{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Gradient Boosted Regression Trees\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Scikit-learn\n", "\n", " * Easy-to-use Machine Learning toolkit\n", " * Classical, well-established machine learning algorithms\n", " * BSD 3 license\n", "\n", "### Estimator\n", "\n", "\"*An estimator is any object that learns from data; it may be a classification, regression or clustering algorithm or a transformer that extracts/filters useful features from raw data.*\"" ] }, { "cell_type": "code", "collapsed": false, "input": [ "class Estimator(object):\n", " \n", " def fit(self, X, y=None):\n", " \"\"\"Fits estimator to data. \"\"\"\n", " # set state of ``self``\n", " return self\n", " \n", " def predict(self, X):\n", " \"\"\"Predict response of ``X``. \"\"\"\n", " # compute predictions ``pred``\n", " return pred" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Scikit-learn provides two estimators for gradient boosting: ``GradientBoostingClassifier`` and ``GradientBoostingRegressor``, both are located in the ``sklearn.ensemble`` package:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.ensemble import GradientBoostingClassifier\n", "from sklearn.ensemble import GradientBoostingRegressor" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Estimators support arguments to control the fitting behaviour -- these arguments are often called _hyperparameters_. Among the most important ones for GBRT are:\n", "\n", " * number of regression trees (``n_estimators``)\n", " * depth of each individual tree (``max_depth``)\n", " * loss function (``loss``)\n", "\n", "For example if you want to fit a regression model with 100 trees of depth 3 using least-squares:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "est = GradientBoostingRegressor(n_estimators=100, max_depth=3, loss='ls')" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "est?" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is an self-contained example that shows how to fit a ``GradientBoostingClassifier`` to a synthetic dataset:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.datasets import make_hastie_10_2\n", "from sklearn.cross_validation import train_test_split\n", "\n", "# generate synthetic data from ESLII - Example 10.2\n", "X, y = make_hastie_10_2(n_samples=5000)\n", "X_train, X_test, y_train, y_test = train_test_split(X, y)\n", "\n", "# fit estimator\n", "est = GradientBoostingClassifier(n_estimators=200, max_depth=3)\n", "est.fit(X_train, y_train)\n", "\n", "# predict class labels\n", "pred = est.predict(X_test)\n", "\n", "# score on test data (accuracy)\n", "acc = est.score(X_test, y_test)\n", "print('ACC: %.4f' % acc)\n", "\n", "# predict class probabilities\n", "est.predict_proba(X_test)[0]" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "ACC: 0.9224\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "array([ 0.74435614, 0.25564386])" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The state of the estimator is stored in instance attributes that have a trailing underscore ('\\_'). For example, the sequence of regression trees (``DecisionTreeRegressor`` objects) is stored in ``est.estimators_``:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "est.estimators_[0, 0]" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 6, "text": [ "DecisionTreeRegressor(compute_importances=None,\n", " criterion=,\n", " max_depth=3, max_features=None, max_leaf_nodes=None,\n", " min_density=None, min_samples_leaf=1, min_samples_split=2,\n", " random_state=,\n", " splitter=)" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gradient Boosted Regression Trees in Practise\n", "\n", "### Function approximation\n", "\n", " * Sinoide function + random gaussian noise \n", " * 80 training (blue), 20 test (red) points" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline\n", "import numpy as np\n", "from sklearn.cross_validation import train_test_split\n", "\n", "FIGSIZE = (11, 7)\n", "\n", "def ground_truth(x):\n", " \"\"\"Ground truth -- function to approximate\"\"\"\n", " return x * np.sin(x) + np.sin(2 * x)\n", "\n", "def gen_data(n_samples=200):\n", " \"\"\"generate training and testing data\"\"\"\n", " np.random.seed(15)\n", " X = np.random.uniform(0, 10, size=n_samples)[:, np.newaxis]\n", " y = ground_truth(X.ravel()) + np.random.normal(scale=2, size=n_samples)\n", " train_mask = np.random.randint(0, 2, size=n_samples).astype(np.bool)\n", " X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=3)\n", " return X_train, X_test, y_train, y_test\n", "\n", "X_train, X_test, y_train, y_test = gen_data(100)\n", "\n", "# plot ground truth\n", "x_plot = np.linspace(0, 10, 500)\n", "\n", "def plot_data(alpha=0.4, s=20):\n", " fig = plt.figure(figsize=FIGSIZE)\n", " gt = plt.plot(x_plot, ground_truth(x_plot), alpha=alpha, label='ground truth')\n", "\n", " # plot training and testing data\n", " plt.scatter(X_train, y_train, s=s, alpha=alpha)\n", " plt.scatter(X_test, y_test, s=s, alpha=alpha, color='red')\n", " plt.xlim((0, 10))\n", " plt.ylabel('y')\n", " plt.xlabel('x')\n", " \n", "annotation_kw = {'xycoords': 'data', 'textcoords': 'data',\n", " 'arrowprops': {'arrowstyle': '->', 'connectionstyle': 'arc'}}\n", " \n", "plot_data()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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IyAsdPSpGRObmKh3J1CbLYlRpSAiwYoXS0fgHFhwRERF5mZoaoLcXyMlROpKpT5JEMVdr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\nocDq1UBFhdhKbt68ibe6u7dXNJK/75FIhAU/K261q1Rihf5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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Regression Trees\n", "\n", " * ``max_depth`` argument controlls the depth of the tree\n", " * The deeper the tree the more variance can be explained" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.tree import DecisionTreeRegressor\n", "plot_data()\n", "est = DecisionTreeRegressor(max_depth=1).fit(X_train, y_train)\n", "plt.plot(x_plot, est.predict(x_plot[:, np.newaxis]),\n", " label='RT max_depth=1', color='g', alpha=0.9, linewidth=2)\n", "\n", "est = DecisionTreeRegressor(max_depth=3).fit(X_train, y_train)\n", "plt.plot(x_plot, est.predict(x_plot[:, np.newaxis]),\n", " label='RT max_depth=3', color='g', alpha=0.7, linewidth=1)\n", "\n", "plt.legend(loc='upper left')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 8, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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H3+qBqqVWGDLEbI6/fLlZwe8pVkMjn75GyaeIiIiPOlNcdNVVcMUVbXcdm7Nl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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Function approximation with Gradient Boosting\n", "\n", " * ``n_estimators`` argument controls the number of trees\n", " * ``staged_predict`` method allows us to step through predictions as we add more trees" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from itertools import islice\n", "\n", "plot_data()\n", "est = GradientBoostingRegressor(n_estimators=1000, max_depth=1, learning_rate=1.0)\n", "est.fit(X_train, y_train)\n", "\n", "ax = plt.gca()\n", "first = True\n", "\n", "# step through prediction as we add 10 more trees.\n", "for pred in islice(est.staged_predict(x_plot[:, np.newaxis]), 0, est.n_estimators, 10):\n", " plt.plot(x_plot, pred, color='r', alpha=0.2)\n", " if first:\n", " ax.annotate('High bias - low variance', xy=(x_plot[x_plot.shape[0] // 2],\n", " pred[x_plot.shape[0] // 2]),\n", " xytext=(4, 4), **annotation_kw)\n", " first = False\n", "\n", "pred = est.predict(x_plot[:, np.newaxis])\n", "plt.plot(x_plot, pred, color='r', label='GBRT max_depth=1')\n", "ax.annotate('Low bias - high variance', xy=(x_plot[x_plot.shape[0] // 2],\n", " pred[x_plot.shape[0] // 2]),\n", " xytext=(6.25, -6), **annotation_kw)\n", "plt.legend(loc='upper left')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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PTyc3dy8JCVZnsfM9e4w86/zzfRxobY7uUl82w65f3/h9Dx82tuXlYK6ZuhIG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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model complexity\n", "\n", " * The number of trees and the depth of the individual trees control model complexity\n", " * Model complexity comes at a price: **overfitting**\n", " \n", " \n", "### Deviance plot\n", "\n", " * Diagnostic to determine if model is overfitting\n", " * Plots the training/testing error (deviance) as a function of the number of trees (=model complexity)\n", " * Training error (deviance) is stored in ``est.train_score_``\n", " * Test error is computed using ``est.staged_predict``" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def deviance_plot(est, X_test, y_test, ax=None, label='', train_color='#2c7bb6', \n", " test_color='#d7191c', alpha=1.0, ylim=(0, 10)):\n", " \"\"\"Deviance plot for ``est``, use ``X_test`` and ``y_test`` for test error. \"\"\"\n", " n_estimators = len(est.estimators_)\n", " test_dev = np.empty(n_estimators)\n", "\n", " for i, pred in enumerate(est.staged_predict(X_test)):\n", " test_dev[i] = est.loss_(y_test, pred)\n", "\n", " if ax is None:\n", " fig = plt.figure(figsize=FIGSIZE)\n", " ax = plt.gca()\n", " \n", " ax.plot(np.arange(n_estimators) + 