBOxlbzfxn82bN1OuXDnWrl2rihcoUECKIPFMpBASIp35e9XdIFvpBuWuk2vSdpR/lEPBtGnyBWSMh0ij1+sZPXo0rVq1Iioqil69enHp0iWt0xJWSG6NCfGIu3HJLD1wWRVrX6MEpYpINyhXXD0M69PtPaizgY6LwesFbXISFufKlSt06tSJgwcPmmINGzZU3R4T4llJR0iIR8zfk7EbNLhxBQ0zykfuR0BoZzAkq+NvfgkVmmqTk7A4P//8M/7+/qYiyN7enmnTprF+/Xo8PDw0zk5YI+kICfH/ouKSWXpAPTbonerSDcoVSbFp0+Tj1Rth8kofqPWeNjkJi5KSksLo0aP54YcfTDE/Pz/CwsJ45RVZT0pknxRCQvy/eXsvkqg3mB6ndYNkbFCOMxrgf73h9il1vNzr8OZXMkNMcPnyZTp27MiRI0dMsfbt27NgwQIKFSqkXWIiT5BbY0IA0fEpLEvXDWrrX4Iynq4aZZSPbP0Yzm1VxzwrQYfFYCt/qwmws7MzDYR2cHBg5syZrF69WoogYRZSCAlB2kyxhJT/ukE2Ohj8unSDctzhhXBwljrmUiRthphzIU1SEpanZMmS/PTTT1SsWJGDBw8ycOBAdNIpFGYihZDI96LjU/hp/2VVrG31EvhJNyhnXdgBm0epY7YOEBQCHn7a5CQswvnz54mJiVHFWrVqxd9//0316tU1ykrkVVIIiXxvQSbdoCGvy0yxHHXnX1jVAxSDOt7mRyhdR5OUhGUIDQ2lRo0a9O3b17Rr/EP29vYaZSXyMimERL52L5Nu0Nv+0g3KUfFRsCIQktV/8dPgA6jWSZuchOYSExPp168fnTt35sGDB6xevZply5ZpnZbIB2QkosjXFvxxkXgZG5R7UpMh7F24d1kdf+FtaDxOk5SE9s6cOUNgYCAnT540xbp27Uq7du00zErkF9IREvnW/YQUftqvninWppoP5YoW0CijPE5RYOP7ELFfHfepAW3ngI38OsqPli1bRs2aNU1FkLOzM4sWLeKnn36iQAH5WRQ5TzpCIt9a+Mcl4pJTTY91OhgsY4Nyzh9T4cRKdcytBHReCQ6yaGV+Ex8fz+DBg1myZIkp9sILL7B69WpeeEG2UxG5RwohkS/dT0hh8b7Lqlibaj6ULyZ/geaIUz/D9k/VMXtX6BwKBYtrk5PQzN27d2nYsCGnTv23iGavXr348ccfcXGRoljkLulFi3xpUSbdoCEyNihnXD8Ga/ulC+qg/QLwrqpJSkJbRYoUoWLFigC4urqybNkyFi5cKEWQ0IR0hES+E5Ogz9ANal3Vh/LFCmqTUF4Wcx1WdobURHW82WdQuaU2OQnN6XQ6Fi1ahMFg4JtvvqFSpUpapyTyMSmERL6zcN8lHqTrBg2VbpD5JcfByiCIu6mO1+gOdQZrk5PQxF9//cW9e/do2LChKVa4cGE2bNigYVZCpJFbYyJfiUnUs3jfJVWs1cveVPCSbpBZGQ2wti/cPKmO+70Grb6TjVTzCUVRmDt3LrVq1aJjx47cuHFD65SEyEAKIZGvLN53iQdJ6bpBb8hMMbP7fSL8u1kdK1IeApeCrawOnB/ExsbSuXNn+vfvT3JyMnfu3OHzzz/XOi0hMpBbYyLfiEnUs/APdTeo5cveVJRukHkdWwr7p6tjToUgeBU4F9YkJZG7jh07RmBgIBcuXDDFBg8ezDfffKNhVkJkTjpCIt9Ysu+yqhsEMFTWDTKvS3vgl+HqmI09BC2HIuW0yUnkGkVRmDFjBnXq1DEVQe7u7qxZs4Yff/wRJycnjTMUIiPpCIl8ITZJz8I/LqpiLV8uTqXi0g0ym7vnIawrGNXFJm9NA78GmqQkcs/9+/fp3bs3a9euNcVeeeUVwsLC8PPz0zAzIZ5MCiGRLyzZd5nY9N0gGRtkPgnRaRupJt1Xx+u9D9Xf1SQlkXuMRiONGjXixIkTptjw4cP58ssvcXBw0DAzIZ5Obo2JPO9BUsaxQS1eKk7l4m4aZZTHpKbAqm4QfUEdr9wa3pioSUoid9nY2DB27FggbVr8zz//zNSpU6UIElZBOkIiz/tp/2ViEvWqmHSDzERRYNMIuLxXHS9eFdrNk41U85GgoCBu3LhB+/btKVWqlNbpCPHM5LeUyNMeJOmZv1fdDXrzxeJU8ZZukFns/xGOL1PHCnpDcBg4uGqTk8hxBw4cYNy4cRniw4cPlyJIWB3pCIk8bemBK9INyilnNsG2T9QxO+e03eTdfLTJSeQoo9HIt99+y0cffYTBYKBKlSq8+66MARPWTTpCIs+KS05l/l71TLFmL3jxgo90g55b5An4Xx9AUcfbzQOf6pqkJHLW3bt3ad26NR9++CEGgwGAFStWoCjKU44UwrJJISTyrJ/2X+Z+gnSDzC42ElZ0An2COv7GBHihjTY5iRy1d+9e/P39+fXXX4G0TVPHjRvHhg0b0Ml2KcLKya0xkSfFJ6eyIF03qOkLXrxUwl2jjPKIlAQI7QwP0u0ZVS0Y6g/P/BhhtYxGI1OmTOGTTz7BaDQCULRoUUJCQmjatKnG2QlhHlIIiTxp6YEr3EvXDXpfukHPx2iEdf3gxnF1vHQ9eOsH2Ug1j7l16xZdu3Zl27Ztpljjxo0JCQnB29tbw8yEMC+5NSbynPjkVObtUa9p06SKdIOe287JcHqDOlbYDwKXgZ2sF5PXjBgxwlQE6XQ6Jk6cyLZt26QIEnmOdIREnrPsoHSDzC58Jez9Th1zdE/bSNW1iDY5iRw1depUduzYAaQNim7cuLHGGQmRM6QQEnlKQkoq8/aoxwa9UbkYL5eUblC2XdkPG4aoYzpbCPwJilbUJidhdoqiqAY+e3l5sXHjRnx9ffHy8tIwMyFyltwaE3nKsgNXiI5PUcXebyLdoGyLvgihXcCo7rDR6jsoJx2CvGLbtm288sorREVFqeI1a9aUIkjkeVIIiTwjs27Q65WLUbVkIW0SsnaJ92FFECRGq+OvDoKaPTVJSZhXamoqH3/8Mc2bN+fo0aP06NFD1gUS+Y7cGhN5RsjBCKLSd4NkbFD2GPSwugfcPauOV2gOzT7TJCVhXteuXSM4OJi9e//bJ85gMJCQkICrq2yPIvIP6QiJPCExxcDcdDPFGlcqSjXfQtokZM0UBX4dDRd3quPFXoQOC8HGVpu8hNls3rwZf39/UxFka2vL119/zS+//CJFkMh3pCMk8oSQP69wNy792CAZyJsdNofnwZFF6qBrsbSNVB0LapOUMAu9Xs+4ceP45ptvTLFSpUoRGhpKnTp1NMxMCO1IISSsXmKKgTm71WODGlYsir90g7LMKyYcm/Bp6qCdU9pGqoV8NclJmEdERASdOnXiwIEDplibNm1YvHgxHh4eGmYmhLbk1piweisORXA3LlkVk5li2XD7FDUvz0KnGNXxtrOhZE1tchJms337dlMRZG9vz/fff8/69eulCBL5nnSEhFVL0huYs1s9Nui1ikWpUaqwRhlZqbjb2IUFozMmqeONx8FL7bTJSZhVjx49+P3339m/fz+rVq3ilVde0TolISyCFELCqq34M4I7D9J1g2SmWNboEyE0GF3sNXX85UB4bZQ2OYnndu/ePQoX/u8PAp1Ox5w5czAYDBQqVEi7xISwMHJrTFitzLpBDSp4ElBaukHPTFHg50Fw7bA67lsb2vwoG6laqbVr11K2bFk2bFDvDVewYEEpgoRIRwohYbVWHorgdrpu0DAZG5Q1u76Ev/+nCinupSAoBOydNEpKZFdSUhJDhgyhffv23L9/nx49enDlyhWt0xLCosmtMWGVMusG1S/vSUBpGfj5zP5aDbu/VIX0Nk4QtAL7AkU1Skpk1/nz5wkMDOT48eOmWLNmzVS3x4QQGUlHSFilsMNXuRUrM8Wy7eqhtFtij1B0NhzxGwxFK2uUlMiusLAwatSoYSqCHB0dmTt3LitXrsTNzU3j7ISwbNIRElYnSW9g1q7zqli98kV4pYx0g57JvSuwsjMY1IWksekX3L7jo1FSIjsSExMZPnw4c+fONcUqVarEqlWrqFq1qoaZCWE9pCMkrM6qI5l0g96QVaSfSVJs2kaqCXfV8VrvYXyljzY5iWw5f/48r776qqoIevfddzly5IgUQUJkgRRCwqokpxqYtVM9NqhuuSLU8pNu0FMZUmFNL7hzWh0v9wY0n6JNTiLbHBwcuHr1KgDOzs4sXLiQpUuXUqBAAY0zE8K6SCEkrMqqw1e5Gate9E/WDXpGW8fB+W3qWNHK0HEx2MpdcmtTqlQpfvrpJ1544QUOHz5Mr1690MlyB0JkmRRCwmokpxqYtUvdDXq1rAe1yxbRKCMrcmg+/DlHHXPxTNtI1cldm5xElpw+fZoHDx6oYm+99RYnTpzgxRdf1CgrIayfFELCaqw+co3ImPTdIBkb9FTnf4dfP1THbB2g0wooXEaTlMSzUxSFxYsXExAQQL9+/VAURfVxOzvp5gnxPDQvhGbNmoWfnx9OTk4EBASwd+/eJz4/OTmZcePGUbp0aRwdHSlXrhyLFi3KpWyFVtLGBqlnitX286BOOekGPdHtM7C6JygGdfztmVCqtjY5iWcWFxdH9+7d6dWrF4mJiaxcuZKwsDCt0xIiT9H0T4mwsDCGDRvGrFmzqFevHnPnzqVFixacOnWKUqVKZXpMYGAgt27dYuHChZQvX57bt2+Tmpqay5mL3Lbm6DVupO8GybpBTxZ/F1YEQnKsOv7aaKgaqE1O4pldvnyZ0aNHc/bsWVOsX79+vP322xpmJUTeo2khNHXqVHr37k2fPmnTdqdNm8Zvv/3G7NmzmTIl4yyWLVu2sHv3bi5evIiHR9osoTJlyuRmykIDKanGDDPFavl5UEfGBj1eajKEdoH76bZXePEdaDRWm5zEM1EUhQULFjB69GhSUlKAtD3C5s2bR6dOnTTOToi8R7NCKCUlhaNHjzJmzBhVvFmzZuzfvz/TYzZs2EDNmjX5+uuvWbZsGa6urrRp04bPPvsMZ2fnTI9JTk4mOfm/NWdiY9P+Otbr9ej1ejN9NiK7Hl6DJ12LsMPXuH4/URUb3MhPOoGPoyjYbhiEzdWDqrDRpwaGVtPBYEj7l86zXAuRs2JjYxk4cCCrVq0yxfz9/QkJCaFChQpybTQgPxeWI6eugWaF0N27dzEYDHh5eaniXl5e3Lx5M9NjLl68yB9//IGTkxPr1q3j7t27DBw4kOjo6MeOE5oyZQqTJk3KEN+5cycuLi7P/4kIs9i2bVum8VQjfB9uC/w3LbhsQYXo03+y+UwuJWdlKt7cQJXINapYgr0Hezx6kLxt51OPf9y1EDnr/v37jB07lsjISFOsZcuW9OjRg3PnznHu3DkNsxPyc6G9hISEHHldzacbpF/3QlGUx66FYTQa0el0hISE4O6eNuV36tSpdOjQgZkzZ2baFRo7diwjRowwPY6NjcXX15fGjRtTpIjcWtGaXq9n27ZtNG3aFHt7+wwfX3XkGtHJp1SxCe1rUlcGSWdKd/pn7I6riyDFwRX7but4w+vJU6yfdi1EzlIUhdWrV7Np0ybc3d3p168fEyZMkGuhMfm5sBxRUVE58rqaFUKenp7Y2tpm6P7cvn07Q5foIW9vb0qUKGEqggCqVKmCoihcu3aNChUyDp51dHTE0dExQ9ze3l6+qS1IZtdDbzAye88lVaxm6cK8VslLFo7LzPWjsGFQuqAOXftF2Jf0f+aXkZ8N7SxdupQ+ffowZcoUzpw5I9fCgsi10F5Off01mz7v4OBAQEBAhnbjtm3bqFu3bqbH1KtXjxs3bhAXF2eKnT17FhsbG0qWLJmj+Yrct/bYNa7dU48Ner9JBSmCMhNzLW0j1VT1zDqafw6V3tQmJ/FEhw8fZs+ePaqYh4cHa9eupWzZshplJUT+o+k6QiNGjGDBggUsWrSI06dPM3z4cCIiIujfvz+QdlurW7dupucHBwdTpEgRevbsyalTp9izZw+jRo2iV69ejx0sLayT3mBkRrp1gwJKF6Z+eU+NMrJgyXGwohPE3VLHA3rAqwM1SUk8nqIoTJs2jXr16hEYGPjYMZFCiNyhaSEUFBTEtGnT+PTTT/H392fPnj1s3ryZ0qVLAxAZGUlERITp+QUKFGDbtm3cv3+fmjVr0qVLF9566y2mT5+u1acgcsi6Y9e5Gp2uG/SGdIMyMBrgf33g1kl13K8htPwW5OtlUaKjo2nbti3Dhw9Hr9dz69Ytvv76a63TEiJf03yw9MCBAxk4MPO/WpcsWZIhVrlyZRm9n8dl1g2qXqoQDSpINyiDbZ/A2V/VsSIVIPAnsJXxDJbkwIEDdOrUSfXH3ahRo/j88881zEoIofkWG0Kkt/74dSKi1dMkhzWpKN2g9I4ugQMz1DHnwmkbqToX1iQlkZHRaOSbb77htddeMxVBRYoU4ZdffuHrr7+WAbhCaEzzjpAQj0rNpBvk71uI16QbpHZxF2waqY7Z2ENQCBQpp0lKIqO7d+/SvXt3Nm/ebIrVr1+flStXygQPISyEdISERVkffoMrUepukMwUS+fuOVjVDYzpVtZ+6wcoU0+bnEQGqampNGjQwFQE6XQ6PvroI3bu3ClFkBAWRAohYTFSDUZm7FCvnlvNtxCNKhbVKCMLlBCdtpFqUow6Xn84VO+iTU4iU3Z2dnz88ccAFC1alC1btvD5559jZyeNeCEsifxECovxc/gNLqfrBg2TmWL/SU2BsK4QfVEdr9waXv9Em5zEE3Xp0oU7d+4QFBSEt7e31ukIITIhHSFhETIbG1S1pDuNKkk3CABFgU3D4cof6rh3NWg3D2zkR1lrO3fuZNy4cRniw4YNkyJICAsmHSFhETadvMmlu/Gq2DAZG/SffT/A8eXqWEFv6BwKDq7a5CQAMBgMfPbZZ3z66acoisLLL79Mp06dtE5LCPGM5M9IoTmjAjN3qW/3VC3pTuNKxTTKyMKc3gi/T1TH7F3SiiA3H01SEmkiIyNp2rQpkyZNQlEUAFavXq1xVkKIrJBCSGju2F0dl9KNDRr6unSDALgRDmvfA5RHgjpoNx98/LXJSQBp+yL6+/uzc+dOAGxsbJg8ebIUQkJYGbk1JjRlMCr8dk1dj79Uwo03qkg3iNgbsLIT6NVFIk0mQpXWmqQk0qbFT5w4kS+++MLUBfLx8WHlypW89tprGmcnhMgqKYSEpjadvMntJHXn5/03ZBVpUuLTiqAHkep49Xeh3vva5CS4du0awcHB7N271xR78803Wbp0KUWLysB+IayR3BoTmjEYlQxjg170caNJfu8GGY1pt8MiT6jjpetDq+9lI1UNDR8+3FQE2dra8tVXX7Fp0yYpgoSwYtIREprZdDKSi+lmiskO88COT+HML+qYR1kIWgZ2DtrkJACYPn06e/bswdHRkdDQUOrWrat1SkKI5ySFkNCEwagwfbt6FekXvN1o+oKXRhlZiOMh8Mf36piTOwSvAhcPbXLKx4xGIzaPrNHk7e3Npk2bKFu2LB4ecj2EyAvk1pjQxOaTkZy/HaeKDc3v3aDL+2BjuvE/NnYQuBQ8K2iTUz62YcMGatasSXR0tCpes2ZNKYKEyEOkEBK5zphJN6iyVwGa5eduUNQFCOsCRr063uo7KNtIk5Tyq5SUFEaMGMHbb7/N8ePH6dWrl2l2mBAi75FbYyLXbf47knPpukGDG5fDxiafdoMS78GKoLT/PqrOYAjooUlK+dWlS5cICgri8OHDppiNjQ1JSUk4OztrmJkQIqdkqxCKj4/nyy+/ZPv27dy+fRuj0aj6+MWLFx9zpMjvMusGebsoNM2vM8UMeljVHaLUXxMqtoCmn2qTUz61du1aevXqRUxMDAAODg589913DBo0KH/fshUij8tWIdSnTx92795N165d8fb2ll8S4plt+ecmZ2+pu0FvljTmz26QosDmD+DSbnXc62VovwBsbLXJK59JTk7mgw8+YMaMGaZYuXLlCAsLIyAgQMPMhBC5IVuF0K+//sqmTZuoV6+eufMReZjRqPDD7+rOR8ViBajqcV+bhLR2cBYcXaKOFfCC4FBwLKBJSvnN+fPnCQoK4tixY6ZYYGAg8+fPx83NTcPMhBC5JVuDpQsXLiyzJkSW/fbPTf699UAVG9y4LPmxGcS/v8Jv49QxOyfovBLcS2qTUz60Y8cOUxHk6OjInDlzCA0NlSJIiHwkW4XQZ599xieffEJCQsLTnywE/98NSjc2qKJXAZrnx5liN0/Cmt6oN1IF3pkDJeRWTG7q27cvgYGBVKxYkT///JN+/frJrX4h8pls3Rr77rvvuHDhAl5eXpQpUwZ7e3vVxx9tMwsBsPXUTc7cVHeDhr5RIf+NDXpwC1Z0Ar16RW1e/xhefEebnPKRqKgoihQpYnqs0+mYP38+Op2OggULapiZEEIr2SqE2rZta+Y0RF6W1g06r4pVKFaAli95YzCkapSVBvSJENoZYq+p41WDoMEH2uSUjyxfvpwBAwawcuVKWrdubYrLbTAh8rdsFUITJkwwdx4iD9t2+hanI2NVsSH/3w0yGDRKKrcZjbB+AFw/qo77vgptfpSNVHNQQkICQ4YMYdGiRQB0796d8PBwfH19Nc5MCGEJZEFFkaMUJeNMsfLFCtDqZW+NMtLIrinwzzp1rFBp6BQCdo7a5JQPnDp1io4dO3Lq1ClTrE2bNjLZQwhh8syFkIeHB2fPnsXT05PChQs/cUBh+r15RP617dQtTqXvBr1eHtv8NDbor1Ww52t1zNEtbSNVV09tcsoHlixZwsCBA0lMTATAxcWF2bNn061bN40zE0JYkmcuhL7//nvTYMJp06blVD4iD1GUjDPFyhV1pXVVH40y0kDEQfh5kDqms4WOi6FYZW1yyuPi4uIYNGgQS5cuNcVeeuklVq9eTeXK8jUXQqg9cyHUvXv3TP9fiMf5/fRt/rmh7gYNfaNC/ukG3bsMoV3AkKKOt/gKyjfRJKW87vTp07Rr144zZ86YYn379uWHH36QvcKEEJl67jFCiYmJ6PXqHbNlFoZI6wadVcXK5qduUFJM2kaqCXfV8dr9oVZfbXLKB5ydnYmMjASgQIECzJs3j86dO2uclRDCkmVrQcX4+HgGDx5MsWLFKFCgAIULF1b9E2LHmdv8fT2fjg0ypMLqnnDnjDpevik0+1ybnPKJMmXKsHjxYqpXr86xY8ekCBJCPFW2CqHRo0ezY8cOZs2ahaOjIwsWLGDSpEn4+Pio7suL/ElRFKalmylW1tOVt/JLN+i3sXBhuzpWtAp0WAS2MlHTnE6cOMGDB+qFOt955x0OHTpEhQoVNMpKCGFNslUIbdy4kVmzZtGhQwfs7Oxo0KABH3/8MV988QUhISHmzlFYmZ3/3ubk9RhVbPDr5bGzzda3m3X5cx4cmqeOuXhCcBg4yS1jc1EUhVmzZlGrVi0GDBiAoqi3K7Gzk4JTCPFssvXOFB0djZ+fH5A2HujhdPn69euzZ88e82UnrE5m6waVKeJCm2r5oBt07nfY8qE6ZuuYtpFq4dLa5JQHxcTEEBgYyKBBg0hJSSEkJIS1a9dqnZYQwkplqxAqW7Ysly9fBuCFF15g1apVQFqnqFChQubKTVihXf/e4cQ1dTdoyOsV8n436NYpWN0DFKM63nYW+NbSJKW86PDhw1SvXp01a9aYYu+//75qywwhhMiKbL079ezZkxMnTgAwduxY01ih4cOHM2rUKLMmKKyHoihM256xG/S2fx7vBsXdgZVBkKIeq0LDMfByB21yymMUReGHH36gXr16XLp0CYBChQqxbt06pk2bhqOjrM4thMiebN1IHz58uOn/GzduzJkzZzhy5AjlypWjWrVqZktOWJfdZ+9w4up9VWxQ4zw+NkifBGFd4H6EOv5Se2g0Rpuc8ph79+7Rq1cv1q9fb4rVrl2bsLAwSpeWW45CiOeTpUIoMTGR7du3m9rQY8eOJTk52fTxgwcPUqlSJZycnMybpbB4mc0UK13EhXeql9Aoo1ygKLBhMFz9Ux0v+Qq8PVM2UjWDa9euUb9+fa5cuWKKffDBB3zxxRfY29trmJkQIq/IUiG0dOlSfvnlF1MhNGPGDF588UXTiq1nzpzB29tb1TES+cOec3cJz2/doD3fwMnV6pi7L3RaAfayirE5+Pj48MILL3DlyhU8PDxYunQprVq10jotIUQekqV3qZCQEHr16qWKrVixgp07d7Jz506++eYb08BpkX+kzRRTryLt6+Gct7tBf/8PdqZbHNGhQNo0+QLFtMkpD7KxsWHp0qV07NiR8PBwKYKEEGaXpULo7NmzVKxY0fTYyckJG5v/XqJWrVqcOnXKfNkJq7D33F2ORdxXxYY0roB9Xu0GXTsC6weqYzqbtAUTvV7UJqc84o8//siwBIenpyerVq3C19dXo6yEEHlZlt6pYmJiVAuV3blzhzJlypgeG41G1ZghkfdltsO8r4cz79TIo92g+1dhZWdITVLHm38BFZtrk1MeYDQamTJlCo0aNSIoKIjbt29rnZIQIp/IUiFUsmRJ/v7778d+/K+//qJkyZLPnZSwHvvOR3H0yj1VbFCj8nmzG5T8IG0j1fh0b9I1e6Vtpiqy5fbt27Ro0YKPPvoIg8HAzZs3+f7777VOSwiRT2Tp3aply5Z88sknJCUlZfhYYmIikyZNknv4+UjaTDH12KCShZ1pVyMPFsNGA6zpDbf/UcfLNoYWX8sMsWzatWsX/v7+bN26FQCdTscnn3zCZ599pnFmQoj8Ikuzxj766CNWrVpFpUqVGDx4MBUrVkSn03HmzBlmzJhBamoqH330UU7lKizM/gtRHEnfDWpcHge7PNgN2joezv2mjnlWhI5LwFamcWeVwWBg8uTJfPrppxiNaatxe3l5ERISwhtvvKFxdkKI/CRLhZCXlxf79+9nwIABjBkzxrTRoU6no2nTpsyaNQsvL68cSVRYlsz2FCtRyJn2ebEbdGQRHJypjjl7pM0Qcy6kSUrW7ObNm3Tp0oUdO3aYYm+88QbLly+nePHiGmYmhMiPsryytJ+fH1u2bCE6Oprz588DUL58eTw8PMyenLBcBy5EcehytCqWJ7tBF3bCpg/UMRt76BQCHmW1ycmK6fV66tWrx8WLF4G06fGTJk1i7Nix2NraapydECI/ytYWGwAeHh7UqiWbSeZX6fcUK1HImQ4BeawbdOcsrOoOikEdb/MjlK6rTU5Wzt7enokTJ9KtWzd8fHxYsWIFDRs21DotIUQ+lu1CSORfBy5EceiSuhs0oFG5vNUNio+CFYGQHKOONxgJ/p21ySmP6Nq1K/fu3aNz584ULVpU63SEEPlcHnrnErkl/UwxH3cnOtbMQ92g1GQIexfuXVLHq7SBxh9rk5OV2rJlC+PGjcsQHzp0qBRBQgiLIB0hkSUHL0bxZ/puUOPyONrlkfEdigIbh0HEfnXc2x/emQs28rfDs9Dr9YwfP56vvvoKAH9/fzp27KhxVkIIkZH8VhdZkn6mmLe7E4F5qRv0x/dwYoU65lYCOoeCg4s2OVmZiIgIGjVqZCqCAH7++WcNMxJCiMeTQkg8sz8vRnHgYpQqNrBRubzTDTq1AbZPUsfsXdOKIDdvbXKyMhs3bqR69ers35/WUbOzs+O7775j2bJlGmcmhBCZk1tj4pml31OsuJsTga/kkY0wbxyHte+lC+qg/XzwrqpJStYkJSWFsWPHMnXqVFOsdOnShIWFUbt2bQ0zE0KIJ5NCSDyTQ5ei2X9B3Q0akFe6QbE3/n8j1UR1vOmnUFm2jHmaS5cu0alTJw4dOmSKtW3blkWLFlG4cGENMxNCiKeTW2PimfywXT1TzMvNkaC80A1KjkvbSPVBpDpevSvUHaJNTlZm+PDhpiLIwcGB6dOns3btWimChBBWQTpC4qmOXI5m3/l03aCG5XCyt/JukNGYdjvs5l/qeJkG0GqqbKT6jGbOnMm+fftwc3Nj1apVBAQEaJ2SEEI8MymExFOlHxtUrKAjnWqV0igbM9o+Ef7dpI55lIPApWDnoElK1sBoNGLzyDICJUqU4Ndff6VChQq4u7trmJkQQmSd3BoTT3T0SjR7z91VxQY0ygPdoGPLYN8P6phTIQheBS6yb97jrFq1iho1anD//n1VvGbNmlIECSGskhRC4ommpVs3qGhBRzpbezfo0l74ZZg6ZmMHQcvAs7wmKVm6xMRE+vfvT1BQECdOnKB3794oiqJ1WkII8dzk1ph4rGMR9zJ0g/pb+9igqAuwqisYU9Xx1t+D32va5GTh/v33XwIDA/nrr//GUjk7O5OSkoKjo6OGmQkhxPOTjpB4rPSrSBct6EiX2lbcDUqITttINfGeOl53KNTopk1OFi4kJISAgABTEeTs7MzChQtZtmyZFEFCiDxBOkIiU8cj7rH77B1VrN9rZa23G2TQw6puEHVeHa/UCppM1CQlS5aQkMDQoUNZuHChKValShVWrVrFSy+9pGFmQghhXpp3hGbNmoWfnx9OTk4EBASwd+/eZzpu37592NnZ4e/vn7MJ5lPpZ4p5FnCkS+3SGmXznBQFNo2Ay+m+t4q/DO3mgY2VFnc55NSpU9SqVUtVBHXv3p3Dhw9LESSEyHM0LYTCwsIYNmwY48aN4/jx4zRo0IAWLVoQERHxxONiYmLo1q0bb7zxRi5lmr+EX73Prn/V3aD+Dcvi7GClBcOBGXBsqTpWoDh0DgPHAtrkZMH27t3LP//8A4CLiwtLlixhyZIluLq6apyZEEKYn6aF0NSpU+nduzd9+vShSpUqTJs2DV9fX2bPnv3E4/r160dwcDB16tTJpUzzlx9+V68i7VnAwXq7QWc2w9bx6pidM3ReCe4ltMnJwr333nt06NCBl156iSNHjtC9e3etUxJCiByj2RihlJQUjh49ypgxY1TxZs2amXauzszixYu5cOECy5cvZ/LkyU89T3JyMsnJyabHsbGxAOj1evR6fTazz7v+uhbDznTdoN71ymCnM6LXG81+vofXIEeuxc2T2P2vDzrU07xT356FUuxlkOsPwO3btylWrJjpGqSmpjJnzhzs7OxwcXGRnxMN5OjPhcgSuRaWI6eugWaF0N27dzEYDHh5eaniXl5e3Lx5M9Njzp07x5gxY9i7dy92ds+W+pQpU5g0aVKG+M6dO3Fxccl64nncvDM2PNooLGCnUOTeKTZvPpWj5922bZtZX89Rf5+G/07EXh+vip/y7si5i7ZwcbNZz2eNFEVh27ZtLFy4kNGjR5u2xjD3tRDZJ9fCcsi10F5CQkKOvK7ms8Z06fZzUhQlQwzAYDAQHBzMpEmTqFix4jO//tixYxkxYoTpcWxsLL6+vjRu3JgiRYpkP/E86OT1GP458KcqNvCNirxT3y/HzqnX69m2bRtNmzbF3t7eTC+agO2yt7HRR6vCxpeDqPDWDCrIHmLExsYycOBAVq1aBcDs2bM5cOAA//zzj3mvhciWHPm5ENki18JyREVFPf1J2aBZIeTp6YmtrW2G7s/t27czdIkAHjx4wJEjRzh+/DiDBw8G0vY8UhQFOzs7tm7dyuuvv57hOEdHx0zXO7G3t5dv6nRm7b6keuzh6kCPemWxt8/5bxOzXQ+jEdYNgcjj6niputi8/SM2socYx48fJzAwkPPn/1tKIDAwEC8vL/755x/52bAgci0sh1wL7eXU11+zwdIODg4EBARkaDdu27aNunXrZni+m5sbJ0+eJDw83PSvf//+VKpUifDwcGrXrp1bqedJf1+P4ffTt1Wx914ri4uD5k3DrNn5OZz6WR0rXAaCloNd/l4AUFEUZs2aRZ06dUxFkJubG6tXr2bmzJk4OTlpnKEQQuQ+Td/lRowYQdeuXalZsyZ16tRh3rx5RERE0L9/fyDtttb169dZunQpNjY2GdYwKVasGE5OTrK2iRmk31PMw9WBrq9a2UyxE6Gw91t1zNE9bSNV1/x9GzQmJoY+ffqwZs0aUywgIICwsDDKlSunYWZCCKEtTQuhoKAgoqKi+PTTT4mMjOSll15i8+bNlC6d9gYcGRn51DWFxPNL6wbdUsX6NPDD1dGKukFXDsCGIeqYzhYCl0DRSpqkZCn++usv3nnnHS5evGiKvf/++3z11VeyTYYQIt/T/J1u4MCBDBw4MNOPLVmy5InHTpw4kYkTJ5o/qXxmerpVpAu72NOtThltksmO6EsQ1gUMKep4y2+gXMZxY/lNgQIFuHs3bfPcQoUKsXjxYtq2battUkIIYSE032JDaOufGzFsPZW+G1SWAtbSDUq8DyuCICHdbILaA+CV3pqkZGnKli3LggULqF27NsePH5ciSAghHiGFUD6XvhtUyMWe7nXLaJNMVhlSYXUPuPuvOl6hOTT/XJOULMGRI0eIj1evn9SxY0f27dtHmTJltElKCCEslBRC+dipG7H89o+6G9TXWrpBigK/joaLO9XxYi9Ch4X5ciNVo9HIt99+S506dRg0aFCGj9va5r+viRBCPI0UQvlY+m6Qu7M93epYyUyxQ/PgyEJ1zLUoBIeCY0FtctLQ3bt3adOmDaNGjSI1NZWffvqJjRs3ap2WEEJYPCv401/khNORsWz5R72YZZ/6fhR0soIFw85uhS3qPeqwdYROK6FQKW1y0tAff/xB586duXbtmik2duxYWrRooWFWQghhHaQjlE/9uCNjN6h7vTLaJJMVt/6BNb1ASbcB7DuzwfcVbXLSiNFoZMqUKTRq1MhUBBUtWpQtW7bwxRdfPPN+fEIIkZ/Jb8p86MzNWDafVHeDetf3w83Su0Fxt2FFJ0h5oI43+gheaq9NThq5ffs2Xbt2ZevWraZYw4YNWbFiBT4+PhpmJoQQ1kUKoXzox+3nVY/dnOzoYendIH0ShAZDTLoFNl/qAA1Ha5OTRi5fvkzdunWJjIwE0jYuHj9+POPHj5cukBBCZJH81sxn/r35gM1/R6piveuXtexukKLAz4Pg2mF1vGQteHsm5LPd5EuVKkXVqlWJjIzEy8uLkJAQ3njjDa3TEkIIqyRjhPKZ6TvOoSj/PS5oDd2g3V/B32vUMfdS0CkE7PPfRqE2NjYsXbqU4OBgwsPDpQgSQojnIB2hfOTcrQdsPqnuBvWq54e7swV3g06ugV1T1DGHghAcBgWKaZNTLvv9999xcnKifv36plixYsUICQnRMCshhMgbpCOUj0zfcT5DN6hXfT/tEnqaq4dhfbp96HQ20HExeL2gTU65KDU1lfHjx9OsWTOCgoK4c+eO1ikJIUSeI4VQPnHu1gN++euGKtbTkrtB9yMgtDMYktXxN7+ECk21ySkXXb9+nTfeeIPJkyejKAo3btxg1qxZWqclhBB5jtwayyd+TN8NcrSjdz0L7QYlxaZtpBqfrgPySh+o9Z42OeWiLVu20LVrV9OO8ba2tnz++eeMGjVK48yEECLvkUIoHzh/O46NGbpBZXB3scBukCE1bcHE26fU8XKvw5tf5ekZYnq9nvHjx/PVV1+ZYiVLliQ0NJR69eppmJkQQuRdUgjlAz+mmylWwNGCxwZt/RjOb1PHilaGjkvANu9+u169epVOnTqxf/9+U6x169YsWbKEIkWKaJiZEELkbXn3nUUAcOFOHBtPqLtBPeqWoZCLg0YZPcHhBfDnbHXMpQh0DgUnd21yygXJycnUq1ePq1evAmBnZ8eXX37JiBEj0OXhDpgQQlgCGSydx83YcR5jum5QbwvsBuku7oTN6VaItnWAoBDwsLx8zcnR0ZFJkyYBULp0afbu3cvIkSOlCBJCiFwgHaE87OKdOH4Ov66Kda9bmsKultUNKph4Hdu1X4BiUH+gzQwoXUebpHJZjx49iI+Pp0uXLhQuXFjrdIQQIt+QjlAelr4b5OpgS5/6ZbVLKDPxd6l9cSq65HQbqb42CqoFaZNTDlu3bh3jxo1TxXQ6HYMHD5YiSAghcpl0hPKoS3fjWZ+hG1TGsrpBqcnY/q8Hrinppsm/0DZtR/k8Jjk5mVGjRvHjjz8CEBAQQLt27TTOSggh8jfpCOVRP+44p+oGuTjY0qeBBXWDFAU2vo/N1YPquE8NaDsbbPLWt+aFCxeoV6+eqQgC+PXXXzXMSAghBEghlCddvhvPz+HqmWLd6pTBw5K6QXu/gxMr1TG3ktB5JTi4aJNTDlm9ejU1atTg6NGjQNrg6NmzZzNv3jyNMxNCCCG3xvKgGTvPY3ikHeTiYEvfBhY08+qf9bDjM1VIsXdFFxwKBYtrk1MOSEpKYsSIEcye/d+SABUqVGDVqlX4+/trl5gQQggTKYTymCtR8aw7rh4b1LVOaYoUcNQoo3SuH4V1/VUhBR2GtnOxK/6yRkmZ39mzZwkMDOTEiROmWHBwMHPmzKFgwYIaZiaEEOJRcmssj5mxQ90Ncra35T1LGRsUcw1WdobURFX4nxKdUCq+qVFSOWPYsGGmIsjJyYkFCxawfPlyKYKEEMLCSEcoD4mISmBtum5QN0vpBiXHwcpOEHdLFTb6d+UCTaikUVo5Zd68efj7+1OsWDFWrVrFSy+9pHVKQgghMiEdoTxkxs5zGbpBfV+zgG6Q0QBr+8LNk+q432sY3vw6T2ykajCoF4MsWbIkW7du5fDhw1IECSGEBZNCKI+4Gp3A2mPqbtC7r5bC0xK6Qb9PgH83q2NFykPgUrC11yYnM/rpp5+oUaMGMTExqniNGjVwdXXVKCshhBDPQgqhPGLmzvOkPtINcrK34b3XymmY0f87+hPs/1Edcy4MwavS/mvF4uPj6dGjBz169OCvv/6ib9++KIry9AOFEEJYDBkjlAdcjU5gzdFrqti7tUtTtKDG3aBLe2DTCHXMxh6ClkMRCyjSnsPJkycJDAzkzJkzppi7uzupqanY21t/l0sIIfIL6QjlAbN2qbtBjnY2vNdQ47FBd89DWFcwpqrjb02DMvU1SckcFEVhwYIF1KpVy1QEFShQgJCQEObPny9FkBBCWBnpCFm5a/cSWH0kXTfo1dIUK+ikUUZAQjSs6AhJ99Xxeu9D9Xc1SckcHjx4QP/+/VmxYoUpVq1aNVatWkXFihU1zEwIIUR2SUfIys3ceSFDN6iflt2g1BRY1Q2iL6rjlVvDGxM1SckcwsPDCQgIUBVBAwYM4ODBg1IECSGEFZOOkBW7fj+RNUevqmLBtUtp1w1SFNg0HC7vVceLV4V286x6I9U9e/Zw7tw5ANzc3Jg/fz6BgYEaZyWEEOJ5SSFkxWbtPI/eoO4GDWio4SDk/dPh+HJ1rKA3BIeBg3VPIx8yZAg7d+7k6tWrhIWFUa6cdQ/2FkIIkUYKISt1/X4iq46ou0Gda5WimJtG3aDTv8C2CeqYvUvabvJuPtrk9Bxu3rxJ8eL/bQCr0+n46aefcHR0xNHRAtZmEkIIYRbWe68in5u9S90NcrCzYUAjjboUkSfSVo4m3Ro67eaBT3VNUsouRVGYPn06ZcqUYevWraqPubm5SREkhBB5jBRCVujG/URWHVbPFAuuVQovLbpBsZGwohPoE9TxJhOhylu5n89zuHfvHu3bt+f9998nOTmZd999l8jISK3TEkIIkYPk1pgVmr3rAikGo+mxg60N/bUYG5SSkLaR6oMb6rh/F6g3LPfzeQ5//vknQUFBXLlyxRTr1q0bRYoU0TArIYQQOU06QlYmMiaRsMPqsUGdavlS3D2Xu0FGI6x7DyLD1fHS9aD1NKvZSFVRFL777jvq169vKoI8PDzYsGED3377LQ4ODhpnKIQQIidJR8jKzMmkG6TJ2KAdn8HpjepYYT8IXAZ21lE8REVF0aNHD3755RdTrG7duoSGhuLr66thZkIIIXKLdISsyM2YJFYeUneDgl7xxdvdOXcTCV8Bf0xVx5zc0zZSdbWOW0lHjhzB399fVQSNGTOGXbt2SREkhBD5iHSErMic3epukL2tLve7QVf2w4ah6pjOFgKXQlHrWWG5UKFCxMTEAODp6cmyZct48803Nc5KCCFEbpOOkJW4FZvEikMRqljQK774FMrFblDUBQjtAka9Ot7qOyjbKPfyMIPy5cszf/58XnvtNcLDw6UIEkKIfEoKISsxe9cFUlLTd4PK514CifdgRRAkRqvjrw6Cmj1zL49s2r9/PwkJ6in+QUFB7Ny5kxIlSmiUlRBCCK1JIWQFbscmsTJdN6hjTV9K5FY3yKCH1T0g6pw6XvFNaPZZ7uSQTQaDgcmTJ9OgQQOGDh2a4eM2Vrz/mRBCiOcn7wJWYM7uiySn6wYNzK2xQYoCm0fBxV3quNdL0H4B2NjmTh7ZcPPmTZo3b8748eMxGo0sXLiQ3377Teu0hBBCWBAphCzc7dgkQv68oop1CPClZGGX3EngzzlwdLE65loMOoeCY8HcySEbtm/fjr+/P9u3bwfSOj+ffvopTZo00TgzIYQQlkRmjVm4uXvU3SA7m1zsBp39DX77SB2zc0rbSLWQZU4xNxgMfPrpp3z22WcoStreZ97e3qxcuZKGDRtqnJ0QQghLI4WQBbv9IGM3qGPNkvh65EI36ObfsKYXKEZ1vO1sKFkz58+fDTdu3CA4OJjdu3ebYs2bN2fp0qUUK1ZMw8yEEEJYKimELNi83RdJ0qfvBuXCTLEHt9L2EEuJU8cbfwwvtcv582fD+fPnqVu3Lnfu3AHA1taWyZMnM3r0aBkQLYQQ4rHkHcJC3XmQzPJ03aD2NXKhG6RPhNBgiFGvYM3LgfDaBzl77ufg5+dHtWrVAChZsiS7du1izJgxUgQJIYR4InmXsFDz92bsBg1qnMPdIKMR1g+E60fUcd/a0OZHi95I1dbWluXLl9O9e3fCw8OpX7++1ikJIYSwAnJrzALdjUtm6YHLqli7GiUoVSSHu0G7v4R/1qpjhUpBUAjY5/Lu9k+xadMmChcuTN26dU0xLy8vlixZol1SQgghrI50hCzQ/D3qbpCtjY7BjSvk7En/WgW7v1LHHN3SNlItUDRnz50Fer2eDz74gNatWxMUFERUVJTWKQkhhLBiUghZmKi4ZJYeUI8Nalc9h7tBEX/Cz4PUMZ0NdFwMxark3Hmz6PLlyzRo0IDvvvsOgGvXrrFgwQKNsxJCCGHNpBCyMPP2XiRRbzA9trXRMfj1HBwbdO9K2uBoQ4o63uJrKG85iw+uX7+e6tWr8+effwJgb2/PDz/8wOjRozXOTAghhDWTMUIWJDo+hWXpukFt/UtQuohrzpwwKSZtI9WEu+p4rfegVt+cOWcWJScn8+GHH/LDDz+YYmXLliUsLIyaNS1zPSMhhBDWQwohCzJ/70USUtTdoCE51Q0ypKYtmHjntDpevgk0n5Iz58yiixcvEhgYyNGjR02xDh06sGDBAtzd3TXMTAghRF4hhZCFiI5P4af9l1Wxt/19KOOZQ92g3z6C87+rY0WrQIdFYKv9t0ViYiL16tXj5s2bADg6OvL999/Tv39/dBY8jV8IIYR1kTFCFmJBum6QjQ6GvJ5DM8UOzYdDc9UxF08IDgUny+i0ODs789lnnwFQoUIFDh48yIABA6QIEkIIYVba/+kvuJdJN6itfwn8cqIbdP53+PVDdczWATqtgMJlzH++59C7d2/0ej3vvvsuBQta7k73QgghrJfmHaFZs2bh5+eHk5MTAQEB7N2797HPXbt2LU2bNqVo0aK4ublRp04dfvvtt1zMNmcs+OMi8em6QTkyU+z2aVjdExSDOv72TChV2/zny4LQ0FDGjx+viul0OgYMGCBFkBBCiByjaSEUFhbGsGHDGDduHMePH6dBgwa0aNGCiIiITJ+/Z88emjZtyubNmzl69CiNGzfmrbfe4vjx47mcufncT0jhp/3qmWJtqvlQtmgB854o/i6sCITkWHW84YdQNdC858qCxMREZs6cSbdu3Zg8eTIbNmzQLBchhBD5j6aF0NSpU+nduzd9+vShSpUqTJs2DV9fX2bPnp3p86dNm8bo0aN55ZVXqFChAl988QUVKlRg48aNuZy5+Sz84xJxyammx2ndIDOPDdInpa0VdD9dgfliO2g01rznyoLTp09Tt25dtm3bZopt375ds3yEEELkP5qNEUpJSeHo0aOMGTNGFW/WrBn79+9/ptcwGo08ePAADw+Pxz4nOTmZ5ORk0+PY2LSOiF6vR6/XZyNz87mfoGfRvkuqWKuXi1O6sKP5clMUbDcMxubqn6qw0acGhlY/QGrqYw7MWcuWLWPIkCEkJCQA4OLiwvTp0+nWrZvm1yW/evh1l6+/9uRamJ/RaESv16MoSpaOS01Nxc7Ojri4OOzsZFhtTtLpdNjb22Njk3mPJqd+HjS7qnfv3sVgMODl5aWKe3l5maZMP813331HfHw8gYGPv7UzZcoUJk2alCG+c+dOXFxyeBPTp9gcYUN88n8XXIfCS7prbN58zWznqHjzZ6pE/k8VS7D3YI9HD5K37TTbeZ5VUlIS8+bNY8eOHaZYqVKlGDVqFJ6enmzevDnXcxJqj3bohLbkWpiHra0tnp6e2NvbZ+v44sWLc/HiRTNnJTKj1+u5c+cORqMxw8ce/uFsbpqXt+mnQyuK8kxTpFeuXMnEiRP5+eefKVas2GOfN3bsWEaMGGF6HBsbi6+vL40bN6ZIkSLZT/w5xSTqGffdXuC/jkyrl73p1aGq2c6hO7Ueu+PqIkhxcMW+2zre8HrRbOd5Vn///TfBwcGcOXPGFOvRowctWrSgdevW2f4lJcxDr9ezbds2mjZtKtdCY3ItzEdRFK5fv05qaire3t6P7TY86fj4+HhcXV1l+Y4cZjQaiYyMxMvLixIlSmT4eufUJtuaFUKenp7Y2tpm6P7cvn07Q5covbCwMHr37s3q1atp0uTJ+2E5Ojri6OiYIW5vb6/pL5ilu9Rjg3Q6GNa0ovlyunYUNg5Wx3Q26Dosxr6kv3nOkUWjRo0yFUEFChRg7ty5dOzYkc2bN2t+PcR/5FpYDrkWz0+v15OUlISPjw8FCmR9EsrDW2rOzs5ZLqJE1hUrVowbN26YbpM9Kqd+FjS7qg4ODgQEBGRo/W7bto26des+9riVK1fSo0cPVqxYQatWrXI6zRwRk6hncYaxQd6UL2amaeL3r8LKTpCapI43+xwqNjfPObJh0aJFFC5cmGrVqnH06FGCg4M1y0UIkT8YDGnLhTg4OGiciXgWD6/Tw+uWGzS9NTZixAi6du1KzZo1qVOnDvPmzSMiIoL+/fsDabe1rl+/ztKlS4G0Iqhbt2788MMPvPrqq6ZukrOzs1XtPbV43yUeJKm7QUPfMNNMseQHaUVQ/G11PKAnvDrAPOd4Rg8HGT5UqlQptm/fTpUqVXBycsrVXIQQ+Zvc1rIOWlwnTft8QUFBTJs2jU8//RR/f3/27NnD5s2bKV26NACRkZGqNYXmzp1LamoqgwYNwtvb2/Tv/fff1+pTyLKYRD2L/lB3g1q+7E1FLzN0g4wG+F8fuPW3Ol62EbT8Jq3iygWKojBnzhxq1KjBgwcPVB+rXr26FEFCCCEshuaDpQcOHMjAgQMz/diSJUtUj3ft2pXzCeWwJfsuE5uknrI+1FzrBm37BM5uUcc8K0LHn8A2d8YZxMTE8N5777Fq1SoA+vXrR0hIiPw1JoQQOUCn07Fu3Tratm2rdSpWS0Z+5aLYJD0L/1BPwWz1sjeVipuhG3RkMRyYoY45e0BwGDgXev7XfwZHjx4lICDAVARB2qD43LzXK4QQecXNmzcZMmQIZcuWxdHREV9fX9566y2LWXhWURQmTpyIj48Pzs7ONGrUiH/++UfrtLJM845QfvJTJt2gIW+YYU+xi7tg8wfqmI09BC0Hj7LP//pPoSgKM2bM4IMPPiAlJQUAd3d3Fi1aRLt27XL8/EII8SyMRoV7CSlZPMbIgwQ9eptks8waK+zigI3N0zvkly9fpl69ehQqVIivv/6aqlWrotfr+e233xg0aJBqGRKtfP3110ydOpUlS5ZQsWJFJk+eTNOmTfn333+tao9IKYRyyYMkPQvSjQ1q8VJxKhd3e74XvnMWVnUDY7oVot/6AcrUe77Xfgb37t2jd+/erFu3zhSrVasWoaGh+Pn55fj5hRDiWd1LSCFg8u+a5nD04yYUKZBxSZf0Bg4ciE6n49ChQ7i6upriL774Ir169XrscR9++CHr1q3j2rVrFC9enC5duvDJJ5+Ypp6fOHGCYcOGceTIEXQ6HRUqVGDu3LnUrFmTK1euMHjwYP744w9SUlIoU6YM33zzDS1btsxwHkVRmDZtGuPGjTP9wfvTTz/h5eXFihUr6NevX1a/NJqRQiiX/LT/MjGJ6uXBn3umWEJ02kaqSTHqeP3hUL3L8732M/jzzz/p1KkTly9fNsVGjhzJF198IVNVhRAim6Kjo9myZQuff/65qgh6qFChQo89tmDBgixZsgQfHx9OnjxJ3759KViwIKNHjwagS5cuVK9endmzZ2Nra0t4eLipSBo0aBApKSns2bMHV1dXTp069di1ly5dusTNmzdp1qyZKebo6EjDhg3Zv3+/FEJCLbNu0JsvFqeK93N0g1JTIOxduKd+Xaq8Ba9/kv3XzYJ9+/aZiiAPDw+WLFnCW2+9lSvnFkKIvOr8+fMoikLlypWzfOzHH39s+v8yZcowcuRIwsLCTIVQREQEo0aNMr12hQr//UEeERFB+/btefnllwEoW/bxQyseLl+T2TZZV65cyXLeWpJCKBcsPXCF+wlm7AYpCvwyHK7sU8e9/eGduZBLq58OHz6cnTt3Eh0dzcqVKylVqlSunFcIIfKyhxvDZme27Zo1a5g2bRrnz58nLi6O1NRU3Nz++6N7xIgR9OnTh2XLltGkSRM6duxIuXLlABg6dCgDBgxg69atNGnShPbt21O16pO3fcruNlmWRAqhHBaXnMr8veqZYs1f9OIFn+foBu2bBuHL1bGCPtA5FBwytlHN5fr165QoUcL0WKfTERISgrOzs2wDIISweIVdHDj68ZO3ZUrPaDTyIC6OggUKmG2w9NNUqFABnU7H6dOnszQt/uDBg3Tq1IlJkybRvHlz3N3dCQ0N5bvvvjM9Z+LEiQQHB7Np0yZ+/fVXJkyYQGhoKO+88w59+vShefPmbNq0ia1btzJlyhS+++47hgwZkuFcxYsXB9I6Q97e3qb4s2yTZWlk+nwOW3rgsnm7Qac2wO8T1TF7F+i8Ety8Mz3keRmNRr766ivKli2bYdqmm5ubFEFCCKtgY6OjSAHHLP/zcLHP1nGZ/XuWGWMeHh40b96cmTNnEh8fn+Hj9+/fz/S4ffv2Ubp0acaNG0fNmjWpUKFCprepKlasyPDhw9m6dSvt2rVj8eLFpo/5+vrSv39/1q5dy8iRI5k/f36m5/Lz86N48eKqbbJSUlLYvXv3E7fJskRSCOWg+ORU5u9Rd4OavuDFiz7Z3A7kxnFY+166oA7azQcf/+y95lPcuXOH1q1bM2bMGFJSUujSpQu3b99++oFCCCGybdasWRgMBmrVqsX//vc/zp07x+nTp5k+fTp16tTJ9Jjy5csTERFBaGgoFy5cYPr06aoZvYmJiQwePJhdu3Zx5coV9u3bx+HDh6lSpQoAw4YN47fffuPSpUscO3aMHTt2mD6Wnk6nY9iwYXzxxResW7eOv//+mx49euDi4mJ1+0jKrbEctPTAFe6l6wa9n91uUOwNWNkZUhPV8aaToErrbGb4ZHv27KFz587cuHEDSPvG79u3Lx4eHjlyPiGEEGn8/Pw4duwYn3/+OSNHjiQyMpKiRYsSEBDA7NmzMz3m7bffZvjw4QwePJjk5GRatWrF+PHjmThxIgC2trZERUXRrVs3bt26haenJ+3atWPSpElA2kangwYN4tq1a7i5ufHmm2/y/fffPzbH0aNHk5iYyMCBA7l37x61a9dm69atVrWGEIBOeTgqK5+IjY3F3d2du3fvUqRIkRw7T3xyKg2+3kl0/H+LdzWp4sWC7jWz/mIp8bC4BUSeUMervwttZph9DzGDwcCUKVOYMGECRqMRgGLFihESEkKTJlm7v/40er2ezZs307JlS7nFpjG5FpZDroX5JCUlcenSJfz8/LK1z6HRaCQ2NhY3NzezjBEST/ak6xUVFYWnpycxMTGqAeDPSzpCOWTZwSuqIgiy2Q0yGtNuh6UvgkrXh1bfm70IunXrFu+++y6///7fomOvv/46y5cvVw2IE0IIIfICKW9zQEJKxrFBTaoU4+WS2RgbtH0SnPlFHfMoB0HLwM68ixbu37+fatWqmYogGxsbJk2axNatW6UIEkIIkSdJRygHLD94hagM3aCKWX+h48vTpso/yqkQBK8CF/OP0ylSpAhxcXEAeHt7s2LFCho1amT28wghhBCWQjpCZpaQksrc3epu0OuVs9ENuvwHbBymjtnYQeBS8DTDRq2ZqFSpEnPnzqV58+aEh4dLESSEECLPk0LIzEIORmTSDcri2KCoC2nbZxjVM85oNRXKNnzODP+ze/duEhPVs9C6dOnCr7/+SrFixcx2HiGEEMJSSSFkRokpBubuuaCKNa5UlGq+hbLwIvfSNlJNvKeO1xkMAd2fP0kgNTWVjz76iEaNGjFs2LAMH7e25dGFEEKI7JJCyIxC/rzC3bh03aAmWRgbZNDDqm4QdV4dr9QSmn5qhgzh2rVrNG7cmClTpgAwb948duzYYZbXFkIIIayNFEJmkphiYE66sUGNKhXF/1m7QYoCmz+AS3vUca+X01aOtrF97hw3bdqEv78/f/zxBwB2dnZ88803MhZICCFEviWFkJmsOBTB3bhkVSxLY4MOzoKjS9SxAl4QHAqOBZ4rN71ez6hRo2jdujVRUVEAlCpVij179vDBBx/IImFCCGGldDod69ev1zoNqybvgGaQpDcwZ7d6bNBrFYtSvVThZ3uBf3+F38apY3ZOaRupupd8rtyuXLnCa6+9xrfffmuKvf322xw/fvyx+9UIIYTQ3s2bNxkyZAhly5bF0dERX19f3nrrrQybX2tl7dq1NG/eHE9PT3Q6HeHh4VqnlC2yjpAZrPgzgjsPstkNunkS1vQG0u108s5cKBHwXHmdOnWKevXqmXYqtre355tvvmHo0KEyIFoIISzY5cuXqVevHoUKFeLrr7+matWq6PV6fvvtNwYNGsSZM2e0TpH4+Hjq1atHx44d6du3r9bpZJsUQs8ps25QgwqeBJR+hm7Qg5uwohPo49Xx18fDi22fO7dKlSpRvXp1du7ciZ+fH2FhYbzyyivP/bpCCGGVjEZIjM7yMbqEB2CbAuYYRuDs8UyvM3DgQHQ6HYcOHcLV1dUUf/HFF+nVq9djj/vwww9Zt24d165do3jx4nTp0oVPPvnEtGfdiRMnGDZsGEeOHEGn01GhQgXmzp1LzZo1uXLlCoMHD+aPP/4gJSWFMmXK8M0339CyZctMz9W1a1cgrWizZlIIPaeVhyK4na4bNKzJM3SD9Ilpu8nHXlPHq3aCBiPNkputrS0hISFMmDCBr7/+mkKFCpnldYUQwiolRsM35bJ0iA2Qjc2RHm/UBXD1fOJToqOj2bJlC59//rmqCHroSb/LCxYsyJIlS/Dx8eHkyZP07duXggULMnr0aCBtrbjq1asze/ZsbG1tCQ8PNxVJgwYNIiUlhT179uDq6sqpU6coUOD5xqhaAymEnsPju0FP2f7CaIR1/eHGMXXc91VoMz3bG6n+73//o0SJErz66qummLe3N/PmzcvW6wkhhMh958+fR1EUKleunOVjP/74Y9P/lylThpEjRxIWFmYqhCIiIhg1apTptStU+O8P94iICNq3b8/LL78MQNmyZZ/n07AaMlj6OYQdvsqt2GyMDdr1BZxar44VKg2dQsDOMct5JCUlMXjwYDp06EBQUBDR0Vls/QohhLAYipI2ZjQ7YznXrFlD/fr1KV68OAUKFGD8+PFERESYPj5ixAj69OlDkyZN+PLLL7lw4b8/5ocOHcrkyZOpV68eEyZM4K+//nr+T8YKSCGUTUl6A7N2qRc+rFe+CDXLPKUbdCIM9nyjjjm6pW2k+pR2aWbOnTtH3bp1mTlzJpBW0S9dujTLryOEEMIyVKhQAZ1Ox+nTp7N03MGDB+nUqRMtWrTgl19+4fjx44wbN46UlP8W+p04cSL//PMPrVq1YseOHbzwwgusW7cOgD59+nDx4kW6du3KyZMnqVmzJj/++KNZPzdLJLfGsmnVkcy6QU9ZRTriIGwYrI7pbKHjEiiW9RZoaGgoffv2Ne0Y7+TkxPTp0+nTp0+WX0sIIfI8Z4+0MTpZYDQaefDgAQULFjTPmmvOT/ljGfDw8KB58+bMnDmToUOHZhgndP/+/UzHCe3bt4/SpUszbtx/y7FcuXIlw/MqVqxIxYoVGT58OJ07d2bx4sW88847APj6+tK/f3/69+/P2LFjmT9/PkOGDMniJ2ldpBDKhuRUA7N2qn+Y6pYrQi2/J3yDR1+C0GAwqLfgoOXXUP6NLJ0/MTGRYcOGqcb+VKpUiVWrVlG1atUsvZYQQuQbNjZZ77wbjSgGB3B1M8+ssWc0a9Ys6tatS61atfj000+pWrUqqampbNu2jdmzZ2faLSpfvjwRERGEhobyyiuvsGnTJlO3B9LeO0aNGkWHDh3w8/Pj2rVrHD58mPbt2wMwbNgwWrRoQcWKFbl37x47duygSpUqj80xOjqaiIgIbty4AcC///4LQPHixSlevLg5vxw5Sm6NZcOqw1e5GZukij1xbFBSDKzsBAlR6njt/vBK1ro3Z86coXbt2qoiqGvXrhw5ckSKICGEyCP8/Pw4duwYjRs3ZuTIkbz00ks0bdqU7du3M3v27EyPefvttxk+fDiDBw/G39+f/fv3M378eNPHbW1tiYqKolu3blSsWJHAwEBatGjBpEmTADAYDAwaNIgqVarw5ptvUqlSJWbNmvXYHDds2ED16tVp1aoVAJ06daJ69erMmTPHjF+JnKdTHo7KyidiY2Nxd3fn7t27FClSJMvHJ6caaPTNLiJj/iuE6pQtwsr3Xs38AEMqrOgIF9JtbFq+KXQOBdtnb8rFxcVRpkwZ0zYZzs7OzJw5kx49eljtAol6vZ7NmzfTsmVL0xROoQ25FpZDroX5JCUlcenSJfz8/HBycsry8UajkdjYWNzc3GQ7olzwpOsVFRWFp6cnMTExuLm5me2cclWzaPWRa6oiCOD9J60btGVMxiKo2AvQYVGWiiCAAgUKMHnyZCBtUa0jR47Qs2dPqy2ChBBCCK3JGKEsSBsbpJ4pVtvPg1fLPqaz9Oc8ODxfHXMtmtYJcspeNduvXz9sbGx49913cXFxydZrCCGEECKNdISyYM3Ra9xI1w0a1uQxM8XObYMtH6pjto7QaQUULv3UcymKwqJFi1T3dyFtXYn33ntPiiAhhBDCDKQj9IxSUo0ZZorV8vOgTrlMukG3TsHqnqAY1fG2s8C31lPPFRcXx4ABA1i+fDkAr776qmkwmhBCCCHMRzpCz2jN0Wtcv5+oig3LbKZY3B1YEQQpD9TxhmPg5Q5PPc9ff/1FQECAqQgC2Lt3b7ZyFkIIIcSTSSH0DFJSjcxMNzaoVplMukH6pLS1gmIi1PGXOkCjMU88h6IozJ07l1q1anH27FkgbfO8lStX8uWXXz735yCEEEKIjOTW2DNYeyxjN+j9JhXUs7UUJW3V6GuH1AeXfAXenvnEjVRjY2N57733CAsLM8Vq1KhBWFgY5cuXN8vnIIQQQoiMpCP0FHqDkRnpukE1Sxembvpu0O6v4eRqdczdN21wtP3j1644duyYqeh5aPDgwezfv1+KICGEECKHSUfoKdYeu8a1e+nGBjWpqO4GnVyTtqP8oxwKQnAYFCj22NdWFIXhw4ebdv91d3dn4cKFpuXOhRBCCJGzpCP0BJl1gwJKF6Ze+Ue6QVcPw/qB6gN1NmkLJnq9+MTX1+l0/PTTTxQqVIhXXnmF48ePSxEkhBDCIpQpU4Zp06aZHut0OtavX69ZPjlFCqEnWHfsOlej040NeuORsUH3IyC0MxjUu9DTfApUbJbpa+r1etXjMmXKsHPnTv744w/8/PzMlrsQQgjr9XDrpIf/ihQpwptvvslff/2lWU6RkZG0aNFCs/PnFCmEHiOzblCNUoVoUOH/dy5OioUVnSD+jvrAmr2hdr8Mr6coCtOmTSMgIIC4uDjVx/z9/XFwcDBr/kIIIazbm2++SWRkJJGRkWzfvh07Oztat26tWT7FixfH0dFRs/PnFCmEHmP98etERCeoYu8/HBtkNMD/esPtf9QHlW0MLb7KMEMsOjqatm3bMnz4cE6ePMmAAQPIZ3vdCiGEyCJHR0eKFy9O8eLF8ff358MPP+Tq1avcuZP2B/iHH35IxYoVcXFxoWzZsowfP1511+HEiRM0btyYggUL4ubmRkBAAEeOHDF9fP/+/bz22ms4Ozvj6+vL0KFDiY+Pf2w+j94au3z5MjqdjrVr19K4cWNcXFyoVq0aBw4cUB2T1XNoQQqhTKRm0g3y9y3Eaw+7QVs/hnNb1Qd5VoKOS8BWvVP0gQMH8Pf3Z8OGDaaYj4+PFEJCCCGeWVxcHCEhIZQvX54iRdLGqRYsWJAlS5Zw6tQpfvjhB+bPn8/3339vOqZLly6ULFmSw4cPc/ToUcaMGYO9fdp71MmTJ2nevDnt2rXjr7/+IiwsjD/++IPBgwdnKa9x48bxwQcfEB4eTsWKFencuTOpqalmPUdOk1ljmVgffoMrUepu0LCH6wYdXggHZ6kPcPZImyHmXMgUMhqNfPvtt3z00UcYDAYAihQpwtKlS2nZsmVOfwpCCCGeYOrUqUydOvWpz6tevTrLli1Txdq0acOxY8eeeuyIESMYMWJEtnP85ZdfKFCgAADx8fF4e3vzyy+/YGOT1sP4+OOPTc8tU6YMI0eOJCwsjNGjRwMQERHBqFGjqFy5MgAVKvy3G8I333xDcHAww4YNM31s+vTpNGzYkNmzZ+Pk9PhlXx71wQcfmLaAmjRpEi+++CLnz5+ncuXKZjtHTpNCKJ1Ug5EZO86pYtV8C9GwYlG4sBM2j1IfYOuQtlaQx38Dne/cuUP37t359ddfTbH69euzcuVKSpYsmaP5CyGEeLrY2FiuX7/+1Of5+vpmiN25c+eZjo2Njc1Wbg81btyY2bNnA2lDLGbNmkWLFi04dOgQpUuXZs2aNUybNo3z588TFxdHamoqbm5upuNHjBhBnz59WLZsGU2aNKFjx46UK1cOgKNHj3L+/HlCQkJMz1cUBaPRyKVLl6hSpcoz5Vi1alXT/3t7ewNw+/ZtKleubLZz5DQphNL5OfwGl9N3g96ogO7uWVjVHRSD+oC3pkPpOqaHe/fupVOnTty4cQNIu6f60UcfMXHiROzs5MsthBCWwM3NjRIlSjz1eZ6enhliRYsWfaZjHy1KssPV1VW1sG5AQADu7u7Mnz+f1q1b06lTJyZNmkTz5s1xd3cnNDSU7777zvT8iRMnEhwczKZNm/j111+ZMGECoaGhvPPOOxiNRvr168fQoUMznLdUqVLPnOPDW22AaUa10Wg0/dcc58hp8s78iMzGBlUr6U4jXxtYEAjJMeoDGowE/86q0MGDB01FULFixVi+fDlNmzbN0byFEEJkzbPetjIajRk6O4+O+cxNOp0OGxsbEhMT2bdvH6VLl2bcuHGmj1+5ciXDMRUrVqRixYoMHz6czp07s3jxYt555x1q1KjBP//8k6M7GOTGOcxBBks/YuNfN7h0Vz2afVjj0ujCusK9y+onv/A2NP6Y9EaOHEmLFi1o3Lgx4eHhUgQJIYTIluTkZG7evMnNmzc5ffo0Q4YMIS4ujrfeeovy5csTERFBaGgoFy5cYPr06axbt850bGJiIoMHD2bXrl1cuXKFffv2cfjwYdPtqA8//JADBw4waNAgwsPDOXfuHBs2bGDIkCFmyz83zmEO0hH6fwajwo/b1d2gqiXcaHT2c4jYr36yT3VoOwdsbLh69arqHrKNjQ2hoaG4urpia2ubG6kLIYTIg7Zs2WIad1OwYEEqV67M6tWradSoEQDDhw9n8ODBJCcn06pVK8aPH8/EiRMBsLW1JSoqim7dunHr1i08PT1p164dkyZNAtLG9uzevZtx48bRoEEDFEWhXLlyBAUFmS3/3DiHOeiUfDaPOzY2Fnd3d+7evWuagghp6wYNCwtXPff3V45Q/mS6WQVuJaDvDgwuRZk8eTKff/45W7duNX1jiqzR6/Vs3ryZli1bqu41i9wn18JyyLUwn6SkJC5duoSfn1+2Zik9vDXm5uZmmq0lcs6TrldUVBSenp7ExMQ89/irR0lHiLRu0PR0M8X6ef6dsQiyd4XOoUTGKXR5uyk7d+4EIDg4mJMnT6oKKyGEEEJYPimEgF/+usHFO/+NDXpZd5HRienXl9BB+wVs+/sW777blNu3bwNpt8IGDx5M4cKFczFjIYQQQphDvi+EDEaF6dv/6wYVJ4olTlOxNSSpnpf6+kQmLt/PF198YVoVukSJEqxcuZIGDRrkZspCCCGEMJN8XwhtOhnJhf/vBrmQxEKHbymiRKuec61UO4I/XsvevXtNsRYtWrB06dJM15gQQgghhHXI14XQo90gG4xMs5/JizbqdRh2Jb1Ah9EbiYqKAtJG4k+ZMoWRI0fKwDkhhBDCyuXrd/LNJyM5fzsOgNF2oTSzPap+QpHyeAVOJTExEUhbCXPv3r2MGjVKiiAhhLAi+WyCtNXS4jrl23dz4yPdoEDbnfS3+0X9BKdCELyKKjXqMHv2bNq0acPx48epU6dOxhcTQghhkR6u55aSkqJxJuJZPLxOubkOX769Nfb76ducux3Hqzan+NxukSm+7UIqDco44hS0HIqkbU7XrVs3unbtatpHRQghhHWws7PDxcWFO3fuYG9vn+VuvtFoJCUlhaSkJLkTkMOMRiN37tzBxcUlV/fmzLeF0Lw/LuGni2SO/ffY6wykGBQ+3JbMtD9TGNixDjP91DPBpAgSQgjro9Pp8Pb25tKlS5nuxfU0iqKQmJiIs7OzvA/kAhsbG0qVKpWrX+t8WwjduXObDQW/oZAunkv3jAStSeDwjbQdc2et3k7nP/6gfv36GmcphBDieTk4OFChQoVs3R7T6/Xs2bOH1157TVb5zgUODg653nnTvBCaNWsW33zzDZGRkbz44otMmzbtievy7N69mxEjRvDPP//g4+PD6NGj6d+/f5bP+739LMra3OR/p/T03pBITHJa3MHBgalTp1KvXr3sfkpCCCEsjI2NTba22LC1tSU1NRUnJycphPIoTW94hoWFMWzYMMaNG8fx48dp0KABLVq0ICIiItPnX7p0iZYtW9KgQQOOHz/ORx99xNChQ/nf//6X5XNXU84weHMiHVb/VwSVK1vWtFOutECFEEKIvE/TQmjq1Kn07t2bPn36UKVKFaZNm4avry+zZ8/O9Plz5syhVKlSTJs2jSpVqtCnTx969erFt99+m+VzN10az8zDetPjoHZtOHb8ODVq1Mj25yOEEEII66JZIZSSksLRo0dp1qyZKt6sWTP279+f6TEHDhzI8PzmzZtz5MgR9Hp9psc8zl+309YqcLSDuV+OY+Wa9WbdzVYIIYQQlk+zMUJ3797FYDDg5eWlint5eXHz5s1Mj7l582amz09NTeXu3bt4e3tnOCY5OZnk5GTT45iYGNP/lyusY+H3n/FS6/5ER0dnOFbkPL1eT0JCAlFRUXL/XWNyLSyHXAvLIdfCcjx8nzb3oouaD5ZOPxZHUZQnjs/J7PmZxR+aMmUKkyZNyvRjF+4pNOrxMfBxFjIWQgghhFaioqJwd3c32+tpVgh5enpia2uboftz+/btDF2fh4oXL57p8+3s7ChSpEimx4wdO5YRI0aYHt+/f5/SpUsTERFh1i+kyJ7Y2Fh8fX25evWq3JrUmFwLyyHXwnLItbAcMTExlCpVCg8PD7O+rmaFkIODAwEBAWzbto133nnHFN+2bRtvv/12psfUqVOHjRs3qmJbt26lZs2aj21ZOjo64ujomCHu7u4u39QWxM3NTa6HhZBrYTnkWlgOuRaWw9zrDGk6a2zEiBEsWLCARYsWcfr0aYYPH05ERIRpXaCxY8fSrVs30/P79+/PlStXGDFiBKdPn2bRokUsXLiQDz74QKtPQQghhBBWTNMxQkFBQURFRfHpp58SGRnJSy+9xObNmyldujQAkZGRqjWF/Pz82Lx5M8OHD2fmzJn4+Pgwffp02rdvr9WnIIQQQggrpvlg6YEDBzJw4MBMP7ZkyZIMsYYNG3Ls2LFsn8/R0ZEJEyZkertM5D65HpZDroXlkGthOeRaWI6cuhY6xdzz0IQQQgghrISmY4SEEEIIIbQkhZAQQggh8i0phIQQQgiRb0khJIQQQoh8K08WQrNmzcLPzw8nJycCAgLYu3fvE5+/e/duAgICcHJyomzZssyZMyeXMs37snIt1q5dS9OmTSlatChubm7UqVOH3377LRezzfuy+rPx0L59+7Czs8Pf3z9nE8xHsnotkpOTGTduHKVLl8bR0ZFy5cqxaNGiXMo2b8vqtQgJCaFatWq4uLjg7e1Nz549iYqKyqVs8649e/bw1ltv4ePjg06nY/369U89xizv30oeExoaqtjb2yvz589XTp06pbz//vuKq6urcuXKlUyff/HiRcXFxUV5//33lVOnTinz589X7O3tlTVr1uRy5nlPVq/F+++/r3z11VfKoUOHlLNnzypjx45V7O3tlWPHjuVy5nlTVq/HQ/fv31fKli2rNGvWTKlWrVruJJvHZedatGnTRqldu7aybds25dKlS8qff/6p7Nu3Lxezzpuyei327t2r2NjYKD/88INy8eJFZe/evcqLL76otG3bNpczz3s2b96sjBs3Tvnf//6nAMq6deue+HxzvX/nuUKoVq1aSv/+/VWxypUrK2PGjMn0+aNHj1YqV66sivXr10959dVXcyzH/CKr1yIzL7zwgjJp0iRzp5YvZfd6BAUFKR9//LEyYcIEKYTMJKvX4tdff1Xc3d2VqKio3EgvX8nqtfjmm2+UsmXLqmLTp09XSpYsmWM55kfPUgiZ6/07T90aS0lJ4ejRozRr1kwVb9asGfv378/0mAMHDmR4fvPmzTly5Ah6vT7Hcs3rsnMt0jMajTx48MDsG+zlR9m9HosXL+bChQtMmDAhp1PMN7JzLTZs2EDNmjX5+uuvKVGiBBUrVuSDDz4gMTExN1LOs7JzLerWrcu1a9fYvHkziqJw69Yt1qxZQ6tWrXIjZfEIc71/a76ytDndvXsXg8GQYfd6Ly+vDLvWP3Tz5s1Mn5+amsrdu3fx9vbOsXzzsuxci/S+++474uPjCQwMzIkU85XsXI9z584xZswY9u7di51dnvpVoansXIuLFy/yxx9/4OTkxLp167h79y4DBw4kOjpaxgk9h+xci7p16xISEkJQUBBJSUmkpqbSpk0bfvzxx9xIWTzCXO/feaoj9JBOp1M9VhQlQ+xpz88sLrIuq9fioZUrVzJx4kTCwsIoVqxYTqWX7zzr9TAYDAQHBzNp0iQqVqyYW+nlK1n52TAajeh0OkJCQqhVqxYtW7Zk6tSpLFmyRLpCZpCVa3Hq1CmGDh3KJ598wtGjR9myZQuXLl0ybRYucpc53r/z1J95np6e2NraZqjkb9++naFqfKh48eKZPt/Ozo4iRYrkWK55XXauxUNhYWH07t2b1atX06RJk5xMM9/I6vV48OABR44c4fjx4wwePBhIezNWFAU7Ozu2bt3K66+/niu55zXZ+dnw9vamRIkSuLu7m2JVqlRBURSuXbtGhQoVcjTnvCo712LKlCnUq1ePUaNGAVC1alVcXV1p0KABkydPlrsIuchc7995qiPk4OBAQEAA27ZtU8W3bdtG3bp1Mz2mTp06GZ6/detWatasib29fY7lmtdl51pAWieoR48erFixQu65m1FWr4ebmxsnT54kPDzc9K9///5UqlSJ8PBwateunVup5znZ+dmoV68eN27cIC4uzhQ7e/YsNjY2lCxZMkfzzcuycy0SEhKwsVG/ddra2gL/dSNE7jDb+3eWhlZbgYdTIRcuXKicOnVKGTZsmOLq6qpcvnxZURRFGTNmjNK1a1fT8x9Ovxs+fLhy6tQpZeHChTJ93kyyei1WrFih2Nn9X3v3HxNlHccB/H0gHPdDgrDkBOQClKCg+CHNtQLzjMtcxxxy0zMgYdJKB4jh2MI/YEVnAg5GNJs7LrP44cwZUYbFjwMnFNxWwqlwHl4yypVT6Ijf3/5wPnmKCGUSd5/Xxsb3+zzf7/P5Pt/B89nzfO+eRaysrIwNDAxwP9euXZuvIdiUuc7H7ehTY/fPXOdiaGiIeXt7s/j4eNbV1cWamprYihUrWGpq6nwNwWbMdS40Gg1btGgR++CDD5jRaGQtLS0sMjKSRUVFzdcQbMbQ0BDT6/VMr9czAKyoqIjp9Xruqwz+q+u3zSVCjDFWVlbGfH19mbOzMwsPD2dNTU3ctqSkJBYdHW21f2NjIwsLC2POzs5MKpWy8vLyBxyx7ZrLXERHRzMAd/wkJSU9+MBt1Fz/Nm5FidD9Nde5MBgMTCaTMYFAwLy9vdmuXbvY8PDwA47aNs11LkpKSlhwcDATCARMIpEwlUrFLl++/ICjtj0NDQ0zXgP+q+s3jzG6l0cIIYQQ+2RTa4QIIYQQQuaCEiFCCCGE2C1KhAghhBBitygRIoQQQojdokSIEEIIIXaLEiFCCCGE2C1KhAghhBBitygRIoSQaRw8eBA+Pj5wcHDAgQMH5jucOeHxeDh+/Ph8h0HIgkCJECELRHJyMng8Hng8HpycnODn54fdu3fDYrHMd2j3JJVKF1QyMTg4iB07dmDPnj3o7+/H9u3b5zskQsh/xKbePk+IrZPL5dBoNBgfH4dOp0NqaiosFgvKy8vn3BdjDJOTk1i0iP4N3M5sNmN8fBwvv/wyvU2cEBtHd4QIWUD4fD48PT3h4+ODLVu2QKVScY9AGGPYt28f/Pz8IBAI8NRTT+Ho0aNc28bGRvB4PJw8eRKRkZHg8/nQ6XSYmpqCWq1GQEAA+Hw+li9fjnfeeYdr19/fD6VSCXd3d3h4eEChUKCvr4/bnpycjLi4OOzfvx8SiQQeHh548803MT4+DgCIiYnBpUuXkJmZyd3RAoDff/8dmzdvhre3N4RCIUJCQvDZZ59ZjXdoaAgqlQoikQgSiQTFxcWIiYlBRkYGt8/Y2Biys7Ph5eUFkUiEZ555Bo2NjTOeR7PZDIVCAbFYDFdXVyQkJODXX38FAFRUVCAkJAQA4OfnBx6PZzXeW4+7Y8cOSCQSuLi4QCqVoqCggNteVFSEkJAQiEQi+Pj44I033rB6e3xFRQXc3NxQW1uLwMBACIVCxMfHw2KxQKvVQiqVwt3dHTt37sTk5CTXTiqVIj8/H1u2bIFYLMayZctQWlo643jvNYeE2DNKhAhZwAQCAZdwvP3229BoNCgvL0dXVxcyMzOxdetWNDU1WbXJzs5GQUEBDAYDQkNDkZOTA7VajdzcXHR3d+PTTz/F0qVLAQDDw8NYs2YNxGIxmpub0dLSArFYDLlcjrGxMa7PhoYGGI1GNDQ0QKvVoqKiAhUVFQCAY8eOwdvbG3l5eRgYGMDAwAAAYGRkBBEREaitrcXZs2exfft2vPrqq2hra+P63bVrF1pbW3HixAnU19dDp9Ohs7PTajyvvfYaWltbUVlZiR9//BGbNm2CXC5HT0/PtOeMMYa4uDhcvXoVTU1NqK+vh9FohFKpBAAolUqcOnUKANDe3o6BgQH4+Pjc0U9JSQlOnDiB6upqnD9/Hp988gmkUim33cHBASUlJTh79iy0Wi2+++47ZGdnW/UxPDyMkpISVFZW4uuvv0ZjYyM2btyIuro61NXV4fDhwzh48KBVQgsA77//PkJDQ9HZ2YmcnBxkZmaivr5+2vHOdg4JsVv/7l2xhJAHJSkpiSkUCq7c1tbGPDw8WEJCAvvjjz+Yi4sLO336tFWblJQUtnnzZsbY3292Pn78OLd9cHCQ8fl89tFHH017zEOHDrHAwEA2NTXF1Y2OjjKBQMBOnjzJxeXr68smJia4fTZt2sSUSiVX9vX1ZcXFxfcc4/r161lWVhYXm5OTE6upqeG2X7t2jQmFQpaens4YY6y3t5fxeDzW399v1c/atWtZTk7OtMf45ptvmKOjIzObzVxdV1cXA8Da29sZY4zp9XoGgJlMprvGunPnTvbCCy9YnZuZVFdXMw8PD66s0WgYANbb28vVpaWlMaFQyIaGhri62NhYlpaWxpV9fX2ZXC636lupVLKXXnqJKwNgn3/+OWNsdnNIiD2jxQGELCC1tbUQi8WYmJjA+Pg4FAoFSktL0d3djZGREaxbt85q/7GxMYSFhVnVRUZGcr8bDAaMjo5i7dq10x6vo6MDvb29WLx4sVX9yMgIjEYjV37iiSfg6OjIlSUSCX766acZxzI5OYn33nsPVVVV6O/vx+joKEZHRyESiQAAFy9exPj4OKKiorg2Dz30EAIDA7lyZ2cnGGNYuXKlVd+jo6Pw8PCY9rgGgwE+Pj5Wd3mCg4Ph5uYGg8GAVatWzRj3TcnJyVi3bh0CAwMhl8uxYcMGvPjii9z2hoYGvPvuu+ju7sbg4CAmJiYwMjICi8XCjVEoFMLf359rs3TpUkilUojFYqu6K1euWB179erVd5Tvthh9tnNIiL2iRIiQBWTNmjUoLy+Hk5MTli1bBicnJwCAyWQCAHz55Zfw8vKyasPn863KNy/CwI1HazOZmppCREQEjhw5cse2Rx55hPv9Zhw38Xg8TE1Nzdh3YWEhiouLceDAAW4tTUZGBve4hjHG9XWrm/U343N0dERHR4dVIgbAKpm4vf3tfc5Ufzfh4eEwmUz46quvcOrUKSQkJEAmk+Ho0aO4dOkS1q9fj9dffx35+fl4+OGH0dLSgpSUFO5RJjD9efsn5/LmftOZ7RwSYq8oESJkARGJRAgICLijPjg4GHw+H2azGdHR0bPub8WKFRAIBPj222+Rmpp6x/bw8HBUVVXh0Ucfhaur6z+O29nZ2WrBLwDodDooFAps3boVwI0Ldk9PD4KCggAA/v7+cHJyQnt7O3f3ZnBwED09PdwYw8LCMDk5iStXruC5556bVSzBwcEwm834+eefuX67u7tx/fp17tiz5erqCqVSCaVSifj4eMjlcly9ehU//PADJiYmUFhYCAeHG0sxq6ur59T3TM6cOXNH+fHHH5923/s1h4TYKlosTYgNWLx4MXbv3o3MzExotVoYjUbo9XqUlZVBq9XetZ2Liwv27NmD7OxsfPzxxzAajThz5gwOHToEAFCpVFiyZAkUCgV0Oh1MJhOampqQnp6Oy5cvzzo+qVSK5uZm9Pf347fffgMABAQEoL6+HqdPn4bBYEBaWhp++eUXqzElJSXhrbfeQkNDA7q6urBt2zY4ODhwdz9WrlwJlUqFxMREHDt2DCaTCd9//z3UajXq6uqmjUUmkyE0NBQqlQqdnZ1ob29HYmIioqOjrR4b3ktxcTEqKytx7tw5XLhwATU1NfD09ISbmxv8/f0xMTGB0tJSXLx4EYcPH8aHH344677vpbW1Ffv27cOFCxdQVlaGmpoapKenT7vv/ZpDQmwVJUKE2Ij8/Hzs3bsXBQUFCAoKQmxsLL744gs89thjM7bLzc1FVlYW9u7di6CgICiVSm5NilAoRHNzM5YvX46NGzciKCgI27Ztw59//jmnuwt5eXno6+uDv78/9zgmNzcX4eHhiI2NRUxMDDw9PREXF2fVrqioCKtXr8aGDRsgk8nw7LPPIigoCC4uLtw+Go0GiYmJyMrKQmBgIF555RW0tbVN+0kv4O9vXXZ3d8fzzz8PmUwGPz8/VFVVzXo8wI1Hb2q1GpGRkVi1ahX6+vpQV1cHBwcHPP300ygqKoJarcaTTz6JI0eOWH20/t/KyspCR0cHwsLCkJ+fj8LCQsTGxk677/2aQ0JsFY/d+sCdEEL+xywWC7y8vFBYWIiUlJT5DmdeSKVSZGRkWH2XEiHkn6M1QoSQ/y29Xo9z584hKioK169fR15eHgBAoVDMc2SEEFtBiRAh5H9t//79OH/+PJydnREREQGdToclS5bMd1iEEBtBj8YIIYQQYrdosTQhhBBC7BYlQoQQQgixW5QIEUIIIcRuUSJECCGEELtFiRAhhBBC7BYlQoQQQgixW5QIEUIIIcRuUSJECCGEELtFiRAhhBBC7NZfm3OITQ3CY8cAAAAASUVORK5CYII=\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week47_73_2.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.ensemble import AdaBoostClassifier\n",
|
||
"\n",
|
||
"ada_clf = AdaBoostClassifier(\n",
|
||
" DecisionTreeClassifier(max_depth=2), n_estimators=200,\n",
|
||
" algorithm=\"SAMME.R\", learning_rate=0.01, random_state=42)\n",
|
||
"ada_clf.fit(X_train, y_train)\n",
|
||
"y_pred = ada_clf.predict(X_test)\n",
|
||
"skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)\n",
|
||
"plt.show()\n",
|
||
"y_probas = ada_clf.predict_proba(X_test)\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": "4bf435d0",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent\n",
|
||
"\n",
|
||
"Gradient boosting is again a similar technique to Adaptive boosting,\n",
|
||
"it combines so-called weak classifiers or regressors into a strong\n",
|
||
"method via a series of iterations.\n",
|
||
"\n",
|
||
"In order to understand the method, let us illustrate its basics by\n",
|
||
"bringing back the essential steps in linear regression, where our cost\n",
|
||
"function was the least squares function."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6f9bf84b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The Squared-Error again! Steepest Descent\n",
|
||
"\n",
|
||
"We start again with our cost function ${\\cal C}(\\boldsymbol{y}m\\boldsymbol{f})=\\sum_{i=0}^{n-1}{\\cal L}(y_i, f(x_i))$ where we want to minimize\n",
|
||
"This means that for every iteration, we need to optimize"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bceb5dce",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"(\\hat{\\boldsymbol{f}}) = \\mathrm{argmin}_{\\boldsymbol{f}}\\hspace{0.1cm} \\sum_{i=0}^{n-1}(y_i-f(x_i))^2.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b334a5df",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We define a real function $h_m(x)$ that defines our final function $f_M(x)$ as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "df096d69",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f_M(x) = \\sum_{m=0}^M h_m(x).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f0367c24",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"In the steepest decent approach we approximate $h_m(x) = -\\rho_m g_m(x)$, where $\\rho_m$ is a scalar and $g_m(x)$ the gradient defined as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7e83582e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"g_m(x_i) = \\left[ \\frac{\\partial {\\cal L}(y_i, f(x_i))}{\\partial f(x_i)}\\right]_{f(x_i)=f_{m-1}(x_i)}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6b43e044",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"With the new gradient we can update $f_m(x) = f_{m-1}(x) -\\rho_m g_m(x)$. Using the above squared-error function we see that\n",
|
||
"the gradient is $g_m(x_i) = -2(y_i-f(x_i))$.\n",
|
||
"\n",
|
||
"Choosing $f_0(x)=0$ we obtain $g_m(x) = -2y_i$ and inserting this into the minimization problem for the cost function we have"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "5e5567eb",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"(\\rho_1) = \\mathrm{argmin}_{\\rho}\\hspace{0.1cm} \\sum_{i=0}^{n-1}(y_i+2\\rho y_i)^2.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bc4464a3",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Steepest Descent Example\n",
|
||
"\n",
|
||
