{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lesson 4 - Introduction to gradient boosting \n", "\n", "> A first look at how gradient boosting combines several weak models into a strong model." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/lewtun/hepml/master?urlpath=lab/tree/notebooks%2Flesson04_intro-to-gradient-boosting.ipynb) [![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/lewtun/hepml/blob/master/notebooks/lesson04_intro-to-gradient-boosting.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Learning objectives\n", "* Understand the conceptual difference between bagging and boosting ensembles\n", "* Understand how gradient boosting works for regression tasks\n", "* Learn how to tune the key hyperparameters of gradient boosting ensembles" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "This lesson is based on the gradient boosting example from\n", "\n", "* Chapter 7 of _Hands-On Machine Learning with Scikit-Learn and TensorFlow_ by Aurèlien Geron\n", "\n", "with parts of the theory coming from\n", "\n", "* _[How to explain gradient boosting](https://explained.ai/gradient-boosting/index.html)_ by Terence Parr and Jeremy Howard\n", "* _[Gradient boosting explained](https://www.gormanalysis.com/blog/gradient-boosting-explained/)_ by Ben Gorman" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What is gradient boosting?\n", "Boosting refers to an ensemble technique that combines multiple simple or \"weak\" models into a single composite model. Unlike the bagging method we saw in previous lessons, boosting methods train the models _sequentially_, where each model is chosen to improve the overall performance. \n", "\n", "
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Figure reference: https://www.quora.com/Whats-the-difference-between-boosting-and-bagging

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\n", "\n", "In gradient boosting, the trick is to fit each new model to the _residual errors_ made by the previous one, e.g. the algorithm runs as follows:\n", "\n", "1. Fit a crappy model to the data $F_1(X) = y$\n", "2. Fit a crappy model to the residuals $h_1(X) = y - F_1(X)$\n", "3. Create a composite model $F_2(X) = F_1(X) + h_1(X)$\n", "4. Repeat steps 2 and 3 recursively $F_{m+1}(X) = F_m(X) + h_m(X)$ for $M$ steps until $F_M(X)$ is good enough. Note that our task at each step is to train the model $h_m(X) = y - F_m(X)$ on the residual errors.\n", "\n", "For sufficiently large $M$, the result is a strong composite model $F_M(X) = \\hat{y}$ that estimates the target values $y$.\n", "\n", "> Note: although $h_m$ can be any model you want, in practice most boosting algorithms are based on tree regressors.\n", "\n", "The \"gradient\" part of gradient boosting is related to the fact that the loss function we wish to optimise is generically given by\n", "\n", "$$ L(y, F_M(X)) = \\frac{1}{N}\\sum_{i=1}^N L(y_i, F_M(x_i)) $$\n", "\n", "and for regression tasks it turns out that training models on the residual errors is equivalent to optimising the Mean Squared Error (MSE):\n", "\n", "$$ L(y, F_M(X)) = \\frac{1}{N}\\sum_{i=1}^N \\left(y_i - F_M(x_i) \\right)^2 $$\n", "\n", "In particular, for each $m\\in 1, \\ldots, M$ we calculate the gradient\n", "\n", "$$ r_{im} = - \\left[ \\frac{\\partial L(y_i, F(x_i)}{\\partial F(x_i)} \\right]_{F(x)=F_{m-1}(x)} \\,, \\qquad i = 1, \\ldots , N$$\n", "\n", "and fit a weak learner to these gradient components. The update step with gradient descent then looks like\n", "\n", "$$ F_{m+1}(X) = F_m(X) + \\gamma_m h_m(X)$$\n", "\n", "where $\\gamma_m$ is the learning rate or \"shrinkage\" parameter that controls the contribution of each tree (or how \"far\" a step we take in the direction of the average gradient).\n", "\n", "In this lesson we look at the basic mechanics behind gradient boosting for _regression_ tasks. The classification case is conceptually the same, but involves a different loss function and some technical details on how to combine predictions to build the ensemble." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Import libraries" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# reload modules before executing user code\n", "%load_ext autoreload\n", "# reload all modules every time before executing Python code\n", "%autoreload 2\n", "# render plots in notebook\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# uncomment this if running locally or on Google Colab\n", "# !pip install --upgrade hepml" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# data wrangling\n", "import pandas as pd\n", "import numpy as np\n", "\n", "# data viz\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "from hepml.core import plot_regression_tree\n", "\n", "sns.set(color_codes=True)\n", "sns.set_palette(sns.color_palette(\"muted\"))\n", "\n", "# ml magic\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "from sklearn.tree import DecisionTreeRegressor\n", "from sklearn.model_selection import train_test_split\n", "from sklearn.metrics import mean_squared_error" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate the data\n", "To keep things simple in this lesson, we will generate a noisy quadratic training set that has just a single feature per example, along with a continuous target:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Xy
0-0.1254600.051573
10.4507140.594480
20.2319940.166052
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" ], "text/plain": [ " X y\n", "0 -0.125460 0.051573\n", "1 0.450714 0.594480\n", "2 0.231994 0.166052\n", "3 0.098658 -0.070178\n", "4 -0.343981 0.343986" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" } ], "source": [ "number_of_examples = 100\n", "# fix the seed for reproducibility\n", "np.random.seed(42)\n", "# generate features\n", "X = np.random.rand(number_of_examples, 1) - 0.5\n", "# generate target\n", "y = 3 * X[:, 0] ** 2 + 0.05 * np.random.randn(number_of_examples)\n", "# create pandas.DataFrame\n", "data = pd.DataFrame(data=np.stack([X[:, 0], y], axis=1), columns=[\"X\", \"y\"])\n", "data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, let's visualise our training set:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.scatterplot(x=\"X\", y=\"y\", data=data)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 1 - build a model on the data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To create a boosted regression model, we start by creating a crappy model that predicts the initial approximation of $y$. As discussed above it is common to use shallow Decision Trees, so let's fix the `max_depth` to a small number:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DecisionTreeRegressor(ccp_alpha=0.0, criterion='mse', max_depth=2,\n", " max_features=None, max_leaf_nodes=None,\n", " min_impurity_decrease=0.0, min_impurity_split=None,\n", " min_samples_leaf=1, min_samples_split=2,\n", " min_weight_fraction_leaf=0.0, presort='deprecated',\n", " random_state=None, splitter='best')" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tree_1 = DecisionTreeRegressor(max_depth=2)\n", "tree_1.fit(X, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The resulting tree can be visualised with a helper function from our `hepml` library:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_regression_tree(tree_1, data.columns, fontsize=24)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that this tree looks similar to the classification trees we have analysed in previous lessons. The main difference is that instead of predicting a discrete class like \"signal\" or \"background\" in each leaf node, a regression tree predicts a continuous _value_. This value is simply the average target value of the training examples associated with a given node. \n", "\n", "The CART algorithm is also similar to classification, except we now split the training set to minimise the Mean Squared Error (MSE) instead og Gini impurity:\n", "\n", "$$J(k, t_k) = \\frac{m_\\mathrm{left}}{m}\\mathrm{MSE}_\\mathrm{left} + \\frac{m_\\mathrm{right}}{m}\\mathrm{MSE}_\\mathrm{right} $$\n", "\n", "where \n", "\n", "$$ \\mathrm{MSE}_\\mathrm{node} = \\sum_{i\\in \\mathrm{node}} \\left(\\hat{y}_\\mathrm{node} - y^{(i)}\\right)^2 \n", "\\qquad \\mathrm{and} \\qquad\n", "\\hat{y}_\\mathrm{node} = \\frac{1}{m_\\mathrm{node}} \\sum_{i\\in \\mathrm{node}} y^{(i)}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, let's add a new column of predictions to our `pandas.DataFrame`" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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XyTree 1 prediction