1, test_dev, color=test_color, label='Test %s' % label, \n", " linewidth=2, alpha=alpha)\n", " ax.plot(np.arange(n_estimators) + 1, est.train_score_, color=train_color, \n", " label='Train %s' % label, linewidth=2, alpha=alpha)\n", " ax.set_ylabel('Error')\n", " ax.set_xlabel('n_estimators')\n", " ax.set_ylim(ylim)\n", " return test_dev, ax\n", "\n", "test_dev, ax = deviance_plot(est, X_test, y_test)\n", "ax.legend(loc='upper right')\n", "\n", "# add some annotations\n", "ax.annotate('Lowest test error', xy=(test_dev.argmin() + 1, test_dev.min() + 0.02),\n", " xytext=(150, 3.5), **annotation_kw)\n", "\n", "ann = ax.annotate('', xy=(800, test_dev[799]), xycoords='data',\n", " xytext=(800, est.train_score_[799]), textcoords='data',\n", " arrowprops={'arrowstyle': '<->'})\n", "ax.text(810, 3.5, 'train-test gap')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 10, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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Y2CrvY3O5FDhFRCzM0qHT5zMxnE5wOqG4uORXUFCgyxJpkkyfj8L1fxHc+Shw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\n1h7Pdn1Hr2e6/vuaoc+tUcrco64axLofPT+hWsSFarkQPhE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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Overfitting\n", "\n", " * Model has too much capacity and starts fitting the idiosyncracies of the training data\n", " * Indicated by a large gap between train and test error\n", " * GBRT provides a number of knobs to control overfitting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Regularization\n", "\n", " * Tree structure\n", " * Shrinkage\n", " * Stochastic Gradient Boosting\n", "\n", "## Tree Structure\n", "\n", " * The ``max_depth`` of the trees controls the degree of features interactions (variance++)\n", " * Use ``min_samples_leaf`` to have a sufficient number of samples per leaf (bias++)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def fmt_params(params):\n", " return \", \".join(\"{0}={1}\".format(key, val) for key, val in params.iteritems())\n", "\n", "fig = plt.figure(figsize=FIGSIZE)\n", "ax = plt.gca()\n", "for params, (test_color, train_color) in [({}, ('#d7191c', '#2c7bb6')),\n", " ({'min_samples_leaf': 3}, ('#fdae61', '#abd9e9'))]:\n", " est = GradientBoostingRegressor(n_estimators=1000, max_depth=1, \n", " learning_rate=1.0)\n", " est.set_params(**params)\n", " est.fit(X_train, y_train)\n", " test_dev, ax = deviance_plot(est, X_test, y_test, ax=ax, label=fmt_params(params),\n", " train_color=train_color, test_color=test_color)\n", " \n", "ax.annotate('Higher bias', xy=(900, est.train_score_[899]), xytext=(600, 3), **annotation_kw)\n", "ax.annotate('Lower variance', xy=(900, test_dev[899]), xytext=(600, 3.5), **annotation_kw)\n", "plt.legend(loc='upper right')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 11, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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7D+ukU5k0Al5vqMMQQgjRBhQUFIQ6BCHatbCeXtdNJpCz14UQQgghWr2wTjox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\nE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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Shrinkage\n", "\n", " * Slow learning by shrinking the predictions of each tree by some small scalar (``learning_rate``)\n", " * A lower ``learning_rate`` requires a higher number of ``n_estimators``\n", " * Its a trade-off between runtime against accuracy." ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=FIGSIZE)\n", "ax = plt.gca()\n", "for params, (test_color, train_color) in [({}, ('#d7191c', '#2c7bb6')),\n", " ({'learning_rate': 0.1},\n", " ('#fdae61', '#abd9e9'))]:\n", " est = GradientBoostingRegressor(n_estimators=1000, max_depth=1, learning_rate=1.0)\n", " est.set_params(**params)\n", " est.fit(X_train, y_train)\n", " \n", " test_dev, ax = deviance_plot(est, X_test, y_test, ax=ax, label=fmt_params(params),\n", " train_color=train_color, test_color=test_color)\n", " \n", "ax.annotate('Requires more trees', xy=(200, est.train_score_[199]), \n", " xytext=(300, 1.75), **annotation_kw)\n", "ax.annotate('Lower test error', xy=(900, test_dev[899]),\n", " xytext=(600, 1.75), **annotation_kw)\n", "plt.legend(loc='upper right')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 12, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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Nvic1NTUceuihAAwbNiyy68CuH1dccUWkzbp16/B4PJF+ly9fHqm4xrIuTzpT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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stochastic Gradient Boosting\n", "\n", " * Subsampling the training set before growing each tree (``subsample``)\n", " * Subsampling the features before finding the best split node (``max_features``)\n", " * Latter usually works better if there is a sufficient large number of features" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig = plt.figure(figsize=FIGSIZE)\n", "ax = plt.gca()\n", "for params, (test_color, train_color) in [({}, ('#d7191c', '#2c7bb6')),\n", " ({'learning_rate': 0.1, 'subsample': 0.5},\n", " ('#fdae61', '#abd9e9'))]:\n", " est = GradientBoostingRegressor(n_estimators=1000, max_depth=1, learning_rate=1.0,\n", " random_state=1)\n", " est.set_params(**params)\n", " est.fit(X_train, y_train)\n", " test_dev, ax = deviance_plot(est, X_test, y_test, ax=ax, label=fmt_params(params),\n", " train_color=train_color, test_color=test_color)\n", " \n", "ax.annotate('Even lower test error', xy=(400, test_dev[399]),\n", " xytext=(500, 3.0), **annotation_kw)\n", "\n", "est = GradientBoostingRegressor(n_estimators=1000, max_depth=1, learning_rate=1.0,\n", " subsample=0.5)\n", "est.fit(X_train, y_train)\n", "test_dev, ax = deviance_plot(est, X_test, y_test, ax=ax, label=fmt_params({'subsample': 0.5}),\n", " train_color='#abd9e9', test_color='#fdae61', alpha=0.5)\n", "ax.annotate('Subsample alone does poorly', xy=(300, test_dev[299]), \n", " xytext=(500, 5.5), **annotation_kw)\n", "plt.legend(loc='upper right', fontsize='small')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 13, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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8++67mDBhAhQKBfz8/LB7924kJiYiMTFR8liLFy9GYmIi/va3v2HOnDlwcnJC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JaNlPxiOdLrpftdd9DtO7fwRbH5H7dVcfjGL76AQcNirk86g3/87h5B0Zc8egxsXBdy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\nrYZa5Tc6VcKI/GOuhxbDQ5uh4j/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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Hyperparameter tuning\n", "\n", "I usually follow this recipe to tune the hyperparameters:\n", "\n", " 1. Pick ``n_estimators`` as large as (computationally) possible (e.g. 3000)\n", " 2. Tune ``max_depth``, ``learning_rate``, ``min_samples_leaf``, and ``max_features`` via grid search\n", " 3. Increase ``n_estimators`` even more and tune ``learning_rate`` again holding the other parameters fixed" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.grid_search import GridSearchCV\n", "\n", "param_grid = {'learning_rate': [0.1, 0.01, 0.001],\n", " 'max_depth': [4, 6],\n", " 'min_samples_leaf': [3, 5] ## depends on the nr of training examples\n", " # 'max_features': [1.0, 0.3, 0.1] ## not possible in our example (only 1 fx)\n", " }\n", "\n", "est = GradientBoostingRegressor(n_estimators=3000)\n", "# this may take some minutes\n", "gs_cv = GridSearchCV(est, param_grid, scoring='mean_squared_error', n_jobs=4).fit(X_train, y_train)\n", "\n", "# best hyperparameter setting\n", "print('Best hyperparameters: %r' % gs_cv.best_params_)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Best hyperparameters: {'learning_rate': 0.001, 'max_depth': 6, 'min_samples_leaf': 5}\n" ] } ], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "# refit model on best parameters\n", "est.set_params(**gs_cv.best_params_)\n", "est.fit(X_train, y_train)\n", "\n", "# plot the approximation\n", "plot_data()\n", "plt.plot(x_plot, est.predict(x_plot[:, np.newaxis]), color='r', linewidth=2)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 15, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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zOcDa2tqorq6mra3N30MZ+oKDzbpPBU8R6acrV8wsbVdVz+sUPgOfl3a732rO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\n+8VYcOSTiCYNrVaLLVvuQ2FhIfT6HoSFZaChQTx7enubERtbhCtXknD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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Caution: Hyperparameters interact with each other (``learning_rate`` and ``n_estimators``, ``learning_rate`` and ``subsample``, ``max_depth`` and ``max_features``).\n", "\n", "See [G. Ridgeway, \"Generalized boosted models: A guide to the gbm package\", 2005](http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=540A0A638283F64E251B1342248CDBCF?doi=10.1.1.151.4024&rep=rep1&type=pdf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Use-case: California Housing\n", "\n", "