"Optimizing with respect to $\\rho$ we obtain (taking the derivative) that $\\rho_1 = -1/2$. We have then that"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "74a990d2",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"f_1(x) = f_{0}(x) -\\rho_1 g_1(x)=-y_i.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "11ac33af",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"We can then proceed and compute"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "31fad8d3",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"g_2(x_i) = \\left[ \\frac{\\partial {\\cal L}(y_i, f(x_i))}{\\partial f(x_i)}\\right]_{f(x_i)=f_{1}(x_i)=y_i}=-4y_i,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "664e354f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"and find a new value for $\\rho_2=-1/2$ and continue till we have reached $m=M$. We can modify the steepest descent method, or steepest boosting, by introducing what is called **gradient boosting**."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bdcc9bb0",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Gradient Boosting, algorithm\n",
|
||
"\n",
|
||
"Steepest descent is however not much used, since it only optimizes $f$ at a fixed set of $n$ points,\n",
|
||
"so we do not learn a function that can generalize. However, we can modify the algorithm by\n",
|
||
"fitting a weak learner to approximate the negative gradient signal. \n",
|
||
"\n",
|
||
"Suppose we have a cost function $C(f)=\\sum_{i=0}^{n-1}L(y_i, f(x_i))$ where $y_i$ is our target and $f(x_i)$ the function which is meant to model $y_i$. The above cost function could be our standard squared-error function"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "91ea379e",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"C(\\boldsymbol{y},\\boldsymbol{f})=\\sum_{i=0}^{n-1}(y_i-f(x_i))^2.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "191fcbc6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"The way we proceed in an iterative fashion is to\n",
|
||
"1. Initialize our estimate $f_0(x)$.\n",
|
||
"\n",
|
||
"2. For $m=1:M$, we\n",
|
||
"\n",
|
||
"a. compute the negative gradient vector $\\boldsymbol{u}_m = -\\partial C(\\boldsymbol{y},\\boldsymbol{f})/\\partial \\boldsymbol{f}(x)$ at $f(x) = f_{m-1}(x)$;\n",
|
||
"\n",
|
||
"b. fit the so-called base-learner to the negative gradient $h_m(u_m,x)$;\n",
|
||
"\n",
|
||
"c. update the estimate $f_m(x) = f_{m-1}(x)+h_m(u_m,x)$;\n",
|
||
"\n",
|
||
"4. The final estimate is then $f_M(x) = \\sum_{m=1}^M h_m(u_m,x)$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8257c200",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Gradient Boosting, Examples of Regression"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"id": "97cc442d",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Max depth: 1\n",
|
||
"Error: 0.5069860830630872\n",
|
||
"Bias^2: 0.28951491799791806\n",
|
||
"Var: 0.21747116506516934\n",
|
||
"0.5069860830630872 >= 0.28951491799791806 + 0.21747116506516934 = 0.5069860830630875\n",
|
||
"Max depth: 2\n",
|
||
"Error: 0.5222413718621189\n",
|
||
"Bias^2: 0.28962869031035515\n",
|
||
"Var: 0.23261268155176382\n",
|
||
"0.5222413718621189 >= 0.28962869031035515 + 0.23261268155176382 = 0.5222413718621189\n",
|
||
"Max depth: 3\n",
|
||
"Error: 0.522240032475565\n",
|
||
"Bias^2: 0.2896287710119233\n",
|
||
"Var: 0.2326112614636416\n",
|
||
"0.522240032475565 >= 0.2896287710119233 + 0.2326112614636416 = 0.5222400324755649\n",
|
||
"Max depth: 4\n",
|
||
"Error: 0.5222400329453616\n",
|
||
"Bias^2: 0.28962877060331055\n",
|
||
"Var: 0.2326112623420511\n",
|
||
"0.5222400329453616 >= 0.28962877060331055 + 0.2326112623420511 = 0.5222400329453616\n",
|
||
"Max depth: 5\n",
|
||
"Error: 0.5222400329453616\n",
|
||
"Bias^2: 0.28962877060331055\n",
|
||
"Var: 0.2326112623420511\n",
|
||
"0.5222400329453616 >= 0.28962877060331055 + 0.2326112623420511 = 0.5222400329453616\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/ensemble/_gb.py:494: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
|
||
" y = column_or_1d(y, warn=True)\n",
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/ensemble/_gb.py:494: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
|
||
" y = column_or_1d(y, warn=True)\n",
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/ensemble/_gb.py:494: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
|
||
" y = column_or_1d(y, warn=True)\n",
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/ensemble/_gb.py:494: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
|
||
" y = column_or_1d(y, warn=True)\n",
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/ensemble/_gb.py:494: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
|
||
" y = column_or_1d(y, warn=True)\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week47_92_2.png"
|
||
}
|
||
},
|
||
"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.ensemble import GradientBoostingRegressor\n",
|
||
"import scikitplot as skplt\n",
|
||
"from sklearn.metrics import mean_squared_error\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"maxdegree = 6\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",
|
||
"\n",
|
||
"error = np.zeros(maxdegree)\n",
|
||
"bias = np.zeros(maxdegree)\n",
|
||
"variance = np.zeros(maxdegree)\n",
|
||
"polydegree = np.zeros(maxdegree)\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n",
|
||
"\n",
|
||
"for degree in range(1,maxdegree):\n",
|
||
" model = GradientBoostingRegressor(max_depth=degree, n_estimators=100, learning_rate=1.0) \n",
|
||
" model.fit(X_train,y_train)\n",
|
||
" y_pred = model.predict(X_test)\n",
|
||
" polydegree[degree] = degree\n",
|
||
" error[degree] = np.mean( np.mean((y_test - y_pred)**2) )\n",
|
||
" bias[degree] = np.mean( (y_test - np.mean(y_pred))**2 )\n",
|
||
" variance[degree] = np.mean( np.var(y_pred) )\n",
|
||
" print('Max depth:', 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",
|
||
"plt.xlim(1,maxdegree-1)\n",
|
||
"plt.plot(polydegree, error, label='Error')\n",
|
||
"plt.plot(polydegree, bias, label='bias')\n",
|
||
"plt.plot(polydegree, variance, label='Variance')\n",
|
||
"plt.legend()\n",
|
||
"save_fig(\"gdregression\")\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e29cb10a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Gradient Boosting, Classification Example"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"id": "5e71ebb0",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"(426, 30)\n",
|
||
"(143, 30)\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[0.93333333 0.93333333 0.8 0.85714286 1. 0.92857143\n",
|
||
" 1. 0.92857143 0.92857143 0.92857143]\n",
|
||
"Test set accuracy with Gradient boosting and scaled data: 0.97\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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\n",
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"text/plain": [
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"<Figure size 640x480 with 2 Axes>"
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]
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},
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"metadata": {
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"filenames": {
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"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week47_94_2.png"
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}
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},
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"output_type": "display_data"
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},
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{
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"data": {
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"image/png": 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\n",
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||
"text/plain": [
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||
"<Figure size 640x480 with 1 Axes>"
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]
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},
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"metadata": {
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"filenames": {
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"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week47_94_3.png"
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}
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},
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"output_type": "display_data"
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},
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{
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"data": {
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"image/png": 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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week47_94_4.png"
|
||
}
|
||
},
|
||
"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",
|
||
"import scikitplot as skplt\n",
|
||
"from sklearn.ensemble import GradientBoostingClassifier\n",
|
||
"from sklearn.model_selection import cross_validate\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",
|
||
"#now scale the data\n",
|
||
"from sklearn.preprocessing import StandardScaler\n",
|
||
"scaler = StandardScaler()\n",
|
||
"scaler.fit(X_train)\n",
|
||
"X_train_scaled = scaler.transform(X_train)\n",
|
||
"X_test_scaled = scaler.transform(X_test)\n",
|
||
"\n",
|
||
"gd_clf = GradientBoostingClassifier(max_depth=3, n_estimators=100, learning_rate=1.0) \n",
|
||
"gd_clf.fit(X_train_scaled, y_train)\n",
|
||
"#Cross validation\n",
|
||
"accuracy = cross_validate(gd_clf,X_test_scaled,y_test,cv=10)['test_score']\n",
|
||
"print(accuracy)\n",
|
||
"print(\"Test set accuracy with Gradient boosting and scaled data: {:.2f}\".format(gd_clf.score(X_test_scaled,y_test)))\n",
|
||
"\n",
|
||
"import scikitplot as skplt\n",
|
||
"y_pred = gd_clf.predict(X_test_scaled)\n",
|
||
"skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)\n",
|
||
"save_fig(\"gdclassiffierconfusion\")\n",
|
||
"plt.show()\n",
|
||
"y_probas = gd_clf.predict_proba(X_test_scaled)\n",
|
||
"skplt.metrics.plot_roc(y_test, y_probas)\n",
|
||
"save_fig(\"gdclassiffierroc\")\n",
|
||
"plt.show()\n",
|
||
"skplt.metrics.plot_cumulative_gain(y_test, y_probas)\n",
|
||
"save_fig(\"gdclassiffiercgain\")\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7704ba08",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## XGBoost: Extreme Gradient Boosting\n",
|
||
"\n",
|
||
"[XGBoost](https://github.com/dmlc/xgboost) or Extreme Gradient\n",
|
||
"Boosting, is an optimized distributed gradient boosting library\n",
|
||
"designed to be highly efficient, flexible and portable. It implements\n",
|
||
"machine learning algorithms under the Gradient Boosting\n",
|
||
"framework. XGBoost provides a parallel tree boosting that solve many\n",
|
||
"data science problems in a fast and accurate way. See the [article by Chen and Guestrin](https://arxiv.org/abs/1603.02754).\n",
|
||
"\n",
|
||
"The authors design and build a highly scalable end-to-end tree\n",
|
||
"boosting system. It has a theoretically justified weighted quantile\n",
|
||
"sketch for efficient proposal calculation. It introduces a novel sparsity-aware algorithm for parallel tree learning and an effective cache-aware block structure for out-of-core tree learning.\n",
|
||
"\n",
|
||
"It is now the algorithm which wins essentially all ML competitions!!!"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8f314f34",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Regression Case"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"id": "c6b184a5",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.\n",
|
||
" from pandas import MultiIndex, Int64Index\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"[15:38:29] WARNING: /var/folders/nz/j6p8yfhx1mv_0grj5xl4650h0000gp/T/abs_eek2t0c4ro/croots/recipe/xgboost-split_1659548960591/work/src/learner.cc:576: \n",
|
||
"Parameters: { \"colsaobjective\" } might not be used.\n",
|
||
"\n",
|
||
" This could be a false alarm, with some parameters getting used by language bindings but\n",
|
||
" then being mistakenly passed down to XGBoost core, or some parameter actually being used\n",
|
||
" but getting flagged wrongly here. Please open an issue if you find any such cases.\n",
|
||
"\n",
|
||
"\n",
|
||
"Max depth: 0\n",
|
||
"Error: 0.35587778675776993\n",
|
||
"Bias^2: 0.35587778675776993\n",
|
||
"Var: 0.0\n",
|
||
"0.35587778675776993 >= 0.35587778675776993 + 0.0 = 0.35587778675776993\n",
|
||
"[15:38:29] WARNING: /var/folders/nz/j6p8yfhx1mv_0grj5xl4650h0000gp/T/abs_eek2t0c4ro/croots/recipe/xgboost-split_1659548960591/work/src/learner.cc:576: \n",
|
||
"Parameters: { \"colsaobjective\" } might not be used.\n",
|
||
"\n",
|
||
" This could be a false alarm, with some parameters getting used by language bindings but\n",
|
||
" then being mistakenly passed down to XGBoost core, or some parameter actually being used\n",
|
||
" but getting flagged wrongly here. Please open an issue if you find any such cases.\n",
|
||
"\n",
|
||
"\n",
|
||
"Max depth: 1\n",
|
||
"Error: 0.3001669239476101\n",
|
||
"Bias^2: 0.2731899981798276\n",
|
||
"Var: 0.0269769337028265\n",
|
||
"0.3001669239476101 >= 0.2731899981798276 + 0.0269769337028265 = 0.3001669318826541\n",
|
||
"[15:38:29] WARNING: /var/folders/nz/j6p8yfhx1mv_0grj5xl4650h0000gp/T/abs_eek2t0c4ro/croots/recipe/xgboost-split_1659548960591/work/src/learner.cc:576: \n",
|
||
"Parameters: { \"colsaobjective\" } might not be used.\n",
|
||
"\n",
|
||
" This could be a false alarm, with some parameters getting used by language bindings but\n",
|
||
" then being mistakenly passed down to XGBoost core, or some parameter actually being used\n",
|
||
" but getting flagged wrongly here. Please open an issue if you find any such cases.\n",
|
||
"\n",
|
||
"\n",
|
||
"Max depth: 2\n",
|
||
"Error: 0.30000279381576256\n",
|
||
"Bias^2: 0.2711099029541577\n",
|
||
"Var: 0.02889288030564785\n",
|
||
"0.30000279381576256 >= 0.2711099029541577 + 0.02889288030564785 = 0.30000278325980556\n",
|
||
"[15:38:29] WARNING: /var/folders/nz/j6p8yfhx1mv_0grj5xl4650h0000gp/T/abs_eek2t0c4ro/croots/recipe/xgboost-split_1659548960591/work/src/learner.cc:576: \n",
|
||
"Parameters: { \"colsaobjective\" } might not be used.\n",
|
||
"\n",
|
||
" This could be a false alarm, with some parameters getting used by language bindings but\n",
|
||
" then being mistakenly passed down to XGBoost core, or some parameter actually being used\n",
|
||
" but getting flagged wrongly here. Please open an issue if you find any such cases.\n",
|
||
"\n",
|
||
"\n",
|
||
"Max depth: 3\n",
|
||
"Error: 0.2999692169766251\n",
|
||
"Bias^2: 0.2710765113417533\n",
|
||
"Var: 0.028892725706100464\n",
|
||
"0.2999692169766251 >= 0.2710765113417533 + 0.028892725706100464 = 0.2999692370478538\n",
|
||
"[15:38:29] WARNING: /var/folders/nz/j6p8yfhx1mv_0grj5xl4650h0000gp/T/abs_eek2t0c4ro/croots/recipe/xgboost-split_1659548960591/work/src/learner.cc:576: \n",
|
||
"Parameters: { \"colsaobjective\" } might not be used.\n",
|
||
"\n",
|
||
" This could be a false alarm, with some parameters getting used by language bindings but\n",
|
||
" then being mistakenly passed down to XGBoost core, or some parameter actually being used\n",
|
||
" but getting flagged wrongly here. Please open an issue if you find any such cases.\n",
|
||
"\n",
|
||
"\n",
|
||
"Max depth: 4\n",
|
||
"Error: 0.2999728858924457\n",
|
||
"Bias^2: 0.2710867359084896\n",
|
||
"Var: 0.02888614870607853\n",
|
||
"0.2999728858924457 >= 0.2710867359084896 + 0.02888614870607853 = 0.2999728846145681\n",
|
||
"[15:38:29] WARNING: /var/folders/nz/j6p8yfhx1mv_0grj5xl4650h0000gp/T/abs_eek2t0c4ro/croots/recipe/xgboost-split_1659548960591/work/src/learner.cc:576: \n",
|
||
"Parameters: { \"colsaobjective\" } might not be used.\n",
|
||
"\n",
|
||
" This could be a false alarm, with some parameters getting used by language bindings but\n",
|
||
" then being mistakenly passed down to XGBoost core, or some parameter actually being used\n",
|
||
" but getting flagged wrongly here. Please open an issue if you find any such cases.\n",
|
||
"\n",
|
||
"\n",
|
||
"Max depth: 5\n",
|
||
"Error: 0.29998782047173667\n",
|
||
"Bias^2: 0.2711004934923823\n",
|
||
"Var: 0.02888733707368374\n",
|
||
"0.29998782047173667 >= 0.2711004934923823 + 0.02888733707368374 = 0.29998783056606604\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
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\n",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week47_97_2.png"
|
||
}
|
||
},
|
||
"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",
|
||
"import xgboost as xgb\n",
|
||
"import scikitplot as skplt\n",
|
||
"from sklearn.metrics import mean_squared_error\n",
|
||
"\n",
|
||
"n = 100\n",
|
||
"maxdegree = 6\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",
|
||
"\n",
|
||
"error = np.zeros(maxdegree)\n",
|
||
"bias = np.zeros(maxdegree)\n",
|
||
"variance = np.zeros(maxdegree)\n",
|
||
"polydegree = np.zeros(maxdegree)\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n",
|
||
"\n",
|
||
"for degree in range(maxdegree):\n",
|
||
" model = xgb.XGBRegressor(objective ='reg:squarederror', colsaobjective ='reg:squarederror', colsample_bytree = 0.3, learning_rate = 0.1,max_depth = degree, alpha = 10, n_estimators = 200)\n",
|
||
"\n",
|
||
" model.fit(X_train,y_train)\n",
|
||
" y_pred = model.predict(X_test)\n",
|
||
" polydegree[degree] = degree\n",
|
||
" error[degree] = np.mean( np.mean((y_test - y_pred)**2) )\n",
|
||
" bias[degree] = np.mean( (y_test - np.mean(y_pred))**2 )\n",
|
||
" variance[degree] = np.mean( np.var(y_pred) )\n",
|
||
" print('Max depth:', 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",
|
||
"plt.xlim(1,maxdegree-1)\n",
|
||
"plt.plot(polydegree, error, label='Error')\n",
|
||
"plt.plot(polydegree, bias, label='bias')\n",
|
||
"plt.plot(polydegree, variance, label='Variance')\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "59a68c8d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Xgboost on the Cancer Data\n",
|
||
"\n",
|
||
"As you will see from the confusion matrix below, XGBoots does an excellent job on the Wisconsin cancer data and outperforms essentially all agorithms we have discussed till now."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"id": "6a3f228b",
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"(426, 30)\n",
|
||
"(143, 30)\n",
|
||
"[15:38:29] WARNING: /var/folders/nz/j6p8yfhx1mv_0grj5xl4650h0000gp/T/abs_eek2t0c4ro/croots/recipe/xgboost-split_1659548960591/work/src/learner.cc:1115: Starting in XGBoost 1.3.0, the default evaluation metric used with the objective 'binary:logistic' was changed from 'error' to 'logloss'. Explicitly set eval_metric if you'd like to restore the old behavior.\n",
|
||
"Test set accuracy with Gradient Boosting and scaled data: 1.00\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/xgboost/sklearn.py:1224: UserWarning: The use of label encoder in XGBClassifier is deprecated and will be removed in a future release. To remove this warning, do the following: 1) Pass option use_label_encoder=False when constructing XGBClassifier object; and 2) Encode your labels (y) as integers starting with 0, i.e. 0, 1, 2, ..., [num_class - 1].\n",
|
||
" warnings.warn(label_encoder_deprecation_msg, UserWarning)\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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\n",
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||
"text/plain": [
|
||
"<Figure size 640x480 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
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||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week47_99_2.png"
|
||
}
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||
},
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"output_type": "display_data"
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||
},
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||
{
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||
"data": {
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||