0-0.1254600.0515730.123566
10.4507140.5944800.528568
20.2319940.1660520.123566
30.098658-0.0701780.123566
4-0.3439810.3439860.123566
\n", "
" ], "text/plain": [ " X y Tree 1 prediction\n", "0 -0.125460 0.051573 0.123566\n", "1 0.450714 0.594480 0.528568\n", "2 0.231994 0.166052 0.123566\n", "3 0.098658 -0.070178 0.123566\n", "4 -0.343981 0.343986 0.123566" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data[\"Tree 1 prediction\"] = tree_1.predict(X)\n", "data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and visualise the quality of the predictions on the training set:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def plot_predictions(regressors, X, y, axes, label=None, style=\"r-\", data_style=\"b.\", data_label=None):\n", " x1 = np.linspace(axes[0], axes[1], 500)\n", " y_pred = sum(regressor.predict(x1.reshape(-1, 1)) for regressor in regressors)\n", " plt.plot(X[:, 0], y, data_style, label=data_label)\n", " plt.plot(x1, y_pred, style, linewidth=2, label=label)\n", " if label or data_label:\n", " plt.legend(loc=\"upper center\", fontsize=16)\n", " plt.axis(axes)\n", " plt.ylabel(\"$y$\", fontsize=16)\n", " plt.xlabel(\"$X$\", fontsize=16)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_predictions(\n", " [tree_1], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"$h(X)=h_1(X)$\", style=\"g-\", data_label=\"Training set\"\n", ")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 2 - build a model on the residuals" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Unsurprisingly, the weak model above is barely able to capture the structure of the data (i.e. it has high bias). However, we can improve the predictions by training a second regression tree on the _residual errors_ made by the first tree:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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XyTree 1 predictionTree 1 residual
0-0.1254600.0515730.123566-0.071993
10.4507140.5944800.5285680.065911
20.2319940.1660520.1235660.042485
30.098658-0.0701780.123566-0.193744
4-0.3439810.3439860.1235660.220420
\n", "
" ], "text/plain": [ " X y Tree 1 prediction Tree 1 residual\n", "0 -0.125460 0.051573 0.123566 -0.071993\n", "1 0.450714 0.594480 0.528568 0.065911\n", "2 0.231994 0.166052 0.123566 0.042485\n", "3 0.098658 -0.070178 0.123566 -0.193744\n", "4 -0.343981 0.343986 0.123566 0.220420" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data[\"Tree 1 residual\"] = data[\"y\"] - data[\"Tree 1 prediction\"]\n", "data.head()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DecisionTreeRegressor(ccp_alpha=0.0, criterion='mse', max_depth=2,\n", " max_features=None, max_leaf_nodes=None,\n", " min_impurity_decrease=0.0, min_impurity_split=None,\n", " min_samples_leaf=1, min_samples_split=2,\n", " min_weight_fraction_leaf=0.0, presort='deprecated',\n", " random_state=None, splitter='best')" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tree_2 = DecisionTreeRegressor(max_depth=2)\n", "tree_2.fit(X, data[\"Tree 1 residual\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 3 - create a composite model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we have an ensemble consisting of two trees. We can get the predictions from the ensemble by simply summing the predictions across all trees:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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XyTree 1 predictionTree 1 residualTree 2 predictionTree 1 + tree 2 prediction
0-0.1254600.0515730.123566-0.071993-0.0903980.033168
10.4507140.5944800.5285680.0659110.0399130.568481
20.2319940.1660520.1235660.0424850.0399130.163479
30.098658-0.0701780.123566-0.193744-0.0903980.033168
4-0.3439810.3439860.1235660.2204200.1598380.283404
\n", "
" ], "text/plain": [ " X y Tree 1 prediction Tree 1 residual Tree 2 prediction \\\n", "0 -0.125460 0.051573 0.123566 -0.071993 -0.090398 \n", "1 0.450714 0.594480 0.528568 0.065911 0.039913 \n", "2 0.231994 0.166052 0.123566 0.042485 0.039913 \n", "3 0.098658 -0.070178 0.123566 -0.193744 -0.090398 \n", "4 -0.343981 0.343986 0.123566 0.220420 0.159838 \n", "\n", " Tree 1 + tree 2 prediction \n", "0 0.033168 \n", "1 0.568481 \n", "2 0.163479 \n", "3 0.033168 \n", "4 0.283404 " ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data[\"Tree 2 prediction\"] = tree_2.predict(X)\n", "data[\"Tree 1 + tree 2 prediction\"] = sum(tree.predict(X) for tree in (tree_1, tree_2))\n", "data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As before, we can plot the predictions of both our second tree on the residuals, along with the predictions from the ensemble on the training set:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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Ag4MDrKys8Mknn0BXVxfLly8X9ktKSsKVK1fUjpowNzcHAMybNw8WFhY4ePAgfv31V4jFYnTu3BlLly5VSeABQEpKCkxNTQs8V3HJ5XIEBgZi7969yMrKgrW1tZDgzK1v/KbVq1dj7dq1+Omnn3D48GHo6Oigb9++WLRokTDa9k0ymQybN29Gamoq6tevDxcXF0il0nzXePN4sVgs7JOSkgI7O7u3am8uAwMDlREbuY845u1Y55WYmIikpCSkp6erJEpzFTV64c04c9/P5ORkYZ2ZmZnKPklJSdi7dy/27t2b73zx8fHCsW/eB3Xq1CkwjuTk5HzXKYmUlBRhFHNeZmZmQmkSIOdDm1j8X+Wp3N9zawSW5F4nIiIiKo68/fKi5O1zvtlPmTBhAvT19fG///0PS5cuxdKlS9G6dWsEBgbC2tq6WP16QP2cKnkTrero6OigVq1aKutq166Ne/fu5ds3t/86Y8YMzJgxI9/2+Pj4Aq+jrg9du3btIvumRfWFS9pfz71eaft/ycnJkEql+Z6SzO0Pp6WlCX3+wj5ntGnTBuvWrcPWrVsRFhaGdevWoUGDBli4cCE6depUqtiIqPJiQpmINK5Dhw4YNmwY9u/fj969ewvfthsaGsLd3V14zCqv3M5mjRo14OfnBz8/P9y7dw/Hjh3DunXrEBwcjC+//FLlGBMTEzx//jzfufLWMc79Rj1v0lapVKpM6iaTybBv3z58/fXX6Ny5MwwMDJCeno7//e9/BbbRxMQEc+fOxdy5c3Hz5k38+OOP2Lp1K2xsbDBhwoR8+//www8IDg7GggUL0L9/fxgZGQmvVUmoa3NiYmKJzlEQIyMjiEQifPfdd5BIJPm2m5qawsjICGZmZtiwYUOJz/9mfencSVsKS+4aGhqie/fu8PDwUBtP7ujuvBPAqLtWXkZGRmrrPRf2iGhexsbGePbsWb71z549U1vupCAludeJiIiINEkikWDs2LEYO3YsHj16hBMnTiA0NBSLFi3Cpk2bitWvL62srCykp6erJJ6fPXumNuGa26eeP3++UGYsrwYNGhR4HXX9xefPn6std5f3ekX1hUvaX89tQ2JiIiwtLYX1N2/ehFKpFMrTFcTY2BjZ2dlISkpS6Yvm9ldL0j/t1q0bunXrhtTUVJw+fRoymQz+/v44c+ZMvhHuRFS1cVI+ItKK6dOnw8jICIGBgULSr3Xr1rh37x5sbW3h4OAABwcHNGvWDGvWrMGFCxcgl8vRv39/bNu2DUBOHTMfHx84Ozvj8ePH+a7h6uqK1NRUREZGCuvu3bunkizMfZwuLi5OWHf58mWVR9QuX74Me3t79OnTR/j2PnfCEXUjlBMSEtClSxccP34cQE65hFmzZqFevXpq4wRyyizUrVsXHh4eQqfxxo0bSEhIKHAUtDqurq44e/YsUlJShHWnT58u8ri8I2UL0rp1ayiVSqSlpQnvj4ODAyIjI7Ft2zZIpVK0bt0aCQkJMDAwUNknIiICP/74Y6HnP336tEpbT5w4AUNDw0I7ybn3jL29vXAtKysrfPPNN7hz5w4aN24MCwsL4b3IlTu5iDouLi64c+cOYmNjhXV3797FhAkTcOvWLbXJ9DdjOnv2rEoSOyEhAZGRkWjVqlWhx+Yq6b1OREREpEmffvqpMDdGvXr14OnpiR49egj9lKL69W8rty8O5PTjL1++jHbt2uXbr0mTJjAxMcHTp09V+qZJSUkIDg5GWlpagddISEgQytwBwK1bt/DgwYMCS2QAKFZfuKT9dUdHR0il0nwTdc+fP18o4VZYX75169YAgKNHj6qsP3LkCMzMzFRK3BUmNDQUH374IYCcJHe/fv3g5eWF1NTUQl9HIqqaOEKZiLSidu3a8Pb2xsqVK7Fjxw54eXnhk08+wcGDBzFu3Dh4enpCR0cHW7ZsweXLlzFt2jRIJBI4Ojpi7dq10NPTQ5MmTXDlyhVcuHBB7YjN9957D23btkVAQABmzpwJAwMDBAUFqZResLW1haWlJYKDgyGVSpGWloaQkBAhqQvklOnYuHEjdu7ciWbNmuHatWtYu3YtRCIRXr16pbZtDRs2xJIlS/Dy5UtYWVnht99+w6NHj9CzZ0+1r4eDg4MwS3K7du1w9+7dQq9RkDFjxmDv3r0YP348Jk6ciCdPnhRr5uVatWrh5s2bOHv2LJycnNTu07x5c/Tq1QsBAQHw9fVF06ZN8ddff0Emk2HcuHEQi8Xo2rUrHBwcMGHCBPj6+sLKygrHjh3D7t27ixxVGx0dDX9/f2Fm7x07dmDGjBmFjnaYNGkSRowYgalTp2Lo0KHIzMzEunXr8PjxY7Ro0QIikQh+fn744osvYGZmhvfeew8//fQTbty4UWBieOjQodi2bRu8vb0xZcoUSCQSBAcHw9HREe3btxfejzNnzqBRo0b5HlkcO3Ysvv/+e3z66afw8fEBAGGywTFjxhT6GuQq6b1OREREVBwpKSm4fPmy2m1GRkZo2rRpsc7TunVryGQymJubw8HBAXfv3sXRo0eFvk5R/fq3IRaLsXTpUqSnp6NmzZpYs2YNTExMhAnn8pJKpZgyZYpQn7hDhw54+PAhvvnmGzRq1KjQEcoikQjTpk3DzJkzAeSUtGvevDnef//9Ao8pTl+4pP11MzMzjBgxAjKZTJiD46effsLNmzeFiQYL68vb2dmhV69eCAwMxIsXL2Bra4tffvkFhw8fxvz584s1sATISYSvXbsW8+bNQ79+/ZCcnIz169ejdevWLMdGVA0xoUxEWjNmzBjs2bMHMpkMgwcPRr169bB7926sWLECAQEBEIlEaNmyJbZu3SrUpJ03bx4MDAywfv16PH/+HPXr11eZ5TkvkUgEmUyGpUuXYsmSJZBKpfj000/x888/C/tIJBIEBQVhyZIl8PX1RYMGDRAQEACZTCbsM2HCBMTHx2PNmjXIyMhAo0aNMH/+fERERODSpUtq27Zq1SosX74cK1euRFJSEho3boyVK1cKsz2/aciQIbh//z6+++47bNq0CfXr14eXlxfu3r1bolEcZmZm2LlzJ5YsWYJp06ahbt26+PLLLzF58uRCjxs7diz8/f0xbtw4bN++vcD9Vq5cieDgYISFhQmv/4wZM+Dl5QUg5/XcvHkzVq5ciRUrViAtLQ0NGzbEsmXLVGaQVmfw4MHIzMyEr68vzM3NMWfOHIwaNarQY+zt7bF9+3YEBQXBz88Penp6aNWqFZYvXy48Eph7b4SFhWHXrl1wc3PDxIkTsXHjRrXnrFWrFnbu3InAwEDMnj0burq6cHd3x+zZsyGVSmFoaIjx48dj586duHTpEiIiIlSOt7Kywq5du7BixQrMnj0bEokErq6uWL16tTChTXGU5F4nIiIiKo6LFy/io48+UrutQ4cOwtNRRZk4cSIUCgX27NmDoKAgmJubY8yYMfD19QWAYvXrS0sqlWLevHlYtmwZ4uPj0bZtW4SEhBRYuuHjjz9GjRo1sG3bNmzZsgUmJibo3bs3/P39C51QTl9fH76+vli6dClevXqFrl27Ys6cOZBKC06jFKcvXJr++pw5c2Bqaopdu3YhMTER7777LjZu3CjUwy6qL5/bh9+2bRuSkpLQpEkTrFixAgMHDizwmm9q164dVq1ahbCwMBw6dAh6enpCH5mIqh+RsiTPUhMREZWDbt26oUuXLsIoCyIiIiIibQkNDcWWLVsKHDxCRFTdsYYyERERERERERERERULE8pERERERJVIREQE+vbti549e2LXrl35tt+4cQNDhw7FwIED4e3trTLxExERERHR22LJCyIiIiKiSuLp06fw8PBAeHg4dHV1MWLECKxatQo2NjbCPiNHjoS3tzc6d+6MwMBA6Onpwd/fX4tRExEREVFVwhHKRERERESVxJkzZ9C+fXuYmJjAwMAAvXr1wtGjR1X2USgUePHiBQAgPT0dNWrU0EaoRERERFRFMaFMRERERFRJxMXFwdzcXFi2sLDA06dPVfaZPXs25s6di44dO+LMmTMYMWKEpsMkIiIioiqMCWUiIiIiokpCXbU6kUgk/P7q1SvMnTsX27dvx++//46RI0di1qxZmgyRiIiIiKo4qbYDqCgSE19Aoaie5aTNzAzx/HmatsMgLeI9QADvA+I9QLwHxGIRTE1rajuMQllaWuL8+fPCclxcHCwsLITl27dvQ09PD46OjgCAjz76CMHBwSW6RnXuFwP8OyDeA8R7gHgPUI7qfB8U1S9mQvk1hUJZrTvO1bntlIP3AAG8D4j3APEeqOjc3NwQGhqKhIQE6Ovr4/jx41i8eLGwvWHDhnjy5Anu3buHJk2a4JdffoGDg0OJrlHd+8UA/w6I9wDxHiDeA5SD94F6TCgTEREREVUSlpaW8Pf3h6enJ7KysjBs2DA4Ojpi/Pjx8PPzg4ODA5YtW4Zp06ZBqVTCzMwMS5cu1XbYRERERFSFMKFMRERERFSJDBgwAAMGDFBZt3HjRuH3zp07o3PnzpoOi4iIiIiqCU7KR0RERERERERERETFwoQyERERERERERERERULE8pEREREREREREREVCysoUxElEd6+gukpSVBLs/WdigaFxcnhkKh0HYYGiUWSyCV6sLIyAQ6OrraDoeIiIiquKysTKSmJiE7OxMKhVzb4VABqmO/uLKRSKQwNDSBvn5NbYdCVC0xoUxE9Fp6+gukpibCxMQcOjq6EIlE2g5Jo6RSMbKzq0/HWalUQqGQIyMjHYmJcTAyMmWHlIiIiMpNbl/T0NAYenq1IRZLql1/s7Kobv3iykapVCIrKxNJSfEAwD48kRaw5AUR0WtpaUkwMTGHrq4eO/fVgEgkgkQihYGBEUxM6uDFi2Rth0REVKFExybjcOR9RMfy30eispCWlgwTkzowMDCCRCJlf5OolEQiEXR19WBiYo60tCRth0NULXGEMhHRa3J5NsseVFM6OnrIzs7SdhhERBVGdGwyVuy5hGy5AlKJGAEeLrCpb6ztsIgqNbk8Czo6etoOg6jK0NHRrZalCokqAo5QJiLKgyNFqie+70REqqJiEpEtV0CpBORyBaJiErUdElGVwD4HUdnh3xOR9jChTEREREREKmytTSGViCEWARKJGLbWptoOiYiIiIjKyNuWNmPJCyIiIiIiUmFT3xgBHi6IikmErbUpy10QERERVRFlUdqMCWUioirK13cCLl++qLJOIpHAyMgI9vaO8PHxQ8OGjcrkWkuWLMStW39jx459Be4zbNgAuLl1xPTps8rkmgBw5EgEli79EocOnYCJiUmZnZeIiHKSykwkExEREVUt6kqblbTPx5IXRERVmIODE9av3yr8BAWtw5gx43D16hX4+09GRkZGmVxn7NhxWLBgSZmci4iIiIgql/v3/0HHjm1w7tyfRe4bFLQCn3027Y11K9GzZyekpKg+eh0X9xSDBvXGuHGeyMh4hX37dsPT8yMoFIoyjV+dkrSpMOram7O+erW5IraXqLoqi9JmTCgTEVVhOaORHYQfF5fWGD58BHx8piAu7ikuXjxXJtepX78BbGzeLZNzEREREVHlEhV1EwBga9ui0P1iYx/ihx8O4NNPJ6isHzFiFDIzMxEevl9Y9+rVK8yePQNisRiBgaugp1cDgwYNQVJSEn766VDZN+INxW1TYQpqL1D92lwR20tUXeWWNhvs3qRU5S4AJpSJiMqdTBaq7RDyMTAwUFl++PABPvtsOnr2dEfv3l2wePEXSEpKEranp6cjMHAxBg3qhW7d3sOnn47CqVMnhe1LlizE6NEfCsvPnz/DvHmz0KtXZ3zwQZ98HcKLF8+jY8c2uHXrb5X1vXt3webNG4Tlv/++jpkz/dC7dxd06dIeHh5D8MMPBwps1/Pnz/DFF7PRr193dO/+HiZNGodLly6U7MUhIqJie9sJXYioaoiKuon69RugVq1ahe63b99u2Ng0g52dasKybl0rdOvWEwcO7ENGRgaUSiW++mo+YmLuIzBwFerUqQMA0NOrgd69+2LPnp3l1pZcxW1TYQpqL1D+bR42bIBKv7o4yrPNFfE9JqrObOobo1+HRqUub8aEMhFROduwYa3Wrq1UKpGdnS38vHz5EhcvnkdY2DpYWi07qHYAACAASURBVNaFk1MrJCQ8x6RJ4/DkyWPMm/clZs78HNevX8P06ZORlZUFAAgOXokLF85j6tQArFwZjEaNmuCLL2bj/v1/8l1TLpdj+vQpiIq6ic8+mwtf32nYsiUM8fFxJYr9yZMn8PObCH19AyxeHIhly77BO+80xMqVy3D3brTaYxYtmo/Y2Af4/PMFCAz8BjVq1MBnn03L92gdERG9vdwJXcJP38OKPZeYVCaqxm7fjoKdXQscPXoYn346Ct26vYePPx6OixfPC/tkZmbi2LGf0LNnL7XnGDnSE4mJCThyJAKbNq3HqVO/Yt68L2Fra6eyX/fuvXD//j1cu3ZF620qTFHtBapfmytae4mo9DgpHxFRFRYZ+Qe6dGmvsk5PTw9t2rTDlCnTYWBggG+/3YLMzAyEhKyDoWHOt5MtWtjDw2MITpw4hj59+uPq1cto27YdunXrASCnNrOpaW3I5XI11/wdd+/ewfr1W2Fv7wAAeOedhvDy+rhEsf/zz120bOmIBQu+glSa899Vy5YO6Nu3Gy5fvoCmTW3yHXPt2mV88sl4dOzoDgBo3NgGe/fuQnp6OmrV4sRSRERlqSwmdCGiyk+pVOL27SgYGT1CamoqxozxgkQixbp1wfjqqwUIDz8MALhx4xrS0lLh5OSi9jzvvtsM7dp1QFjYOqSmpmDcuIno0qW72v0MDGri7NlIODg4qY1HXR/1TSKRCBKJ5K3aVJii2pvblrJoc1nQRJsrUnuJ6O0woUxEVA5kslCVkcnOzjnfunt7T4aPzxSNxeHo6Aw/v+kAgHv37mLNmiC0adMO8+Z9CV1dXQA55SdatnSEoaERsrOzAQAWFpZo1KgxLlw4hz59+sPJyQURET/g+fNncHPrhPfe64QpU/zVXvPq1SswMqolJJMBwNbWDlZW9UoUe4cO76FDh/eQkZGBf/65h4cPY3Dz5g0AQGZmVoHt3bRpPaKj78DNrSM6dHgPkydPLdF1iYioeHIndJHLFaWe0IWIgNjgVXhx7apWY6jp4Ij6U6eX6tgHD/7Fy5cv0LZtOyxZskJYHxf3FKtWfY2MjFfQ06uBGzeuQSQSoWnTgufd6Nq1O/76KxIdO7pj7NhxavcRi8WwsXkXN25cU7v90qUL8PObWGTczs6tsGZNmNptMTHFa1NhitNeoGzaXFASPfdpxVyFJdGL+z4WRlPvMRFpHxPKRETlwMdnipA4dna2w+XLt7QSh6GhoVC/zM6uBSwt62LatEnQ0dHBF18sAgCkpCTj77+vo2PHdvmOr13bDAAwbdpM1KljjqNHj+CPP/4P33wjRvv272HOnAUwMTFROSY1NRXGxiYFnqu45HI51qwJwsGD4cjOzkK9eg3g7Jwz2kGpVKo9ZtGiZdi6dRNOnvwZv/xyHFKpFN27v4/PPptTZAeYiIhKJndCl6iYRNham3J0MlE1FRWV08/19p6ssj45OQk1a9YU+mDPnj1DzZo1oaOjo/Y8jx8/EgZkxMUVXirNxMQUDx78q3abnV1zbNr0bZFxvzmnSF7FbdO2bZtw9OgRxMY+wJIlK+Du3kXYt6j2AmXX5oKS6Nu2bcK2bZuE5cKS6MVpc0pKyuu6xzHQ09ND7dq1MWPGbDRo8A4Azb3HRKR9TCgTEVUjrVu3Rf/+gxAR8QO6du2Bjh3dUbOmIdq3d4O39yTI5QqV/XM72np6NeDl5Q0vL2/ExNzHr7/+gu3bN2PTJhlmzvxc5RhjY2MkJSXku3Zy8n+1NUUiEQBAofjvekqlEunp6cLyt99uwY8/hmPevC/RocN70NfXx6tXr3Do0MEC21erljGmTp2BqVNn4M6dKBw/fhTffbcTjRs3wccfjy3+C0VERMViU9+YiWSit1TakcEVRVTULVhZ1YO1dSOV9bdvR6mMVM3MzICOjq7ac7x4kYbPPpsGQ0NDjBvnjZUrA3Hu3Fm0beuqdn89PT1kZGSo3aavbwAbm2ZFxp3bH1Xn1q2bxWpTmzau6NmzN5YtW5TvHIW1FyjbNqtLos+aNR1ubp0waNBgYV1RSfSi2iwSiTB8uIcQ4/793yEwcLGQpNbUe0xE2lcpJuWLiIhA37590bNnT+zatavA/X777Td069ZNg5ERERXtzW/5tc3b2xeGhoZYs2Y1srKy4OjojH///RdNm9rAzq4F7OxaoHHjptiyJQxXr16GXC7H6NEfYt++3QAAa+tGGDPGCy1bOuDp0yf5zt+qVRukpaXhwoVzwrqYmPt49OihsFyzZk0AOaMYct24cU3lUb3r16/Bzq4FunXrAX19fQDA2bNnXm/NP0I5KSkJQ4b0w6lTJwEA775ri8mTp6JuXSs8ffq0lK8WERERERUmKuommjWzzbf+zp0oNGv232RrxsYmSEtLzbefXC7H/PlzEB8fj+XLV2PgwCFo0OAd7N5d8CjjlJQUtU/EATmjdbt0aV/kz9SpPgWe/9at4rXJ3t4B9es3UHuOgtpbHm02MKgp9ONzf3R0dFCnTh2VdW8mi/MqzvtoZGSkkgB2cHDEkyePi2xzWbeXiLSvwo9Qfvr0KVavXo3w8HDo6upixIgRcHV1hY2N6mRMz549w9dff62lKImICqbJmsnFYWJigtGjP4FMFor9+7/DRx+NwtGjh+Hv74thw0ZAKpXiu+924fr1qxg/3gcSiQQtWthjy5aN0NXVhbV1I9y4cR1Xr15GQMDn+c7ftq0rnJ1bYdGiefDx8YO+vj42bpRBKv3v0bemTd+FubkFNm2SQSqV4sWLNGzevAGGhobCPs2bt8DOndtw4MBeNGlig5s3/8a2bZsgEonw6tUrte165x1rBAd/g/T0dFhYWCIy8g88efJY5fFDIiIiIiobSqUSd+5EYcQI1cmXU1JS8OTJY5UEpbV1Q2RlZSEu7iksLCyF9cHBK3H+/FmsXBkiJDw9PEZjxYqluHMnCu++mz/J+fhxLJo3b6k2prcteZEzOd2tYrWpMAW1Fyj7Nr+tkryPee3btwcdO3YWljX1HhOR9lX4EcpnzpxB+/btYWJiAgMDA/Tq1QtHjx7Nt9+8efPg6+urhQiJiCqf4cM9YGVVD99+uxl6enpYt24TatSogUWL5mPBgrlQKBQIClondO6mTQtA79598e23WzFjxhQcPvwjJk+ehv79P8h3bpFIhMDAVXB1dUNQ0EqsWLEMffr0h43Nf48HSiQSLFq0DLq6epg7NwBbt26Ej48f6td/R9jn44/Hok+f/ti6dSM++8wfJ04chb9/ANq2dcX16+on6Fi4cAlatWoDmSwEM2ZMwV9/RWL+/MUFPkpHRETlLzo2GYcj7yM6NrnIfYmocomNfYi0tDTY2tqprL9zJwoAVEbzOju3AgBhkmUAOHBgL8LD92PatACV/lqfPv1hZmaGXbvyJ4ZTU1Px4EGMcL43qRutq+6noNG6JWlTYdS1t7za/LZK0+YtW8Lw6FEsJk78Lw+jqfeYiLSvwo9QjouLg7m5ubBsYWGBq1dVZ8D99ttv0aJFCzg5OZX6OmZmhkXvVIWZmxtpOwTSMt4DQFycGFJphf+erdjWr99U4DaptAa+//6QsGxuboZvvgkpcH8jo5qYOXMWZs6cpXb7ggWqdeNMTGph/vwvVdaNGfOJyrKLiwu2bdupsq579+7C74aGBpg7dz6A+Sr7DBgwUPh94MBBGDhwUJ521MHChYsLbEdhxGIx/w7AfwuI90BlEBERAZlMhqysLIwdOxajRo0Stt28eROzZ88WlhMSEmBsbIxDhw6pO1W5i45Nxoo9l5AtV0AqESPAw4U1l4mqkKiomwDyJxxv346Crq4uGjVqLKyzsqqH5s1b4o8//g+dO3fD2bORCAlZhaFDP8TgwcNUjtfV1cWwYR7YtEkGb+/JsLKqJ2yLjPwdOjo65fYEWknaVJg32wugyrR527ZNiIz8A6tXr0WNGv9NfF1Z3mMiensipVKZvxBlBbJ+/Xqkp6fD398fALB//35cu3YNixblJC9u376NRYsWYdu2bXjy5Ak8PT1x8uTJEl/n+fM0KBQV+qUoN+bmRoiPV1/biaoH3gM5njz5F3XrNtR2GFojlYqRna0oescqqrq//wD/LSDeA2KxqMIPMnj69Ck8PDxUysGtWrUqXzk4AEhPT8fw4cOxcOFCtGnTptjXKMt+8eHI+wg/fQ9KJSAWAYPdm6Bfh0Zlcu7yUt3/Dqj87gH2NYAjRyIQHLwSBw8eU0lElsSMGX4wMTHGF1+UbhBBcZS0X+zrOwEffjgyXwK0LNoLaKbNxbVlS5iQTM5bri6Xpt/j8vq74v8FBFTv+6CofnGFH4pnaWmpMmlTXFwcLCwshOWjR48iPj4eQ4cOxYQJExAXF4eRI0dqI1QiIiIionJV3HJwALBhwwa0bdu2RMnksmZrbQqpRAyxCJBIxLC1NtVaLESkfe+/3wd16pgjPHx/qY6/cycKFy+ewyefTCjjyEpn8+YNGDy4L27cuIavv16MwYP7Ii7uv8mg37a9QMVq8717d7FlSxhSUpLh6zsBY8eOhJfXaJV9qtp7TETqVfiSF25ubggNDUVCQgL09fVx/PhxLF7837dUfn5+8PPzAwA8fPgQnp6e2L17t7bCJSIiIiIqN8UpBwfkTKS0b98+REREaDK8fGzqGyPAwwVRMYmwtTZluQuiak4qleLzzxfg9u1bpTr++fPnmDNnARo0eKfonTXAy8sbXl7eBW5/2/YCFavNTZo0xe+/ny90n6r2HhORehU+oWxpaQl/f394enoiKysLw4YNg6OjI8aPHw8/Pz84ODhoO0QiIiIiIo1QV61OJBLlWxcREYEePXrAzMysxNco67If5uZG6ODcoEzPWd5YS5zK4x6oavN1lJazsxOcnUs3/1HHjh3LOJqCldV79TbtBTTb5rKiyfe4POdB4f8FBPA+KEiFTygDwIABAzBgwACVdRs3bsy3X4MGDUpVP5mIiIiIqDKwtLTE+fP/jQ57sxxcrhMnTsDbu+BRc4UpbQ3l6NjkKjESuTrXS6Qc5XUPKBSKaj1fRWVS3ecWqUwUCkW5/L3y/wICqvd9UOlrKBMRERERUQ43NzdERkYiISEB6enpOH78ONzd3VX2USqVuHHjBlxcXDQWV3RsMlbsuYTw0/ewYs8lRMcma+zaRERERKRZTCgTEREREVUSecvBffDBB+jfv79QDu7atWsAgISEBOjo6EBPT09jcUXFJCJbroBSCcjlCkTFJGrs2kRERESkWZWi5AUREREREeUoqhycmZkZ/vjjD43GZGttCqlEDLlcAYlEDFtrU41en4iIiKi602T5MSaUiYiIiIjordjUN0aAh0uVqKFMVJ6USqXaiTSJqOTUTVRLVF3llh/LlisglYgR4OFSrv0xJpSJiIiIiOit2dQ3ZiKZqBASiQ6ysjKgq1tD26EQVQlZWZmQSJjWIgLUlx8rz34ZaygTERERERERlTNDQ2MkJT3DixepkMuzObqSqJSUSiUyMzOQlBQPQ0MTbYdDVCHklh8Ti6CR8mP8KoeIqIq7f/8ffPzxcKxevQZt27Yv9XmCglbg0aNYLF8elGfdShw+fBAHDhxCrVr/ffsZF/cU48ePgbm5BdauDcPBg+E4dOggtm3bA7GY32USERFR9aOvXxNSqQ7S0pLw4kUyFAq5tkOiAojFYigUCm2HQYWQSKQwMjKFvn5NbYdCVCFouvwYE8pERFVcVNRNAICtbYtSnyM29iF++OEA1q/forJ+xIhR+P77/QgP34+xY8cBAF69eoXZs2dALBYjMHAV9PRqYNCgIdi5czt++ukQ+vUbWPrGEBEREVViOjq6MDW10HYYVARzcyPEx6dqOwwiohLRZPkxJpSJiKq4qKibqF+/AWrVqlXqc+zbtxs2Ns1gZ6ealK5b1wrduvXEgQP74OExGrq6uvjqq/mIibmPtWs3oU6dOgAAPb0a6N27L/bs2cmEMhFRBZf060lkv3ih7TAEz5NfIT45HebG+jAzVq09q9ewEWq2tNdSZERERETVExPKRERV3O3bUbCza4GjRw9j377duH//PurVq4fp02ehVas2RR6fmZmJY8d+wiefjFO7feRIT/z881EcORKBZ8/icerUr1i8OBC2tnYq+3Xv3gu7d+/AtWtX4ODgVCZtIyKispd47Agy4uK1HYaKOgCUAJ69sV4klaJp8FqI9fS0EBURERFR9cSEMhFRFaZUKnH7dhSMjB4hNTUVY8Z4QSKRYt26YHz11QKEhx8u8hw3blxDWloqnJxc1G5/991maNeuA8LC1iE1NQXjxk1Ely7d1e5nYFATZ89GMqFMRFSBGXfphqzUNG2HAQC4G5uMqAdJgBIQiYBm75ig6etHOZN++RnKzEwoXr1iQpmIiIhIg5hQJiIqxLorW3Dj+S2txtDSzA6TnD4t1bEPHvyLly9foG3bdliyZIWwPi7uKVat+hoZGa+gp1ejkDPkJJRFIhGaNn23wH26du2Ov/6KRMeO7kIt5TeJxWLY2LyLGzeulaotRESkGbV794VCodR2GACA5NhkbN1zCXK5AhKJGG5DXWD+OqGc+ucZZGdmQinP1nKURERERNULE8pERFVYVFROMtzbe7LK+uTkJNSsWRN6ejWQkpKCr76ajwcPYqCrq4fatWtjxozZaNDgHQDAs2fPULNmTejo6Ki9xuPHj7Bhw1oAQFxcXKHxmJiY4sGDf9+2WUREVE0UNmO5SJrzUUaZLddWeERERETVEhPKRESFKO3I4IoiKuoWrKzqwdq6kcr627ejhBHHIpEIw4d7oEOHDsjOVmD//u8QGLgYa9aEAQAyMzOgo6Or9vwvXqThs8+mwdDQEOPGeWPlykCcO3cWbdu6qt1fT08PGRkZZddAIiKq8gqasVwkyU0oc4QyERERkSaJtR0AERGVn6iom2jWzDbf+jt3otCsWc6keUZGRioJYAcHRzx58lhYNjY2QVpaar5zyOVyzJ8/B/Hx8Vi+fDUGDhyCBg3ewe7d3xYYT0pKCoyNTd6mSURERDmEEcpZWg6EiIiIqHphQpmIqIpSKpW4cycK776rmlBOSUnBkyeP1SaaAWDfvj3o2LGzsGxt3RBZWVmIi3uqsl9w8EqcP38WixcHwtq6EcRiMTw8RuPcubO4cydK7bkfP46FtXXDt2wZERFVJdGxyTgceR/RscklOo4lL4iIiIi0gwllIqIqKjb2IdLS0mBra6eyPjfZmztCOa8tW8Lw6FEsJk70FdY5O7cCANy8eUNYd+DAXoSH78e0aQEqo5v79OkPMzMz7NqVf5RyamoqHjyIEc5HREQUHZuMFXsuIfz0PazYc6lESeXchDI4KR8RERGRRjGhTERURUVF3QSQP3F8+3YUdHV10ahRY5X1W7ZsQmTkH1i5MgQ1atQQ1ltZ1UPz5i3xxx//BwA4ezYSISGrMHTohxg8eJjKOXR1dTFsmAd+/fUEHj9+pLItMvJ36OjowN29S1k1kYiIKrmomERkyxVQKgG5XIGomMRiH/vfCGUmlImIiIg0iQllIqIqqnv39/H77+dhZlZHZb2Hx8c4efIMpNL/5mXdsiUMv/9+GqtXr4WhoWG+cw0ePAynTp3Eq1ev4OraAadOnYW//2dqrzt69FicOnUWVlb1VNYfO/YTunbtzhrKREQksLU2hVQihlgESCRi2FqbFvtYkUQCgAllIiIiIk2TFr0LERFVZffu3cWWLWFo0KABfH0nAAAkEgk2b94h7PP++32wa9d2hIfvx8iRo0t8jTt3onDx4jns2LGvzOImIqLKz6a+MQI8XBAVkwhba1PY1Dcu9rEcoUxERESkHUwoExFVc02aNMXvv5+HVCpGdrZC7T5SqRSff74At2/fKtU1nj9/jjlzFqBBg3feJlQiIqqCbOoblyiRnEtIKLOGMhEREZFGMaFMRETFYm/vAHt7h1Id2769WxlHQ0RE1R1HKBMRERFpB2soExERERFRpSOSMKFMREREpA1MKBMRERERUaXDEcpERERE/4mOTcbhyPuIjk0u92sxoUxVmkwWqu0QiIiIiKgciKQSAIAyW/7W59LkBzAiIiKishYdm4wVey4h/PQ9rNhzqdz7NEwoU5W2YcNabYdAREREVKYiIiLQt29f9OzZE7t27cq3/d69exg9ejQGDhwILy8vJCdXnSRp3sSvSKoD4O0n5XvzA9it+wllECkRERGR5kTFJCJbroBSCcjlCkTFJJbr9ZhQJiLKQ6lUajsE0gK+70RUWTx9+hSrV6/G7t27cfDgQezduxfR0dHCdqVSCR8fH4wfPx4//vgjmjdvjrCwMC1GXHbeTPwmpuckkt+25MWbH8Cu3X1WFuESERERlUppnpyytTaFVCKGWARIJGLYWpuWX4AApOV6diItkMlCVUYmOzvbAQC8vSfDx2eKtsKiSkAikSIrKxO6unraDoU0LCsrA9LXI92IiCqyM2fOoH379jAxMQEA9OrVC0ePHoWvry8A4MaNGzAwMIC7uzsAYOLEiUhJSdFavGXpzcTv87QsmOHtE8q5H8DkcgUkEjEcmtYpm4CJiIiISij3C/RsuQJSiRgBHi6wqW9c5HE29Y0R4OGCqJhE2FqbFuuYt8GEMlU5Pj5ThMSxs7MdLl++peWIqLIwNDRBUlI8TEzMoaOjC5FIpO2QqBwplUooFHK8epWOFy+SYWRUvt/gEhGVhbi4OJibmwvLFhYWuHr1qrAcExODOnXqYNasWfj777/RrFkzfPHFFyW6hpmZYZnFW5baO9ZHxJn7yM5WQCoVo0E9U6RfAvR1xTA3Nyr1ec3NjbDUxADX7j6DQ9M6sGtUuwyjpsrqbe4pqhp4DxDvAQI0fx/8dvUx5K+/QM/OVuBS9HN0cG5QrGPNzY2Kve/bYkKZiOg1ff2aAIDk5GeQv2U9xspILBZDoVBoOwyNEosl0NHRhampBXR0dLUdDhFRkdSV6Mn7BWh2djb++usv7Ny5Ew4ODggKCkJgYCACAwOLfY3nz9OgUFS8UkBmNXUwc8R/I29qXj+DdAAvU14iPj71rc/dxdFKWH7b81HlZm5uxHugmuM9QLwHCNDOfdDAzABisQgKuRJKAMf/+hcuNmblPuL4TWKxqNBBBkwoU5Xm7T1Z2yFQJaOvX1NILFc37DQREVV8lpaWOH/+vLAcFxcHCwsLYdnc3BwNGzaEg4MDAKB///7w8/PTeJzlxaa+sfCBKvFWzkeZt52Uj4iIiKiisKlvjI4OVvjt8iMAgFKhRFRMosYTykXhpHxUpbFmMhEREVUlbm5uiIyMREJCAtLT03H8+HGhXjIAuLi4ICEhAbdu5ZT8OnnyJFq2bKmtcMuVSPo6ofyWNZSJiIiItKGgyffcHKygI9XcBHulwRHKRERERESVhKWlJfz9/eHp6YmsrCwMGzYMjo6OGD9+PPz8/ODg4IC1a9di3rx5SE9PR926dbF8+XJth12momOTERWTiGapmQCYUCYiIqLKp7DJ9zQ9wV5pMKFMFY5MFsqRxUREREQFGDBgAAYMGKCybuPGjcLvTk5O+N///qfpsDQi74cv+7SH6AdAmS3XdlhEREREJRIVk4js15PvyeWKfGUt8pb5qohY8oIqnA0b1mo7BCIiIiLSgIIe9SxI3g9fWcqcjzKsoUxERESVja21KaSSil3WojAcoUxERERERBpX2KOeBcn98CWXKwCJBABLXhAREVHlUxnKWhSGCWWqEGSyUJWRyc7OdgAAb+/JLH9BREREVAUV9ainOnk/fDXLMIBy50kmlImIiCoY+cuXgEKh7TDeWpYeIE9LK7fzNzaWoLFDHQDle51SkUoAM8OCN2swFKIC+fhMERLHzs52uHz5lpYjIiIiIqLylHe0cUke9cytKfjy5ks8BEcoExERVSQJRw7hWXjVmMvhrrYD0CI9C3OYb1xf4HYmlImIiIiISOPe9lFPkVQHABPKREREFUn63WgAgEivBkRSiZajeTtisQgKhVLbYWiFWN+g0O1MKFOF4+09WdshEBEREZEGvM0M5rkfUpVyeVmGRERERG/jdakLK++JMHR01nIwb8fc3Ajx8anaDkMrxGJR4ds1FAdRsZVVzWSZLLRMzkNEREREFY9ImjM2RpmVBQD47XIsvtl7Cb9djtVmWERERNWa8nVCWSRiylETomOTcTjyPqJjkzV6Xb67VOGUVSI47yR/RERERPyyuYqRvE4oy7Px2+VYfHs0Cjf+ScS3R6OYVCYiItIW5esSEWKmHMtbdGwyVuy5hPDT97BizyWNJpX57lKFw0QwERERlQf2MaqW3BHKyJbjQlScyrY3l4mIiEgzhBHKTCiXu6iYRGTLFVAqAblcgaiYRI1dm+8uVSkyWSicne3g7GwHAMLvHJFEREREVLUIJS/k2Whta6Gy7c1lIiIi0pDXCWWICq/BS2/P1toUUokYYhEgkYhha22qsWtzUj6qEGSyUJVRQ7kJYW/vyQXWVJbJQvNt8/GZIqxzdrbD5cu3yiliIiIiqgxK08egykFIKGdno4tzfQA5I5Nb21oIy0RERKRhLHmhMTb1jRHg4YKomETYWpuWeqLj0mBCmSqE0iSCN2xYyw+CREREVCh+2Vx1iaQSADkJZQDo4lyfiWQiIiItq+qT8kXHJheawC1qe1mzqW+s0URyrkqRUI6IiIBMJkNWVhbGjh2LUaNGqWw/ceIEQkNDoVQq0aBBAyxbtgzGxpp/Mali8faerO0QiIiIiKiciCT/jVAmIiKiCkL5uuSFuOqVvMidBC9broBUIkaAh4tKMreo7VVJhf+64OnTp1i9ejV2796NgwcPYu/evYiOjha2p6WlYeHChQgLC8OPP/4IW1tbhIayXm5lVlgiuCQ1kjl6mYiIiPLil81Vi0hHBwATykRERBWJUvG65EUVHKFc1CR42pwkT9Mq/Lt75swZtG/fHiYmWdyE6gAAIABJREFUJjAwMECvXr1w9OhRYXtWVhYWLlwIS0tLAICtrS0eP36srXCpDBSWCPbxmYLLl28Jj6vm/s7kMRERERWF/YWqRSQW50z4o1QKj9cSERGRluWWvKiCNZSLmgRPm5PkaVqFL3kRFxcHc3NzYdnCwgJXr14Vlk1NTdGjRw8AwKtXrxAWFobRo0drPE4iIiIiItIskVQKZVYWlFlZEOnpaTscIiIiqsIlL4qaBE+bk+RpWoVPKCtzZ4fMQyTKf1OmpqZi0qRJsLOzw+DBg0t8HTMzw1LFV1WYmxtpO4QSmz59eqWMu6Lia0kA7wPiPVBc33zzDWbMmKHtMMoF7wGqTISEsjwbABPKRERE2pZb8qKqTspX1CR42pokT9MqfELZ0tIS58+fF5bj4uJgYWGhsk9cXBy8vLzQvn17zJkzp1TXef48DQpF/uR1dWBuboT4+FSNXEsmCy2zx009PScUGHdZXqc60OQ9QBUX7wPiPVB8q1atgqfnBG2HUeaq+z0gFouq/SCDyua/ifnkWo6EiIiIAOQZoVw1E8qUo8K/u25uboiMjERCQgLS09Nx/PhxuLu7C9vlcjkmTpyIPn36YO7cuWpHL1PFsWHD2ip1HSIiIiLSHpFObkKZE/MRERFVBMK8BszPVWkVPqFsaWkJf39/eHp64oMPPkD//v3h6OiI8ePH49q1azh58iT+/vtvHDt2DIMGDcKgQYMwd+5cbYdNlYBMFqrtEIiIqBKRyULh7GwHZ2c7ABB+5/8nRNojjFCWM6FMRERUIbwuXVsVJ+Wj/1T4khcAMGDAAAwYMEBl3caNGwEADg4OuHXrljbComKSyUJVRgznfhD39p5cpmUpSnqdDRvWsiwGEREVm4/PFOH/DWdnO1y+zP4HkdZJJQAAZRYTykRERBWCgiUvqoNKkVCmyk1TH8D5QZ+IiIiqg4iICMhkMmRlZWHs2LEYNWqUyvY1a9bgwIEDqFWrFgDgww8/zLdPVZE7QhkcoUxERFQh5Ja8YEnaqo0JZapWNDVamoiIqjZv78naDoGqqadPn2L16tUIDw+Hrq4uRowYAVdXV9jY2Aj7XL9+HatWrYKLi4sWI/1/9u49Pqr6zv/4e2YSrgkBMUltXKSKDbKCQbQgVawKRtBUUdsKarZWEaOIRUGtUNFSl64IrqUakbX1UsjSbVWKIOKl1f0VtGJhsRVpA1raICSQGLnKXM7vj2SG3DMzOWfOZV7PPnyUzEzmfGfmm5kzn/M5729q+DIzJVmboVxZVa9tO+tUOKBfWqzaDgBAlzRGXtCh7G0UlJFSqfoC3t526GIGAJiBg5Cwy/r16zVq1Cj17dtXklRcXKy1a9dq2rRpsdv8+c9/1tKlS/WPf/xDZ599tu655x51797driFbyhdojLwIhS25/8qqei2o2KRQOKKMgF+zJg2nqAwAQAcMIi/SAq8uUipVX8D5og8ASFbLRfZYdA9OUl1drdzc3NjPeXl52rNnT+zngwcP6rTTTtM999yjF198UZ9//rmeeOIJO4aaEr6MxkX5QkFL7n/bzjqFwhEZhhQOR7RtZ50l2wEAwDNcEHlRWVWv1Rs+UWVVvd1DcS06lJEShmFo7+FaGYrYPZSY7067WdWHauwehqW6B7orp3sfu4cBAK7SctFWFnGFkxjR00ibaPqFrXfv3rHFqyXpe9/7nu677z7NmDEj7m3075/VtUGmUHXP7josqU9WN/XLzTbtfnMb72vUsAKtWv+JQqGIMjL8GjWsIHYdvI3XGcwBMAeS87FPCkvqn9tH3fo67zn86JNaPfLfm2Kf7Q/d8nUNHnhcu7dnHrSNgjJSomLbb/SHXX+0exjNnSw9+M4Cu0dhuZuHluqM3NPtHgYAAJYoL1+cVgX//Px8bdy4MfZzdXW18vLyYj/v2rVL69ev19VXXy2poQCdkZHYLv++fQcUibQuXDtRsLFX4bN9+xWq2W/KfebmZqum8b76987UzGuGxzKU+/fOjF0H72o6B5CemANgDiQv3BhDVVt3SIGgdcEIya5x8M6WKgVDDWcfhUIRvbOlSv17Z7Z523SeB36/r8MmAwrKSIl/7N8lSerbPUeZfvdNu507/64BA06yexgJORg8pEOhw9p1YDcFZQDoRHuLtrb8mUVcnSfdOshHjx6txYsXq7a2Vj179tS6des0b9682PU9evTQggULNHLkSJ144olatmyZxo0bZ+OIrRVdlO/Iju2xPOWuysjpqYP1h2M/nyDphCxJtZ/rYG3X79/fO0s9vvIVR58KDABA0qIZyhZ+znVljYPCAf2UEfArHI4oEPCrcEA/y8bpZe6r7MGVQpGGlbfLht2gE7O/bPNoEldUNlg/d9kCfqs/fk1rPn5NYcOaRWoAwEs6WrSVRVzhJPn5+ZoxY4ZKS0sVDAZ19dVXa9iwYZoyZYqmT5+uoUOH6kc/+pHKysoUDAZ15pln6oYbbrB72JaJFpRr17xs2n1WmXZP7fvy9O8ra1hRCrYEAECKReO5LFyUr601DuItKA8qyNGsScOT6m7GMRSUkRLRgrKbupPb61ZzS3dawNfQpRM2nJNbDQCAGdz+Gd1VJSUlKikpaXZZ09zk4uJiFRcXp3pYtuh74ThFjhyREQqZdp/dumXo6FHz7q+po7uqFKqtVWifCa3OAAA4kBFdlM/CgnJXu4wHFeRQSO4i91T34GrBxoJyhosKyh11q7lBwNfw5k2HMgAkZurU2zr8GfZz+2c0zNPz5JNVMO0OU+/TyrzE6uXP67M335ARZv8MAOBRKYi8oMvYfu6p7sHVQrGCcttB5zBfwN/QoRyJ0KEMAIlo2eGaDh2vAJKT6IJAvkDD1y8jbE0HNAAAdjMaIy+s7FCW6DK2m7WvLtAoZEQjL8xZLMVs5eWLO7zejd1pfjqUAQBpwI2f0fCG6IJAL7y9QwsqNqmyqr7zX4ouHEiHMgDAq6JNbRYXlGGvpDqUP/74Y1VWVmrfvn3y+Xw67rjjdOqpp2rgwIEmDw9eEXR4h3JnK8S7sTvtWIYyX1gAAN7lxs9oeEMyCwL5Mhr2z