\n", "\n", " * Predict the median house value for census block groups in California\n", " * 20.000 groups, 8 features: *median income*, *average house age*, *latitude*, *longitude*, ...\n", " * Mean Absolute Error on 80-20 train-test split" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.datasets.california_housing import fetch_california_housing\n", "\n", "cal_housing = fetch_california_housing()\n", "\n", "# split 80/20 train-test\n", "X_train, X_test, y_train, y_test = train_test_split(cal_housing.data,\n", " cal_housing.target,\n", " test_size=0.2,\n", " random_state=1)\n", "names = cal_housing.feature_names" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Challenges\n", "\n", " * heterogenous features (different scales and distributions, see plot below)\n", " * non-linear feature interactions (interaction: latitude and longitude)\n", " * extreme responses (robust regression techniques)\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import pandas as pd\n", "X_df = pd.DataFrame(data=X_train, columns=names)\n", "X_df['MedHouseVal'] = y_train\n", "_ = X_df.hist(column=['Latitude', 'Longitude', 'MedInc', 'MedHouseVal'], figsize=FIGSIZE)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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JtEHL7YQesP5IT9jpVI/HJ4cnOTjUDiA7o841ZsRyGbFM1Pvo7TzWW15Aj5kdagdwm/7q\nWF7sdBIRERGR4nh73Q28vU6kDVpuJ/SA9Ud6wtvr6uHtdSIiIiLSHXY6PcKhdgDZGXVcihHLZcQy\nGVVDQwMiIiIwZ84cAE2zhMTExGD06NGIjY1FRUWF9NzU1FQEBQUhODgYe/bskdbn5OQgNDQUQUFB\nWLp0qcfLoBS9ncd6ywvoMbND7QBu018dy4udTiIijVizZg1CQkKkb3iz2+2IiYlBfn4+oqOjYbfb\nAQB5eXnYtm0b8vLykJGRgSVLlki3wJKTk5GWloaCggIUFBQgIyNDtfIQEV2KYzrdwDGdRNqg5Xai\nu5xOJ5KSkvDYY4/hT3/6E9566y0EBwdj79690jfARUVF4YsvvkBqaiq8vLyQkpICAJg5cyaeeuop\nDB8+HDfddBOOHj0KANi6dSscDgdeeeWVFvsyYv2RcXFMp3o4ppOIyIAeeughPPfcc/Dy+r5ZLisr\ng9lsBtD01cNlZWUAgJKSElitVul5VqsVLper1XqLxQKXy+WhEhARdYydTo9wqB1AdkYdl2LEchmx\nTEbzn//8B/7+/oiIiGj3qoLJZJJuu/dGejuP9ZYX0GNmh9oB3Ka/OpaXt9oBiIh6u48//hjp6enY\ntWsXamtrUVlZiQULFki31QMCAlBaWgp/f38ATVcwi4uLpdc7nU5YrVZYLBY4nc4W6y0WS5v7TEpK\ngs1mAwD4+fkhPDwcUVFRAL7/xail5dzcXE3lMVreS2klT/Pyd6kARF3yf1z2GNp4vLNleCS/npYd\nDgc2btwIAFL7ICeO6XQDx3QSaYOW24me2rt3L/7v//4Pb731Fh555BFcc801SElJgd1uR0VFBex2\nO/Ly8nDHHXcgOzsbLpcL06dPx7Fjx2AymTBlyhSsXbsWkZGRmD17Nh588EHMnDmzxT6MXH9kPBzT\nqR652wpe6SQi0pjm2+grVqxAfHw80tLSYLPZsH37dgBASEgI4uPjERISAm9vb6xbt056zbp165CU\nlISamhrExcW16nASEamFVzrd0P2/thz4/rJ+p3vRbPkv5XA4Lrv1YQxGLJcRy6TldkIP9Fh/ejuP\n9ZYX0G7m9n/3OtD1361tbtnj7wOt1nF7VPn0ekVFBW6//XZcf/31CAkJwf79+zlpMRERERF1WZeu\ndCYmJuKGG27AokWLUF9fjwsXLuDZZ5/Ftddei0ceeQSrV6/G2bNnW4w1+vTTT6WxRgUFBTCZTIiM\njMSf//xnREZGIi4uTndjjTimk0gbtNxO6AHrj/SEYzrV4/ErnefOncMHH3yARYsWAQC8vb0xYMAA\npKenIzExEUBTp3THjh0AgJ07dyIhIQE+Pj6w2WwIDAzE/v37UVpaiqqqKkRGRgIAFi5cKL2GiIiI\niIyt005nYWEhBg8ejLvvvhsTJkzAvffeiwsXLnDSYrc41A4gu8un2DAKI5bLiGWi3kdv57He8gJ6\nzOxQO4Db9FfH8uq001lfX48DBw5gyZIlOHDgAK666irp+3+b9fZJi4mIiIioY51OmWS1WmG1WjF5\n8mQAwO23347U1FQEBAT0ykmLezoJbefPb/npNrXL29uWm9dpJY9cy5eWTQt5upPf4XCgqKgI1Dvp\n6RO/gP7yAnrMHKV2ALfpr47l1aUPEv30pz/F3//+d4wePRpPPfUUqqurAaDXTVrMDxIRaYOW2wk9\nYP2RnvCDROpRZcqkl156CXfeeSfCwsJw6NAhPPbYY1ixYgXeeecdjB49Gu+99x5WrFgBoOWkxbNm\nzWo1afHixYsRFBSEwMDAXjRpsUPtALIz6rgUI5bLiGWi3kdv57He8gJ6zOxQO4Db9FfH8urSNxKF\nhYXh008/bbU+MzOzzeevXLkSK1eubLV+4sSJOHz4sJsRiYiItMnXdxCqqs7Kvt3+/QeisrJc9u0S\nqYnfSOQG3l4n0gYttxN6wPqTD2/9Ko91rB5Vbq8TEREREfUEO50e4VA7gOyMOi7FiOUyYpmo99