"image/png": 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R8cb2AdBa7jKnC844mXKn6LqZswBoy12mWFy8j40ATJG77OSzk3DaP7DoupHtAfSUu2x25DdYv/9skXWlz1wBNJK7rMWfVoi6VfiL7V/eckv5HPGfunyOAMDnCJm6FXSO6BUwALSDgAtFbuKjVKlECAAkEonMcyKSW15gxYoVWLJkSek2rkCQ6hedoaNW0ctItYS6akVnxFItafF1i/mhI9UjSDWKqJtXTBauhOL3qVl0XVIv4VhVijlW7RKOVf7bCEhK2Kd2Me+NSgnHql5MvJol7FepmLq6xdRVLea9USwhXq1i3hu1EuItpkFDWquE96aYHoXF1ksv5r1RLqGuRjHHqvER741OCcdaFD5H/IvPEQD4HCGjAs4R/2QkguYRUNzvlo9UpRIhExMTJCXJvhrJyclQUlKCgYGB3Drz58+Hp6en8Dw9PR3m5kVca5dKoJBa9DtJrxVQ1MdL8q74utKsov57AYU3CsXXzStyERReSqCQJb8uvZIUGS9yUfyxZhRdV5JZwrFmF3Os6SUca1E7pRLem/Ri3pvs4o9VmllMvBklHGtuMXVfSaAgKeK9eVvMe5NXwnvzppj3JquEeItp2VZ4XcJ7U9z5r7h404p5b3JKqFvM6yR5+xHvTZoCFDSLqVvkAj5HCHX5HAGAzxEydcv5HJFDuVjxz0mg4EqoGoAsOSt+pCqVCNnZ2eHo0aMyZSdPnoStrW2R/YNUVVWhqlo4xTXTz4B5np7w3KKONura1EXekKLPKJfNn8DjdOGOkDpNDeD4pQfchwQWWfenp5ex90lEoY6QsK2NfU6/Fd8R8nDhjpBNddWBprXxalBa8R0hAwp3hKxjoQc7exvkDVlT5D6PqN7FivDCHSHVrYywuPsqLB7yR5F1vSJO4XR64Y6QsKmN0L5Xiu8Iua1wR8iGxlrQbm5a7Htz69YzTDxWuCOkvqU+ujmMR96QHUXW9U27gR0xhTtCKraujZ977cbPxXWEPHkE/0gKd4RE89qIH/Ck+I6Q2wp3hKxbVxdf2Fkjb8iyIvd5Sv8hFl4q3BFSq7khPLp6w2NI0XdRLr9/AUefF+4ICdvaONH7VPEdIXcV7ghpaaAJWBoX+948fPgSrvsLd4Q0bqSPnp3aIW/I5iLr7sm9hQ23C3eWVmlpjDU9t2JNcZ2lQ4Nx5V3hztKwro1b/aKK7yzdvnBnaT5HyOJzBJ8j3lfe5wizRoYItFwCx73fwN7eHlu3boWVlVWR2/lQEiq4tiSCN2/e4MGDBwCAVq1aYe3atejSpQv09fVRr149zJ8/HwkJCfjll18A5N8+37x5c0yaNAkTJkzApUuXMHnyZOzZs6fUd42lp6dDR0cHEn8JpKM/oGmcMcYYY+WOiJCVlQV1dXWZ8pMnT6Jr1654+/YtdHR0kJaWBm1t+X2RPoSo4wiFhYWhVatWaNWqFQDA09MTrVq1grd3fkfFxMRExMfHC+s3aNAAx48fx9mzZ9GyZUssXboUGzZsKPOt84wxxhirPFJTUzFs2DAMHToU77fP9OzZE0pKFXcBS9QWITFwixBjjDFWeZw5cwZubm5ISMgfjmHLli2YMqXwXWQF39/VqkWIMcYYYzVTdnY25s6di27duglJkJ6eHkxMiu6HVBGqVGfp8tQkqXZ+B8FiOkwyxhhjrPzduXMHLi4uCA8PF8q6du2KgIAA1K0rf9ylilJjW4Qur/IEppwUOwzGGGOsxiAibNu2Da1btxaSIGVlZaxevRohISGfPAkCanCLEGOMMcY+nXfv3mHIkCEyw+A0bdoUgYGBwk1TYqixLUKMMcYY+3RUVVVRq1Yt4fnUqVOFu8fFxC1CjDHGGPskNm/ejPv378Pb2xt9+hQ9v9unxIkQY4wxxsrdzZs38fTpU/Tq1Uso09XVxZUrV4qcH1QMNfbS2IyhB4CZtmKHwRhjjFUrUqkU69atQ5s2beDi4oInT57ILK9MSRBQgxOhX9pfA4qZH4YxxhhjZVPQAuTp6Yns7Gy8fPkSy5cvFzusYtXYRIgxxhhj5ee3336DlZUVQkJChLLZs2dj3bp1IkZVMu4jxBhjjLEPlpGRAQ8PD/j4+AhlderUwS+//ILu3buLGFnpcCLEGGOMsQ8SFhYGV1dX3Lt3TygbMGAAfHx8YGBgIGJkpceJEGOMMcbKLCsrC1999RUSExMBABoaGtiwYQPGjRtX6TpEF4f7CDHGGGOszNTU1LBlyxYAQJs2bRAREQF3d/cqlQQB3CLEGGOMsVLKzs6GioqK8Lx///44fPgwevfuDWVlZREj+3DcIsQYY4yxYqWlpcHNzQ0jR44EEcks69+/f5VNgoAa3CI09VwnoNY9YKCl2KEwxhhjlVZoaChGjhyJuLg4AEDv3r0xevRocYMqRzW2RWj5730An0ixw2CMMcYqpZycHHh7e6Nz585CEqStrQ01NTVxAytnNbZFiDHGGGPyPXjwACNHjsSVK1eEMnt7e+zevRv169cXL7AKUGNbhBhjjDEmi4jg5+eHli1bCkmQoqIili5dirNnz1a7JAjgFiHGGGOMIX9cIDc3Nxw4cEAoa9SoEQIDA9GuXTsRI6tY3CLEGGOMMaiqqiInJ0d47u7ujoiIiGqdBAE1uEWomfdyPHFJEDsMxhhjrFKQSCTw9fXFgwcPsGTJEgwaNEjskD6JGpsIPdVNA4w0xA6DMcYYE8WdO3fw7NkzODg4CGWGhoa4efMmFBRqzgWjmnOkjDHGGAMRYdu2bWjdujWGDh2KZ8+eySyvSUkQwIkQY4wxVmMkJyejX79+mDJlCjIzM5GcnIylS5eKHZaoauylMcYYY6wmOXHiBMaOHSvTAjRt2jSsWrVKxKjExy1CjDHGWDWWmZmJGTNmwNnZWUiCjI2NcezYMWzatAkaGjW7vyy3CDHGGGPVVGRkJFxdXXH79m2hzNnZGTt37kTt2rVFjKzy4ESIMcYYq4YyMzPRs2dPJCcnAwDU1NSwevVqTJ06FRKJROToKg++NMYYY4xVQ+rq6li3bh0AwNraGtevX8e0adM4CXpPjW0ROrjdHbh3AVjWSexQGGOMsXKRl5cHRUVF4bmLiwuICIMHD4aqqqqIkVVeNTYR6nbXEtBJEjsMxhhj7KNlZGTAw8MDOTk58PPzk1nm6uoqUlRVQ41NhBhjjLHqICwsDK6urrh37x6A/M7QQ4YMETmqqoP7CDHGGGNVUF5eHlasWAE7OzshCdLQ0MC7d+9Ejqxq4RYhxhhjrIqJj4+Hm5sbzp8/L5TZ2toiMDAQlpaWIkZW9dTYFqFok2dAPW2xw2CMMcbKZO/evbCyshKSIIlEAi8vL1y8eJGToA8gISISO4hPKT09HTo6OpD4SyAdLRU7HMYYY6xUMjMzMWnSJOzatUsoq1evHnbv3o1Onar/HdAF399paWnQ1i6/howa2yLEGGOMVSWqqqoy84S5uLggMjKyRiRBFYkTIcYYY6wKUFBQgL+/Pxo1aoTdu3cjMDAQurq6YodV5XFnacYYY6wSevDgAVJSUtCuXTuhrE6dOrhz5w6UlPjru7xwixBjjDFWiRAR/Pz80LJlSwwaNAipqakyyzkJKl+cCDHGGGOVRGpqKoYOHYpx48YhIyMDCQkJWLJkidhhVWucVjLGGGOVwJkzZ+Dm5oaEhAShzN3dHcuWLRMxquqPW4QYY4wxEWVnZ2Pu3Lno1q2bkATp6enhwIED8PX1hZaWlsgRVm/cIsQYY4yJ5M6dO3BxcUF4eLhQ1rVrVwQEBKBu3boiRlZz1NgWoVeePwBO+8UOgzHGWA319u1bdO7cWUiClJWVsXr1aoSEhHAS9AnV2ESIMcYYE5OGhobQ/6dp06a4evUqZs+eDQUF/mr+lPjSGGOMMfaJEBEkEonwfPz48SAijBw5EhoaGiJGVnNxIsQYY4xVsMzMTHz77bcgImzcuFEol0gkmDhxooiRMU6EGGOMsQoUGRkJV1dX3L59GwDQq1cv9O7dW+SoWIEaeyFys8MFoL+l2GEwxhirpqRSKdatW4e2bdsKSZCamhqeP38ucmTsvyRERGIH8Smlp6dDR0cHEn8JpKOlYofDGGOsGnr69CnGjBmDkJAQocza2hpBQUFo1qyZiJFVXQXf32lpadDW1i637dbYFiHGGGOsIhw+fBhWVlYySdDs2bNx5coVToIqIe4jxBhjjJWDrKwszJgxAz4+PkKZqakpAgIC0L17dxEjY8XhFiHGGGOsHCgrK+POnTvC8wEDBuDmzZucBFVynAgxxhhj5UBRURG7du2CmZkZfH19cfDgQRgYGIgdFisBXxpjjDHGPsCjR4/w8uVLtGzZUiizsLBATEwMVFVVxQuMlQm3CDHGGGNltGfPHlhbW2PgwIFIT0+XWcZJUNXCiRBjjDFWSmlpaXBzc4OLiwvS0tIQGxuLJUuWiB0W+wiiJ0JbtmxBgwYNoKamBhsbG1y4cKHY9QMDA2FtbQ0NDQ3UqVMHY8eORUpKSpn32+2OJRCW9KFhM8YYq2FCQ0PRsmVL7N69WyhzcXGBt7e3iFGxjyVqIrRv3z7MmjULXl5eCA8PR6dOneDk5IT4+Hi56//9998YNWoU3N3dcfv2bezfvx/Xrl3D+PHjy7zvgz+7A4uKT7oYY4yxnJwceHt7o3PnzoiLiwMAaGtrY/fu3QgMDISOjo64AbKPImoitHbtWri7u2P8+PFo2rQp1q9fD3Nzc2zdulXu+pcvX0b9+vUxY8YMNGjQAB07dsSkSZMQFhb2iSNnjDFWE8TExKBTp05YunQppNL82Qg6duwozB/Gqj7REqHs7Gxcv34dPXv2lCnv2bMnLl68KLdOhw4d8OTJExw/fhxEhGfPnuHAgQPFTl737t07pKenyzwYY4yxkmRkZKB9+/a4cuUKgPzb47///nucPXsW9evXFzc4Vm5ES4RevHiBvLw81K5dW6a8du3aSEqS33enQ4cOCAwMxLBhw6CiogITExPo6upi48aNRe5nxYoV0NHRER7m5ublehyMMcaqJ01NTSxcuBAA0KhRI1y8eBFeXl5QVFQUOTJWnkTvLC2RSGSeE1GhsgJRUVGYMWMGvL29cf36dQQHByM2NhaTJ08ucvvz589HWlqa8Hj8+HG5xs8YY6z6eH8e8unTp2Pt2rWIiIhA27ZtRYqKVSTRBlQ0NDSEoqJiodaf5OTkQq1EBVasWAF7e3vMmTMHAGBlZQVNTU106tQJ33//PerUqVOojqqqqtwxHQZN3IGQQWc/+jgYY4xVfdnZ2Vi4cCEUFBSwcuVKoVxBQQEeHh4iRsYqmmgtQioqKrCxsZGZnRcAQkJC0KFDB7l13r59CwUF2ZALmijfz+JLcqrJPcDWpEx1GGOMVT/R0dFo3749fvzxR6xatQpnzpwROyT2CYl6aczT0xO+vr7YuXMnoqOj4eHhgfj4eOFS1/z58zFq1Chh/b59++LQoUPYunUrHj58iNDQUMyYMQNt27aFqampWIfBGGOsCiIibN26FTY2NggPDwcAKCkpISYmRuTI2Kck6lxjw4YNQ0pKCr777jskJiaiefPmOH78OCwsLAAAiYmJMmMKjRkzBq9fv8amTZswe/Zs6OrqomvXrvjhhx/EOgTGGGNVUHJyMtzd3XHs2DGhrGnTpggKCpKZO4xVfxIq6zWlKi49PR06OjqQ+EsgHS0VOxzGGGOf2IkTJzBmzBgkJycLZVOnTsWPP/4IDQ0NESNjxSn4/k5LS4O2tna5bVf0u8YYY4yxTyErKwszZsyAs7OzkAQZGRnh6NGj2Lx5MydBNRQnQowxxmoERUVFXL58WXju7OyMW7duoU+fPiJGxcTGiRBjjLEaQVlZGYGBgTA0NMSmTZtw7NixIodrYTWHqJ2lGWOMsYry9OlTpKWloWnTpkLZZ599hri4OGhqaooYGatMamyL0LLf+wDbI8UOgzHGWAU4fPgwrKysMGjQILx9+1ZmGSdB7L9qbCI07Vwn4Ld7YofBGGOsHGVkZGDixIkYOHAgUlJSEB0dje+++07ssFglxpfGGGOMVQthYWFwdXXFvXv//sgdMGCAMC0TY/LU2BYhxhhj1UNeXh5WrFgBOzs7IQnS0NCAr68vDh48CAMDA5EjZJUZtwgxxhirsuLj4+Hm5obz588LZW3atEFgYCA+++wzESNjVQUnQowxxqqk169fw9bWFs+fPwcASCQSLFiwAIsXL4aysrLI0bGqosZeGtNd+y1wYojYYTDGGPtAtWrVwqxZswAA9erVw7lz5/D9999zEsTKhFuEGGOMVVnffvstpFIpvv76a+jq6oodDquCOBFijDFW6eXm5mLp0qVQUlLCokWLhHJFRUUsXLhQxMhYVceJEGOMsUotJiYGrq6uuHLlChQUFNC9e3fY2dmJHRarJmpsHyHGGGOVGxHB398fLVu2xJUrVwDkd4iOjORZAVj54RYhxhhjlU5qaiomTZqEAwcOCGWNGjVCYGAg2rVrJ2JkrLrhFiHGGGOVypkzZ2BlZSWTBLm7uyMiIoKTIFbuOBFijDFWKWRnZ+Pbb79Ft27dkJCQAADQ09PDgQMH4OvrCy0tLZEjZNURXxpjjDFWKUilUpw4cQJEBADo2rUrAgICULduXZEjY9VZjW0RurTKE5j0p9hhMMYY+39qamoICgqCtrY2Vq9ejZCQEE6CWIWrsS1CTZNqA/HpYofBGGM1VnJyMl6/fo1GjRoJZc2bN8ejR494cET2ydTYFiHGGGPiOXHiBFq0aIHBgwfj3bt3Mss4CWKfEidCjDHGPpnMzEzMmDEDzs7OSE5ORkREBJYtWyZ2WKwGq7GXxhhjjH1akZGRcHV1xe3bt4UyZ2dnTJs2TcSoWE1XY1uETn1+D2htInYYjDFW7UmlUqxbtw5t27YVkiA1NTVs2rQJx44dQ+3atUWOkNVkEiq4T7GGSE9Ph46ODiT+EkhHS8UOhzHGqrWnT59i9OjR+Ouvv4Qya2trBAUFoVmzZiJGxqqagu/vtLQ0aGtrl9t2+dIYY4yxCpGWloaWLVvi+fPnQtns2bOxbNkyqKqqihgZY/+qsZfGGGOMVSwdHR1MnDgRAGBqaoqQkBCsXr2akyBWqXCLEGOMsQqzePFiSKVSzJ49GwYGBmKHw1ghH9QilJubi7/++gvbt2/H69evAeRfB37z5k25BscYY6xqyMvLw4oVK7Bu3TqZcmVlZSxfvpyTIFZplblF6NGjR+jVqxfi4+Px7t079OjRA7Vq1cKqVauQlZWFbdu2VUScjDHGKqn4+Hi4ubnh/PnzUFZWxpdffolWrVqJHRZjpVLmFqGZM2fC1tYWL1++hLq6ulA+YMAAnDp1qlyDY4wxVrnt3bsXVlZWOH/+PID8KwYXL14UOSrGSq/MLUJ///03QkNDoaKiIlNuYWGBhISEcguMMcZY5ZWeno6vv/4au3btEsrq1auH3bt3o1OnTiJGxljZlLlFSCqVIi8vr1D5kydPUKtWrXIJ6lMwfaUDPH8rdhiMMVblhIaGwtraWiYJcnFxQWRkJCdBrMopcyLUo0cPrF+/XngukUjw5s0bLF68GM7OzuUZW4WK+m4BMOoPscNgjLEqIycnB97e3ujcuTPi4uIAANra2ti9ezcCAwN5slRWJZX50ti6devQpUsXNGvWDFlZWXBxccH9+/dhaGiIPXv2VESMjDHGKoHs7Gzs27cPUmn+qPwdO3bErl27UL9+fXEDY+wjlDkRMjU1RUREBPbu3Yvr169DKpXC3d0drq6uMp2nGWOMVS+ampoIDAxE586d4eXlhXnz5kFRUVHssBj7KGWea+z8+fPo0KEDlJRkc6iCOwU6d+5crgGWN2GuEv1V0G5bHzgxROyQGGOsUkpNTUVGRgbMzc1lypOTk2FsbCxSVKymqqi5xsrcR6hLly5ITU0tVJ6WloYuXbqUS1CMMcbEdebMGVhZWWHo0KHIzc2VWcZJEKtOypwIEREkEkmh8pSUFGhqapZLUJ/Cgn7HgAnWYofBGGOVSnZ2NubOnYtu3bohISEBly9fxg8//CB2WIxVmFL3ERo4cCCA/LvExowZIzNpXl5eHm7evIkOHTqUf4QVZIvDBWwaaCl2GIwxVmlER0fD1dUV4eHhQlnXrl0xevRoEaNirGKVOhHS0dEBkN8iVKtWLZmO0SoqKmjfvj0mTJhQ/hEyxhirUESE7du3w9PTE5mZmQD+nSPM09MTCgofNC0lY1VCqRMhPz8/AED9+vXxzTffVKnLYIwxxuRLTk7G+PHjcfToUaGsadOmCAwM5PnCWI1Q5tvnFy9eXBFxMMYY+8RevXoFa2trJCUlCWVTp07Fjz/+CA0NDREjY+zTKXMiBAAHDhzAr7/+ivj4eGRnZ8ssu3HjRrkExhhjrGLp6upi+PDhWL9+PYyMjLBz50706dNH7LAY+6TKfOF3w4YNGDt2LIyNjREeHo62bdvCwMAADx8+hJOTU0XEyBhjrIKsWLECM2bMwK1btzgJYjVSmQdUbNKkCRYvXowRI0agVq1aiIyMRMOGDeHt7Y3U1FRs2rSpomItFwUDMkn8JZCOloodDmOMfRJSqRQ//fQTNDU1MXHiRLHDYazMKs2AivHx8cJt8urq6nj9+jUAwM3NjecaY4yxSujp06fo1asXPD09MXPmTERHR4sdEmOVRpkTIRMTE6SkpAAALCwscPnyZQBAbGwsyti4JKpRl9sAwbFih8EYYxXq8OHDsLKyQkhICAAgKytL+Jsx9gGJUNeuXYXbLN3d3eHh4YEePXpg2LBhGDBgQLkHWFE2/DoY+ClM7DAYY6xCZGRkYOLEiRg4cKDw49XU1BQhISGYMWOGyNExVnmU+a6xn3/+GVJpft+ayZMnQ19fH3///Tf69u2LyZMnl3uAjDHGyiYsLAyurq64d++eUDZgwAD4+PjAwMBAxMgYq3zKnAgpKCjIjDI6dOhQDB06FACQkJAAMzOz8ouOMcZYqeXl5WHVqlXw9vYWJkrV0NDAhg0bMG7cOLnzRDJW05XLuOlJSUmYPn06GjduXB6bY4wx9gEyMjKwfft2IQlq06YNIiIi4O7uzkkQY0UodSL06tUruLq6wsjICKamptiwYQOkUim8vb3RsGFDXL58GTt37qzIWBljjBVDW1sbu3btgrKyMry8vBAaGorPPvtM7LAYq9RKPY7Q1KlTcfToUQwbNgzBwcGIjo6Go6MjsrKysHjxYjg4OFR0rOWiYByCpitNEDXsDlBfR+yQGGPsg6Snp+Pt27cwMTGRKX/8+DHMzc1FioqxiiH6OEJ//PEH/Pz8sHr1ahw5cgREBEtLS5w+fbrKJEH/dcfkGSdBjLEqKzQ0FNbW1nBxcRFuYCnASRBjpVfqROjp06do1qwZAKBhw4ZQU1PD+PHjKywwxhhjheXk5MDb2xudO3dGXFwczpw5g3Xr1okdFmNVVqnvGpNKpVBWVhaeKyoqQlNTs0KCYowxVtiDBw8wcuRIXLlyRSjr2LEjBg0aJGJUjFVtpU6EiAhjxoyBqqoqgPzRSSdPnlwoGTp06FD5RsgYYzUcEcHf3x/Tp09HRkYGgPwfo0uWLMG8efOgqKgocoSMVV2lvjQ2evRoGBsbQ0dHBzo6Ohg5ciRMTU2F5wWPstqyZQsaNGgANTU12NjY4MKFC8Wu/+7dO3h5ecHCwgKqqqpo1KgR363GGKu2UlNTMXToUIwbN05Igho1aoSLFy/Cy8uLkyDGPlKpW4T8/PzKfef79u3DrFmzsGXLFtjb22P79u1wcnJCVFQU6tWrJ7fO0KFD8ezZM+zYsQONGzdGcnKyMGYGY4xVJy9fvoS1tTWePHkilLm7u2P9+vXQ0tISMTLGqo9S3z5fEdq1a4fWrVtj69atQlnTpk3Rv39/rFixotD6wcHBGD58OB4+fAh9ff0P2mfB7XcSfwmko6UlV2CMMRFNmjQJP//8M/T09ODj48P9gViNJfrt8+UtOzsb169fR8+ePWXKe/bsiYsXL8qtc+TIEdja2mLVqlUwMzODpaUlvvnmG2RmZn6KkBlj7JNbu3Yt3N3dcfPmTU6CGKsAZZ5rrLy8ePECeXl5qF27tkx57dq1kZSUJLfOw4cP8ffff0NNTQ2HDx/GixcvMHXqVKSmphbZT+jdu3d49+6d8Dw9PR0A4B/gCjy5BHjZldMRMcbYhyMibN++HVpaWhg5cqRQrqmpCV9fXxEjY6x6Ey0RKvD+/DdEVOScOFKpFBKJBIGBgULH7LVr12Lw4MHYvHkz1NXVC9VZsWIFlixZUqi8f6QVoPqkUDljjH1qycnJGD9+PI4ePQotLS3Y2dmhUaNGYofFWI0g2qUxQ0NDKCoqFmr9SU5OLtRKVKBOnTowMzOTuTutadOmICKZzoT/NX/+fKSlpQmPx48fl99BMMbYRzpx4gSsrKxw9OhRAMCbN29w7NgxkaNirOb4oERo165dsLe3h6mpKR49egQAWL9+PX7//fdSb0NFRQU2NjYICQmRKQ8JCUGHDh3k1rG3t8fTp0/x5s0boezevXtQUFBA3bp15dZRVVWFtra2zIMxxsSWmZmJGTNmwNnZGc+ePQMAGBkZ4ejRo5g5c6bI0TFWc5Q5Edq6dSs8PT3h7OyMV69eIS8vDwCgq6uL9evXl2lbnp6e8PX1xc6dOxEdHQ0PDw/Ex8dj8uTJAPJbc0aNGiWs7+LiAgMDA4wdOxZRUVE4f/485syZg3Hjxsm9LMYYY5XRzZs30aZNG2zcuFEoc3Z2xq1bt9CnTx8RI2Os5ilzIrRx40b4+PgUGsjL1tYWt27dKtO2hg0bhvXr1+O7775Dy5Ytcf78eRw/fhwWFhYAgMTERMTHxwvra2lpISQkBK9evYKtrS1cXV3Rt29fbNiwoayHgQTdNMCAkyfG2KcjlUqxbt06tGnTBrdv3wYAqKmpYdOmTTh27FiR3QIYYxWnzOMIqaur486dO7CwsECtWrUQGRmJhg0b4v79+7Cysqr0t7LzOEKMMbG8fPkSX3zxBRITEwEAVlZWCAoKwhdffCFyZIxVfpVmHKEGDRogIiKiUPmJEyeE2ekZY4wVpqenh4CAACgoKGD27Nm4evUqJ0GMiazMt8/PmTMH06ZNQ1ZWFogIV69exZ49e7BixQoe64Ixxv4jIyMDWVlZMDAwEMp69OiBu3fvonHjxiJGxhgrUOZEaOzYscjNzcXcuXPx9u1buLi4wMzMDD/99BOGDx9eETEyxliVExYWBldXVzRu3BjHjh2TGR+NkyDGKo+PmmvsxYsXkEqlMDY2Ls+YKhT3EWKMVaS8vDysWrUK3t7ewoTQmzdvxtSpU0WOjLGqrdL0EVqyZAliYmIA5A+KWJWSIMYYq0jx8fHo2rUrFixYICRBbdq0QY8ePUSOjDFWlDInQgcPHoSlpSXat2+PTZs24fnz5xURF2OMVSl79+6FlZUVzp8/DwBQUFCAl5cXQkND8dlnn4kcHWOsKGVOhG7evImbN2+ia9euWLt2LczMzODs7IygoCC8ffu2ImJkjLFKKz09HaNGjcKIESOQlpYGAKhXrx7Onj2L77//HsrKyiJHyBgrzkf1EQKA0NBQBAUFYf/+/cjKyhJmd6+suI8QY6y8pKSkoE2bNoiNjRXKXFxcsHnzZujq6ooXGGPVUKXpI/Q+TU1NqKurQ0VFBTk5OeUR0ycRv+A7YOBvYofBGKvCDAwMYG9vDwDQ1tbG7t27ERgYyEkQY1XIByVCsbGxWLZsGZo1awZbW1vcuHED//vf/wrNJF+ZaWepAplVJ3FjjFVOmzZtwogRIxAZGQlXV1exw2GMlVGZxxGys7PD1atX0aJFC4wdO1YYR4gxxqozIkJAQAC0tbUxcOBAoVxHRwdBQUEiRsYY+xhlToS6dOkCX19fHhaeMVZjpKamYtKkSThw4AB0dXXRpk0bmJubix0WY6wclPnS2PLlyzkJYozVGGfOnIGVlRUOHDgAAHj16pXwN2Os6itVi5CnpyeWLl0KTU1NeHp6Frvu2rVryyWwivZLu2v4ukcXscNgjFVS2dnZWLhwIVavXo2Cm2v19PTg4+ODQYMGiRwdY6y8lCoRCg8PF+4ICw8Pr9CAPpUZww7g69G/ih0GY6wSunPnDlxcXGTOd127dkVAQADq1q0rYmSMsfJWqkTozJkzcv9mjLHqhIiwfft2eHp6IjMzEwCgrKyMFStWwMPDAwoKHz3iCGOskinzf/W4cePw+vXrQuUZGRkYN25cuQTFGGNiSE1NxaJFi4QkqGnTprh69Spmz57NSRBj1VSZ/7MDAgKEk8R/ZWZm4pdffimXoBhjTAwGBgbw9fUFAEydOhVhYWFo2bKluEExxipUqW+fT09PBxGBiPD69WuoqakJy/Ly8nD8+HGeiZ4xVqVkZmYiOzsbOjo6Qlm/fv1w8+ZNtGjRQsTIGGOfSqkTIV1dXUgkEkgkElhaWhZaLpFIsGTJknINjjHGKsrNmzfh4uKCpk2b4tdff4VEIhGWcRLEWM1R6kTozJkzICJ07doVBw8ehL6+vrBMRUUFFhYWMDU1rZAgGWOsvEilUvz000+YN28esrOzcfv2bQQEBGDMmDFih8YYE0GpEyEHBwcA+fOM1atXT+bXE2OMVQVPnz7FmDFjEBISIpRZW1ujbdu2IkbFGBNTqRKhmzdvonnz5lBQUEBaWhpu3bpV5LpWVlblFlxFahNnAUS9AJoZih0KY+wTOHz4MCZMmICUlBShbPbs2Vi2bBlUVVVFjIwxJiYJFQyZWgwFBQUkJSXB2NgYCgoKkEgkkFdNIpEgLy+vQgItL+np6dDR0UGa/ipot60PnBgidkiMsQqUkZEBDw8P+Pj4CGWmpqYICAhA9+7dRYyMMVYWwvd3Whq0tbXLbbulahGKjY2FkZGR8DdjjFUFz58/R8eOHXHv3j2hbMCAAfDx8YGBgYGIkTHGKotSJUIWFhZy/2aMscrM0NAQX3zxBe7duwcNDQ1s2LAB48aN4z6OjDHBBw2o+McffwjP586dC11dXXTo0AGPHj0q1+AYY+xjSCQS+Pj44KuvvkJERATc3d05CWKMyShzIrR8+XKoq6sDAC5duoRNmzZh1apVMDQ0hIeHR7kHyBhjpbV3716cOHFCpszAwAC///47PvvsM5GiYoxVZqW+fb7A48eP0bhxYwDAb7/9hsGDB2PixImwt7fHl19+Wd7xVZgxowNxqP9RscNgjJWD9PR0fP3119i1axeMjIxw69Yt1K5dW+ywGGNVQJlbhLS0tITbT0+ePCncdaGmpiZ3DrLK6jfrm0Bnc7HDYIx9pNDQUFhbW2PXrl0A8jtIBwYGihwVY6yqKHOLUI8ePTB+/Hi0atUK9+7dQ+/evQEAt2/fRv369cs7PsYYkysnJwdLly7FsmXLIJVKAQDa2trYsmULXF1dRY6OMVZVlLlFaPPmzbCzs8Pz589x8OBB4RbU69evY8SIEeUeIGOMve/Bgwfo1KkTli5dKiRBHTt2RGRkJCdBjLEyKdWAitVJwYBMEn8JpKOlYofDGCsDIoK/vz+mT5+OjIwMAICioiKWLFmCefPmQVFRUeQIGWMVRdQBFd/36tUr7NixA9HR0ZBIJGjatCnc3d2ho6NTboExxtj7nj9/Dg8PDyEJatSoEQIDA9GuXTuRI2OMVVVlvjQWFhaGRo0aYd26dUhNTcWLFy+wbt06NGrUCDdu3KiIGBljDABgbGyMbdu2AQDc3d0RERHBSRBj7KOU+dJYp06d0LhxY/j4+EBJKb9BKTc3F+PHj8fDhw9x/vz5Cgm0vPClMcaqjuzsbOTk5EBTU1Om/OrVqzxjPGM1TEVdGvugFqFvv/1WSIIAQElJCXPnzkVYWFi5BcYYq9nu3LkDOzs7TJs2rdAyToIYY+WlzImQtrY24uPjC5U/fvwYtWrVKpegPoVvg7sDu26LHQZj7D1EhG3btqF169a4ceMGAgIC8Ouvv4odFmOsmipzIjRs2DC4u7tj3759ePz4MZ48eYK9e/di/PjxVer2+fknewBBUWKHwRj7j+fPn6Nfv36YMmWKMEBr06ZNeXoMxliFKfNdY6tXr4ZEIsGoUaOQm5sLAFBWVsaUKVOwcuXKcg+QMVYzBAcHY8yYMXj27JlQNnXqVPz444/Q0NAQMTLGWHX2weMIvX37FjExMSAiNG7cuMqcqITOVvqroN22PnBiiNghMVajZWZmYt68ediwYYNQZmRkhJ07d6JPnz4iRsYYq0xE7yz99u1bTJs2DWZmZjA2Nsb48eNRp04dWFlZVZkkiDFWuSQnJ6Nt27YySZCzszNu3brFSRBj7JModSK0ePFi+Pv7o3fv3hg+fDhCQkIwZcqUioyNMVbNGRoawszMDED+xM2bNm3CsWPHeOZ4xtgnU+pLY40aNcKyZcswfPhwAPnjeNjb2yMrK6tKDWtf0LSmvU0NaSPTAU1lsUNirEZLTEzEqFGj8NNPP6FZs2Zih8MYq6Qq6tJYqRMhFRUVxMbGCr/eAEBdXR337t2Dubl5uQVU0XhARcbE89tvv0FXVxdffvml2KEwxqoY0fsI5eXlQUVFRaZMSUlJuHOMMcaKkpGRgYkTJ2LAgAEYOXIkUlNTxQ6JMcYAlOH2eSLCmDFjoKqqKpRlZWVh8uTJMsPfHzp0qHwjZIxVaWFhYXB1dcW9e/cAAAkJCfD394enp6fIkTHGWBkSodGjRxcqGzlyZLkGwxirPvLy8rBq1Sp4e3sLLccaGhrYsGEDxo0bJ3J0jDGWr9SJkJ+fX0XGwRirRuLj4+Hm5iYzCbOtrS0CAwNhaWkpYmSMMSarzFNsMMZYcfbu3QsrKyshCZJIJPDy8sLFixc5CWKMVTplnmKDMcaKkpSUhPHjxyMjIwMAUK9ePezevRudOnUSOTLGGJOPW4QYY+XGxMQEP/30EwBgxIgRiIyM5CSIMVap1dgWoZMbpgIRp4F1XcUOhbEqKycnB3l5eVBTUxPKxo0bh4YNG6JLly4iRsYYY6VTY1uE2sZZAHdSxA6DsSrrwYMH6NSpE2bPni1TLpFIOAlijFUZH5QI7dq1C/b29jA1NcWjR48AAOvXr8fvv/9ersExxiofIoKfnx9atmyJK1euYMuWLTh27JjYYTHG2AcpcyK0detWeHp6wtnZGa9evUJeXh4AQFdXF+vXry/v+BhjlUhqaiqGDh2KcePGCR2iGzVqBGNjY5EjY4yxD1PmRGjjxo3w8fGBl5eXzGSrtra2uHXrVrkGxxirPM6cOQMrKyscOHBAKHN3d0dERATatm0rYmSMMfbhypwIxcbGolWrVoXKVVVVhV+IVcHV+o+AJgZih8FYpZednY25c+eiW7duSEhIAADo6enhwIED8PX1hZaWlsgRMsbYhyvzXWMNGjRAREQELCwsZMpPnDiBZs2alVtgFa3njC2Qjt4kdhiMVWrJycno1asXwsPDhbJu3bohICAAZmZmIkbGGGPlo8yJ0Jw5czBt2jRkZWWBiHD16lXs2bMHK1asgK+vb0XEyBgTiYGBAWrVqgUAUFZWxooVK+Dh4QEFhRp7wyljrJop89ls7NixWLx4MebOnYu3b9/CxcUF27Ztw08//YThw4eXOYAtW7agQYMGUFNTg42NDS5cuFCqeqGhoVBSUkLLli3LvE/GWOkoKipi165d6NChA65evYrZs2dzEsQYq1YkREQfWvnFixeQSqUffMfIvn374Obmhi1btsDe3h7bt2+Hr68voqKiUK9evSLrpaWloXXr1mjcuDGePXuGiIiIUu8zPT0dOjo6kPhLIB0t/aC4GauuTpw4AT09PbRv316mnIggkUhEiooxxv79/k5LS4O2tna5bfejftoZGhp+1G2za9euhbu7O8aPH4+mTZti/fr1MDc3x9atW4utN2nSJLi4uMDOzu6D980Y+1dmZiZmzJgBZ2dnuLi4ID09XWY5J0GMserqgzpLF3dSfPjwYam2k52djevXr2PevHky5T179sTFixeLrOfn54eYmBjs3r0b33//fYn7effuHd69eyc8f/8Ez1hNFxkZCVdXV9y+fRtA/p2hO3bsgIeHh8iRMcZYxStzIjRr1iyZ5zk5OQgPD0dwcDDmzJlT6u28ePECeXl5qF27tkx57dq1kZSUJLfO/fv3MW/ePFy4cAFKSqULfcWKFViyZEmp42KsppBKpfjpp58wb948ZGdnAwDU1NSwZs0aTJkyReToGGPs0yhzIjRz5ky55Zs3b0ZYWFiZA3i/damovgh5eXlwcXHBkiVLYGlpWertz58/H56ensLz9PR0mJublzlOxqqTp0+fYsyYMQgJCRHKrK2tERQUVKWGwWCMsY9Vbrd/ODk54eDBg6Ve39DQEIqKioVaf5KTkwu1EgHA69evERYWhq+//hpKSkpQUlLCd999h8jISCgpKeH06dNy96OqqgptbW2ZBwDUylIFMnLKcISMVQ+HDx+GlZWVTBI0e/ZsXLlyhZMgxliNU26J0IEDB6Cvr1/q9VVUVGBjYyNzMgaAkJAQdOjQodD62trauHXrFiIiIoTH5MmT8fnnnyMiIgLt2rUrU7yPF3wHDP6tTHUYq+qePn2KESNGICUlBQBgamqKkJAQrF69GqqqqiJHxxhjn16ZL421atVK5tIVESEpKQnPnz/Hli1byrQtT09PuLm5wdbWFnZ2dvj5558RHx+PyZMnA8i/rJWQkIBffvkFCgoKaN68uUx9Y2NjqKmpFSpnjMlnamqKH3/8ETNmzMCAAQPg4+MDAwOeaoYxVnOVORHq37+/zHMFBQUYGRnhyy+/RJMmTcq0rWHDhiElJQXfffcdEhMT0bx5cxw/flyYviMxMRHx8fFlDZEx9v/y8vIglUqhrKwslH399ddo2LAhnJ2d+bZ4xliNV6YBFXNzcxEYGAhHR0eYmJhUZFwVRhiQSX8VtNvWB04METskxipEfHw83Nzc0K5dO6xatUrscBhj7KNUigEVlZSUMGXKFJlxeRhjlc/evXthZWWF8+fP48cff8SpU6fEDokxxiqlMneWbteuncxM1FXVip4hgAvfIcOql/T0dIwaNQojRoxAWloaAKBevXpQU1MTOTLGGKucytxHaOrUqZg9ezaePHkCGxsbaGpqyiy3srIqt+Aq0g+9/sIKty/EDoOxchMaGoqRI0ciLi5OKHNxccHmzZuhq6srWlyMMVaZlbqP0Lhx47B+/Xq5J1SJRCIMhJiXl1feMZYrnnSVVTc5OTlYunQpli1bBqk0/zOtra2NLVu2wNXVVeToGGOsfFRUH6FSJ0KKiopITExEZmZmsesV3PFVWXEixKqT5ORkfPXVV7hy5YpQ1rFjR+zatQv169cXLzDGGCtnFZUIlfrSWEG+VNkTHcZqEj09PeF/U1FREUuWLMG8efOgqKgocmSMMVY1lKmzNI85wljloqysjMDAQLRs2RIXL16El5cXJ0GMMVYGZeosbWlpWWIylJqa+lEBMcaKdubMGejp6aFly5ZCWePGjXHjxg3+ocIYYx+gTInQkiVLoKOjU1GxMMaKkJ2djYULF2L16tX4/PPPcf36dWhoaAjLOQlijLEPU6ZEaPjw4TA2Nq6oWBhjcty5cwcuLi7C+F137tyBj48PZs6cKXJkjDFW9ZW6j1B1+8XZP9IKOP9Y7DAYKxIRYdu2bWjdurWQBCkrK2P16tWYPn26yNExxlj1UOa7xqoL/wBXIPoy0Nlc7FAYKyQ5ORnjx4/H0aNHhbKmTZsiKChIpn8QY4yxj1PqFiGpVMqXxRj7BE6cOAErKyuZJGjq1KkICwvjJIgxxspZmafYYIxVnCdPnqBfv37IyckBABgZGWHnzp3o06ePyJExxlj1VOZJVxljFadu3br47rvvAABOTk64desWJ0GMMVaBuEWIMRFJpVIQkcwgiHPmzEGjRo0wePDganeTAmOMVTY1tkWox4wtwJouYofBarCnT5+iV69eWLp0qUy5oqIihgwZwkkQY4x9AjU2EbpW/xHQzFDsMFgNdfjwYVhZWSEkJARLly7FxYsXxQ6JMcZqpBqbCDEmhoyMDEycOBEDBw5ESkoKAKB27dpC52jGGGOfFvcRYuwTCQsLg6urK+7duyeUDRgwAD4+PjAwMBAxMsYYq7m4RYixCpaXl4cVK1bAzs5OSII0NDTg6+uLgwcPchLEGGMi4hYhxipQcnIyhgwZgvPnzwtlbdq0QWBgID777DMRI2OMMQZwixBjFUpbWxuvXr0CkD9fn5eXF0JDQzkJYoyxSoITIcYqkJqaGoKCgvD555/j3Llz+P7776GsrCx2WIwxxv4fXxpjrByFhoZCT08PzZo1E8q++OIL3L59W2bQRMYYY5VDjW0R2rBvMLAuTOwwWDWRk5MDb29vdO7cGS4uLnj37p3Mck6CGGOscqqxidCoK22Ak7Fih8GqgZiYGHTq1AlLly6FVCpFZGQkfv75Z7HDYowxVgo1NhFi7GMREfz9/dGyZUtcuXIFQH7Lz/fff4+pU6eKHB1jjLHS4D5CjH2A1NRUTJo0CQcOHBDKGjVqhKCgILRt21bEyBhjjJUFtwgxVkanT5+GlZWVTBLk7u6OiIgIToIYY6yKqbEtQulq76Ctzrcxs7KJj4+Ho6MjcnNzAQB6enrw8fHBoEGDRI6MMcbYh6ixLUL1lnsDh/qLHQarYurVq4f58+cDALp27YqbN29yEsQYY1VYjW0RYqw0iAhEBAWFf38zLFq0CI0aNYKbm5tMOWOMsaqHz+KMFSE5ORn9+vXDmjVrZMqVlZUxevRoToIYY6wa4DM5Y3KcOHECVlZWOHr0KLy8vHDjxg2xQ2KMMVYBOBFi7D8yMzMxY8YMODs749mzZwAAXV1dvHz5UuTIGGOMVQTuI8TY/4uMjISrqytu374tlDk5OcHPzw+1a9cWMTLGGGMVhVuEWI0nlUqxbt06tG3bVkiC1NTUsHHjRvzxxx+cBDHGWDXGLUKsRnv+/DlcXFzw119/CWVWVlYICgrCF198Ue77y8vLQ05OTrlvlzHGqgMVFZVPfiMKJ0KsRtPQ0EB8fLzwfPbs2Vi2bBlUVVXLdT9EhKSkJLx69apct8sYY9WJgoICGjRoABUVlU+2TwkR0SfbWyWQnp4OHR0dRDX0QlO79sDuPmKHxER2/fp1DB48GD4+PujevXuF7CMxMRGvXr2CsbExNDQ0IJFIKmQ/jDFWVUmlUjx9+hTKysqoV69eofNkwfd3WloatLW1y22/NbZFyOyVDpCSKXYY7BMLCwuDnp4eGjVqJJTZ2Njg3r17UFaumClX8vLyhCTIwMCgQvbBGGPVgZGREZ4+fYrc3NwKOye/jztLsxohLy8PK1asgJ2dHVxdXQv106nIf7iCfWloaFTYPhhjrDoouCSWl5f3yfbJiRCr9uLj49G1a1csWLAAubm5uHLlCnx9fT95HHw5jDHGiifGeZITIVat7d27F1ZWVjh//jyA/H8yLy8vjB8/XuTIGGOMVQY1NhH6zfom0LGu2GGwCpKeno5Ro0ZhxIgRSEtLA5A/c/y5c+fw/ffff7Jrz4wVJTQ0FC1atICysjL69+9f5vpnz56FRCKpcnci3r17FyYmJnj9+rXYoVQ733zzDWbMmCF2GFVOjU2ExowOBLzsxA6DVYCLFy+iZcuW2LVrl1Dm4uKCyMhIdOrUScTIqp4xY8ZAIpFAIpFASUkJ9erVw5QpU+ROOXLx4kU4OztDT08PampqaNGiBdasWSP3Wv+ZM2fg7OwMAwMDaGhooFmzZpg9ezYSEhI+xWFVCp6enmjZsiViY2Ph7+8vdjhl9vLlS7i5uUFHRwc6Ojpwc3MrVVLm5eWFadOmoVatWhUfpAhu376NQYMGoX79+pBIJFi/fn2p6t26dQsODg5QV1eHmZkZvvvuO7x/U/e5c+dgY2MDNTU1NGzYENu2bZNZPnfuXPj5+SE2Nra8DqdGqLGJEKue4uLi4ODgIJwItLW1sXv3bgQGBkJXV1fc4KqoXr16ITExEXFxcfD19cXRo0cxdepUmXUOHz4MBwcH1K1bF2fOnMGdO3cwc+ZMLFu2DMOHD5c5oW/fvh3du3eHiYkJDh48iKioKGzbtg1paWlYs2bNJzuu7OzsT7YveWJiYtC1a1fUrVu3Sn42XVxcEBERgeDgYAQHByMiIgJubm7F1nny5AmOHDmCsWPHftS+xX7vivP27Vs0bNgQK1euhImJSanqpKeno0ePHjA1NcW1a9ewceNGrF69GmvXrhXWiY2NhbOzMzp16oTw8HAsWLAAM2bMwMGDB4V1jI2N0bNnz0IJEisB1TBpaWkEgCT+ErFDYRXEw8ODAJC9vT3FxsaKHQ5lZmZSVFQUZWZmih1KmY0ePZr69esnU+bp6Un6+vrC8zdv3pCBgQENHDiwUP0jR44QANq7dy8RET1+/JhUVFRo1qxZcvf38uXLImN5+fIlTZgwgYyNjUlVVZW++OILOnr0KBERLV68mKytrWXWX7duHVlYWBQ6luXLl1OdOnXIwsKC5s2bR+3atSu0rxYtWpC3t7fwfOfOndSkSRNSVVWlzz//nDZv3lxknEREWVlZNH36dDIyMiJVVVWyt7enq1evEhFRbGwsAZB5+Pn5FbmdOXPmUN26dUlFRYUaN25Mvr6+RER05swZAiC8Zi9evKDhw4eTmZkZqaurU/PmzSkoKEhme/v376fmzZuTmpoa6evrU7du3ejNmzfC9tq0aUMaGhqko6NDHTp0oLi4OLlxRUVFEQC6fPmyUHbp0iUCQHfu3CnydVmzZg3Z2trKlJUmbgcHB5o2bRp5eHiQgYEBde7cmYiIbt++TU5OTqSpqUnGxsY0cuRIev78uVDvxIkTZG9vTzo6OqSvr0+9e/emBw8eFBlfebOwsKB169aVuN6WLVtIR0eHsrKyhLIVK1aQqakpSaVSIiKaO3cuNWnSRKbepEmTqH379jJl/v7+ZG5u/vHBi6S482XB93daWlq57pNbhFiVRkSFmo+XL1+OzZs34+zZs6hfv744gVVTDx8+RHBwsEwfq5MnTyIlJQXffPNNofX79u0LS0tL7NmzBwCwf/9+ZGdnY+7cuXK3X1TLiFQqhZOTEy5evIjdu3cjKioKK1euhKKiYpniP3XqFKKjoxESEoJjx47B1dUVV65cQUxMjLDO7du3cevWLbi6ugIAfHx84OXlhWXLliE6OhrLly/HokWLEBAQUOR+5s6di4MHDyIgIAA3btxA48aN4ejoiNTUVJibmyMxMRHa2tpYv349EhMTMWzYMLnbGTVqFPbu3YsNGzYgOjoa27Ztg5aWltx1s7KyYGNjg2PHjuGff/7BxIkT4ebmhitXrgDIH9RzxIgRGDduHKKjo3H27FkMHDgQRITc3Fz0798fDg4OuHnzJi5duoSJEycWeQfPpUuXoKOjg3bt2gll7du3h46ODi5evFjk63L+/HnY2tqWKe4CAQEBUFJSQmhoKLZv347ExEQ4ODigZcuWCAsLQ3BwMJ49e4ahQ4cKdTIyMuDp6Ylr167h1KlTUFBQwIABAyCVSouMcfny5dDS0ir2ceHChSLrf4hLly7BwcFBZkR7R0dHPH36FHFxccI6PXv2lKnn6OiIsLAwmeFA2rZti8ePH+PRo0flGmN1VmMHVGRVX2pqKiZNmoQvv/wS06ZNE8rV1NQKXbqpjGxtbZGUlPTJ92tiYoKwsLBSr3/s2DFoaWkhLy8PWVlZACDTZH/v3j0AQNOmTeXWb9KkibDO/fv3oa2tjTp16pQp5r/++gtXr15FdHQ0LC0tAQANGzYs0zYAQFNTE76+vjLD9xfMLbdo0SIAQGBgINq0aSPsZ+nSpVizZg0GDhwIAGjQoAGioqKwfft2jB49utA+MjIysHXrVvj7+8PJyQlAfjIVEhKCHTt2YM6cOTAxMYFEIoGOjk6Rl0/u3buHX3/9FSEhIcKI58Uds5mZmUwyOn36dAQHB2P//v1o164dEhMTkZubi4EDB8LCwgIA0KJFCwD5/0tpaWno06ePMNhoUe8nACQlJcHY2LhQubGxcbGf6bi4ONjY2JQp7gKNGzfGqlWrhOfe3t5o3bo1li9fLpTt3LkT5ubmuHfvHiwtLTFo0CCZfe3YsQPGxsaIiopC8+bN5cY4efJkmWRKHjMzs2KXl1VSUlKhH20Fkz0nJSWhQYMGSEpKKjQBdO3atZGbm4sXL14I/1MFscXFxQnvMyseJ0KsSjpz5gzc3NyQkJCAY8eO4csvv6yQSVIrUlJSUpXoHNylSxds3boVb9++ha+vL+7du4fp06cXWu/9lrn/lhe0LPz377KIiIhA3bp1heTkQ7Vo0aLQHEaurq7YuXMnFi1aBCLCnj17MGvWLAD5k/I+fvwY7u7umDBhglAnNzcXOjo6cvcRExODnJwc2NvbC2XKyspo27YtoqOjSx1rREQEFBUV4eDgUKr18/LysHLlSuzbtw8JCQl49+4d3r17B01NTQCAtbU1unXrhhYtWsDR0RE9e/bE4MGDoaenB319fYwZMwaOjo7o0aMHunfvjqFDhxabsMp7H0t6fzMzM6GmplamuAu835J0/fp1nDlzRm4LWUxMDCwtLRETE4NFixbh8uXLePHihdASFB8fX2QipK+vD319/SKPoaK8/7oV/D/9t7w066irqwPI76vESocTIValZGdnY+HChVi9erVwElBXV0dCQkKVS4RK25FS7P1qamqicePGAIANGzagS5cuWLJkCZYuXQoAQnISHR2NDh06FKp/584dNGvWTFg3LS0NiYmJZWoVKji5F0VBQaFQIvb+6OEFx/I+FxcXzJs3Dzdu3EBmZiYeP36M4cOHA4Dwxenj4yPTOgGgyMty8r6cCsrLkgSWdMzvW7NmDdatW4f169ejRYsW0NTUxKxZs4SOxYqKiggJCcHFixdx8uRJbNy4EV5eXrhy5QoaNGgAPz8/zJgxA8HBwdi3bx8WLlyIkJAQtG/fvtC+TExM8OzZs0Llz58/L9Rq8V+GhoaF7jgsKe4C7793UqkUffv2xQ8//FBoPwWfrb59+8Lc3Bw+Pj4wNTWFVCpF8+bNi+1svXz5cplWJnlOnDhRrnegmpiYFGpJS05OBvBvy1BR6ygpKclM3ZOamgogf6oKVjqcCLEqIzo6Gq6urggPDxfKunbtioCAANStW/XGhCrL5anKZPHixXBycsKUKVNgamqKnj17Ql9fH2vWrCmUCB05cgT3798XkqbBgwdj3rx5WLVqFdatW1do269evZLbT8jKygpPnjwRLnm8z8jICElJSTLJRkRERKmOp27duujcuTMCAwORmZmJ7t27C18+tWvXhpmZGR4+fCj0GSpJ48aNoaKigr///hsuLi4A8pOysLAwoaWpNFq0aAGpVIpz586VajLgCxcuoF+/fhg5ciSA/ETh/v37Mpe4JBIJ7O3tYW9vD29vb1hYWODw4cPw9PQEALRq1QqtWrXC/PnzYWdnh6CgILmJkJ2dHdLS0nD16lW0bdsWAHDlyhWkpaXJTYYLtGrVClFRUWWOW57WrVvj4MGDqF+/PpSUCn+VpaSkIDo6Gtu3bxeSlr///rvYbQLiXBqzs7PDggULkJ2dLbRYnjx5EqampsIlMzs7Oxw9elSm3smTJ2FrayvTZ++ff/6BsrJylfthKKpy7XpdBRT0Om+60oQo9pXY4bBSkEqltGXLFlJXVxfuslFWVqbVq1dTXl6e2OGVqLrdNUZEZGNjQ9OmTROe79+/nxQVFWnChAkUGRlJsbGx5OvrS3p6ejR48GDhzhcios2bN5NEIqFx48bR2bNnKS4ujv7++2+aOHEieXp6FhnLl19+Sc2bN6eTJ0/Sw4cP6fjx43TixAkiyr+LSSKR0MqVK+nBgwe0adMm0tPTk3vXmDw///wzmZqakqGhIe3atUtmmY+PD6mrq9P69evp7t27dPPmTdq5cyetWbOmyFhnzpxJpqamdOLECbp9+zaNHj2a9PT0KDU1VVhHR0enyLvFCowZM4bMzc3p8OHD9PDhQzpz5gzt27ePiArfNTZr1iwyNzen0NBQioqKovHjx5O2trZwzJcvX6Zly5bRtWvX6NGjR/Trr7+SiooKHT9+nB4+fEjz5s2jixcvUlxcHP3555+kr69PW7ZsKTK2Xr16kZWVFV26dIkuXbpELVq0oD59+hR7PEeOHCFjY2PKzc0VykqKmyj/rrGZM2fKbCshIYGMjIxo8ODBdOXKFYqJiaE///yTxo4dS7m5uZSXl0cGBgY0cuRIun//Pp06dYratGlDAOjw4cPFxvkx3r17R+Hh4RQeHk516tShb775hsLDw+n+/fvCOhs3bqSuXbsKz1+9ekW1a9emESNG0K1bt+jQoUOkra1Nq1evFtZ5+PAhaWhokIeHB0VFRdGOHTtIWVmZDhw4ILP/xYsXy2y7qhHjrrEamwil6a8i6vWr2OGwErx48YL69Okjc6tx06ZN6caNG2KHVmrVMREKDAwkFRUVio+PF8rOnz9PvXr1Ih0dHVJRUaFmzZrR6tWrZb70CoSEhJCjoyPp6emRmpoaNWnShL755ht6+vRpkbGkpKTQ2LFjycDAgNTU1Kh58+Z07NgxYfnWrVvJ3NycNDU1adSoUbRs2bJSJ0IvX74kVVVV0tDQoNevX8s93pYtW5KKigrp6elR586d6dChQ0XGmpmZSdOnTydDQ8NCt88XKE0ilJmZSR4eHlSnTh3h9vmdO3cSUeFEKCUlhfr160daWlpkbGxMCxcupFGjRgnHHBUVRY6OjsIt/ZaWlrRx40YiIkpKSqL+/fsL+7GwsCBvb+9if2ikpKSQq6sr1apVi2rVqkWurq7FDn9ARJSbm0tmZmYUHBwss53i4iaSnwgREd27d48GDBhAurq6pK6uTk2aNKFZs2YJiXdISAg1bdqUVFVVycrKis6ePVvhiZC84REAkIODg7DO4sWLZT6bREQ3b96kTp06kaqqKpmYmND//vc/mR8QRERnz56lVq1akYqKCtWvX5+2bt1aaP+Wlpa0Z8+eiji0T0KMREhCVEQPx2oqPT0dOjo6SNNfBe229YETQ8QOiRUjLS0N1tbWwq2gU6dOxY8//lilZnLPyspCbGwsGjRoUKijKGM1zZYtW/D777/jzz//FDuUauePP/7AnDlzcPPmTbmXC6uC4s6Xwvd3Whq0tbXLbZ88jhCr1HR0dLB7927UqVMHR48exebNm6tUEsQYkzVx4kR07tyZ5xqrABkZGfDz86uySZBY+NVilUpkZCT09fVhbm4ulHXs2BEPHz7k1hTGqgElJSV4eXmJHUa1VFInbyaf6C1CW7ZsEZrAbGxsih2x89ChQ+jRoweMjIygra0NOzs7bl6tJqRSKdatW4e2bdvCzc2t0ESdnAQxxhirCKImQvv27cOsWbPg5eWF8PBwdOrUCU5OToiPj5e7/vnz59GjRw8cP34c169fR5cuXdC3b1+Z26lLa8bQA8BM25JXZBXu6dOn6NWrFzw9PZGdnY1z585h586dYofFGGOsBhC1s3S7du3QunVrbN26VShr2rQp+vfvjxUrVpRqG1988QWGDRsGb2/vUq1f0NlK4i+BdHTR882wT+Pw4cOYMGECUlJShLLZs2dj2bJlMvPuVGXcWZoxxkpHjM7SovURys7OxvXr1zFv3jyZ8p49exY7ad9/SaVSvH79utjh0AuGay+Qnp7+YQGzcpWRkQEPDw/4+PgIZaampggICCjV4HGMMcZYeRDt0tiLFy+Ql5cndxK50k5EuWbNGmRkZBTbQWzFihXQ0dERHv/thMvEERYWhtatW8skQQMHDsTNmzc5CWKMMfZJid5Z+kPn49mzZw/+97//Yd++fXJnQS4wf/58pKWlCY/Hjx9/dMzswz18+BB2dnbCbOSamprYsWMHDhw4IDNfDmOMMfYpiJYIGRoaQlFRUe4kcsVN2gfkd7J2d3fHr7/+WmILgqqqKrS1tWUeTDwNGzaEu7s7AKBNmzYIDw/HuHHjPmhGcsYYY+xjiZYIqaiowMbGBiEhITLlISEhxU7at2fPHowZMwZBQUHo3bt3RYfJKsCaNWuwevVqhIaG4rPPPhM7HMZEERoaihYtWkBZWRn9+/cvc/2zZ89CIpHg1atX5R5bRbp79y5MTEx4QMUK8M0332DGjBlih1HliHppzNPTE76+vti5cyeio6Ph4eGB+Ph4TJ48GUD+Za1Ro0YJ6+/ZswejRo3CmjVr0L59eyQlJSEpKQlpaWliHQIrRnp6OkaNGgU/Pz+Zck1NTcyePVtmxmRWOY0ZMwYSiQQSiQRKSkqoV68epkyZgpcvXxZa9+LFi3B2doaenh7U1NTQokULrFmzptCYUABw5swZODs7w8DAABoaGmjWrBlmz56NhISET3FYlYKnpydatmyJ2NhY+Pv7ix1OmS1btgwdOnSAhoYGdHV1S13Py8sL06ZNQ61atSouOBHdvn0bgwYNQv369SGRSLB+/fpS1bt16xYcHBygrq4OMzMzfPfdd3j/pu5z587BxsYGampqaNiwIbZt2yazfO7cufDz80NsbGx5HU6NIGoiNGzYMKxfvx7fffcdWrZsifPnz+P48eOwsLAAACQmJsqMKbR9+3bk5uZi2rRpqFOnjvCYOXOmWIfAinDx4kW0bNkSu3btwowZM/DgwQOxQ2IfqFevXkhMTERcXBx8fX1x9OhRTJ06VWadw4cPw8HBAXXr1sWZM2dw584dzJw5E8uWLcPw4cNlTujbt29H9+7dYWJigoMHDyIqKgrbtm1DWloa1qxZ88mOKzs7+5PtS56YmBh07doVdevWLVMiUVlkZ2djyJAhmDJlSqnrPHnyBEeOHMHYsWM/et+V1du3b9GwYUOsXLkSJiYmpaqTnp6OHj16wNTUFNeuXcPGjRuxevVqrF27VlgnNjYWzs7O6NSpE8LDw7FgwQLMmDEDBw8eFNYxNjZGz549CyVIrATlOoVrFVAwe+20sZ2JDt4VO5xqJycnh7y9vUlBQUGYdVlbW5tOnDghdmiiqW6zz3t6epK+vr7w/M2bN2RgYEADBw4sVP/IkSMEgPbu3UtERI8fPyYVFRWaNWuW3P0VN3v5y5cvacKECWRsbEyqqqr0xRdf0NGjR4kofzZva2trmfXXrVsnd/b55cuXU506dcjCwoLmzZtH7dq1K7SvFi1akLe3t/B8586d1KRJE1JVVaXPP/+cNm/eXGScRERZWVk0ffp0Yab3/84+L2928qJmoc/KyqI5c+ZQ3bp1hdnnfX19iajw7PMvXryg4cOHk5mZGamrq1Pz5s0pKChIZnv79++n5s2bk5qaGunr61O3bt3ozZs3wvbatGlDGhoapKOjQx06dKC4uLhij5OIyM/Pj3R0dEpcj4hozZo1ZGtrK1NWmrgdHBxo2rRp5OHhQQYGBtS5c2ciIrp9+zY5OTmRpqYmGRsb08iRI+n58+dCvRMnTpC9vT3p6OiQvr4+9e7dmx48eFCqWMuDhYUFrVu3rsT1tmzZQjo6OpSVlSWUrVixgkxNTYUZ6OfOnUtNmjSRqTdp0iRq3769TJm/vz+Zm5t/fPAiEWP2+Ro719jy3/sAiZHAQEuxQ6k2YmJi4OrqiitXrghlHTt2xK5du1C/fn3xAqukbK/aIim7dENFlCcTFROEtQ37oLoPHz5EcHCwzGXNkydPIiUlBd98802h9fv27QtLS0vs2bMHw4YNw/79+5GdnY25c+fK3X5RLSNSqRROTk54/fo1du/ejUaNGiEqKgqKiopliv/UqVPQ1tZGSEiI0Eq1cuVKxMTEoFGjRgDyL23cunULBw4cAAD4+Phg8eLF2LRpE1q1aoXw8HBMmDABmpqaGD16tNz9zJ07FwcPHkRAQAAsLCywatUqODo64sGDBzA3N0diYiI+//xzfPfddxg2bBh0dHTkbmfUqFG4dOkSNmzYAGtra8TGxuLFixdy183KyoKNjQ2+/fZbaGtr448//oCbmxsaNmyIdu3aITExESNGjMCqVaswYMAAvH79GhcuXAARITc3F/3798eECROwZ88eZGdn4+rVq+V+E8P58+dhays7on9JcRcICAjAlClTEBoaCiJCYmIiHBwcMGHCBKxduxaZmZn49ttvMXToUJw+fRpA/nhlnp6eaNGiBTIyMuDt7Y0BAwYgIiICCgryL4gsX74cy5cvL/Y4Tpw4gU6dOn3kq/GvS5cuwcHBQWYQWUdHR8yfPx9xcXFo0KABLl26hJ49e8rUc3R0xI4dO5CTkyP8T7Zt2xaPHz/Go0ePhKsrrHg1NhFi5YeIEBAQgOnTp+PNmzcAAEVFRSxZsgTz5s0r85dVTZGUnYSEd5W/T8yxY8egpaWFvLw8ZGVlAYBMk33BUAhNmzaVW79JkybCOvfv34e2tjbq1KlTphj++usvXL16FdHR0bC0zP/x0rBhwzIfi6amJnx9faGioiKUWVlZISgoCIsWLQIABAYGok2bNsJ+li5dijVr1mDgwIEAgAYNGiAqKgrbt2+XmwhlZGRg69at8Pf3h5OTE4D8ZCokJAQ7duzAnDlzYGJiAolEAh0dnSIvn9y7dw+//vorQkJChLtjiztmMzMzmWR0+vTpCA4Oxv79+4VEKDc3FwMHDhS+IFu0aAEASE1NRVpaGvr06SMkhEW9nx8jLi4ONjY2ZYq7QOPGjbFq1Srhube3N1q3bi2TtOzcuRPm5ua4d+8eLC0tMWjQIJl97dixA8bGxoiKikLz5s3lxjh58uQSJy81MzMr+WDLICkpqdCPxYK7p5OSktCgQQMkJSXJHXcvNzcXL168EP6nCmKLi4vjRKiUOBFiH+Xly5eYOHGi8OsZABo1aoSgoCC0bdtWxMgqPxOV0vUfEHu/Xbp0wdatW/H27Vv4+vri3r17mD59eqH1qIjZeug/Y4NRKccJe19ERATq1q0rJCcfqkWLFjJJEAC4urpi586dWLRoEYgIe/bswaxZswAAz58/x+PHj+Hu7o4JEyYIdXJzc4tsxYmJiUFOTg7s7e2FMmVlZbRt2xbR0dGljjUiIgKKiopwcHAo1fp5eXlYuXIl9u3bh4SEBGFUfU1NTQCAtbU1unXrhhYtWsDR0RE9e/bE4MGDoaenB319fYwZMwaOjo7o0aMHunfvjqFDh5Y5YS1JZmZmoWkTSoq7wPstSdevX8eZM2egpaVVaD8xMTGwtLRETEwMFi1ahMuXL+PFixeQSvOnVYqPjy8yEdLX1y92toKKIm9MvffLS7OOuro6gPy+Sqx0OBFiH0UqlcpMieLu7o7169fLPTkxWR96eepT09TUROPGjQEAGzZsQJcuXbBkyRIsXboUAITkJDo6Wu7QF3fu3EGzZs2EddPS0pCYmFimL9mCk3tRFBQUCiViOTk5co/lfS4uLpg3bx5u3LiBzMxMPH78GMOHDwcA4YvTx8dHpnUCQJEtnfK+nArKy5IElnTM71uzZg3WrVuH9evXo0WLFtDU1MSsWbOEjsWKiooICQnBxYsXcfLkSWzcuBFeXl64cuUKGjRoAD8/P8yYMQPBwcHYt28fFi5ciJCQELRv375McRTH0NCw0B2HJcVd4P33TiqVom/fvvjhhx8K7afgs9W3b1+Ym5vDx8cHpqamkEqlaN68ebGdrcW4NGZiYiJ3TD3g35ahotZRUlKSGYw2NTUVAGBkZFRu8VV3oo8szao2AwMDBAQEwMDAAAcOHICvry8nQdXc4sWLsXr1ajx9+hRA/vyA+vr6cu/4OnLkCO7fv48RI0YAAAYPHgwVFRWZSxz/VdSYOFZWVnjy5Ilwie19RkZGSEpKkkmGIiIiSnU8devWRefOnREYGIjAwEB0795d+PKpXbs2zMzM8PDhQzRu3Fjm0aBBA7nba9y4MVRUVPD3338LZTk5OQgLCyvT5aYWLVpAKpXi3LlzpVr/woUL6NevH0aOHAlra2s0bNgQ9+/fl1lHIpHA3t4eS5YsQXh4OFRUVHD48GFheatWrTB//nxcvHgRzZs3R1BQUKnjLY1WrVohKiqqzHHL07p1a9y+fRv169cv9N5oamoiJSUF0dHRWLhwIbp164amTZvKHfbhfZMnT0ZERESxj/dbpz6WnZ0dzp8/L5OgnTx5EqampsIlMzs7u0Lj7p08eRK2trYyffb++ecfKCsr44svvijXGKu1cu16XQUU9Do3W69LlJwhdjhVTlRUFCUlJRUqT09PFyGaqqG63TVGRGRjY0PTpk0Tnu/fv58UFRVpwoQJFBkZSbGxseTr60t6eno0ePBg4c4XIqLNmzeTRCKhcePG0dmzZykuLo7+/vtvmjhxInl6ehYZy5dffknNmzenkydP0sOHD+n48ePC3YhRUVEkkUho5cqV9ODBA9q0aRPp6enJvWtMnp9//plMTU3J0NCQdu3aJbPMx8eH1NXVaf369XT37l26efMm7dy5k9asWVNkrDNnziRTU1M6ceIE3b59m0aPHk16enqUmpoqrKOjo1Pk3WIFxowZQ+bm5nT48GF6+PAhnTlzhvbt20dEhe8amzVrFpmbm1NoaChFRUXR+PHjSVtbWzjmy5cv07Jly+jatWv06NEj+vXXX0lFRYWOHz9ODx8+pHnz5tHFixcpLi6O/vzzT9LX16ctW7YUGdujR48oPDyclixZQlpaWhQeHk7h4eH0+vXrIuscOXKEjI2NKTc3VygrKW6i/LvGZs6cKbOthIQEMjIyosGDB9OVK1coJiaG/vzzTxo7dizl5uZSXl4eGRgY0MiRI+n+/ft06tQpatOmDQGgw4cPF/u6f4x3794Jr0WdOnXom2++ofDwcLp//76wzsaNG6lr167C81evXlHt2rVpxIgRdOvWLTp06BBpa2vT6tWrhXUePnxIGhoa5OHhQVFRUbRjxw5SVlamAwcOyOx/8eLFMtuuasS4a6zGJkISf4nYoVQpUqmUtm7dSurq6uTk5CTzxcaKVx0TocDAQFJRUaH4+Hih7Pz589SrVy/S0dEhFRUVatasGa1evVrmS69ASEgIOTo6kp6eHqmpqVGTJk3om2++oadPnxYZS0pKCo0dO5YMDAxITU2NmjdvTseOHROWb926lczNzUlTU5NGjRpFy5YtK3Ui9PLlS1JVVSUNDQ25X+SBgYHUsmVLUlFRIT09PercuTMdOnSoyFgzMzNp+vTpZGhoWOj2+QKlSYQyMzPJw8OD6tSpI9w+v3PnTiIqnAilpKRQv379SEtLi4yNjWnhwoU0atQo4ZijoqLI0dFRuKXf0tKSNm7cSERESUlJ1L9/f2E/FhYW5O3tTXl5eUXGNnr06ELDAACgM2fOFFknNzeXzMzMKDg4WCgrKW4i+YkQEdG9e/dowIABpKurS+rq6tSkSROaNWuWcH4KCQmhpk2bkqqqKllZWdHZs2crPBGSNzwCAHJwcBDWWbx4scxnk4jo5s2b1KlTJ1JVVSUTExP63//+V+g8e/bsWWrVqhWpqKhQ/fr1aevWrYX2b2lpSXv27KmIQ/skxEiEJERF9HCsptLT06GjowOJvwTS0VKxw6kSkpOTMX78eBw9elQo8/Pzw5gxY8QLqgrJyspCbGwsGjRoUKijKGM1zZYtW/D777/jzz//FDuUauePP/7AnDlzcPPmTSgpVc0uwMWdLwu+v9PS0sp13tCq+UqxTyY4OBhjxozBs2fPhLKpU6eWeHspY4zJM3HiRLx8+RKvX7+uttNsiCUjIwN+fn5VNgkSC79aTK7MzEzMmzcPGzZsEMqMjIywc+dO9OnTR8TIGGNVmZKSEry8vMQOo1riH6gfhhMhVsitW7fg4uKCf/75RyhzdnbGzp07Cw3oxRhjjFVlnAgxGQ8ePICtra1wG6eamhpWr16NqVOnlvtw+4wxxpjYeBwhJqNx48YYNmwYgPyRaK9fv45p06ZxEsQYY6xa4hYhVsimTZvw2WefYe7cuTKTADLGGGPVTY1tETq43R3wuiB2GKLKyMjAxIkTsW/fPplybW1tLFq0iJMgxhhj1V6NTYS63bUEbiSVvGI1FRYWhtatW8PHxweTJ0/G48ePxQ6JMcYY++RqbCJUU+Xl5WHFihWws7MT5m3Kzs7GzZs3RY6MVRdnz56FRCIpct4wxiqTHTt2oGfPnmKHUS21adMGhw4dEjuMEnEiVIPEx8eja9euWLBgAXJzcwHkf1AjIiLQu3dvkaNj1UWHDh2QmJgIHR0dsUOpMSQSifDQ0tKCtbU1/P39C62Xl5eHdevWwcrKCmpqatDV1YWTkxNCQ0MLrZudnY1Vq1bB2toaGhoaMDQ0hL29Pfz8/JCTk/MJjqrivXv3Dt7e3li0aJHYoVSYQ4cOwdHREYaGhpBIJKWejPjgwYNo1qwZVFVV0axZM5nJeQts2bJFGAHaxsYGFy7IdjdZtGgR5s2bB6m0cs/iwIlQDbF3715YWVnh/PnzAPJPnF5eXggNDcVnn30mcnSsOlFRUYGJickH32n43xm4qwIiEn5YiMnPzw+JiYmIjIzEsGHDMHbsWJlpLIgIw4cPx3fffYcZM2YgOjoa586dg7m5Ob788kv89ttvwrrZ2dlwdHTEypUrMXHiRFy8eBFXr17FtGnTsHHjRty+ffuTHVdFJl0HDx6ElpYWOnXq9FHbqcyJYUZGBuzt7bFy5cpS17l06RKGDRsGNzc3REZGws3NDUOHDsWVK1eEdfbt24dZs2bBy8sL4eHh6NSpE5ycnBAfHy+s07t3b6SlpVX+6VTKdeayKqBg0rbLzWYTTQwuuUIVl5aWRm5ubjKT/9WrV4/Onz8vdmg1RrGTrvb6tfBjW0TJG72WKL/utcRyjd3BwYG+/vprmjlzJunq6pKxsTFt376d3rx5Q2PGjCEtLS1q2LAhHT9+XKjz/mSgRER///03de7cmdTV1UlXV5d69uwpzMTu4OBA06ZNIw8PDzIwMKDOnTsTUf4Ek23atCEVFRUyMTGhb7/9lnJycoqN9+rVq9S9e3cyMDAgbW1t6ty5M12/fl1YPnz4cBo2bJhMnezsbDIwMBAmM5VKpfTDDz9QgwYNSE1NjaysrGj//v2Fji84OJhsbGxIWVmZTp8+TQ8ePKCvvvqKjI2NSVNTk2xtbSkkJERmX0+fPiVnZ2dSU1Oj+vXrU2BgIFlYWNC6deuEdV69ekUTJkwgIyMjqlWrFnXp0oUiIor/TEDORKL6+vrk6ekpPN+7dy8BoCNHjhSqP3DgQDIwMKA3b94QEdEPP/xACgoKdOPGjULrZmdnC+vJU9x7/f6xEhFZW1vT4sWLZY5l69at9NVXX5GGhgYtXLiQzMzMCk0wev36dQJAMTExRPRhr1vfvn3pm2++kSkr6TMkL0Zvb28iIjpy5Ai1bt2aVFVVqUGDBvS///1P5jO7Zs0aat68OWloaFDdunVpypQpcif5rQgFk8GGh4eXuO7QoUOpV69eMmWOjo40fPhw4Xnbtm1p8uTJMus0adKE5s2bJ1M2ZswYcnNzK3WcYky6WmNbhOzmrgW2O4odRoV7+/YtTpw4ITwfMWIEIiMjP/oXECsnYc8KP56kl1wv/Z38uunvyj3EgIAAGBoa4urVq5g+fTqmTJmCIUOGoEOHDrhx4wYcHR3h5uaGt2/fyq0fERGBbt264YsvvsClS5fw999/o2/fvsjLy5PZh5KSEkJDQ7F9+3YkJCTA2dkZbdq0QWRkJLZu3YodO3bg+++/LzbW169fY/To0bhw4QIuX76Mzz77DM7Oznj9+jUAwNXVFUeOHMGbN2+EOn/++ScyMjIwaNAgAMDChQvh5+eHrVu34vbt2/Dw8MDIkSNx7tw5mX3NnTsXK1asQHR0NKysrPDmzRs4Ozvjr7/+Qnh4OBwdHdG3b1+ZX8ijRo3C06dPcfbsWRw8eBA///wzkpOTheVEhN69eyMpKQnHjx/H9evX0bp1a3Tr1g2pqamler/y8vLw66+/IjU1FcrKykJ5UFAQLC0t0bdv30J1Zs+ejZSUFISEhAAAAgMD0b17d7Rq1arQusrKytDU1JS779K816WxePFi9OvXD7du3cL48eMxfPhwBAYGyqwTFBQEOzs7NGzY8INftwsXLsDW1lamrKTPkLwYx40bhz///BMjR47EjBkzEBUVhe3bt8Pf3x/Lli0T6igoKGDDhg34559/EBAQgNOnT2Pu3LnFvhZOTk7Q0tIq9lHeLl26VKjflKOjIy5evAggv8Xw+vXrhdbp2bOnsE6Btm3bFrpkVumUa1pVBRRklBJ/idihfDK///47aWtr0+7du8UOpUYqtkXIcGPhx8JStNadipNf91Rcucbu4OBAHTt2FJ7n5uaSpqamzC+8xMREAkCXLl0iosItQiNGjCB7e/ti99GyZUuZsgULFtDnn39OUqlUKNu8eTNpaWlRXl5eqePPzc2lWrVq0dGjR4kovzXD0NCQfvnlF2GdESNG0JAhQ4iI6M2bN6SmpkYXL16U2Y67uzuNGDFC5vh+++23EvffrFkz2rhxIxERRUdHEwC6du2asPz+/fsEQGglOXXqFGlra1NWVpbMdho1akTbt28vcj8ASE1NjTQ1NUlRUZEAkL6+Pt2/f19Yp0mTJtSvXz+59VNTUwkA/fDDD0REpK6uTjNmzCjx+N5X0ntd2hahWbNmyaxz48YNkkgkFBeX//nOy8sjMzMz2rx5MxF92Ov28uVLAlBi6/j7n6GiYuzUqRMtX75cpmzXrl1Up06dIrf966+/koGBQbH7f/LkCd2/f7/YR2mUpUVIWVmZAgMDZcoCAwNJRUWFiIgSEhIIAIWGhsqss2zZMrK0tJQp+/3330lBQaHU/7ditAjxgIrVzIMHD6CnpwcDAwOh7KuvvkJsbCz09fVFjIxVVVZWVsLfioqKMDAwQIsWLYSygvnn/tuy8V8REREYMmRIsft4/1d5dHQ07OzsZPoZ2dvb482bN3jy5AkAoFmzZsKyBQsWYMGCBUhOToa3tzdOnz6NZ8+eIS8vD2/fvhVaZZSVlTFkyBAEBgbCzc0NGRkZ+P333xEUFAQAiIqKQlZWFnr06CETT3Z2dqHWkfdjzsjIwJIlS3Ds2DE8ffoUubm5yMzMFPZ99+5dKCkpoXXr1kKdxo0bQ09PT3h+/fp1vHnzRub/F8ifBDkmJqbY13DdunXo3r07Hj9+DE9PT3h4eKBx48bF1nlfwetNRB/Ux6s073VpvP/atmrVCk2aNMGePXswb948nDt3DsnJycIkox/yumVmZgLIn0bov0r6DBUV4/Xr13Ht2jWZFqC8vDxkZWXh7du30NDQwJkzZ7B8+XJERUUhPT0dubm5yMrKQkZGRpGtbGZmZkW9TBXq/fdf3meiNOuoq6tDKpXi3bt3UFdXr5hgPxInQtUEEcHf3x/Tp09Hr169sH//fpkPJCdB7EP99/IKkH/y+29ZweesqDtDSnPye/9LQN4JlYiE/dWpU0fm7peCz/eYMWPw/PlzrF+/HhYWFlBVVYWdnZ1MB2xXV1c4ODggOTkZISEhUFNTg5OTk8wx/PHHH4W+gN4fYPT9mOfMmYM///wTq1evRuPGjaGuro7BgwcL+y6I/33/LZdKpahTpw7Onj1baD1dXV259QuYmJigcePGaNy4Mfbv349WrVrB1tZWSBgtLS0RFRUlt250dDQACDdOWFpaCmVlUdJ7raCgUOh1kNfRWF5S4OrqiqCgIMybNw9BQUHCnVDAh71uBgYGkEgkePnypUx5aT5D8mKUSqVYsmQJBg4cWGhfampqePToEZydnTF58mQsXboU+vr6+Pvvv+Hu7l5sZ2snJ6cSLy3991JveTAxMUFSkuw4e8nJycKPHkNDQygqKha7ToHU1FRoaGhU2iQI4ESoWkhNTcWkSZNw4MABAPl3QuzZswcuLi4iR8ZKZFu7cFld7ZLraavKr6td+UYDt7KywqlTp7BkyZJS12nWrBkOHjwokxBdvHgRtWrVgpmZGRQUFOS2dly4cAFbtmyBs7MzAODx48d48eKFzDodOnSAubk59u3bhxMnTmDIkCFQUVER9quqqor4+Hg4ODiU6TgvXLiAMWPGYMCAAQDyv5zi4uKE5U2aNEFubi7Cw8NhY2MDIL8F97/jLbVu3RpJSUlQUlJC/fr1y7T//2rcuDEGDRqE+fPn4/fffwcADB8+HC4uLjh69GihfkJr1qyBgYGB0BLm4uKCBQsWIDw8vFBLWG5uLt69eyc3WSnpvTYyMkJiYqLwPD09HbGxsaU6JhcXFyxcuBDXr1/HgQMHsHXrVmHZh7xuKioqaNasGaKiomT6upTmMyRP69atcffu3SJb4cLCwpCbm4s1a9ZAQSG/e+6vv/5a4nZ9fX2F1qtPxc7ODiEhIfDw8BDKTp48iQ4dOgDIf+1sbGwQEhIifN4BICQkBP369ZPZ1j///CPTClopleuFtiqguvUROn36NJmZmcncFebu7v7J7kRgJSu2j1Al5+DgQDNnzpQpk9fPA/+5a+n9PkJ3794lFRUVmjJlCkVGRlJ0dDRt2bKFnj9/XuQ+njx5QhoaGjRt2jSKjo6m3377jQwNDWX6ksjTsmVL6tGjB0VFRdHly5epU6dOpK6uXijeBQsWULNmzUhJSYkuXLggs8zLy4sMDAzI39+fHjx4QDdu3KBNmzaRv7+/3OMr0L9/f2rZsiWFh4dTREQE9e3bl2rVqiVzbN27d6fWrVvTlStX6MaNG9SlSxdSV1en9evXE1H+HWsdO3Yka2trCg4OptjYWAoNDSUvLy+ZvkXv++/rX+DmzZskkUiEelKplAYMGEB6enrk6+tLsbGxFBkZSRMnTiQlJSWZ+llZWdSpUyfS09OjTZs2UUREBMXExNC+ffuodevWRfYzKem9njdvHpmYmND58+fp1q1b1L9/f9LS0irUR+j9YynQoUMHsra2Ji0tLXr79q1Q/qGvm6enJw0aNEimrDSfIXkxBgcHk5KSEi1evJj++ecfioqKor1795KXlxcREYWHhxMAWr9+PcXExNAvv/winLvf/yyVp5SUFAoPD6c//viDANDevXspPDycEhP/vcPUzc1N5m6v0NBQUlRUpJUrV1J0dDStXLmSlJSU6PLly8I6e/fuJWVlZdqxYwdFRUXRrFmzSFNTU+jHVcDBwYG+++67UscrRh8hToSqqHfv3tGcOXNIIpEICZCenh4dOHBA7NDYe2p6IkSUfyt8hw4dSFVVlXR1dcnR0VFYLm8fBXXKevv8jRs3yNbWllRVVemzzz6j/fv3y4339u3bBIAsLCxkOmQT5X+p/vTTT/T555+TsrIyGRkZkaOjI507d67I4yPK74xakNiYm5vTpk2bCh3b06dPycnJiVRVVcnCwoKCgoLI2NiYtm3bJqyTnp5O06dPJ1NTU1JWViZzc3NydXWl+Pj4Io+7qOShR48e5OTkJDzPycmh1atX0xdffEGqqqqkra1Njo6OhZJBovxkaMWKFdSiRQtSU1MjfX19sre3J39//2Lfh+Le67S0NBo6dChpa2uTubk5+fv7y+0sXVQitHnzZgJAo0aNKrTsQ1636OhoUldXp1evXgllpfkMFRVjcHAwdejQgdTV1UlbW5vatm1LP//8s7B87dq1VKdOHVJXVydHR0f65ZdfKjwR8vPzk/mhXPD472vu4OBAo0ePlqm3f/9+4X+gSZMmdPDgwULb3rx5M1lYWJCKigq1bt1a+B8p8OTJE1JWVqbHjx+XOl4xEiEJUREXrqup9PR06OjoQOIvgXR05R7tsih37tyBi4sLwsPDhbKuXbsiICAAdevWFTEyJk9WVhZiY2OFEVgZK/DkyROYm5vjr7/+Qrdu3cQOp0YaOnQoWrVqhfnz54sdSrUzZ84cpKWl4eeffy51neLOlwXf32lpadDWLkUXglLiPkJVzN27d9G6dWvhmrGysjJWrFgBDw8P4bozY6xyOn36NN68eYMWLVogMTERc+fORf369dG5c2exQ6uxfvzxRxw5ckTsMKolY2NjfPPNN2KHUaIa+835yvMHwGm/2GGUmaWlpXCHS9OmTXH16lXMnj2bkyDGqoCcnBwsWLAAX3zxBQYMGAAjIyOcPXu20J157NOxsLDA9OnTxQ6jWpozZ06hu8gqI24RqmIkEgl+/vlnWFpaYtGiRdDQ0BA7JMZYKTk6OsLRsfqPaM9YVcLNCJVYZmYmZsyYgaNHj8qUGxgYYMWKFZwEMcYYYx+JE6FKKjIyEm3atMHGjRsxbty4QgNXMcYYY+zjcSJUyUilUqxbtw5t27bF7du3AeQPzBYWFiZyZIwxxlj1U2MToc0OF4D+lmKHIePp06fo1asXPD09heHcra2tcf36dfTp00fk6BhjjLHqp8YmQl79jgGTrMUOQ3D48GFYWVkhJCREKJs9ezauXLkiM7kkY4wxxsoP3zUmsjdv3sDDwwO+vr5CmampKQICAtC9e3cRI2OMMcaqvxrbIlRZvHz5Evv3/zue0YABA3Dz5k1OghhjTCRubm5Yvny52GFUO8nJyTAyMkJCQoLYocjgREhk5ubm2L59OzQ1NeHr64uDBw/CwMBA7LAYY1XY2bNnIZFIhIeBgQG6du2K0NDQQuumpqZi1qxZqF+/PlRUVFCnTh2MHTsW8fHxhdZNSkrC9OnT0bBhQ6iqqsLc3Bx9+/bFqVOnPsVhfRI3b97EH3/8Ua0HWVy2bBk6dOgADQ0N6OrqlqoOEeF///sfTE1Noa6uji+//FK4oafAu3fvMH36dBgaGkJTUxNfffUVnjx5Iiw3NjaGm5sbFi9eXJ6H89E4EfrE4uPjkZ6eLlM2bNgwPHjwAO7u7pBIJCJFxljllZOTI3YIZVJZ4r179y4SExNx9uxZGBkZoXfv3khOThaWp6amon379vjrr7+wZcsWPHjwAPv27UNMTAzatGmDhw8fCuvGxcXBxsYGp0+fxqpVq3Dr1i0EBwejS5cumDZt2ic7JiJCbm5uhW1/06ZNGDJkCGrVqvXB26joGD9WdnY2hgwZgilTppS6zqpVq7B27Vps2rQJ165dg4mJCXr06IHXr18L68yaNQuHDx/G3r178ffff+PNmzfo06cP8vLyhHXGjh2LwMBAvHz5slyP6aOU6xSuVYCYs8/v2bOHdHR05M6czKqv4mZTbt/et9Bj/fpLJW7z0qXHcuteulT6WZ5Lw8HBgb7++muaOXMm6erqkrGxMW3fvp3evHlDY8aMIS0tLWrYsCEdP35cqJObm0vjxo2j+vXrk5qaGllaWtL69esLbXvHjh3UrFkzYXb5adOmCcsA0NatW+mrr74iDQ0N8vb2JiKiLVu2UMOGDUlZWZksLS3pl19+KfEYdu3aRTY2NqSlpUW1a9emESNG0LNnz4iIKC8vj8zMzGjr1q0yda5fv04AKCYmhoiIXr16RRMmTCAjIyOqVasWdenShSIiIoT1Fy9eTNbW1rRjxw5q0KABSSQSkkqldOLECbK3tycdHR3S19en3r1704MHD2T2FRoaStbW1qSqqko2NjZ0+PBhAkDh4eHCOrdv3yYnJyfS1NQkY2NjGjlyJD1//rzIYz5z5kyhWc1v3rxJAOjIkSNC2eTJk0lTU5MSExNl6r99+5bMzMyoV69eQpmTkxOZmZnRmzdvCu2vpNnTi3qvY2NjCx3ry5cvCQCdOXNG5liCg4PJxsaGlJWVadu2bQSAoqOjZfazZs0asrCwIKlU+kGvW15eHunq6tKxY8dkyov7DBUV4+nTp0kqldIPP/xADRo0IDU1NbKysqL9+/cL9Ur7v1JR/Pz8SEdHp8T1pFIpmZiY0MqVK4WyrKws0tHRoW3bthFR/v+IsrIy7d27V1gnISGBFBQUKDg4WGZ79evXpx07dsjdlxizz3Mi9In26ebmRgCEx4EDBz7Z/pm4ivvHBv5X6OHhESxnK7KCg+/LrRscfL9cY3dwcKBatWrR0qVL6d69e7R06VJSUFAgJycn+vnnn+nevXs0ZcoUMjAwoIyMDCIiys7OJm9vb7p69So9fPiQdu/eTRoaGrRv3z5hu1u2bCE1NTVav3493b17l65evUrr1q37z+sCMjY2ph07dlBMTAzFxcXRoUOHSFlZmTZv3kx3796lNWvWkKKiIp0+fbrYY9ixYwcdP36cYmJi6NKlS9S+fXtycnISls+ePZs6duwoU2f27NlkZ2dHRPlfAvb29tS3b1+6du0a3bt3j2bPnk0GBgaUkpJCRPmJkKamJjk6OtKNGzcoMjKSpFIpHThwgA4ePEj37t2j8PBw6tu3L7Vo0YLy8vKIiCg9PZ309fVp5MiRdPv2bTp+/DhZWlrKJAdPnz4lQ0NDmj9/PkVHR9ONGzeoR48e1KVLlyKP+f1EKCMjgzw8PAgAnThxgoj+/dKfOHGi3G0sW7aMJBIJpaSkUEpKCkkkElq+fHmxr7U8xb3XZUmErKys6OTJk/TgwQN68eIF2djY0MKFC2X2ZWNjQ/Pnz//g1y08PJwAUFJSkkx5SZ+homJcsGABNWnShIKDgykmJob8/PxIVVWVzp49S0Sl+1+RR1NTs9jHfxPY4pQ2EYqJiSEAdOPGDZnyr776Svhhf+rUKQJAqampMutYWVkJP2QKDB06lMaMGSN3X5wIfQKfOhH6+++/qX79+jJJ0IgRI0r8BcWqj6qeCP03ScjNzSVNTU1yc3MTyhITEwkAXbpUdEvW1KlTadCgQcJzU1NT8vLyKnJ9ADRr1iyZsg4dOtCECRNkyoYMGULOzs6lPh4ioqtXrxIAev36NRER3bhxgyQSCcXFxRHRv61EmzdvJqL8E7y2tjZlZWXJbKdRo0a0fft2IspPhJSVlSk5ObnYfScnJxMAunXrFhERbd26lQwMDGQ+Gz4+PjLJwaJFi6hnz54y23n8+DEBoLt378rdT8EXc8EXo0QiIQBkY2ND2dnZRESUlJREAGQS0P86dOgQAaArV67QlStXCAAdOnSo2OOTp7j3uiyJ0G+//SZTd+3atdSwYUPh+d27dwkA3b59m4g+7HU7fPgwKSoqCi1KRXn/MyQvxjdv3pCamhpdvHhRpq67uzuNGDGiyG2//78iz/3794t9PHnypNj6BUqbCIWGhhIASkhIkCmfMGGC8BoHBgaSiopKobo9evQolGx7eHjQl19+KXdfYiRCNbaPULc7lkBYxU1bkZOTA29vb3Tu3BlxcXEAAG1tbezevRtBQUGl7qDGmNisrKyEvxUVFWFgYIAWLVoIZQWzS/+378m2bdtga2sLIyMjaGlpwcfHR+h8m5ycjKdPn6Jbt27F7tfW1lbmeXR0NOzt7WXK7O3tER0dDQAIDAyElpaW8Lhw4QIAIDw8HP369YOFhQVq1aqFL7/8EgCEeFq1aoUmTZpgz549AIBz584hOTkZQ4cOBQBcv34db968gYGBgcz2Y2NjERMTI8RiYWEBIyMjmfhiYmLg4uKChg0bQltbGw0aNJDZ9927d2FlZQU1NTWhTtu2bWW2cf36dZw5c0Zm302aNBG2X5wLFy7gxo0b2LNnDywsLODv71/qme6JCED+RM///bssSvtel8b7n4fhw4fj0aNHuHz5MoD8979ly5bCuGsf8rplZmZCVVW10HGW9BmSF2NUVBSysrLQo0cPmRh++eUXmf0X979SlMaNGxf7MDMzK7b+h3r/dSGiEj8T8tZRV1fH27dvyz2+D1VjxxE6+LM7EHEBODGk3Lf94MEDjBw5EleuXBHK7O3tsXv3btSvX7/c98dYRXr/i1MikciUFZzkpFIpAODXX3+Fh4cH1qxZAzs7O9SqVQs//vij8P+grq5eqv1qamoWKivuRPzVV1+hXbt2wjIzMzNkZGSgZ8+e6NmzJ3bv3g0jIyPEx8fD0dFRGL0dAFxdXREUFIR58+YhKCgIjo6OMPy/9u48qqkz/QP4NyEkbAJ1JQiCUBFsKwqKiEM9tiqKlcrUpcq4cGorRQVhXEenqDOOtR6tYt2OVRgdqDoq1o5WRVsoi9OyuSAoqAzWCkVcUJFF4Pn94eH+CAlLMBBMns85nEPe+96b5+Yh3Cf3vjdv9+7CfsnlciQkJCjF0/ADjap4J06cCFtbW+zZswfW1taoq6vDm2++KTy3qoNEfdFRr66uDhMnTsSGDRuUti+Xy5XaGurbty8sLS3h5OSEyspK+Pv7Izs7GzKZDD169IClpSVycnJUrnvt2jWIRCI4OjoCePHa5+bmYtKkSc0+Z0Mt5VosfvFZvOE+NzXQvPHrK5fLMWrUKMTGxsLT0xPffPMN5s2bJyxvy+vWvXt3PHv2DNXV1ZBKpQDQ6r+hxjHWvx9OnjypVJjIZDIALb9XmmJmZtbscm9vb3z//ffN9lGHlZUVgBd3DTZ87UpKSoQPQlZWVqiursbDhw/x2muvKfTx8vJS2N6DBw+UPjRok94WQu0lNzcXQ4cORXl5OYAXn6BXr16N5cuXQyLhl5sp8vS0UWqzs7NocT0LCyOV61pYGKno3bGSkpLg5eWF4OBgoa3hJ+AuXbrA3t4e58+fx6hRo1q9XRcXFyQnJ2PWrFlCW2pqKlxcXITtNr7TJyMjA6Wlpfj8889ha2sLACrn7ZsxYwZWrVqFjIwMHDlyBDt37hSWubm5obi4GBKJRK0PMvfv30dubi52794Nb29vAEBycrJCH2dnZ8TExKCqqko4ODaOz83NDUePHoW9vf1L/Q+ZOXMm1q5dix07diAsLAxisRhTp05FTEwM1q5dKxzsgBdnRnbs2AEfHx907doVAODj44Pt27cjJCREqSh59OiRyrPcLeW6/mBYVFSEwYMHAwAuXrzY6n0KCAjAsmXLMH36dNy8eRMffvihsKwtr9ugQYMAvDibU//7tWvXWvU31NiAAQMgk8lw+/ZtjBw5UmWflt4rTWnpNWrth43W6tu3L6ysrBAfHy/kqbq6GomJiUKh6e7uDkNDQ8THxwtnU4uKipCdnY0vvvhCYXvZ2dnCWbVOQaMX2l4BwjXGrl8QjTus8e3X1dXRuHHjCAA5OjrSf//7X40/B3u1NHfNu7MbOXIkhYaGKrTZ2dkpjSsBQHFxcUREtGXLFjI3N6fTp0/T9evXadWqVWRubk6urq5C/+joaDIyMqKtW7dSXl4eZWRkUGRkpMrt1YuLiyNDQ0PauXMn5eXlCYOl68eSqFJSUkJSqZSWLFlCN2/epG+//VZpMHI9Ly8vcnV1JTMzM3r27JnQXldXR3/4wx/I1dWVTp8+TQUFBZSSkkIrV66ktLQ0Ivr/u8Yaqq2tpW7dutGf/vQnys/Pp/Pnz9PQoUMV9q2srIy6du1Ks2bNopycHDp9+jQ5OzsTAOGutN9++4169OhBkydPpp9//plu3rxJZ86cocDAQKqpqVG536ruGiMiioyMpJ49ewoD2+/du0eOjo705ptv0qlTp+j