4i8AAB4kWEYxxblszDyAvaLu6C8fft2VVRU6NVXX9XevXslNWljb5wk/fv31/jx43XNNdfolFNOsWC4cCPDMJpEXjizQ9mLYgVlIi8AAABMl8yCQEReAAA8rUkx2UdB2dM6LSjv3LlTjzzyiF577TX16NFDI0aM0He+8x0NGDBAffv2lWEYqq+v186dO7V582b9+te/1i9/+UuNGzdOs2bN0r/8y7+k4nEgSeXli3X//fdZuo1QY4dswBeIxTA4gddXiD+2KB8FZQAAALMlsyCQrzHywgjRoQwA8CDiLtJGpwXlCRMm6Ktf/armz5+viy++WL169erw9ocOHdKrr76q5557ThMmTNAHH3xg2mBhviVLHre+oOzQ7mSvrxAfW5SPyAsAAABLJLwgUIDICwCAdxmNDW10J3tfpwXlxx57TBdddFHcd9irVy9NnDhREydO1Ouvv96lwcEbogXlTIfmJ3sVi/IBAAA0V1lVn1BHsdmikRci8gIA4EWRxsgLOpQ9r9NX+KKLLtLGjRuTuvOxY8cm9XuwVnn5YhUVDY5FPBQUFKioaLDKyxdbsr1jHcpJrQGZEl5cIZ5F+QBYwarPCgCwWmVVvRZUbNILb+/QgopNqqyqT/kYiLwAAHhaNHLTQXGnsEZcr/D3vvc9rVmzxuqxIEXKym7X5s0fxSIeqqqqtHnzR5blBgcjQUnOLih7ITO5pViGMovyATBR0+x5AHCTbTvrFApHZBhSOBzRtp11KR+DL4PICwCAdxmN9Qefn8gLr4uroHzKKado5syZWrp0aVx3un79+i4NCt4SijTsMDu5oOxFxzKUKSgDAAAUDuinjIBffp8UCPhVOKBfyscQjbwwiLwAAHhRNPKCDmXPi+sVXrZsmc4991wtWrRIc+fOVaSdjsc33nhD3/rWt3TjjTeaOshUSrdTeVMR9RDtUM6koJxSRF4AMEvLqKTov930memmsQKwxqCCHM2aNFwTx5ysWZOG25KhHF2UT3QoAwA8KLYonwszlCur6rV6wye2RGK5UVyvcK9evfTkk0/qO9/5jlasWKGysjIdOnRIkmQYhlavXq1vfvObmjZtmv7+97+rrKzM0kFbKd1O5U1F1EOsQ9lHQTmVWJQPgFlaRiVF/93RZ4jTCrjp9vkOoG2DCnJ06TkD7Skmq0nkBRnKAAAvijag+twVeeGEdRbcJu5DBn6/Xw888IBmzpypt99+W9ddd52WL1+uSy65RDNnzlRNTY2+//3v680339T06dOtHDNchg7l5HWlIBPrUCZDGYANKOACQGtEXgAAPM1ojLxwWYeyE9ZZcJuEX+HS0lJdeOGF+vDDDzVv3jwdPHhQ99xzj373u99p6tSpysrKsmKclpsw4SJXn8rrZKFIww4zGcqJ60pBJuCnQxmA+VIRlWQWL0R1APAWX4BF+QAA3nVsUT53FZSdsM6C28Rd4Tt06JAqKir0i1/8Qvv27VNBQYEOHTqkYDCooUOHqkePHlaO03Jr1ryhSMRQUdHg2Cm9MEe0oOzUDuXy8sUpif5ItWiHMovyATBTZzEXTQ+ERQu5U6feZsv7bFnZ7bHt8vnuXV79HIe7VFbVa9vOOhUO6NdxnAYFZQCAl7k08iK6zkJcn+WQFGeH8s9+9jNdcMEFWrBggfr06aP58+dr3bp1qqioUJ8+fXTDDTdozZo1Vo8VLuX0DmWnnZZtVkddgAxlACmWTNYy0FVO+xxH+kkkd9GX0bg/TEEZAOBBRmPkhds6lCX711lwm7gLyl/+8pf12GOPafXq1briiisUCAQ0cOBArVixQoWFhZo5c6aWLl1q9XgtF++pvJwuG7+gwwvKTmNWQcYfy1DmCwuA9NHe57ObojoAuEsiuYvHIi/IUAYAeFC0Q9mFBWUkJq5XeMmSJXrxxRdVXFwsX4u29eOOO07PP/+8zj//fC1atEhz585VxMWLgMVbtKMbJn4hw3kF5XTI1YwtykfkBQAb2FXAbe/zmS5pd4j3czgdPsfhHonkLsYKyiEO+AMAPMilkRdIXFwF5fPPP7/D63v06KHHH39c11xzjVasWKGysjJTBofOlZcvdvyXp6ADM5Tdclp2VwoyLMoHwE5mv586/bMO5oj3gL1bPseRHqK5ixPHnKxZk4Z3eKosi/IBALzMzZEXSIxpr7Df79fcuXN111136X//93/NultHcWI3zJIljzu+W/rYonyZNo/EfbryxZhF+QB4SUefdU78fEbyeN3gRnHnLgYaGiyIvAAAeBKRF2nD9JbRKVOmqKCgwOy7dQRWi0/OsQzlgM0jaZtXczVZlA9AOol+JvP57D7l5YubHTCIHiyfOvW2uA6sevVzHN4U7VBO9aJ8lVX1rFwPALCcQeRF2uj0kMGGDRsSvtMJEyZIktavX5/4iNCplp1YkrO7sUKxgrIzO5S9enosi/IBcLt4O4+dfqYOOtYyvkJSQvEVXv0c78iqVas0YcIEjRs3TsuWLWv3dr///e914YUXpnBk6aOyql6rN3yiyqr6hH7Pl5H6yIvKqnotqNikF97eoQUVmxIeMwAAcSPyIm10+grfdNNNKi0t1e9+9zuF49jxCQaDeu2113Tdddfp5ptvNmWQTmRnN0x7X7ycmh0YcniHslcF/OYtyufEAxUAvC+ZnFy6Vd2h5edK9OBBlJMPlNttz549evTRR7V8+XKtXLlSK1asUGVlZavb7d27V//xH/9hwwi9rysFWl9j5MWRw1+krLC7bWedQuGIDEMKhyPatrMuJdsFAKQhIi/SRqev8IsvvqiMjAyVlZXpvPPO01133aVnn31Wv/vd7/SnP/1J77//vt5880394he/0B133KFzzz1Xt99+u3r06KGXXnopFY/BFk4s3DoVGcr2aBp5EQ3GTxbdfwASZXUhsL3uZbhDy8+V6MGD6AEBJx8ot9v69es1atQo9e3bV7169VJxcbHWrl3b6nZz5szRtGnTbBih93WlQPtx9UFJUvCLYMq6hQsH9FNGwC+/TwoE/Coc0M/ybQIA0lM08sJH5IXndZqh/NWvflU///nPtWnTJi1fvlxvvPGGVq9e3WpyGIahrKwsjRs3TpMmTdKwYcMsG7RblJcvtvyLkBs6sZyeoexVfp9fPvlkNP7PJ2vf0FMx3wG4x5Ilj5v6ntDy8451DbyprOx2DmJ2orq6Wrm5ubGf8/LytGXLlma3ee655zRkyBCdccYZqR5eWogWaMPhSMIF2spP9+sUSX7DiBWjrc40HlSQo1mThpOhDACwXrSZjQ5lz4t7Ub7hw4dr+PDhCofD+stf/qLKykrV1tbK5/PpuOOO06mnnqohQ4bIz6SJMfvLdFvcUMCjQ9k+AZ9fISOscCQsfyCxv82WiyRFO//aWyQpFfMdgPuYdbCJ9xf3i/dzxQ0Hy+3U1llHTRs9/vrXv2rdunV65plntHv37qS20b9/VtLj84rc3OwOr/v3vr30wfa9GnrK8Ro88Li47/fsYSeqVlJAYWVk+DVqWEGH2zJLbm62zik60fLteEkqXhc4G3MAzIHE1Vf30D8kdeue6ZnnzyuPw2xxF5SjAoGAhg0bRgcy4nasQznh6YYu8vsDUjissBFWphIr6NP9ByBR7RUMJfMLwoke9IL94v1c4fXrWH5+vjZu3Bj7ubq6Wnl5ebGf165dq5qaGl111VUKBoOqrq7W5MmTtXz58ri3sW/fAUUiXYvLcrPc3GzV1Ozv8Db9e2fqG8NOkKROb9vs9/r0bCwoG5p5zXD1752Z0O8jNeKZA/A25gCYA8k5VHtAkhQMRTzx/KXzPPD7fR02GdBObLJ4V6RPJ8c6lCkop1rAZ97CfG1hvgNoqq1F9KKXW72tqVNvI3MXaWH06NHasGGDamtrdfjwYa1bt05jxoyJXT99+nS9+uqrWrlypZ566inl5eUlVEyGxRrP5vQZhk45gY4nAIDHEHmRNqjwmYyuztaiBeUMH9MtVaKnmEcX5ot0saDc3unHzHfA/V7f+ZZ+u31tw/uET5IJTYmGYWj0IyW69fVZsf+XGk7Lt2KBjtGPlOgD7dS0N+8x/b7TjklzoDNfX/hNR75eeb37a/Fl8+weRofy8/M1Y8YMlZaWKhgM6uqrr9awYcM0ZcoUTZ8+XUOHDrV7iOiAz+eTAg1nkBnhsHx84QYAeMixRfn4fPM6Syt8R48e1fjx4/XGG29YuRnbsRhZx4i8SL1onvGxDuVwl+6P+Q1415aaD4+9R5hVSPS1v7KzYUG10uf3WXbfaSdVT6HPma9XVw/ApkpJSYlKSkqaXbZ06dJWtzvxxBP15ptvpmpYiJMvEJARDkvhkJTJGiMAAA+J7kv5zW8igbNYXuGrqqqyehO2a28xMhaVaRCioGwbf+NRwXCkawXleDDfAXcKRoKSpLtG3KazTx6imr3mZoSdeeYQ/elPH5p6n1FPPvkzPfXUE60uv/nmW3XLLdMs2abX5R6fbfocsMqTT/7M9NfZz5cfpIAvI0PG0aMyQtbvnwEAkEpGdA2GFHYoV1bVa9vOOhUO6KdBBTkp226663KF76KLLmr3OsMwLDm11S3o6mwQMshQToW2Fqg6876L1PP43l3uUI4H8x1wp2hBuXugm/x+f+xAlFmm3nyb6fcZdWvZdN1aNl0SsTtmsWIOWOWpJU/EXn+z+NN4vxWp4ws0nEFmhDvfP+NLMgDAVaKRFyk6SF9ZVa8FFZsUCkeUEfBr1qThfF6mSJcrfLW1tbrzzjt1wgkntLouGAzqzjvv7OomHInV5eMXLVbQoWy+pnErbeUZ/+idR7TnULVli/IBcL9guOE9OtPf+rRrMyKd+EwEgBbiLCjzJRkA4DqxyIvUNChs21mnUDgiw5DC4Yi27azjszJFulzhO+2009S/f3+NHTu21XVHjx6VYTgvH88MXl+MzMxc6FBj3AIdyuZrL24lyqxF+QB419HGg37dAq0Lyp29xzgJsTvpgQP68AJfRsM+sREOdXg7viQDANwmGnnRdFE+K8+2KRzQTxkBv8LhiAIBvwoH9DP1/tG+Llf4rr/+evXt27ftO8/I0Pz587u6CdjAzCICHcqpFy2sBPyNi/KlIEMZgDtF36Pb6lB2E4qJ1nLKAsReP6CP9BCNvFAnHcp8SQYAuE6LRfmsPttmUEGOZk0aTjyUDbrcgz5+/Hidc845bd+536+JEyd2dROOR1dUx+hQNld5+WIVFQ2OdWVF/11evjh2m+iX7diifE0ylJvezuxxAXCfaORFt8aCcjzvMUg/TbuC28L8AOIXb4Zy9EvyxDEnE3cBAHAFozFDObooX1tn25htUEGOLj1nIJ+TKZZUQTkcDmvnzp3as2eP2eNxJSd07JjBqiJCiA5lU5WV3a7Nmz+KdWVF/93WPAz4GjuUm0RedFYUSJZV9wvYyetFsogRUcgIyydf7D06kfcYIMqOzwAO6MOtYgXlUMeRFxJfkgEALtMYe+trzFCOnm3j94mzbTwm4YLy+++/r/PPP1/FxcX6xje+obPOOkvXX3+9fvKTn+i3v/2ttm/fbnpu8qpVqzRhwgSNGzdOy5Yta3X91q1bddVVV6m4uFizZ89WKI6dM6ezo4hhRRHBMIxYhzIF5dSLZigTeQEkx+sHSoKRhs/LDH+GfL7UrMQM93B6t7rTDnK8/PLLdg8BbhGIZiizfwYA8JhI88gLzrbxroQLyg899JAOHjyoqVOn6vbbb9d5552nPXv26JlnntHdd9+tyy67TCNGjDBtgHv27NGjjz6q5cuXa+XKlVqxYoUqKyub3WbWrFn64Q9/qFdffVWGYehXv/qVadu3i1eKGGEjLEOG/D5/LH4B5umsOyvaobxy1YuWFAWcXmwA0LGj4aOSjsVdtEQHaHrr7EAznwHN3XvvvSotLdX27dvtHgocLt4MZTNVVtVr9YZPVFlVn7JtAgDSTzTyoumifJxt400Jt4zu2LFDN910k6ZNm9bs8v379+svf/mL/vKXv+jDDz80bYDr16/XqFGjYgv/FRcXa+3atbHtV1VV6ciRIyoqKpIkXXnllfrpT3+qyZMnJ7SdH7+7UHsP1Zo27q4a9e8TdOdbc1KyLZ/P16qr/LxHLjdl+9F7JT/ZGp11Z0UX5Ztw6WW6+99mSep8EaNEFl5icSR4UXn54mYH9aLFsqlTb3NcR2RXxRbkC7RdUPba44W5+Axo7je/+Y0efPBBXX755br++us1bdo09e7d2+5hwYHizVA2i9ULIgEAEBOtLflpKPS6hKt8xx9/vI477rhWl2dnZ2vUqFEaNWqUKQOLqq6uVm5ubuznvLw8bdmypd3rc3Nzk8p2Pho+qi8aO7WcINAjw97x+GXq9k/PL1RubrZp94f49OzeTZLUO7tbs+e/rdcietmSJY/r/vvvS2p7vMbux2so3X//fbG/gYKCAlVVVdk8IusEPz8oSeqZ2T322jMH0NYcuPPOOzudG+k+dwoLC7V8+XK9+OKLeuSRR/Tyyy/rnnvu0WWXXWb30OAwvmjkRRwxfZVV9V1eub6tBZEoKAMArGC0iLyAdyVcUJ4wYYL++Mc/JtwBnKy28pib5jx2dn28Zo+8U+FwpPMbpsjXvz5Cf/jD+ynZ1vHHZ2vv3v0J/c5//dcS3XTT1Lhv3z3QXTU1iW0DXRcKNvx91NUfVE33hud/6tTbWr0WubnZzS5L5rVq637hLi3nARp4+TnZvb/h1Ge/Aqqp2c8cQLtzoLT05g7nhlc+A/x+n/r3z+rSfUycOFFjx47VokWLdPfdd2vFihW6//77deqpp5o0SridLyO+DmWzOoujCyKFwxEWRAIAWKuNyAt4U6cF5ZKSEp122mkqLCxUYWGhrrzySt1xxx1atWqVSkpKLB9gfn6+Nm7cGPu5urpaeXl5za7fu3dv7Oeamppm18ere6C7Ij5zFxPsivAXYfXI6JGSbfXM7KEeGcGEfue/nizXtFvusGhEMEtbi/K1dQr7woULtWjRotjPyZziz6nx8CKvZwjHIi/ayVCWEovBQfpijjSXnZ2tuXPn6lvf+pbuueceTZw4Udddd52mTZumrKyuFazhAXFGXpjVWRxdEKmrnc4AAHSKyIu00WlBOTMzU2vXrtVvf/vbWOdvt27ddPfdd2vdunUaP368zjjjDBUUFFgywNGjR2vx4sWqra1Vz549tW7dOs2bNy92fUFBgbp37673339fI0aM0EsvvaQxY8ZYMpZU8noRA6kRzVCOGB133991110qLb1ZEjmYQFNeL5JFF+XrKOd+yZLHPf88AGYJBoPaunWrNm/erP/7v//T5s2bY7E5y5Yt0+rVq/XAAw/ooosusnmksFO8i/LF21kcTyzGoIIcCskAAMvFFuUj8sLzOi0ov/DCCwqHw6qsrNTWrVtj/3300Ud67bXX9Nprr8nn86lPnz4aMmSIhgwZon/913/VhAkTTBlgfn6+ZsyYodLSUgWDQV199dUaNmyYpkyZounTp2vo0KF65JFHNGfOHB08eFBDhgxRaWmpKdu2WkddX0788p5OC1V5RcDX8IUlbKRuFXEA7hHtUO4W6GbzSAD3+853vqOtW7cqGAzK7/ersLBQF1xwgUaMGKEzzzxTvXv31s9+9jPdcccdmj17tiZNmmT3kGETX0Z8GcrxdBaz4B4AwFGiGcpEXnheXBnKgUAgFnlxxRVXxC6vqqrS1q1b9eGHH8YKzRs2bJDP5zOtoCw1xG60jNdYunRp7N+DBw/Wr3/9a9O2lypu6/piNXf38UcjLxIoKNMdD6SPYKShmNEy8oIDiEDisrKydPPNN2vEiBE644wz1KtXr1a3uffee9W/f38tWbKEgnIa88UZeSF13lnMgnsAAEch8iJtJLwoX1MFBQX87GCkAAAgAElEQVQqKCjQ2LFjY5d99tln2rp1a5cHBnORgZmeYh3KkfgXnGSeAN7T3mdAMNx2hjIHEL2L/QHrPP3003Hd7uyzz9bChQstHg0cLYGCcmdYcA8A4CREXqQP0w8Z9O3bV+ecc47Zd+sZ5eWLVVQ0ONbtFf13efliS7fbtNPMDHSxukPAn3iHMgDvae8z4GikIUO5W6BLx5fhImbvDyBxgwcP1hNPPGH3MGAjX+N7rhHuOPIiHtFYjIljTibuAgBgPyIv0gbfIFPMK11fdDe5Q7RDubNF+QCkp/Y6lJviAKKz0GHsfj169NCFF15o9zBgI19G46J8IXMO+LPgHgDAKYzGyAsfkReexyvsYXZ1Q8M5kslQZn4A3hDPZ8DRxgzljhblo3jpLMl0GLM/ADhLIhnKAAA4WWVVvVZv+ESVVfUNF0Q7lIm88Dw6lG1kddeXV7qhkbxjGcrxf2Fx22KRANoWz2dAMBLtUGZ3wMvYHwCcxczICwAA7FJZVa8FFZsUCkeUEfBr1qTh6kvkRdrgFbYRRTtYLVZQdmnkBd1zgLXiibyA/egwBjymsUP5r3/fd6yjy0KtuscAADDBtp11CoUjMgwpHI5o2846iciLtNGlV/jzzz/XP/7xD7PGAguRgZme4l2Ub+HChY4sVrB4lHfZPbfM5vTH095nwNFoh3KAgrKTlZXdrs2bP4p1Fkf/ncyBafYHvGHVqlWaMGGCxo0bp2XLlrW6/rXXXlNJSYkuvfRS3XvvvTp69KgNo0R76g42dCb/9ZN9WlCxydJCb7R77IW3d1i+LQBAeikc0E8ZAb/8PikQ8KtwQL8mi/K1jrzgAKe3dKmg/Nxzz+niiy82ayzoQFeLFXRDp6d4F+W76667TCtWAPHw2sECpz+e9v6Wox3K3ehQThu8r7vfnj179Oijj2r58uVauXKlVqxYocrKytj1hw4d0o9+9CP94he/0OrVq/XFF1/oxRdftHHEaKlm/xeSJL8ROdbRZZE2u8fawJd8AECiBhXkaNak4Zo45mTNmjRcgwpyZDQWlFt2KHOA03voQXcJJxYrnN6Rh+QW5bMbp3YDqRPNUKag7B50GGP9+vUaNWqU+vbtq169eqm4uFhr166NXd+rVy+9+eabOv7443Xo0CHt27dPffr0sXHEaCn3uCxJUkDGsY4ui7TZPdYCX/IBAMkaVJCjS88ZqEEFOQ0XNEZetMxQjvcAJ9yDVXiQNBZvc762FuUrL1/c4evWVrGis98xE4tHeVd5+eJmB8eiBw2mTr3Nle8lXng8RF64j1vmFqxTXV2t3Nzc2M95eXnasmVLs9tkZmbqrbfe0t133628vDyde+65CW2jf/8sU8bqZrm52Zbdd+ik47VD0mn/0kfFN31dgwceZ9m2cnOz9e99e+mD7Xs19JTj29zW77d8qnCTL/n/3HdI5xSdaNmY3MLKOQB3YA6AOZC4Az0yVCcpq0/PZs/fqGEFWrX+E4VCEWVk+DVqWIFrnl+3jDPVKCg7mBeKFbDXsQzlY5EXnR0IaOs6Dh7ADF47WOCFx8OifID7GNHOnyZ8beQUnn/++Xr33Xe1aNEiPfDAA1q4cGHc29i374AikdbbSRe5udmqqdlv2f0fONyQoXxC3+7q3zvT0m1JUv/emfrGsBMkqc1tndi/lwIBvxSOKBDw68T+vSwfk9NZPQfgfMwBMAeSc+jgEUnSwYNHmz1//XtnauY1w7VtZ50KB/RLyeefGdJ5Hvj9vg6bDIi8cDAzF+ExC3EE7hLrUHZR5EVTiZzazRyE1bw4x2IdyhSUAdfIz8/X3r17Yz9XV1crLy8v9vNnn32m//f//l/s55KSEm3bti2lY0THfIGG/TOFnbF/1lYGJgAASYkekPa3Lje2iseAq1FQRkKcWORG+6IF5W1//SjhAwFOOHiQyLxyYs442ufGHNiO5pgbH4/UJEOZyAvANUaPHq0NGzaotrZWhw8f1rp16zRmzJjY9YZhaNasWdq1a5ck6ZVXXtGZZ55p13DRhmhB2Qg5o6As8SUfANC5eBZwNYzoonytz56CtxB54RJTp96W0hzbtti9fSQuuijfyaecEjsIEO+p+V44nR/O5bX3Erc+HiIvAPfJz8/XjBkzVFpaqmAwqKuvvlrDhg3TlClTNH36dA0dOlTz5s3T1KlT5fP5NGjQID344IN2DxtN+DIavoJ98c+d2rdqpc2jSS+9hvyrep4yyO5hAIArVFbVxyIqJGlBxSaFwhFlBPztn9ESaYzb9NG/6nUUlF2irOx2FRUNtrVo0TJH160deekk4I9GXkQ6uaV7ND2wQc44rOb1OUaHMuBOJSUlKikpaXbZ0qVLY/8eO3asxo4dm+phIU7+Xr0kSUd37dK+lS/aPJr0Uv/2Wzp5wSK7hwEAjldZVd+sgPz107+kUJMFXLftrGu7oGy0H3kBb6GgbBMvdPsmOn4vPGa3Cfiii/IdO6UymQMBTjp40PTABl3U3uDk9wavzzEylCE5+28Q8KJeg09T3rXXK1Tf/inDTlW7/wvtqz+s/jk9dVx2d7uHEzcjFFLd2jUKHzpk91AAwBW27axrVkCWpIyAX+HGBVyjXcstGREiL9IFBWWbtOz2bY/d3XFmbj/exwzzRDOUI006lJN5DXjd4kdhJnG8N8TP7PlF5AUk/gaBVPMFAup7wUV2DyNhlVX1WhjtVjvi16wL3bOAXyR4VHVr10gR5+RWA4CTFQ7o16yAPHroCRo99IRYBEa77/9EXqSNLhWUDcOQEW1nhyXs7o6ze/vommhBOezyned4Dmw4pYuawox3OWGOmT2/jhJ5AQCIU8tutXZPd3YgX2MMnBF29z4xAKTKoIIczZo0vFUBubP3/WiN0Efkhef5jC5UhPfv36/PP/9cBQUFZo7JFvv2HVAkYm1xvGVRLCrebl+rCrq5udmqqdlvyfa7+pjRNX+r26H/3PSkfPIp09/+8SOfz2fqwaFgKKTMDGtOgDh8+LB69uxpyX2bobPxWfncdJXZ86AjwVBIoWCw1eUZmZmOfX6cwOz5fzQSlE8+Lb7gJ/L5fHF/HsD92vt8vvPOO1VaerMNI3IGv9+n/v2z7B6G7VKxX+xkvBe2LZqnGe1Wa3dBJgcyDEN/m3KDJOnUpb+Qz9fxqdjMATAHwBxIzqdLn9T+d9/Rl266WX1GjbZ7OF2WzvOgs/3iLn1rz87OVnZ2dlfuIq10tdvX7u64ZLZPh7O9TsjKV3a3LO0/eiDWiZgSflm2vUD3jNQ+lgR1Oj4LnxtX8Tc8Vy0ZMnh+OmDF/C/sN6jTL9bwnvY+n9N5pxlAx9rrVnMDn88nBQJSONxwOnYgYPeQAMCbiLxIG7SBuYjdHb12bx+Jy8rsrYdGz1bI6Pj0vuOPz9LevQdM2+455wzXhg2bTLu/pv5rablumlJmyX2bobPHbsVzY9Z9mj0P4mXlfGmP0+dRe6x4rrqRnwwAiNOgghxXFZKb8vn9MsJhGeGwfBSUAcASRF6kDwrKNrG729gO6fiYnSDgDyigjneae2R0V/fA0S5tp+Xp0yNHDJNkfrzJbbfcYdp9WSFyNKzugW7NLrP6uWlrm8kwYx4kY8oNt5gy/kQsfbLclrnU1UX1zHqtgab4fAaQFvwBSUEW5gMAK0U7lP2cAel1HDKwSTp2+6bjY04nZWW3a/Pmj2KnTUf/nW6ve1uFGSuem/LyxSoqGhxboDD67/LyxUnfp13SaY60lVmbCAp/sEI6/Q0C6FhlVb1Wb/hElVX1dg/FdL5Aw1dfIxyxeSQA4F0GkRdpI+FX+KGHHtKBA6k/JRoA3CBVhRkK+InzQhGe1xcAYJXoonsvvL1DCyo2ea6oHI25MMJ0KAOAZYi8SBsJv8IVFRUaN26c/vu//zuWjQIATdFF2T6eG/vYVYT3QiEbAOB923bWKRSOyDCkcDiibTvr7B6SufyNEXBEXgCAdYi8SBsJF5R/+9vf6vTTT9cDDzygK664Qu+++64V4wLgYmYU6LxabLOieEmR2tnoJgcAuEHhgH7KCPjl90mBgF+FA/rZPSRTEXkBANaLRl74iLzwvIRf4ZNPPllLly7Vk08+qSNHjui73/2upk+frqqqKivGByBNdTVrti0Uqa3hxueVIjwAAM0NKsjRrEnDNXHMyZo1abgGFeTYPSRTEXkBACkQTTIg8sLzkn6Fv/GNb2j16tWaOXOm1q9frwkTJujRRx/VoUOHzBwfAJjGiiJ1R9xYaE1Gqp9XM9hVhKeQDQBwskEFObr0nIGeKyZLIvICAFIg1qFMQdnzuvQKZ2Rk6MYbb9S6det02WWXaenSpSouLtZLL71k1vgApBGvZc26sdCa7qyea3Z3kwMAkK6IvACAFIhmKPvIUPY6Uw4Z1NfX62tf+5rOPPNM1dTU6Ac/+IG+/e1va8uWLWbcPYA0YUXWrNeK1E7h1eeVgwAAAHjTsciLkM0jAeAFlVX1Wr3hE1VW1ds9FGch8iJtZCT6CzU1NdqyZYu2bNmiDz74QH/+85+1f/9+SZLP59Opp56qYcOG6Y9//KOuueYa3XDDDZo5c6Z8HJ0AYIOysttjBemiosGxYrVVyssXNytKRguuU6fe5qnu1Lae16KiwZ56jAAAwENikRd0KAPomsqqei2o2KRQOKKMgN+TufPJYlG+9JFwQfm8886Tz+eTYRjKycnR8OHDdcYZZ2j48OEaOnSosrKyJEmhUEhPP/20fvrTn8rn82nmzJmmDx6Ad7k1azbVBWx0XbocBAAAIJ0di7wgQxlA12zbWadQOCLDkMLhiLbtrHNNQbmyql7bdtapcEA/a8ZsNB6089NU6nUJF5S//e1v68wzz9QZZ5yhr3zlK+3fcUaGpk6dqgMHDujFF1+koAwgIVYU8txapHayaMRF0+gLyV3FWA4CAADgfb5A41dfOpQBdFHhgH7KCPgVDkcUCPhVOKCf3UOKSyo6q41IY+QFHcqel3BB+Uc/+lFCtx88eLD27t2b6GYAwHSpLnCmQwE7VcXY8vLFrilQA6nA3wQAJMhPhzIAcwwqyNGsScPj7vS1vCs4TinprI5GXpCh7HmWv8LnnnuuFi5caPVmAMBxKPaYJ1WL5aXDQQB4AwtIAkgnZix+5fNHF+WjoAyg6wYV5OjScwbGVUxeULFJL7y9QwsqNtm6iF+0s9rvk3Wd1URepI2EO5QTlZOTo0svvdTqzQAAbOaFYiwHAQAAcBbTTtFuzFAm8gJAKjkpbznRzupkRCMvWJTP+3iFASBNRfOPzfods4ux5eWLVVQ0uFk+c1HR4KTGDaSaFfOUvwkAVjKjC9gKbRVjkuEL0KEMIPVS0hWcgHg7q5MW61Cm3Oh1vMIAkKaSOWU+lafZl5Xdrs2bP4rlMkf/TRcx3MCKvxX+JhC1atUqTZgwQePGjdOyZctaXf/666/r8ssv1ze/+U3deuutqq93VoEQzuOkU7JbMqsYQ+QFADtEu4InjjnZkkXwnMaIngXiI/LC6yyPvAAAAABgjj179ujRRx/VCy+8oG7duumaa67RyJEjNWjQIEnSgQMH9MADD+g3v/mN8vPz9dhjj2nx4sWaM2eOzSOHkznplOyWTDtFm8gLADYZVJDjmPdUyxmNkRd0KHserzAApJFkTpl3wmn2VuczExkAM6Tyb8ULmeVIzvr16zVq1Cj17dtXvXr1UnFxsdauXRu7PhgM6oEHHlB+fr4kqbCwUJ9++qldw4VLOO2U7JbMOEX7WORFyKxhAYBj2RZjFCHyIl34DKPx8EGa27fvgCKR9HwqcnOzVVOz3+5hwEbMgfRUVDQ4duq8FN88aPk7XuHVx5Uo3gvM49Y5le5zwO/3qX//LLuH0aElS5bo0KFDmjFjhiTpf/7nf7RlyxbNmzev1W2PHDmiyZMn6/rrr9fEiRNTPVS4zEef1OqD7Xs19JTjNXjgcXYPx3R//c/Fqvnd73XqHdOUd+EFdg8HACzz0Se1mv3kHxQKRZSR4ddDt3w9Ze/rG6fcoi+qazTiqSfUo/HgNryJyAsASGPl5YvJXwUAF2mrF8TXRk7h/v37deutt2rw4MEJF5PTudFCSt8DK/17Z+obw06QJE8+/i+CDdnJn392UL5OHl+6zgEcwxyAk+dAZVV9hzFA72ypUjDUEGMUCkX0zpYq9e+dmZKxhUMN77W1dYeV6Xfm85cIJ88Dq3XWaEEPOgCkqalTb0t44TAvnWbvhCgPeJeX/lbgLPn5+dq7d2/s5+rqauXl5TW7TXV1tSZPnqzBgwfroYceSvUQAUc6FnnBonwA3KujRVSjMRe9e2baFmNkEHmRNniFAcCBUlHUTKYz2UvdzGVlt2vz5o9isQTRf3vpMcI+zCNYZfTo0dqwYYNqa2t1+PBhrVu3TmPGjIldHw6Hdcstt2j8+PGaPXt2m93LQFryNxaUWZQPgIu1tYiq1LzQXPH63zRp7KmaOOZkzZo0PLULAja+x7L/4X0UlAHAgRLtHE5Ee525CxcuTOq+AACpk5+frxkzZqi0tFRXXHGFLrvsMg0bNkxTpkzRBx98oDfffFMffvihXn31VV1++eW6/PLLNXv2bLuHDdjOF2j86kuHMgAXa28R1ZaF5oOHg11ezDQp0WguOpQ9jwxlAEgzZWW3x7onmy4clkw+1JIlj3uiE3PEiLPtHgIAxK2kpEQlJSXNLlu6dKkkaejQofroI/ctCAlYzYzIi85ySwHAaoMKcjRr0vBW70XRQnM4HEl5zEVT0bNAfBSUPc/xBeVdu3Zp1qxZ2rdvn77yla/okUceUe/evZvdprq6Wj/4wQ+0d+9e+f1+3X333TrnnHNsGjEAJKe8fHGzzuRoB/HUqbd5omjrZO+//57dQwAAAFZqjLxQkpEX0dPJQ+GIMgL+1J9GDsCVrDgQNaggp9V9DSrI0aSxp+r9bdUaUZhn3/tT9D2WyAvPc/whgwcffFCTJ0/W2rVrdfrpp+uJJ55odZuHH35YF1xwgVauXKmFCxdq5syZCnMqEwCXsSPTN5mFw1jMDgAAuE008iLZDuX2cksBoD0dLaBnxbYqXv+bPvykThWv/83SbXWIyIu04ehXOBgM6r333lNxcbEk6corr9TatWtb3e7iiy+OnfZ30kkn6YsvvtChQ4dSOlYAcKNkF+bzwmJ2FMYBAEgfPn/XIi/ayy1tqbKqXqs3fGJfMQeAY6TyQJRTDnoReZE+HB15UVdXp6ysLGVkNAwzNzdXe/bsaXW7iy++OPbvp59+Wqeddpqys7MT2lb//lldG6zL5eYm9nzBe5gDznLnnXfa8poks023zp37779P999/nySpoKBAVVVVNo/IGdz6esI8zAEAnhToWuRFe7mlTRGLAaCpprnGfr9P++qPqLKq3pL3BadkKBN5kT4cU1B+5ZVXNH/+/GaXDRw4sNXtfB1MymeeeUYrVqzQL3/5y4S3v2/fAUUiRsK/5wXJLMQFb2EOOE9p6c0pf02SmQdTp97mmbnjlcfRFbwXIN3ngN/vS/smA8CrutqhLLWdW9pUWx2CFJQB9zBCIe198dcK1X2m2h4Z+uJIqEv311vSXZlHtffgEVV/dliqMvSXdT5FTuqn7J7dzBl0G9uSpMivt+hTk7cRj+h7LB3K3ueYgvL48eM1fvz4ZpcFg0GNHDlS4XBYgUBANTU1ysvLa/P3H374Yb311ltatmyZvvSlL6ViyACQ9twWc9GeZLKkAQCAe3Q1QzkejukQBJCUQ3/dprpXG2JWzTy8fnzjfzEffGzq/bfcliTpH+Y+hkT4e/cmQzkNOKag3JbMzEydddZZWrNmjUpKSvTSSy9pzJgxrW73zDPP6N1331VFRYX69Oljw0gBAG7mlcI4AABorrKqXtt21umr+4MNF0SsKyjHE4sBwLkiRxq6e7sP/IpOuvJyfb7/sCn3u6f2kF5e/3dFIhH5/X5dNvok5R/Xy5T7bmrz32r0x63VkiSfpLNPy1PRqbmmb6czPQacRIdyGnB0QVmS5s6dq3vvvVfl5eU64YQTtGjRIklSRUWFqqurNX36dD3++OPKysrS9ddfH/u9p556Svn5+XYNGwAAQFLDApActACA1GuaaTzi8yqNlWSEk8tQjldnsRgAnMsIHpUkdcvLU+7550kmxYD1kVQyrN7yg01fPrFef9u9KXaWxOUXDFcf3o9gEccXlAsKCvT888+3unzSpEmxf7/33nupHBIAAEDclix5nIIyANigaaZxqHG5HCsjLwC4mxFsOJPBl5Fp+n2n4mATZ0kglRxfUAYAAAAAIFFNM43VuCiflZEXANwtVlDONL+gnCqcJYFUIdQEAADAZOXli1VUNFhFRYMlKfbv8vLFNo8MALynsqpeqzd8osqq+maXR7v1Jo45WeNHf0WS9ZEXANwrcrQh8sLXrVur69p7nwHSFR3KAAAAJisruz0Wc1FUNFibN39k84gAwJua5iRnBPyaNWl4s+68aLfe53/crd0i8gJA+6Idyv4WHcqdvc8A6YgOZQAAAACAKzXNSQ6HI9q2s67N2/kCRF4A6JgRajvyIt73GSCdUFAGAACw0NSpt9k9BADwrGhOst8nBQJ+FQ7o1+btfI0ZykbE2sgLTosH3Ku9DOV432eAdELkBQAAgIWi0RcAAPNFc5K37axT4YB+7Z+GHmjspWoSeVFZVd/57yWA0+LhZWb/vThR5GjbBeW432eANEJBGQAAAADgWtGc5I7EOpQbC8pWFH/bOi2ewhO8IF0OlrTXoSzF9z4DpBMiLwAAAAAAnhbNUI5GXliRicpp8fCqdMkQPrYoXzebRwI4Hx3KAAAAAABviy7K19ihHC3+hsORdou/iZ7iz2