27duUmJhI3t7e1LNnT+GuOSKiW7dukZWVFQ0YMICOHDlCeXl5lJOTQ1u3biVnZ+cmc9BSrj09Pcnb25uuXr1KiYmJ5OHhoXKMkKpxlWVlZWRkZESurq707rvvKixry+tGROTm5kbbtm0THrfmb6ipGFeuXEndunWj6OhounHjBmVmZtJXX31F0dHRRNS690p7KCwspKysLFqzZg2ZmZlRVlYWZWVlCWOeiIj69++vMCbs888/JwsLCzp27BhduXKFpk+fTnK5nB4/fiz0CQoKIhsbGzp37hxlZmbSO++8Q66urgqvd3l5ORkbG9NPP/2kMjYeLN0B2rsQInoxeDQ0NFThj4rpL30rhCorK2nOnDlkYWFBlpaW9Omnn9Ly5cuV/rnv2rWL+vfvT4aGhiSXy2nhwoUqt9dQW26fj42NJXt7e5LJZDR8+HA6ceKEykJo+/btBEDl11s8fvyYFi5cSNbW1mRoaEi2trYUEBBAt2/fJiLVhRARUXx8PLm4uJBMJqOBAwdSQkKC0r6lpKTQwIEDSSqVkru7O8XGxhIAunbtmtAnLy+P/P39ydLSkoyNjcnZ2ZkWLVrU5KDepg7MT58+pddee402bNggtN27d48WLlxItra2JJFIqFevXjR79mwqLCxU2u7du3dp/vz5ZGdnR1KplHr37k1+fn7NFqNEzec6JyeHPD09ydjYmAYNGkRnz55tdSFE9GLAPADat2+f0jJ1X7f6WD09PRXaWvobairGuro62rp1q7DvPXr0IB8fH0pMTCSi1r9XNG327NkKN/DU/zTMIwCKiopS2JeIiAiysrIimUxGb7/9tjDov15FRQUtWLCAunbtSsbGxvTee+8J75F6sbGx1L9//yZj00YhJCJqdEFaxz1+/BgWFhYo6/oFzD3sX2qMUHV1Nf76179izJgxPCUGa1JlZSUKCgrQt29fhUGxjKkSExODwMBAlJWVafwSB2tZZWUl+vfvj4MHD2L48OHaDkfneHh4YNGiRZgxY4bK5c39vxSO32VlMDc311hMejto5YNP9iL+g4Q2r3/t2jXMmDEDWVlZ+Ne//oXLly/z1BiMMbXt378fDg4O6N27Ny5duoRly5Zh6tSpXARpiZGREfbv34/S0lJth6JzSkpKMHnyZEyfPl3boSjQ20LovHMeMMSq5Y6NEBF2796N8PBwVFRUAADu3buH1NRUTJw4UdNhMsZ0XHFxMT777DPhjpwpU6Zg3bp12g5LrzU1uJm9nJ49e2Lp0qXaDkOJ3hZCbVFSUoK5c+fiu+++E9pcXFwQGxsr3GHAGGPqWLp0aac8ODCmL/T2CxXVdfr0aQwcOFChCAoODkZ6ejoXQYwxxtgriguhFlRUVCA0NBTjx4/H77//DuDFd19899132L59O0xMTLQcIWOMMcbaiguhFty9exd79+4VHvv6+uLKlSt47733tBgVexXp2Q2ajDGmNm38n+RCqAWOjo6IjIyEkZERvvrqK/znP/8RvlKcsdaon46iM82twxhjnVH9tCUGBgYd9pw8WLqRu3fvwtLSUuGSV2BgIN59913Y2dlpMTL2qjIwMIClpaUwKamJiYnak1cyxpiuq6urw71792BiYtKhU1JxIdRAXFwcPv74Y0yZMkVhriGRSMRFEHsp9fM4NZyhnTHGmCKxWIw+ffp06IdFvS2E1n37HlB5CZjniqdPnyIsLAxff/01AGDXrl2YMGECjwNiGiMSiSCXy9GzZ88mZ9dmjDF9J5VKIRZ37KgdrRdCO3bswMaNG1FUVIQ33ngDW7ZsEWZqViUxMRHh4eG4evUqrK2tsXTpUgQFBan9vPMTvYGKPKS5VSMgIAD5+fnCMn9/f/5qddYuDAwMOvTaN2OMseZpdbD0oUOHsGjRIqxcuRJZWVnw9vbG+PHjcfv2bZX9CwoK4OvrC29vb2RlZeEvf/kLQkJCcPToUbWfu5YI62/GwcvLSyiCTExM8PXXX+Po0aM8XQZjjDGmB7Q66eqwYcPg5uamMB7HxcUFkyZNwvr165X6L1u2DCdOnEBubq7QFhQUhEuXLuHChQutes76Sdu8DByQWntLaB86dChiYmLQr1+/l9gjxhhjjLWH9pp0VWtnhKqrq5GRkYGxY8cqtI8dOxapqakq17lw4YJSfx8fH6Snp6s97qK+CBKLxVi5ciVSUlK4CGKMMcb0jNbGCJWWlqK2tlbpO3l69eqF4uJilesUFxer7F9TU4PS0lLI5XKldaqqqlBVVSU8LisrE363kXXFnuMx8PLyQkVFhTCJKmOMMcY6l8ePHwPQ/Jcuan2wdONb5Iio2dvmVPVX1V5v/fr1WLNmjcpld6oeYPz48eqEyxhjjDEtun//PiwsLDS2Pa0VQt27d4eBgYHS2Z+SkpImv7nZyspKZX+JRNLk4OYVK1YgPDxcePzo0SPY2dnh9u3bGn0hWds8fvwYtra2+PXXXzV6zZepj3PReXAuOg/ORedRVlaGPn36oGvXrhrdrtYKIalUCnd3d8THx8Pf319oj4+Px/vvv69yneHDhyvM/g4AZ8+exZAhQ4RpDBqTyWSQyWRK7RYWFvxH3YmYm5tzPjoJzkXnwbnoPDgXnYemv2dIq7fPh4eH4+uvv8a+ffuQm5uLsLAw3L59W/heoBUrVmDWrFlC/6CgIBQWFiI8PBy5ubnYt28f9u7di8WLF2trFxhjjDH2CtPqGKFp06bh/v37WLt2LYqKivDmm2/i1KlTwnQWRUVFCt8p1LdvX5w6dQphYWHYvn07rK2tERkZiQ8++EBbu8AYY4yxV5jWB0sHBwcjODhY5bLo6GiltpEjRyIzM7PNzyeTyRAREaHychnreJyPzoNz0XlwLjoPzkXn0V650OoXKjLGGGOMaZNWxwgxxhhjjGkTF0KMMcYY01tcCDHGGGNMb3EhxBhjjDG9pZOF0I4dO9C3b18YGRnB3d0dSUlJzfZPTEyEu7s7jIyM4ODggF27dnVQpLpPnVwcO3YMY8aMQY8ePWBubo7hw4fjzJkzHRit7lP3vVEvJSUFEokEgwYNat8A9Yi6uaiqqsLKlSthZ2cHmUwGR0dH7Nu3r4Oi1W3q5iImJgaurq4wMTGBXC5HYGAg7t+/30HR6q6ffvoJEydOhLW1NUQiEY4fP97iOho5fpOOOXjwIBkaGtKePXsoJyeHQkNDydTUlAoLC1X2v3XrFpmYmFBoaCjl5OTQnj17yNDQkI4cOdLBkesedXMRGhpKGzZsoF9++YXy8vJoxYoVZGhoSJmZmR0cuW5SNx/1Hj16RA4ODjR27FhydXXtmGB1XFty4efnR8OGDaP4+HgqKCign3/+mVJSUjowat2kbi6SkpJILBbT1q1b6datW5SUlERvvPEGTZo0qYMj1z2nTp2ilStX0tGjRwkAxcXFNdtfU8dvnSuEPDw8KCgoSKHN2dmZli9frrL/0qVLydnZWaFt3rx55Onp2W4x6gt1c6HKgAEDaM2aNZoOTS+1NR/Tpk2jVatWUUREBBdCGqJuLr7//nuysLCg+/fvd0R4ekXdXGzcuJEcHBwU2iIjI8nGxqbdYtRHrSmENHX81qlLY9XV1cjIyMDYsWMV2seOHYvU1FSV61y4cEGpv4+PD9LT0/H8+fN2i1XXtSUXjdXV1eHJkycan2BPH7U1H1FRUbh58yYiIiLaO0S90ZZcnDhxAkOGDMEXX3yB3r17w8nJCYsXL0ZFRUVHhKyz2pILLy8v3LlzB6dOnQIR4ffff8eRI0cwYcKEjgiZNaCp47fWv1lak0pLS1FbW6s0e32vXr2UZq2vV1xcrLJ/TU0NSktLIZfL2y1eXdaWXDS2adMmlJeXY+rUqe0Rol5pSz7y8/OxfPlyJCUlQSLRqX8VWtWWXNy6dQvJyckwMjJCXFwcSktLERwcjAcPHvA4oZfQllx4eXkhJiYG06ZNQ2VlJWpqauDn54dt27Z1RMisAU0dv3XqjFA9kUik8JiIlNpa6q+qnalP3VzU++abb7B69WocOnQIPXv2bK/w9E5r81FbW4sZM2ZgzZo1cHJy6qjw9Io67426ujqIRCLExMTAw8MDvr6+2Lx5M6Kjo/mskAaok4ucnByEhITgs88+Q0ZGBk6fPo2CggJhsnDWsTRx/Napj3ndu3eHgYGBUiVfUlKiVDXWs7KyUtlfIpGgW7du7RarrmtLLuodOnQIH330Ef79739j9OjR7Rmm3lA3H0+ePEF6ejqysrKwYMECAC8OxkQEiUSCs2fP4p133umQ2HVNW94bcrkcvXv3hoWFhdDm4uICIsKdO3fQr1+/do1ZV7UlF+vXr8eIESOwZMkSAMDAgQNhamoKb29v/P3vf+erCB1IU8dvnTojJJVK4e7ujvj4eIX2+Ph4eHl5qVxn+PDhSv3Pnj2LIUOGwNDQsN1i1XVtyQXw4kzQnDlzEBsby9fcNUjdfJibm+PKlSu4ePGi8BMUFIT+/fvj4sWLGDZsWEeFrnPa8t4YMWIE7t69i6dPnwpteXl5EIvFsLGxadd4dVlbcvHs2TOIxYqHTgMDAwD/fzaCdQyNHb/VGlr9Cqi/FXLv3r2Uk5NDixYtIlNTU/rf//5HRETLly+nmTNnCv3rb78LCwujnJwc2rt3L98+ryHq5iI2NpYkEglt376dioqKhJ9Hjx5paxd0irr5aIzvGtMcdXPx5MkTsrGxocmTJ9PVq1cpMTGR+vXrR3PnztXWLugMdXMRFRVFEomEduzYQTdv3qTk5GQaMmQIeXh4aGsXdMaTJ08oKyuLsrKyCABt3ryZsrKyhK8yaK/jt84VQkRE27dvJzs7O5JKpeTm5kaJiYnCstmzZ9PIkSMV+ickJNDgwYNJKpWSvb097dy5s4Mj1l3q5GLkyJEEQOln9uzZHR+4jlL3vdEQF0KapW4ucnNzafTo0WRsbEw2NjYUHh5Oz5496+CodZO6uYiMjKQBAwaQsbExyeVyCggIoDt37nRw1Lrnxx9/bPYY0F7HbxERn8tjjDHGmH7SqTFCjDHGGGPq4EKIMcYYY3qLCyHGGGOM6S0uhBhjjDGmt7gQYowxxpje4kKIMcYYY3qLCyHGGGOM6S0uhBhjCqKjo2FpaantMNrM3t4eW7ZsabbP6tWrMWjQoA6JhzHWuXEhxJgOmjNnDkQikdLPjRs3tB0aoqOjFWKSy+WYOnUqCgoKNLL9tLQ0fPLJJ8JjkUiE48ePK/RZvHgxzp8/r5Hna0rj/ezVqxcmTpyIq1evqr2dV7kwZayz40KIMR01btw4FBUVKfz07dtX22EBeDGpa1FREe7evYvY2FhcvHgRfn5+qK2tfelt9+jRAyYmJs32MTMzU2t26rZquJ8nT55EeXk5JkyYgOrq6nZ/bsZY63AhxJiOkslksLKyUvgxMDDA5s2b8dZbb8HU1BS2trYIDg5WmNW8sUuXLmHUqFHo0qULzM3N4e7ujvT0dGF5amoq3n77bRgbG8PW1hYhISEoLy9vNjaRSAQrKyvI5XKMGjUKERERyM7OFs5Y7dy5E46OjpBKpejfvz8OHDigsP7q1avRp08fyGQyWFtbIyQkRFjW8NKYvb09AMDf3x8ikUh43PDS2JkzZ2BkZIRHjx4pPEdISAhGjhypsf0cMmQIwsLCUFhYiOvXrwt9mstHQkICAgMDUVZWJpxZWr16NQCguroaS5cuRe/evWFqaophw4YhISGh2XgYY8q4EGJMz4jFYkRGRiI7Oxv//Oc/8cMPP2Dp0qVN9g8ICICNjQ3S0tKQkZGB5cuXw9DQEABw5coV+Pj44I9//CMuX76MQ4cOITk5GQsWLFArJmNjYwDA8+fPERcXh9DQUPz5z39GdnY25s2bh8DAQPz4448AgCNHjuDLL7/E7t27kZ+fj+PHj+Ott95Sud20tDQAQFRUFIqKioTHDY0ePRqWlpY4evSo0FZbW4vDhw8jICBAY/v56NEjxMbGAoDw+gHN58PLywtbtmwRziwVFRVh8eLFAIDAwECkpKTg4MGDuHz5MqZMmYJx48YhPz+/1TExxgCdnH2eMX03e/ZsMjAwIFNTU+Fn8uTJKvsePnyYunXrJjyOiooiCwsL4XGXLl0oOjpa5bozZ86kTz75RKEtKSmJxGIxVVRUqFyn8fZ//fVX8vT0JBsbG6qqqiIvLy/6+OOPFdaZMmUK+fr6EhHRpk2byMnJiaqrq1Vu387Ojr788kvhMQCKi4tT6BMREUGurq7C45CQEHrnnXeEx2fOnCGpVEoPHjx4qf0EQKampmRiYiLMpO3n56eyf72W8kFEdOPGDRKJRPTbb78ptL/77ru0YsWKZrfPGFMk0W4ZxhhrL6NGjcLOnTuFx6ampgCAH3/8Ef/4xz+Qk5ODx48fo6amBpWVlSgvLxf6NBQeHo65c+fiwIEDGD16NKZMmQJHR0cAQEZGBm7cuIGYmBihPxGhrq4OBQUFcHFxURlbWVkZzMzMQER49uwZ3NzccOzYMUilUuTm5ioMdgaAESNGYOvWrQCAKVOmYMuWLXBwcMC4cePg6+uLiRMnQiJp+7+zgIAADB8+HHfv3oW1tTViYmLg6+uL11577aX2s0uXLsjMzERNTQ0SExOxceNG7Nq1S6GPuvkAgMzMTBARnJycFNqrqqo6ZOwTY7qECyHGdJSpqSlef/11hbbCwkL4+voiKCgIf/vb39C1a1ckJyfjo48+wvPnz1VuZ/Xq1ZgxYwZOnjyJ77//HhERETh48CD8/f1RV1eHefPmKYzRqdenT58mY6svEMRiMXr16qV0wBeJRAqPiUhos7W1xfXr1xEfH49z584hODgYGzduRGJiosIlJ3V4eHjA0dERBw8exKeffoq4uDhERUUJy9u6n2KxWMiBs7MziouLMW3aNPz0008A2paP+ngMDAyQkZEBAwMDhWVmZmZq7Ttj+o4LIcb0SHp6OmpqarBp0yaIxS+GCB4+fLjF9ZycnODk5ISwsDBMnz4dUVFR8Pf3h5ubG65evapUcLWkYYHQmIuLC5KTkzFr1iyhLTU1VeGsi7GxMfz8/ODn54f58+fD2dkZV65cgZubm9L2DA0NW3U32owZMxATEwMbGxuIxWJMmDBBWNbW/WwsLCwMmzdvRlxcHPz9/VuVD6lUqhT/4MGDUVtbi5KSEnh7e79UTIzpOx4szZgecXR0RE1NDbZt24Zbt27hwIEDSpdqGqqoqMCCBQuQkJCAwsJCpKSkIC0tTShKli1bhgsXLmD+/Pm4ePEi8vPzceLECSxcuLDNMS5ZsgTR0dHYtWsX8vPzsXnzZhw7dkwYJBwdHY29e/ciOztb2AdjY2PY2dmp3J69vT3Onz+P4uJiPHz4sMnnDQgIQGZmJtatW4fJkyfDyMhIWKap/TQ3N8fcuXMREREBImpVPuzt7fH06VOcP38epaWlePbsGZycnBAQEIBZs2bh2LFjKCgoQFpaGjZs2IBTp06pFRNjek+bA5QYY+1j9uzZ9P7776tctnnzZpLL5WRsbEw+Pj60f/9+AkAPHz4kIsXBuVVVVfThhx+Sra0tSaVSsra2pgULFigMEP7ll19ozJgxZGZmRqampjRw4EBat25dk7GpGvzb2I4dO8jBwYEMDQ3JycmJ9u/fLyyLi4ujYcOGkbm5OZmampKnpyedO3dOWN54sPSJEyfo9ddfJ4lEQnZ2dkSkPFi63tChQwkA/fDDD0rLNLWfhYWFJJFI6NChQ0TUcj6IiIKCgqhbt24EgCIiIoiIqLq6mj777DOyt7cnQ0NDsrKyIn9/f7p8+XKTMTHGlImIiLRbijHGGGOMaQdfGmOMMcaY3uJCiDHGGGN6iwshxhhjjOktLoQYY4wxpre4EGKMMcaY3uJCiDHGGGN6iwshxhhjjOktLoQYY4wxpre4EGKMMcaY3uJCiDHGGGN6iwshxhhjjOktLoQYY4wxprf+D8EsdgVBqXiLAAAAAElFTkSuQmCC\n",
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||
"text/plain": [
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||
"<Figure size 640x480 with 1 Axes>"
|
||
]
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||
},
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||
"metadata": {
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"filenames": {
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||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week47_99_3.png"
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||
}
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||
},
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"output_type": "display_data"
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||
},
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||
{
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||
"data": {
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||
"image/png": 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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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]
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},
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"metadata": {
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"filenames": {
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"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week47_99_4.png"
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}
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},
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"output_type": "display_data"
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},
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{
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"data": {
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\n",
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||
"text/plain": [
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||
"<Figure size 640x480 with 1 Axes>"
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]
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},
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"metadata": {
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"filenames": {
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"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week47_99_5.png"
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}
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},
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"output_type": "display_data"
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},
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{
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"data": {
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|
||
"text/plain": [
|
||
"<Figure size 5000x1000 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week47_99_6.png"
|
||
}
|
||
},
|
||
"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.datasets import load_breast_cancer\n",
|
||
"from sklearn.preprocessing import LabelEncoder\n",
|
||
"from sklearn.model_selection import cross_validate\n",
|
||
"import scikitplot as skplt\n",
|
||
"import xgboost as xgb\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",
|
||
"#now scale the data\n",
|
||
"from sklearn.preprocessing import StandardScaler\n",
|
||
"scaler = StandardScaler()\n",
|
||
"scaler.fit(X_train)\n",
|
||
"X_train_scaled = scaler.transform(X_train)\n",
|
||
"X_test_scaled = scaler.transform(X_test)\n",
|
||
"\n",
|
||
"xg_clf = xgb.XGBClassifier()\n",
|
||
"xg_clf.fit(X_train_scaled,y_train)\n",
|
||
"\n",
|
||
"y_test = xg_clf.predict(X_test_scaled)\n",
|
||
"\n",
|
||
"print(\"Test set accuracy with Gradient Boosting and scaled data: {:.2f}\".format(xg_clf.score(X_test_scaled,y_test)))\n",
|
||
"\n",
|
||
"import scikitplot as skplt\n",
|
||
"y_pred = xg_clf.predict(X_test_scaled)\n",
|
||
"skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)\n",
|
||
"save_fig(\"xdclassiffierconfusion\")\n",
|
||
"plt.show()\n",
|
||
"y_probas = xg_clf.predict_proba(X_test_scaled)\n",
|
||
"skplt.metrics.plot_roc(y_test, y_probas)\n",
|
||
"save_fig(\"xdclassiffierroc\")\n",
|
||
"plt.show()\n",
|
||
"skplt.metrics.plot_cumulative_gain(y_test, y_probas)\n",
|
||
"save_fig(\"gdclassiffiercgain\")\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"\n",
|
||
"xgb.plot_tree(xg_clf,num_trees=0)\n",
|
||
"plt.rcParams['figure.figsize'] = [50, 10]\n",
|
||
"save_fig(\"xgtree\")\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"xgb.plot_importance(xg_clf)\n",
|
||
"plt.rcParams['figure.figsize'] = [5, 5]\n",
|
||
"save_fig(\"xgparams\")\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4756e98c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Summary of course"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0d2f09bc",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## What? Me worry? No final exam in this course!\n",
|
||
"<!-- dom:FIGURE: [figures/exam1.jpeg, width=500 frac=0.6] -->\n",
|
||
"<!-- begin figure -->\n",
|
||
"\n",
|
||
"<img src=\"figures/exam1.jpeg\" width=\"500\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
|
||
"<!-- end figure -->"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "bedc75f8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## What is the link between Artificial Intelligence and Machine Learning and some general Remarks\n",
|
||
"\n",
|
||
"Artificial intelligence is built upon integrated machine learning\n",
|
||
"algorithms as discussed in this course, which in turn are fundamentally rooted in optimization and\n",
|
||
"statistical learning.\n",
|
||
"\n",
|
||
"Can we have Artificial Intelligence without Machine Learning? See [this post for inspiration](https://www.linkedin.com/pulse/what-artificial-intelligence-without-machine-learning-claudia-pohlink)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "25385cd0",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Going back to the beginning of the semester\n",
|
||
"\n",
|
||
"Traditionally the field of machine learning has had its main focus on\n",
|
||
"predictions and correlations. These concepts outline in some sense\n",
|
||
"the difference between machine learning and what is normally called\n",
|
||
"Bayesian statistics or Bayesian inference.\n",
|
||
"\n",
|
||
"In machine learning and prediction based tasks, we are often\n",
|
||
"interested in developing algorithms that are capable of learning\n",
|
||
"patterns from given data in an automated fashion, and then using these\n",
|
||
"learned patterns to make predictions or assessments of newly given\n",
|
||
"data. In many cases, our primary concern is the quality of the\n",
|
||
"predictions or assessments, and we are less concerned with the\n",
|
||
"underlying patterns that were learned in order to make these\n",
|
||
"predictions. This leads to what normally has been labeled as a\n",
|
||
"frequentist approach."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "97a4cbd9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Not so sharp distinctions\n",
|
||
"\n",
|
||
"You should keep in mind that the division between a traditional\n",
|
||
"frequentist approach with focus on predictions and correlations only\n",
|
||
"and a Bayesian approach with an emphasis on estimations and\n",
|
||
"causations, is not that sharp. Machine learning can be frequentist\n",
|
||
"with ensemble methods (EMB) as examples and Bayesian with Gaussian\n",
|
||
"Processes as examples.\n",
|
||
"\n",
|
||
"If one views ML from a statistical learning\n",
|
||
"perspective, one is then equally interested in estimating errors as\n",
|
||
"one is in finding correlations and making predictions. It is important\n",
|
||
"to keep in mind that the frequentist and Bayesian approaches differ\n",
|
||
"mainly in their interpretations of probability. In the frequentist\n",
|
||
"world, we can only assign probabilities to repeated random\n",
|
||
"phenomena. From the observations of these phenomena, we can infer the\n",
|
||
"probability of occurrence of a specific event. In Bayesian\n",
|
||
"statistics, we assign probabilities to specific events and the\n",
|
||
"probability represents the measure of belief/confidence for that\n",
|
||
"event. The belief can be updated in the light of new evidence."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "77dada73",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Topics we have covered this year\n",
|
||
"\n",
|
||
"The course has two central parts\n",
|
||
"\n",
|
||
"1. Statistical analysis and optimization of data\n",
|
||
"\n",
|
||
"2. Machine learning"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "4f784898",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Statistical analysis and optimization of data\n",
|
||
"\n",
|
||
"The following topics have been discussed:\n",
|
||
"1. Basic concepts, expectation values, variance, covariance, correlation functions and errors;\n",
|
||
"\n",
|
||
"2. Simpler models, binomial distribution, the Poisson distribution, simple and multivariate normal distributions;\n",
|
||
"\n",
|
||
"3. Central elements from linear algebra, matrix inversion and SVD\n",
|
||
"\n",
|
||
"4. Gradient methods for data optimization\n",
|
||
"\n",
|
||
"5. Estimation of errors using cross-validation, bootstrapping and jackknife methods;\n",
|
||
"\n",
|
||
"6. Practical optimization using Singular-value decomposition and least squares for parameterizing data.\n",
|
||
"\n",
|
||
"7. Principal Component Analysis to reduce the number of features."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "35722378",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Machine learning\n",
|
||
"\n",
|
||
"The following topics will be covered\n",
|
||
"1. Linear methods for regression and classification:\n",
|
||
"\n",
|
||
"a. Ordinary Least Squares\n",
|
||
"\n",
|
||
"b. Ridge regression\n",
|
||
"\n",
|
||
"c. Lasso regression\n",
|
||
"\n",
|
||
"d. Logistic regression\n",
|
||
"\n",
|
||
"5. Neural networks and deep learning:\n",
|
||
"\n",
|
||
"a. Feed Forward Neural Networks\n",
|
||
"\n",
|
||
"b. Convolutional Neural Networks\n",
|
||
"\n",
|
||
"c. Recurrent Neural Networks\n",
|
||
"\n",
|
||
"4. Decisions trees and ensemble methods:\n",
|
||
"\n",
|
||
"a. Decision trees\n",
|
||
"\n",
|
||
"b. Bagging and voting\n",
|
||
"\n",
|
||
"c. Random forests\n",
|
||
"\n",
|
||
"d. Boosting and gradient boosting\n",
|
||
"\n",
|
||
"5. Support vector machines, not covered this year but included in notes\n",
|
||
"\n",
|
||
"a. Binary classification and multiclass classification\n",
|
||
"\n",
|
||
"b. Kernel methods\n",
|
||
"\n",
|
||
"c. Regression"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c5de1725",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Learning outcomes and overarching aims of this course\n",
|
||
"\n",
|
||
"The course introduces a variety of central algorithms and methods\n",
|
||
"essential for studies of data analysis and machine learning. The\n",
|
||
"course is project based and through the various projects, normally\n",
|
||
"three, you will be exposed to fundamental research problems\n",
|
||
"in these fields, with the aim to reproduce state of the art scientific\n",
|
||
"results. The students will learn to develop and structure large codes\n",
|
||
"for studying these systems, get acquainted with computing facilities\n",
|
||
"and learn to handle large scientific projects. A good scientific and\n",
|
||
"ethical conduct is emphasized throughout the course. \n",
|
||
"\n",
|
||
"* Understand linear methods for regression and classification;\n",
|
||
"\n",
|
||
"* Learn about neural network;\n",
|
||
"\n",
|
||
"* Learn about bagging, boosting and trees\n",
|
||
"\n",
|
||
"* Support vector machines, not covered\n",
|
||
"\n",
|
||
"* Learn about basic data analysis;\n",
|
||
"\n",
|
||
"* Be capable of extending the acquired knowledge to other systems and cases;\n",
|
||
"\n",
|
||
"* Have an understanding of central algorithms used in data analysis and machine learning;\n",
|
||
"\n",
|
||
"* Work on numerical projects to illustrate the theory. The projects play a central role and you are expected to know modern programming languages like Python or C++."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "77f0effd",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Perspective on Machine Learning\n",
|
||
"\n",
|
||
"1. Rapidly emerging application area\n",
|
||
"\n",
|
||
"2. Experiment AND theory are evolving in many many fields. Still many low-hanging fruits.\n",
|
||
"\n",
|
||
"3. Requires education/retraining for more widespread adoption\n",
|
||
"\n",
|
||
"4. A lot of “word-of-mouth” development methods\n",
|
||
"\n",
|
||
"Huge amounts of data sets require automation, classical analysis tools often inadequate. \n",
|
||
"High energy physics hit this wall in the 90’s.\n",
|
||
"In 2009 single top quark production was determined via [Boosted decision trees, Bayesian\n",
|
||