nx8Kp4/l68wAgeldR2hzKA5igoAwAAAAA8zedvODk3GnnRWfE32VP8OS0eXpQuB0s6irwA0BwFZQAAAACAp7WMvJA6Lv6Shww0lw4HSyIUlIG4kaEMAAAAAPC2FpEXnSEPGUg/ZCgD8aOgDAAAALjIqlWrNGHCBI0bN07Lli1r93b33HOPXnjhhRSODHCulpEXnYme4j9xzMlxx10AcLfOIi8qq+q1esMnqqyqT+GoAGci8gIAAABwiT179ujRRx/VCy+8oG7duumaa67RyJEjNWjQoGa3mTt3rjZs2KCRI0faOFrAOY5FXsRXUJbS4xR/AMd0VFBONlcd8Co6lAEAAACXWL9+vUaNGqW+ffuqV69eKi4u1tq1a5vdZtWqVbrooos0fvx4m0YJOJA/GnkR6fh2ANJWrKDcrXVBua1cdSCd0aEMAAAAuER1dbVyc3NjP+fl5WnLli3NbnPTTTdJkt5///2Ujg1wMl8gscgLAOknEjwqSfK30aEczVUPhyPkqgOioAwAAAC4hmEYrS7z+XymbqN//yxT78+NcnOz7R4CTPaF/6g+luSXEdfryxwAc8B7PvqkVh9s36uhpxyvwQOPa3X99lBIknT8lxqKxU3nQG5utv69b68Ofx/exHtB2ygoAwAAAC6Rn5+vjRs3xn6urq5WXl6eqdvYt++AIpHWhet0kZubrZqa/XYPAyYL1R+WJIWDoU5fX+YAmAPeE08GcuRoQ4dybf0Xys9uPQf6987UN4adIEnMjzSRzu8Ffr+vwyYDMpQBAAAAlxg9erQ2bNig2tpaHT58WOvWrdOYMWPsHhbgeLFF+Yi8ANJSZxnIhmF0uCgfgOYoKAMAAAAukZ+frxkzZqi0tFRXXHGFLrvsMg0bNkxTpkzRBx98YPfwAOdqLCgrQkEZSEfRDGS/T21mIBuhxmJyRoZ8fkplQGeIvAAAAABcpKSkRCUlJc0uW7p0aavb/eQnP0nVkADHixaIjEgk7t+prKrXtp11KhzQr9Wp8QDcZVBBjmZNGt7u3zTdyUBiKCgDAAAAADwt0ciLePJWAbjLoIKcdv+OKSgDiaGPHwAAAADgbdFT2MNhGUbni052lreaapVV9Vq94RNVVtXbOg7Aq4yjFJSBRNChDAAAAADwNJ/fL/l8kmE0/OfzdXj7aN5qOBxpM281leiW9javRau49fFE6FAGEkJBGQAAAADgeb5AQEYoJCMcks/frcPbdpa3mkptdUu7qVCH9nntYIGbH090UT5/ZsfvDQAaEHkBAAAAAPC+WOxFfAvzDSrI0aXnDLS9IBbtlvb7ZHu3NMzltGiVrnLz4zGOHpVEhzIQLzqUAQAAAACe5wsEZEgyIvEtzOcUTuqWhrmcFK1iBjc/HhblAxJDQRkAAAAA4H2BgCTJCIeTynm1Mxt2UEEOhWQP8trBAjc/HjKUgcRQUAYAAAAAeJ6vMfLi46rP9MjLOxLKeXVzNiyczW0HCzo7sOK2xxNlBBsiL8hQBuJDhjIAAAAAwPN8gYZ+qh3/SDzn1S3ZsJVV9Vq94RNVVtXbPRR4UPTAygtv79CCik2emmdEXgCJoUMZAAAAAOB9gYZ+qpO/lKWMQF1COa9uyIalixpWa+vAilfmGAVlIDEUlAEAAAAAnufzN2Qon5TbO+GcVzdkw3q52AdncMOBlWTFCsrdKCgD8aCgDAAAAADwPF90Ub5IOKmcV6dlw7bMsvVysQ/O4IYDK8mKLsrnz6CgDMSDgjIAAAAAwPsaF+VTOGzvOEzQXryFV4t9cA6nHVgxC5EXQGIoKAMAAAAAPC/WoRyO2DySrmsv3sIpxb6W3dPoHM9Z/Kx4rigoA4mhoAwAAAAA8L7GDuV9q15SIDu73Zt91iNTR44EUzWqpJx68KgmVNfKMAz5fD6d+qdt2r2tm93DkiR9fvCoPtjRMLb/8/kUOfk49entjLHFK9VzwAvPWapY9Vwd+fhjSZKvG887EA8KygAAAAAAz8vo00dfSDr4f5s7vN3nqRlOlw1t+sMmZ43byWOLhx3jdftzlkpWPlcZOXSHA/GgoAwAAAAA8Lz80ht08M8fSEbHkRfZ2T20f/8RU8RF7wMAABGrSURBVLZZXXdYu2sP6UvH9VJev56m3KfTVdcd1to/7lQkYsjv9+mSrw1o9did/ryYOQfiEc9zhgZWPlf+Xr2VdUaRKfcFeB0FZQAAAACA52X07aucc8/r9Ha5udny1+zv8vYqq+r1SMUmhcLdlLHXr1mTitIiGzdHkm9E+xm3Vj0vZubqmjUH4tXZc4ZjeK4AZ6CgDAAAAACAydpbOC8ddLQ4oBXPS2VVvRZUbFIoHFFGwK9Zk4a77rm2a0FFNy4G6JTFJ4F0RkEZAAAAAACTFQ7op4yAX+FwRIGAX4UD+tk9JEew4nlJ5+J9V9hViHdjERtAcxSUAQAAAAAw2aCCHM2aNJzCWQtWPC8U75NjRyHeC93kACgoAwAAAABgCU7Nb5vZzwvF++TYUYinmxzwBgrKAAAAgIusWrVK5eXlCgaD+u53v6trr7222fVbt27VnDlzdODAAZ111ll68MEHlZHBbj8Ab6N4nzg7CvF0kwPe4Ld7AAAAAADis2fPHj366KNavny5Vq5cqRUrVqiysrLZbWbNmqUf/vCHevXVV2UYhn71q1/ZNFoAgNMNKsjRpecMTFkxPlrEnjjmZOIuABejoAwAAAC4xPr16zVq1Cj17dtXvXr1UnFxsdauXRu7vqqqSkeOHFFRUZEk6corr2x2PQD3qayq1+oNn6iyqt6R94djeG7jk+oiNgDzOb6gvGvXLl177bW65JJLVFZWpoMHD7Z72wMHDmjs2LF69913UzhCAAAAIDWqq6uVm5sb+zkvL0979uxp9/rc3Nxm1wNwl+gCZi+8vUMLKjZ1uVBp9v3Fu810KLLa8dwCgF0cH6b24IMPavLkybr00kv1+OOP64knntCsWbPavO28efP0+eefp3iEAAAAQGoYhtHqMp/PF/f18ejfPyvxgXlMbm623UOAzZwyB36/5VOFmyxg9s99h3RO0YmOub/OfPRJrR75700KhSLKyPDroVu+rsEDj7Nse2ZKdA6k+rmF9ZzyPgB7MQ/a5uiCcjAY1HvvvafHH39cUsMpe9ddd12bBeU1a9aod+/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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (ax0, ax1) = plt.subplots(ncols=2, figsize=(20, 5))\n", "\n", "plt.subplot(ax0)\n", "plot_predictions(\n", " [tree_2],\n", " X,\n", " data[\"Tree 1 residual\"],\n", " axes=[-0.5, 0.5, -0.5, 0.5],\n", " label=\"$h_2(X)$\",\n", " style=\"g-\",\n", " data_style=\"k+\",\n", " data_label=\"Residuals\",\n", ")\n", "plt.ylabel(\"$y - h_1(X)$\", fontsize=18)\n", "plt.title(\"Residuals and tree predictions\", fontsize=16)\n", "\n", "plt.subplot(ax1)\n", "plot_predictions([tree_1, tree_2], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"$h(X) = h_1(X) + h_2(X)$\")\n", "plt.title(\"Ensemble predictions\", fontsize=16)\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the figure, we see that the ensemble's predictions have improved compared to our first crappy model!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Step 4 - rinse and repeat" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is not hard to see how we can continue this procedure by successively adding new models:\n", "\n", "$$ F_{m+1}(x) = F_m(x) + h_m(x)\\,, \\qquad \\mathrm{for} \\, m \\geq 0 $$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " X y Tree 1 prediction Tree 1 residual Tree 2 prediction \\\n", "0 -0.125460 0.051573 0.123566 -0.071993 -0.090398 \n", "1 0.450714 0.594480 0.528568 0.065911 0.039913 \n", "2 0.231994 0.166052 0.123566 0.042485 0.039913 \n", "3 0.098658 -0.070178 0.123566 -0.193744 -0.090398 \n", "4 -0.343981 0.343986 0.123566 0.220420 0.159838 \n", "\n", " Tree 1 + tree 2 prediction Tree 1 + tree 2 residual \n", "0 0.033168 0.018405 \n", "1 0.568481 0.025998 \n", "2 0.163479 0.002573 \n", "3 0.033168 -0.103346 \n", "4 0.283404 0.060582 " ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data[\"Tree 1 + tree 2 residual\"] = data[\"Tree 1 residual\"] - data[\"Tree 2 prediction\"]\n", "data.head()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DecisionTreeRegressor(ccp_alpha=0.0, criterion='mse', max_depth=2,\n", " max_features=None, max_leaf_nodes=None,\n", " min_impurity_decrease=0.0, min_impurity_split=None,\n", " min_samples_leaf=1, min_samples_split=2,\n", " min_weight_fraction_leaf=0.0, presort='deprecated',\n", " random_state=None, splitter='best')" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tree_3 = DecisionTreeRegressor(max_depth=2)\n", "tree_3.fit(X, data[\"Tree 1 + tree 2 residual\"])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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XyTree 1 predictionTree 1 residualTree 2 predictionTree 1 + tree 2 predictionTree 1 + tree 2 residualTree 3 predictionTree 1 + tree 2 + tree 3 predictionFinal residual
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" ], "text/plain": [ " X y Tree 1 prediction Tree 1 residual Tree 2 prediction \\\n", "0 -0.125460 0.051573 0.123566 -0.071993 -0.090398 \n", "1 0.450714 0.594480 0.528568 0.065911 0.039913 \n", "2 0.231994 0.166052 0.123566 0.042485 0.039913 \n", "3 0.098658 -0.070178 0.123566 -0.193744 -0.090398 \n", "4 -0.343981 0.343986 0.123566 0.220420 0.159838 \n", "\n", " Tree 1 + tree 2 prediction Tree 1 + tree 2 residual Tree 3 prediction \\\n", "0 0.033168 0.018405 0.007043 \n", "1 0.568481 0.025998 -0.068529 \n", "2 0.163479 0.002573 0.007043 \n", "3 0.033168 -0.103346 0.007043 \n", "4 0.283404 0.060582 0.007043 \n", "\n", " Tree 1 + tree 2 + tree 3 prediction Final residual \n", "0 0.040212 0.011361 \n", "1 0.499952 0.094528 \n", "2 0.170523 -0.004471 \n", "3 0.040212 -0.110390 \n", "4 0.290448 0.053538 " ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data[\"Tree 3 prediction\"] = tree_3.predict(X)\n", "data[\"Tree 1 + tree 2 + tree 3 prediction\"] = sum(tree.predict(X) for tree in (tree_1, tree_2, tree_3))\n", "data[\"Final residual\"] = data[\"Tree 1 + tree 2 residual\"] - data[\"Tree 3 prediction\"]\n", "data.head()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (ax0, ax1) = plt.subplots(ncols=2, figsize=(20, 5))\n", "\n", "plt.subplot(ax0)\n", "plot_predictions(\n", " [tree_3],\n", " X,\n", " data[\"Tree 1 + tree 2 residual\"],\n", " axes=[-0.5, 0.5, -0.5, 0.5],\n", " label=\"$h_3(X)$\",\n", " style=\"g-\",\n", " data_style=\"k+\",\n", ")\n", "plt.ylabel(\"$y - h_1(X) - h_2(X)$\", fontsize=16)\n", "\n", "plt.subplot(ax1)\n", "plot_predictions(\n", " [tree_1, tree_2, tree_3], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"$h(X) = h_1(X) + h_2(X) + h_3(X)$\",\n", ")\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As promised, adding more models to the ensemble improves the predictions (at least qualitatively)!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gradient boosting with scikit-learn" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Manually building up the gradient boosting ensemble is a drag, so in practice it is better to make use of scikit-learn's [GradientBoostingRegressor](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.GradientBoostingRegressor.html) class. Similar to the Random Forest classes that we've worked with in previous lessons, it has similar hyperparameters like `max_depth` and `min_samples_leaf` that control the growth of each tree, along with parameters like `n_estimators` which control the size of the ensemble. For example, we can reconstruct our hand-crafted ensemble from before as follows:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "GradientBoostingRegressor(alpha=0.9, ccp_alpha=0.0, criterion='friedman_mse',\n", " init=None, learning_rate=1.0, loss='ls', max_depth=2,\n", " max_features=None, max_leaf_nodes=None,\n", " min_impurity_decrease=0.0, min_impurity_split=None,\n", " min_samples_leaf=1, min_samples_split=2,\n", " min_weight_fraction_leaf=0.0, n_estimators=3,\n", " n_iter_no_change=None, presort='deprecated',\n", " random_state=None, subsample=1.0, tol=0.0001,\n", " validation_fraction=0.1, verbose=0, warm_start=False)" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gbrt = GradientBoostingRegressor(max_depth=2, n_estimators=3, learning_rate=1.0)\n", "gbrt.fit(X, y)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_predictions(\n", " [gbrt], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"Ensemble predictions\", style=\"g-\", data_label=\"Training set\"\n", ")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Choosing hyperparameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are two main hyperparameters that you need to tune to prevent a boosted regression ensemble from overfitting the training set:\n", "\n", "* `learning_rate`: this hyperparameter weights the contribution of each tree. Low values like 0.1 imply more trees are needed in the ensemble, but will typically lead to better generalisation error.\n", "* `n_estimators`: this hyperparameter controls the number of trees in the ensemble. Adding too many trees can lead to overfitting." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Effect of learning rate" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To show the effect of the learning rate, let's train two ensembles at different extremes:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "GradientBoostingRegressor(alpha=0.9, ccp_alpha=0.0, criterion='friedman_mse',\n", " init=None, learning_rate=0.1, loss='ls', max_depth=2,\n", " max_features=None, max_leaf_nodes=None,\n", " min_impurity_decrease=0.0, min_impurity_split=None,\n", " min_samples_leaf=1, min_samples_split=2,\n", " min_weight_fraction_leaf=0.0, n_estimators=200,\n", " n_iter_no_change=None, presort='deprecated',\n", " random_state=42, subsample=1.0, tol=0.0001,\n", " validation_fraction=0.1, verbose=0, warm_start=False)" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gbrt_high_lr = GradientBoostingRegressor(max_depth=2, n_estimators=3, learning_rate=0.1, random_state=42)\n", "gbrt_high_lr.fit(X, y)\n", "\n", "gbrt_low_lr = GradientBoostingRegressor(max_depth=2, n_estimators=200, learning_rate=0.1, random_state=42)\n", "gbrt_low_lr.fit(X, y)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (ax0, ax1) = plt.subplots(ncols=2, figsize=(20, 5))\n", "\n", "plt.subplot(ax0)\n", "plot_predictions([gbrt_high_lr], X, y, axes=[-0.5, 0.5, -0.1, 0.8], label=\"Ensemble predictions\")\n", "plt.title(f\"learning_rate={gbrt_high_lr.learning_rate}, n_estimators={gbrt_high_lr.n_estimators}\", fontsize=18)\n", "\n", "plt.subplot(ax1)\n", "plot_predictions([gbrt_low_lr], X, y, axes=[-0.5, 0.5, -0.1, 0.8])\n", "plt.title(f\"learning_rate={gbrt_low_lr.learning_rate}, n_estimators={gbrt_low_lr.n_estimators}\", fontsize=18)\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Early stopping" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In practice the learning rate and number of trees in the ensemble are found via cross-validation. However, it has been observed empircally that small learning rates like 0.1 produce models that generalise better. For fixed learing rate, we can find the optimal number of trees using a technique known as \"early stoppping\". Here the idea is to use a validation set to measure how the error decreases as we add more trees and find the optimal point from the curve:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "GradientBoostingRegressor(alpha=0.9, ccp_alpha=0.0, criterion='friedman_mse',\n", " init=None, learning_rate=0.1, loss='ls', max_depth=2,\n", " max_features=None, max_leaf_nodes=None,\n", " min_impurity_decrease=0.0, min_impurity_split=None,\n", " min_samples_leaf=1, min_samples_split=2,\n", " min_weight_fraction_leaf=0.0, n_estimators=56,\n", " n_iter_no_change=None, presort='deprecated',\n", " random_state=42, subsample=1.0, tol=0.0001,\n", " validation_fraction=0.1, verbose=0, warm_start=False)" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X_train, X_valid, y_train, y_valid = train_test_split(X, y, random_state=49)\n", "\n", "gbrt = GradientBoostingRegressor(max_depth=2, n_estimators=120, random_state=42)\n", "gbrt.fit(X_train, y_train)\n", "\n", "errors = [mean_squared_error(y_valid, y_pred) for y_pred in gbrt.staged_predict(X_valid)]\n", "bst_n_estimators = np.argmin(errors) + 1\n", "\n", "gbrt_best = GradientBoostingRegressor(max_depth=2, n_estimators=bst_n_estimators, random_state=42)\n", "gbrt_best.fit(X_train, y_train)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "min_error = np.min(errors)\n", "\n", "fig, (ax0, ax1) = plt.subplots(ncols=2, figsize=(20, 5))\n", "\n", "plt.subplot(ax0)\n", "plt.plot(errors, \"b.-\")\n", "plt.plot([bst_n_estimators, bst_n_estimators], [0, min_error], \"k--\")\n", "plt.plot([0, 120], [min_error, min_error], \"k--\")\n", "plt.plot(bst_n_estimators, min_error, \"ko\")\n", "plt.text(bst_n_estimators, min_error * 1.2, \"Minimum\", ha=\"center\", fontsize=14)\n", "plt.axis([0, 120, 0, 0.01])\n", "plt.xlabel(\"Number of trees\", fontsize=16)\n", "plt.ylabel(\"MSE\", fontsize=16)\n", "plt.title(\"Validation error\", fontsize=14)\n", "\n", "plt.subplot(ax1)\n", "plot_predictions([gbrt_best], X, y, axes=[-0.5, 0.5, -0.1, 0.8])\n", "plt.title(f\"Best model ({bst_n_estimators} trees)\", fontsize=14)\n", "\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In practice it is better to actually stop the training when the early stopping criterion is met, instead of training many redundant models. In scikit-learn, this is configured by setting `warm_start=True` which allows for incremental training and can be use to stop the training loop when some threshold is met, e.g." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "GradientBoostingRegressor(alpha=0.9, ccp_alpha=0.0, criterion='friedman_mse',\n", " init=None, learning_rate=0.1, loss='ls', max_depth=2,\n", " max_features=None, max_leaf_nodes=None,\n", " min_impurity_decrease=0.0, min_impurity_split=None,\n", " min_samples_leaf=1, min_samples_split=2,\n", " min_weight_fraction_leaf=0.0, n_estimators=120,\n", " n_iter_no_change=5, presort='deprecated',\n", " random_state=42, subsample=1.0, tol=1e-05,\n", " validation_fraction=0.2, verbose=0, warm_start=True)" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gbrt = GradientBoostingRegressor(\n", " n_estimators=120, validation_fraction=0.2, n_iter_no_change=5, tol=1e-5, max_depth=2, random_state=42, warm_start=True\n", ")\n", "gbrt.fit(X, y)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimal number of trees: 60\n", "Minimum validation MSE: 0.0008984023296480315\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print(f\"Optimal number of trees: {gbrt.n_estimators_}\")\n", "print(f\"Minimum validation MSE: {np.min(gbrt.train_score_)}\")\n", "\n", "plot_predictions([gbrt], X, y, axes=[-0.5, 0.5, -0.1, 0.8])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use scikit-learn's [GradientBoostingClassifier](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.GradientBoostingClassifier.html?highlight=gradientboostingclassifier) to explore how the algorithm's hyperparameters influence the [decision boundary](https://en.wikipedia.org/wiki/Decision_boundary) on the following synthetic dataset for binary classification:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import make_moons\n", "\n", "X, y = make_moons(n_samples=500, noise=0.30, random_state=42)\n", "\n", "sns.scatterplot(x=X[:, 0], y=X[:, 1], hue=y)\n", "plt.xlabel(\"$x_1$\")\n", "plt.ylabel(\"$x_2$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In addition, see if you can use early stopping to find the optimal number of trees to include in the ensemble." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" } }, "nbformat": 4, "nbformat_minor": 4 }