"Neural Networks, etc.](https://arxiv.org/pdf/0903.0850.pdf). Similarly, the search for Higgs was a statistical learning tour de force. See this link on [Kaggle.com](https://www.kaggle.com/c/higgs-boson)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1da4f54b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Machine Learning Research\n",
|
||
"\n",
|
||
"Where to find recent results:\n",
|
||
"1. Conference proceedings, arXiv and blog posts!\n",
|
||
"\n",
|
||
"2. **NIPS**: [Neural Information Processing Systems](https://papers.nips.cc)\n",
|
||
"\n",
|
||
"3. **ICLR**: [International Conference on Learning Representations](https://openreview.net/group?id=ICLR.cc/2018/Conference#accepted-oral-papers)\n",
|
||
"\n",
|
||
"4. **ICML**: International Conference on Machine Learning\n",
|
||
"\n",
|
||
"5. [Journal of Machine Learning Research](http://www.jmlr.org/papers/v19/) \n",
|
||
"\n",
|
||
"6. [Follow ML on ArXiv](https://arxiv.org/list/cs.LG/recent)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "960798e1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Starting your Machine Learning Project\n",
|
||
"\n",
|
||
"1. Identify problem type: classification, regression\n",
|
||
"\n",
|
||
"2. Consider your data carefully\n",
|
||
"\n",
|
||
"3. Choose a simple model that fits 1. and 2.\n",
|
||
"\n",
|
||
"4. Consider your data carefully again! Think of data representation more carefully.\n",
|
||
"\n",
|
||
"5. Based on your results, feedback loop to earliest possible point"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3bb0c58d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Choose a Model and Algorithm\n",
|
||
"\n",
|
||
"1. Supervised?\n",
|
||
"\n",
|
||
"2. Start with the simplest model that fits your problem\n",
|
||
"\n",
|
||
"3. Start with minimal processing of data"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "06e070b4",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Preparing Your Data\n",
|
||
"\n",
|
||
"1. Shuffle your data\n",
|
||
"\n",
|
||
"2. Mean center your data\n",
|
||
"\n",
|
||
" * Why?\n",
|
||
"\n",
|
||
"3. Normalize the variance\n",
|
||
"\n",
|
||
" * Why?\n",
|
||
"\n",
|
||
"4. [Whitening](https://multivariatestatsjl.readthedocs.io/en/latest/whiten.html)\n",
|
||
"\n",
|
||
" * Decorrelates data\n",
|
||
"\n",
|
||
" * Can be hit or miss\n",
|
||
"\n",
|
||
"5. When to do train/test split?\n",
|
||
"\n",
|
||
"Whitening is a decorrelation transformation that transforms a set of\n",
|
||
"random variables into a set of new random variables with identity\n",
|
||
"covariance (uncorrelated with unit variances)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8fc31057",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Which Activation and Weights to Choose in Neural Networks\n",
|
||
"\n",
|
||
"1. RELU? ELU?\n",
|
||
"\n",
|
||
"2. Sigmoid or Tanh?\n",
|
||
"\n",
|
||
"3. Set all weights to 0?\n",
|
||
"\n",
|
||
" * Terrible idea\n",
|
||
"\n",
|
||
"4. Set all weights to random values?\n",
|
||
"\n",
|
||
" * Small random values"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "be1f2461",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Optimization Methods and Hyperparameters\n",
|
||
"1. Stochastic gradient descent\n",
|
||
"\n",
|
||
"a. Stochastic gradient descent + momentum\n",
|
||
"\n",
|
||
"2. State-of-the-art approaches:\n",
|
||
"\n",
|
||
" * RMSProp\n",
|
||
"\n",
|
||
" * Adam\n",
|
||
"\n",
|
||
" * and more\n",
|
||
"\n",
|
||
"Which regularization and hyperparameters? $L_1$ or $L_2$, soft\n",
|
||
"classifiers, depths of trees and many other. Need to explore a large\n",
|
||
"set of hyperparameters and regularization methods."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2bf97adf",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Resampling\n",
|
||
"\n",
|
||
"When do we resample?\n",
|
||
"\n",
|
||
"1. [Bootstrap](https://www.cambridge.org/core/books/bootstrap-methods-and-their-application/ED2FD043579F27952363566DC09CBD6A)\n",
|
||
"\n",
|
||
"2. [Cross-validation](https://www.youtube.com/watch?v=fSytzGwwBVw&ab_channel=StatQuestwithJoshStarmer)\n",
|
||
"\n",
|
||
"3. Jackknife and many other"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "af4d612c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Other courses on Data science and Machine Learning at UiO\n",
|
||
"\n",
|
||
"1. [FYS5429 Advanced Machine Learning and Data Analysis for the Physical Sciences](https://www.uio.no/studier/emner/matnat/fys/FYS5429/index-eng.html). Discussed deep learning and generative deep learning.\n",
|
||
"\n",
|
||
"2. [FYS5419 Quantum Computing and Quantum Machine Learning](https://www.uio.no/studier/emner/matnat/fys/FYS5419/index-eng.html)\n",
|
||
"\n",
|
||
"3. [STK2100 Machine learning and statistical methods for prediction and classification](http://www.uio.no/studier/emner/matnat/math/STK2100/index-eng.html). \n",
|
||
"\n",
|
||
"4. [IN3050/IN4050 Introduction to Artificial Intelligence and Machine Learning](https://www.uio.no/studier/emner/matnat/ifi/IN3050/index-eng.html). Introductory course in machine learning and AI with an algorithmic approach. \n",
|
||
"\n",
|
||
"5. [STK-INF3000/4000 Selected Topics in Data Science](http://www.uio.no/studier/emner/matnat/math/STK-INF3000/index-eng.html). The course provides insight into selected contemporary relevant topics within Data Science. \n",
|
||
"\n",
|
||
"6. [IN4080 Natural Language Processing](https://www.uio.no/studier/emner/matnat/ifi/IN4080/index.html). Probabilistic and machine learning techniques applied to natural language processing. o [STK-IN4300 – Statistical learning methods in Data Science](https://www.uio.no/studier/emner/matnat/math/STK-IN4300/index-eng.html). An advanced introduction to statistical and machine learning. For students with a good mathematics and statistics background.\n",
|
||
"\n",
|
||
"7. [IN-STK5000 Adaptive Methods for Data-Based Decision Making](https://www.uio.no/studier/emner/matnat/ifi/IN-STK5000/index-eng.html). Methods for adaptive collection and processing of data based on machine learning techniques. \n",
|
||
"\n",
|
||
"8. [IN5400/INF5860 – Machine Learning for Image Analysis](https://www.uio.no/studier/emner/matnat/ifi/IN5400/). An introduction to deep learning with particular emphasis on applications within Image analysis, but useful for other application areas too.\n",
|
||
"\n",
|
||
"9. [TEK5040 – Dyp læring for autonome systemer](https://www.uio.no/studier/emner/matnat/its/TEK5040/). The course addresses advanced algorithms and architectures for deep learning with neural networks. The course provides an introduction to how deep-learning techniques can be used in the construction of key parts of advanced autonomous systems that exist in physical environments and cyber environments."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "02ca1e2c",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Additional courses of interest\n",
|
||
"\n",
|
||
"1. [STK4051 Computational Statistics](https://www.uio.no/studier/emner/matnat/math/STK4051/index-eng.html)\n",
|
||
"\n",
|
||
"2. [STK4021 Applied Bayesian Analysis and Numerical Methods](https://www.uio.no/studier/emner/matnat/math/STK4021/index-eng.html)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "1bd70651",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## What's the future like?\n",
|
||
"\n",
|
||
"Based on multi-layer nonlinear neural networks, deep learning can\n",
|
||
"learn directly from raw data, automatically extract and abstract\n",
|
||
"features from layer to layer, and then achieve the goal of regression,\n",
|
||
"classification, or ranking. Deep learning has made breakthroughs in\n",
|
||
"computer vision, speech processing and natural language, and reached\n",
|
||
"or even surpassed human level. The success of deep learning is mainly\n",
|
||
"due to the three factors: big data, big model, and big computing.\n",
|
||
"\n",
|
||
"In the past few decades, many different architectures of deep neural\n",
|
||
"networks have been proposed, such as\n",
|
||
"1. Convolutional neural networks, which are mostly used in image and video data processing, and have also been applied to sequential data such as text processing;\n",
|
||
"\n",
|
||
"2. Recurrent neural networks, which can process sequential data of variable length and have been widely used in natural language understanding and speech processing;\n",
|
||
"\n",
|
||
"3. Encoder-decoder framework, which is mostly used for image or sequence generation, such as machine translation, text summarization, and image captioning.\n",
|
||
"\n",
|
||
"4. **Generative deep learning**! Recent textbook by David Foster (and obviously many other ones) at <https://www.oreilly.com/library/view/generative-deep-learning/9781492041931/>\""
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ec41c770",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Types of Machine Learning, a repetition\n",
|
||
"\n",
|
||
"The approaches to machine learning are many, but are often split into two main categories. \n",
|
||
"In *supervised learning* we know the answer to a problem,\n",
|
||
"and let the computer deduce the logic behind it. On the other hand, *unsupervised learning*\n",
|
||
"is a method for finding patterns and relationship in data sets without any prior knowledge of the system.\n",
|
||
"Some authours also operate with a third category, namely *reinforcement learning*. This is a paradigm \n",
|
||
"of learning inspired by behavioural psychology, where learning is achieved by trial-and-error, \n",
|
||
"solely from rewards and punishment.\n",
|
||
"\n",
|
||
"Another way to categorize machine learning tasks is to consider the desired output of a system.\n",
|
||
"Some of the most common tasks are:\n",
|
||
"\n",
|
||
" * Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning.\n",
|
||
"\n",
|
||
" * Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values.\n",
|
||
"\n",
|
||
" * Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.\n",
|
||
"\n",
|
||
" * Other unsupervised learning algortihms like **Boltzmann machines**"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "eb4b2fd3",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Why Boltzmann machines?\n",
|
||
"\n",
|
||
"What is known as restricted Boltzmann Machines (RMB) have received a lot of attention lately. \n",
|
||
"One of the major reasons is that they can be stacked layer-wise to build deep neural networks that capture complicated statistics.\n",
|
||
"\n",
|
||
"The original RBMs had just one visible layer and a hidden layer, but recently so-called Gaussian-binary RBMs have gained quite some popularity in imaging since they are capable of modeling continuous data that are common to natural images. \n",
|
||
"\n",
|
||
"Furthermore, they have been used to solve complicated [quantum mechanical many-particle problems or classical statistical physics problems like the Ising and Potts classes of models](https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.91.045002)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "666fb9a8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Boltzmann Machines\n",
|
||
"\n",
|
||
"Why use a generative model rather than the more well known discriminative deep neural networks (DNN)? **Simplest approach to generative deep learning**.\n",
|
||
"\n",
|
||
"* Discriminitave methods have several limitations: They are mainly supervised learning methods, thus requiring labeled data. And there are tasks they cannot accomplish, like drawing new examples from an unknown probability distribution.\n",
|
||
"\n",
|
||
"* A generative model can learn to represent and sample from a probability distribution. The core idea is to learn a parametric model of the probability distribution from which the training data was drawn. As an example\n",
|
||
"\n",
|
||
"a. A model for images could learn to draw new examples of cats and dogs, given a training dataset of images of cats and dogs.\n",
|
||
"\n",
|
||
"b. Generate a sample of an ordered or disordered phase, having been given samples of such phases.\n",
|
||
"\n",
|
||
"c. Model the trial function for [Monte Carlo calculations](https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.91.045002)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "59961309",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Some similarities and differences from DNNs\n",
|
||
"\n",
|
||
"1. Both use gradient-descent based learning procedures for minimizing cost functions\n",
|
||
"\n",
|
||
"2. Energy based models don't use backpropagation and automatic differentiation for computing gradients, instead turning to Markov Chain Monte Carlo methods.\n",
|
||
"\n",
|
||
"3. DNNs often have several hidden layers. A restricted Boltzmann machine has only one hidden layer, however several RBMs can be stacked to make up Deep Belief Networks, of which they constitute the building blocks.\n",
|
||
"\n",
|
||
"History: The RBM was developed by amongst others [Geoffrey Hinton](https://en.wikipedia.org/wiki/Geoffrey_Hinton), called by some the \"Godfather of Deep Learning\", working with the University of Toronto and Google."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "95115be7",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Boltzmann machines (BM)\n",
|
||
"\n",
|
||
"A BM is what we would call an undirected probabilistic graphical model\n",
|
||
"with stochastic continuous or discrete units.\n",
|
||
"\n",
|
||
"It is interpreted as a stochastic recurrent neural network where the\n",
|
||
"state of each unit(neurons/nodes) depends on the units it is connected\n",
|
||
"to. The weights in the network represent thus the strength of the\n",
|
||
"interaction between various units/nodes.\n",
|
||
"\n",
|
||
"It turns into a Hopfield network if we choose deterministic rather\n",
|
||
"than stochastic units. In contrast to a Hopfield network, a BM is a\n",
|
||
"so-called generative model. It allows us to generate new samples from\n",
|
||
"the learned distribution."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "67240cfb",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## A standard BM setup\n",
|
||
"\n",
|
||
"A standard BM network is divided into a set of observable and visible units $\\hat{x}$ and a set of unknown hidden units/nodes $\\hat{h}$.\n",
|
||
"\n",
|
||
"Additionally there can be bias nodes for the hidden and visible layers. These biases are normally set to $1$.\n",
|
||
"\n",
|
||
"BMs are stackable, meaning they cwe can train a BM which serves as input to another BM. We can construct deep networks for learning complex PDFs. The layers can be trained one after another, a feature which makes them popular in deep learning\n",
|
||
"\n",
|
||
"However, they are often hard to train. This leads to the introduction of so-called restricted BMs, or RBMS.\n",
|
||
"Here we take away all lateral connections between nodes in the visible layer as well as connections between nodes in the hidden layer. The network is illustrated in the figure below."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "34238f91",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The structure of the RBM network\n",
|
||
"\n",
|
||
"<!-- dom:FIGURE: [figures/RBM.png, width=800 frac=1.0] -->\n",
|
||
"<!-- begin figure -->\n",
|
||
"\n",
|
||
"<img src=\"figures/RBM.png\" width=\"800\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
|
||
"<!-- end figure -->"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b5a2f4e8",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The network\n",
|
||
"\n",
|
||
"**The network layers**:\n",
|
||
"1. A function $\\mathbf{x}$ that represents the visible layer, a vector of $M$ elements (nodes). This layer represents both what the RBM might be given as training input, and what we want it to be able to reconstruct. This might for example be given by the pixels of an image or coefficients representing speech, or the coordinates of a quantum mechanical state function.\n",
|
||
"\n",
|
||
"2. The function $\\mathbf{h}$ represents the hidden, or latent, layer. A vector of $N$ elements (nodes). Also called \"feature detectors\"."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8814bf46",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Goals\n",
|
||
"\n",
|
||
"The goal of the hidden layer is to increase the model's expressive\n",
|
||
"power. We encode complex interactions between visible variables by\n",
|
||
"introducing additional, hidden variables that interact with visible\n",
|
||
"degrees of freedom in a simple manner, yet still reproduce the complex\n",
|
||
"correlations between visible degrees in the data once marginalized\n",
|
||
"over (integrated out).\n",
|
||
"\n",
|
||
"**The network parameters, to be optimized/learned**:\n",
|
||
"1. $\\mathbf{a}$ represents the visible bias, a vector of same length as $\\mathbf{x}$.\n",
|
||
"\n",
|
||
"2. $\\mathbf{b}$ represents the hidden bias, a vector of same lenght as $\\mathbf{h}$.\n",
|
||
"\n",
|
||
"3. $W$ represents the interaction weights, a matrix of size $M\\times N$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7fc70e53",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Joint distribution\n",
|
||
"\n",
|
||
"The restricted Boltzmann machine is described by a Boltzmann distribution"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "db48a9df",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto1\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
"\tP_{rbm}(\\mathbf{x},\\mathbf{h}) = \\frac{1}{Z} e^{-\\frac{1}{T_0}E(\\mathbf{x},\\mathbf{h})},\n",
|
||
"\\label{_auto1} \\tag{1}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "62a31f83",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where $Z$ is the normalization constant or partition function, defined as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "cb335a56",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto2\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
"\tZ = \\int \\int e^{-\\frac{1}{T_0}E(\\mathbf{x},\\mathbf{h})} d\\mathbf{x} d\\mathbf{h}.\n",
|
||
"\\label{_auto2} \\tag{2}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "599fa487",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"It is common to ignore $T_0$ by setting it to one."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "114dd535",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Network Elements, the energy function\n",
|
||
"\n",
|
||
"The function $E(\\mathbf{x},\\mathbf{h})$ gives the **energy** of a\n",
|
||
"configuration (pair of vectors) $(\\mathbf{x}, \\mathbf{h})$. The lower\n",
|
||
"the energy of a configuration, the higher the probability of it. This\n",
|
||
"function also depends on the parameters $\\mathbf{a}$, $\\mathbf{b}$ and\n",
|
||
"$W$. Thus, when we adjust them during the learning procedure, we are\n",
|
||
"adjusting the energy function to best fit our problem.\n",
|
||
"\n",
|
||
"An expression for the energy function is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "211cb42a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"$$\n",
|
||
"E(\\hat{x},\\hat{h}) = -\\sum_{ia}^{NA}b_i^a \\alpha_i^a(x_i)-\\sum_{jd}^{MD}c_j^d \\beta_j^d(h_j)-\\sum_{ijad}^{NAMD}b_i^a \\alpha_i^a(x_i)c_j^d \\beta_j^d(h_j)w_{ij}^{ad}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e70c1aa0",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"Here $\\beta_j^d(h_j)$ and $\\alpha_i^a(x_j)$ are so-called transfer functions that map a given input value to a desired feature value. The labels $a$ and $d$ denote that there can be multiple transfer functions per variable. The first sum depends only on the visible units. The second on the hidden ones. **Note** that there is no connection between nodes in a layer.\n",
|
||
"\n",
|
||
"The quantities $b$ and $c$ can be interpreted as the visible and hidden biases, respectively.\n",
|
||
"\n",
|
||
"The connection between the nodes in the two layers is given by the weights $w_{ij}$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8176921d",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Defining different types of RBMs\n",
|
||
"There are different variants of RBMs, and the differences lie in the types of visible and hidden units we choose as well as in the implementation of the energy function $E(\\mathbf{x},\\mathbf{h})$. \n",
|
||
"\n",
|
||
"**Binary-Binary RBM:**\n",
|
||
"\n",
|
||
"RBMs were first developed using binary units in both the visible and hidden layer. The corresponding energy function is defined as follows:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d4559704",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto3\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
"\tE(\\mathbf{x}, \\mathbf{h}) = - \\sum_i^M x_i a_i- \\sum_j^N b_j h_j - \\sum_{i,j}^{M,N} x_i w_{ij} h_j,\n",
|
||
"\\label{_auto3} \\tag{3}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6087f3b1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"where the binary values taken on by the nodes are most commonly 0 and 1.\n",
|
||
"\n",
|
||
"**Gaussian-Binary RBM:**\n",
|
||
"\n",
|
||
"Another varient is the RBM where the visible units are Gaussian while the hidden units remain binary:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "090cbae9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"<!-- Equation labels as ordinary links -->\n",
|
||
"<div id=\"_auto4\"></div>\n",
|
||
"\n",
|
||
"$$\n",
|
||
"\\begin{equation}\n",
|
||
"\tE(\\mathbf{x}, \\mathbf{h}) = \\sum_i^M \\frac{(x_i - a_i)^2}{2\\sigma_i^2} - \\sum_j^N b_j h_j - \\sum_{i,j}^{M,N} \\frac{x_i w_{ij} h_j}{\\sigma_i^2}. \n",
|
||
"\\label{_auto4} \\tag{4}\n",
|
||
"\\end{equation}\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "19c78c3f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## More about RBMs\n",
|
||
"1. Useful when we model continuous data (i.e., we wish $\\mathbf{x}$ to be continuous)\n",
|
||
"\n",
|
||
"2. Requires a smaller learning rate, since there's no upper bound to the value a component might take in the reconstruction\n",
|
||
"\n",
|
||
"Other types of units include:\n",
|
||
"1. Softmax and multinomial units\n",
|
||
"\n",
|
||
"2. Gaussian visible and hidden units\n",
|
||
"\n",
|
||
"3. Binomial units\n",
|
||
"\n",
|
||
"4. Rectified linear units\n",
|
||
"\n",
|
||
"To read more, see [Lectures on Boltzmann machines in Physics](https://github.com/CompPhysics/ComputationalPhysics2/blob/gh-pages/doc/pub/notebook2/ipynb/notebook2.ipynb)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2c32807b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Autoencoders: Overarching view\n",
|
||
"\n",
|
||
"Autoencoders are artificial neural networks capable of learning\n",
|
||
"efficient representations of the input data (these representations are called codings) without\n",
|
||
"any supervision (i.e., the training set is unlabeled). These codings\n",
|
||
"typically have a much lower dimensionality than the input data, making\n",
|
||
"autoencoders useful for dimensionality reduction. \n",
|
||
"\n",
|
||
"More importantly, autoencoders act as powerful feature detectors, and\n",
|
||
"they can be used for unsupervised pretraining of deep neural networks.\n",
|
||
"\n",
|
||
"Lastly, they are capable of randomly generating new data that looks\n",
|
||
"very similar to the training data; this is called a generative\n",
|
||
"model. For example, you could train an autoencoder on pictures of\n",
|
||
"faces, and it would then be able to generate new faces. Surprisingly,\n",
|
||
"autoencoders work by simply learning to copy their inputs to their\n",
|
||
"outputs. This may sound like a trivial task, but we will see that\n",
|
||
"constraining the network in various ways can make it rather\n",
|
||
"difficult. For example, you can limit the size of the internal\n",
|
||
"representation, or you can add noise to the inputs and train the\n",
|
||
"network to recover the original inputs. These constraints prevent the\n",
|
||
"autoencoder from trivially copying the inputs directly to the outputs,\n",
|
||
"which forces it to learn efficient ways of representing the data. In\n",
|
||
"short, the codings are byproducts of the autoencoder’s attempt to\n",
|
||
"learn the identity function under some constraints.\n",
|
||
"\n",
|
||
"[Video on autoencoders](https://www.coursera.org/lecture/building-deep-learning-models-with-tensorflow/autoencoders-1U4L3)\n",
|
||
"\n",
|
||
"See also A. Geron's textbook, chapter 15."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f988bcd6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Bayesian Machine Learning\n",
|
||
"\n",
|
||
"This is an important topic if we aim at extracting a probability\n",
|
||
"distribution. This gives us also a confidence interval and error\n",
|
||
"estimates.\n",
|
||
"\n",
|
||
"Bayesian machine learning allows us to encode our prior beliefs about\n",
|
||
"what those models should look like, independent of what the data tells\n",
|
||
"us. This is especially useful when we don’t have a ton of data to\n",
|
||
"confidently learn our model.\n",
|
||
"\n",
|
||
"[Video on Bayesian deep learning](https://www.youtube.com/watch?v=E1qhGw8QxqY&ab_channel=AndrewGordonWilson)\n",
|
||
"\n",
|
||
"See also the [slides here](https://github.com/CompPhysics/MachineLearning/blob/master/doc/Articles/lec03.pdf)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "c75013bd",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Reinforcement Learning\n",
|
||
"\n",
|
||
"Reinforcement Learning (RL) is one of the most exciting fields of\n",
|
||
"Machine Learning today, and also one of the oldest. It has been around\n",
|
||
"since the 1950s, producing many interesting applications over the\n",
|
||
"years.\n",
|
||
"\n",
|
||
"It studies\n",
|
||
"how agents take actions based on trial and error, so as to maximize\n",
|
||
"some notion of cumulative reward in a dynamic system or\n",
|
||
"environment. Due to its generality, the problem has also been studied\n",
|
||
"in many other disciplines, such as game theory, control theory,\n",
|
||
"operations research, information theory, multi-agent systems, swarm\n",
|
||
"intelligence, statistics, and genetic algorithms.\n",
|
||
"\n",
|
||
"In March 2016, AlphaGo, a computer program that plays the board game\n",
|
||
"Go, beat Lee Sedol in a five-game match. This was the first time a\n",
|
||
"computer Go program had beaten a 9-dan (highest rank) professional\n",
|
||
"without handicaps. AlphaGo is based on deep convolutional neural\n",
|
||
"networks and reinforcement learning. AlphaGo’s victory was a major\n",
|
||
"milestone in artificial intelligence and it has also made\n",
|
||
"reinforcement learning a hot research area in the field of machine\n",
|
||
"learning.\n",
|
||
"\n",
|
||
"[Lecture on Reinforcement Learning](https://www.youtube.com/watch?v=FgzM3zpZ55o&ab_channel=stanfordonline).\n",
|
||
"\n",
|
||
"See also A. Geron's textbook, chapter 16."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "f0ba11de",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Transfer learning\n",
|
||
"\n",
|
||
"The goal of transfer learning is to transfer the model or knowledge\n",
|
||
"obtained from a source task to the target task, in order to resolve\n",
|
||
"the issues of insufficient training data in the target task. The\n",
|
||
"rationality of doing so lies in that usually the source and target\n",
|
||
"tasks have inter-correlations, and therefore either the features,\n",
|
||
"samples, or models in the source task might provide useful information\n",
|
||
"for us to better solve the target task. Transfer learning is a hot\n",
|
||
"research topic in recent years, with many problems still waiting to be studied.\n",
|
||
"\n",
|
||
"[Lecture on transfer learning](https://www.ias.edu/video/machinelearning/2020/0331-SamoryKpotufe)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "7c3f7c5b",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Adversarial learning\n",
|
||
"\n",
|
||
"The conventional deep generative model has a potential problem: the\n",
|
||
"model tends to generate extreme instances to maximize the\n",
|
||
"probabilistic likelihood, which will hurt its performance. Adversarial\n",
|
||
"learning utilizes the adversarial behaviors (e.g., generating\n",
|
||
"adversarial instances or training an adversarial model) to enhance the\n",
|
||
"robustness of the model and improve the quality of the generated\n",
|
||
"data. In recent years, one of the most promising unsupervised learning\n",
|
||
"technologies, generative adversarial networks (GAN), has already been\n",
|
||
"successfully applied to image, speech, and text.\n",
|
||
"\n",
|
||
"[Lecture on adversial learning](https://www.youtube.com/watch?v=CIfsB_EYsVI&ab_channel=StanfordUniversitySchoolofEngineering)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "964dd5f1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Dual learning\n",
|
||
"\n",
|
||
"Dual learning is a new learning paradigm, the basic idea of which is\n",
|
||
"to use the primal-dual structure between machine learning tasks to\n",
|
||
"obtain effective feedback/regularization, and guide and strengthen the\n",
|
||
"learning process, thus reducing the requirement of large-scale labeled\n",
|
||
"data for deep learning. The idea of dual learning has been applied to\n",
|
||
"many problems in machine learning, including machine translation,\n",
|
||
"image style conversion, question answering and generation, image\n",
|
||
"classification and generation, text classification and generation,\n",
|
||
"image-to-text, and text-to-image."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "53d27ff9",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Distributed machine learning\n",
|
||
"\n",
|
||
"Distributed computation will speed up machine learning algorithms,\n",
|
||
"significantly improve their efficiency, and thus enlarge their\n",
|
||
"application. When distributed meets machine learning, more than just\n",
|
||
"implementing the machine learning algorithms in parallel is required."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "263d674f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Meta learning\n",
|
||
"\n",
|
||
"Meta learning is an emerging research direction in machine\n",
|
||
"learning. Roughly speaking, meta learning concerns learning how to\n",
|
||
"learn, and focuses on the understanding and adaptation of the learning\n",
|
||
"itself, instead of just completing a specific learning task. That is,\n",
|
||
"a meta learner needs to be able to evaluate its own learning methods\n",
|
||
"and adjust its own learning methods according to specific learning\n",
|
||
"tasks."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "df2807f3",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The Challenges Facing Machine Learning\n",
|
||
"\n",
|
||
"While there has been much progress in machine learning, there are also challenges.\n",
|
||
"\n",
|
||
"For example, the mainstream machine learning technologies are\n",
|
||
"black-box approaches, making us concerned about their potential\n",
|
||
"risks. To tackle this challenge, we may want to make machine learning\n",
|
||
"more explainable and controllable. As another example, the\n",
|
||
"computational complexity of machine learning algorithms is usually\n",
|
||
"very high and we may want to invent lightweight algorithms or\n",
|
||
"implementations. Furthermore, in many domains such as physics,\n",
|
||
"chemistry, biology, and social sciences, people usually seek elegantly\n",
|
||
"simple equations (e.g., the Schrödinger equation) to uncover the\n",
|
||
"underlying laws behind various phenomena. In the field of machine\n",
|
||
"learning, can we reveal simple laws instead of designing more complex\n",
|
||
"models for data fitting? Although there are many challenges, we are\n",
|
||
"still very optimistic about the future of machine learning. As we look\n",
|
||
"forward to the future, here are what we think the research hotspots in\n",
|
||
"the next ten years will be.\n",
|
||
"\n",
|
||
"See the article on [Discovery of Physics From Data: Universal Laws and Discrepancies](https://www.frontiersin.org/articles/10.3389/frai.2020.00025/full)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "97618d26",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Explainable machine learning\n",
|
||
"\n",
|
||
"Machine learning, especially deep learning, evolves rapidly. The\n",
|
||
"ability gap between machine and human on many complex cognitive tasks\n",
|
||
"becomes narrower and narrower. However, we are still in the very early\n",
|
||
"stage in terms of explaining why those effective models work and how\n",
|
||
"they work.\n",
|
||
"\n",
|
||
"**What is missing: the gap between correlation and causation**. Standard Machine Learning is based on what e have called a frequentist approach. \n",
|
||
"\n",
|
||
"Most\n",
|
||
"machine learning techniques, especially the statistical ones, depend\n",
|
||
"highly on correlations in data sets to make predictions and analyses. In\n",
|
||
"contrast, rational humans tend to reply on clear and trustworthy\n",
|
||
"causality relations obtained via logical reasoning on real and clear\n",
|
||
"facts. It is one of the core goals of explainable machine learning to\n",
|
||
"transition from solving problems by data correlation to solving\n",
|
||
"problems by logical reasoning.\n",
|
||
"\n",
|
||
"**Bayesian Machine Learning is one of the exciting research directions in this field**."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e661ff12",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Scientific Machine Learning\n",
|
||
"\n",
|
||
"An important and emerging field is what has been dubbed as scientific ML, see the article by Deiana et al [Applications and Techniques for Fast Machine Learning in Science, arXiv:2110.13041](https://arxiv.org/abs/2110.13041)\n",
|
||
"\n",
|
||
"The authors discuss applications and techniques for fast machine\n",
|
||
"learning (ML) in science - the concept of integrating power ML\n",
|
||
"methods into the real-time experimental data processing loop to\n",
|
||
"accelerate scientific discovery. The report covers three main areas\n",
|
||
"\n",
|
||
"1. applications for fast ML across a number of scientific domains;\n",
|
||
"\n",
|
||
"2. techniques for training and implementing performant and resource-efficient ML algorithms;\n",
|
||
"\n",
|
||
"3. and computing architectures, platforms, and technologies for deploying these algorithms."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "45e0405a",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Quantum machine learning\n",
|
||
"\n",
|
||
"Quantum machine learning is an emerging interdisciplinary research\n",
|
||
"area at the intersection of quantum computing and machine learning.\n",
|
||
"\n",
|
||
"Quantum computers use effects such as quantum coherence and quantum\n",
|
||
"entanglement to process information, which is fundamentally different\n",
|
||
"from classical computers. Quantum algorithms have surpassed the best\n",
|
||
"classical algorithms in several problems (e.g., searching for an\n",
|
||
"unsorted database, inverting a sparse matrix), which we call quantum\n",
|
||
"acceleration.\n",
|
||
"\n",
|
||
"When quantum computing meets machine learning, it can be a mutually\n",
|
||
"beneficial and reinforcing process, as it allows us to take advantage\n",
|
||
"of quantum computing to improve the performance of classical machine\n",
|
||
"learning algorithms. In addition, we can also use the machine learning\n",
|
||
"algorithms (on classic computers) to analyze and improve quantum\n",
|
||
"computing systems.\n",
|
||
"\n",
|
||
"[Lecture on Quantum ML](https://www.youtube.com/watch?v=Xh9pUu3-WxM&ab_channel=InstituteforPure%26AppliedMathematics%28IPAM%29).\n",
|
||
"\n",
|
||
"[Read interview with Maria Schuld on her work on Quantum Machine Learning](https://physics.aps.org/articles/v13/179?utm_campaign=weekly&utm_medium=email&utm_source=emailalert). See also [her recent textbook](https://www.springer.com/gp/book/9783319964232)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "04188bac",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Quantum machine learning algorithms based on linear algebra\n",
|
||
"\n",
|
||
"Many quantum machine learning algorithms are based on variants of\n",
|
||
"quantum algorithms for solving linear equations, which can efficiently\n",
|
||
"solve N-variable linear equations with complexity of O(log2 N) under\n",
|
||
"certain conditions. The quantum matrix inversion algorithm can\n",
|
||
"accelerate many machine learning methods, such as least square linear\n",
|
||
"regression, least square version of support vector machine, Gaussian\n",
|
||
"process, and more. The training of these algorithms can be simplified\n",
|
||
"to solve linear equations. The key bottleneck of this type of quantum\n",
|
||
"machine learning algorithms is data input—that is, how to initialize\n",
|
||
"the quantum system with the entire data set. Although efficient\n",
|
||
"data-input algorithms exist for certain situations, how to efficiently\n",
|
||
"input data into a quantum system is as yet unknown for most cases."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "6ab01276",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Quantum reinforcement learning\n",
|
||
"\n",
|
||
"In quantum reinforcement learning, a quantum agent interacts with the\n",
|
||
"classical environment to obtain rewards from the environment, so as to\n",
|
||
"adjust and improve its behavioral strategies. In some cases, it\n",
|
||
"achieves quantum acceleration by the quantum processing capabilities\n",
|
||
"of the agent or the possibility of exploring the environment through\n",
|
||
"quantum superposition. Such algorithms have been proposed in\n",
|
||
"superconducting circuits and systems of trapped ions."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "132951d0",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Quantum deep learning\n",
|
||
"\n",
|
||
"Dedicated quantum information processors, such as quantum annealers\n",
|
||
"and programmable photonic circuits, are well suited for building deep\n",
|
||
"quantum networks. The simplest deep quantum network is the Boltzmann\n",
|
||
"machine. The classical Boltzmann machine consists of bits with tunable\n",
|
||
"interactions and is trained by adjusting the interaction of these bits\n",
|
||
"so that the distribution of its expression conforms to the statistics\n",
|
||
"of the data. To quantize the Boltzmann machine, the neural network can\n",
|
||
"simply be represented as a set of interacting quantum spins that\n",
|
||
"correspond to an adjustable Ising model. Then, by initializing the\n",
|
||
"input neurons in the Boltzmann machine to a fixed state and allowing\n",
|
||
"the system to heat up, we can read out the output qubits to get the\n",
|
||
"result."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "06d34a06",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Social machine learning\n",
|
||
"\n",
|
||
"Machine learning aims to imitate how humans\n",
|
||
"learn. While we have developed successful machine learning algorithms,\n",
|
||
"until now we have ignored one important fact: humans are social. Each\n",
|
||
"of us is one part of the total society and it is difficult for us to\n",
|
||
"live, learn, and improve ourselves, alone and isolated. Therefore, we\n",
|
||
"should design machines with social properties. Can we let machines\n",
|
||
"evolve by imitating human society so as to achieve more effective,\n",
|
||
"intelligent, interpretable “social machine learning”?\n",
|
||
"\n",
|
||
"And much more."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8e7e63e1",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## The last words?\n",
|
||
"\n",
|
||
"Early computer scientist Alan Kay said, **The best way to predict the\n",
|
||
"future is to create it**. Therefore, all machine learning\n",
|
||
"practitioners, whether scholars or engineers, professors or students,\n",
|
||
"need to work together to advance these important research\n",
|
||
"topics. Together, we will not just predict the future, but create it."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "8d87fad6",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## AI/ML and some statements you may have heard (and what do they mean?)\n",
|
||
"\n",
|
||
"1. Fei-Fei Li on ImageNet: **map out the entire world of objects** ([The data that transformed AI research](https://cacm.acm.org/news/219702-the-data-that-transformed-ai-research-and-possibly-the-world/fulltext))\n",
|
||
"\n",
|
||
"2. Russell and Norvig in their popular textbook: **relevant to any intellectual task; it is truly a universal field** ([Artificial Intelligence, A modern approach](http://aima.cs.berkeley.edu/))\n",
|
||
"\n",
|
||
"3. Woody Bledsoe puts it more bluntly: **in the long run, AI is the only science** (quoted in Pamilla McCorduck, [Machines who think](https://www.pamelamccorduck.com/machines-who-think))\n",
|
||
"\n",
|
||
"If you wish to have a critical read on AI/ML from a societal point of view, see [Kate Crawford's recent text Atlas of AI](https://www.katecrawford.net/)\n",
|
||
"\n",
|
||
"**Here: with AI/ML we intend a collection of machine learning methods with an emphasis on statistical learning and data analysis**"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "52dd089f",
|
||
"metadata": {
|
||
"editable": true
|
||
},
|
||
"source": [
|
||
"## Best wishes to you all and thanks so much for your heroic efforts this semester\n",
|
||
"\n",
|
||
"<!-- dom:FIGURE: [figures/Nebbdyr2.png, width=500 frac=0.6] -->\n",
|
||
"<!-- begin figure -->\n",
|
||
"\n",
|
||
"<img src=\"figures/Nebbdyr2.png\" width=\"500\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
|
||
"<!-- end figure -->"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.9.10"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
} |