Hf\neexQO4DbWMfK018dy4udTiIiIiJSHMd0uoFjOom0QcvthB6w/uTD8YbKYx2rh2M6iYiIiEh32On0\nCIfaAWRn1HEpRiyXEctEvY/+zmOH2gHcxjpWnv7qWF7sdBIRERGR4jim0w0c00mkDVpuJ/SA9Scf\njjdUHutYPRzTSURERES6w06nRzjUDiA7o45LMWK5jFgm6n30dx471A7gNtax8vRXx/Jip5OIiIiI\nFNelMZ02mw2+vr7o06cPfHx8kJ2djfLycsyfPx8nTpyAzWbD9u3b4efnBwBITU3F+vXr0adPH6xd\nuxaxsbEAgJycHCQlJaG2thZxcXFYs2ZN60AaHmvEMZ1E2qDldkIPWH/y4XhD5bGO1aPKmE6TyQSH\nw4GDBw8iOzsbAGC32xETE4P8/HxER0fDbrcDAPLy8rBt2zbk5eUhIyMDS5YskQInJycjLS0NBQUF\nKCgoQEZGhmwFISIiIiLt6vLt9ct7uunp6UhMTAQAJCYmYseOHQCAnTt3IiEhAT4+PrDZbAgMDMT+\n/ftRWlqKqqoqREZGAgAWLlwovcb4HGoHkJ1Rx6UYsVxGLBP1Pvo7jx1qB3Ab61h5+qtjeXX5Suf0\n6dMxadIk/O1vfwMAlJWVwWw2AwDMZjPKysoAACUlJbBardJrrVYrXC5Xq/UWiwUul0u2ghARERGR\ndnWp0/nRRx/h4MGD2L17N15++WV88MEHLR43mUzfjbmgtkWpHUB2UVFRakdQhBHLZcQyGU1tbS2m\nTJmC8PBwhISE4NFHHwUAlJeXIyYmBqNHj0ZsbCwqKiqk16SmpiIoKAjBwcHYs2ePtD4nJwehoaEI\nCgrC0qVLPV4WpejvPI5SO4DbWMfK018dy8u7K0+67rrrAACDBw/GLbfcguzsbJjNZpw6dQoBAQEo\nLS2Fv78/gKYrmMXFxdJrnU4nrFYrLBYLnE5ni/UWi6XN/SUlJcFmswEA/Pz8EB4eLh2o5kvTai1/\nfzlfqeWmfWqlvFzmshaWm/9fVFQEI+rbty+ysrLQr18/1NfX4yc/+Qk+/PBDpKenIyYmBo888ghW\nr14Nu90Ou93eYuy8y+XC9OnTUVBQAJPJJI2dj4yMRFxcHDIyMjBz5ky1i0hEBIhOXLhwQVRWVgoh\nhDh//rz40Y9+JN5++22xfPlyYbfbhRBCpKamipSUFCGEEEeOHBFhYWHi4sWL4vjx42LkyJGisbFR\nCCFEZGSk2Ldvn2hsbBSzZs0Su3fvbrW/LkRSDQABiG78ZLnxXO2W/1JZWVlqR1CEEctlxDLp5X3S\nHRcuXBCTJk0S//vf/8SYMWPEqVOnhBBClJaWijFjxgghhFi1apXU/gohxIwZM8Qnn3wiSkpKRHBw\nsLT+jTfeEL/85S9b7UOP9afV87j93wvutPva+F3AOlaeVuu4PXLXUadXOsvKynDLLbcAAOrr63Hn\nnXciNjYWkyZNQnx8PNLS0qQpkwAgJCQE8fHxCAkJgbe3N9atWyfdel+3bh2SkpJQU1ODuLg4/vVN\nRPSdxsZGTJgwAV999RWSk5MxduzYDsfOT506VXpt89h5Hx8fjp0nIs3qtNM5YsQI5Obmtlo/aNAg\nZGZmtvmalStXYuXKla3WT5w4EYcPH+5GTL2LUjuA7Iw6LsWI5TJimYzIy8sLubm5OHfuHGbMmIGs\nrKwWj/f2sfP6O4+j1A7gNtax8vRXx/Lq0phOIiLyjAEDBmD27NnIycnptWPn9bas3Fh/eCS/1peb\nOMD6VX7Z4XBg48aNACC1D7KS9Wa9DDQYSQKO6ZTobVxKVxmxXEYsk17eJ111+vRpcfbsWSGEENXV\n1WLatGkiMzOzV46db49Wz+P2fy9wvKFcWMfqkbuOeKWTiEhlpaWlSExMRGNjIxobG7FgwQJER0cj\nIiKCY+eJyDC69N3rnqTl7wTmd68TaYOW2wk9YP3Jh98LrjzWsXpU+e51IiIiIqKeYKfTIxxqB5Dd\npZN2G4kRy2XEMlHvo7/z2KF2ALexjpWnvzqWFzudRERERKQ4jul0A8d0EmmDltsJPWD9yYfjDZXH\nOlYPx3QSERERke6w0+kRDrUDyM6o41KMWC4jlol6H/2dxw61A7iNdaw8/dWxvNjpJCIiIiLFcUyn\nGzimk0gbtNxO6AHrTz4cb6g81rF6VBnT2dDQgIiICMyZMwcAUF5ejpiYGIwePRqxsbGoqKiQnpua\nmoqgoCAEBwdjz5490vqcnByEhoYiKCgIS5cula0ARERERKR9Xep0rlmzBiEhIdLXrNntdsTExCA/\nPx/R0dGw2+0AgLy8PGzbtg15eXnIyMjAkiVLpB5ycnIy0tLSUFBQgIKCAmRkZChUJC1yqB1AdkYd\nl2LEchmxTNT76O88dqgdwG2sY+Xpr47l1Wmn0+l0YteuXVi8eLHUgUxPT0diYiIAIDExETt27AAA\n7Ny5EwkJCfDx8YHNZkNgYCD279+P0tJSVFVVITIyEgCwcOFC6TVEREREZHyddjofeughPPfcc/Dy\n+v6pZWVlMJvNAACz2YyysjIAQElJCaxWq/Q8q9UKl8vVar3FYoHL5ZKtENoXpXYA2UVFRakdQRFG\nLJcRy0S9j/7O4yi1A7iNdaw8/dWxvDrsdP7nP/+Bv78/IiIi2h1IajKZpNvuRERERERt8e7owY8/\n/hjp6enYtWsXamtrUVlZiQULFsBsNuPUqVMICAhAaWkp/P39ATRdwSwuLpZe73Q6YbVaYbFY4HQ6\nW6y3WCzt7jcpKQk2mw0A4Ofnh/DwcOmvg+bxEGotfz+GxJ3lXADLuvj8pn1qpbztLTev00oeuZZf\nfPFFTZ1vcizn5uZi2bJlmsnTneXm/xcVFYF6p0vbRX1wQG9X4npSx76+g1BVdVbeQJ1yoDfVsSGI\nLnI4HOJnP/uZEEKI5cuXC7vdLoQQIjU1VaSkpAghhDhy5IgICwsTFy9eFMePHxcjR44UjY2NQggh\nIiMjxb59+0RjY6OYNWuW2L17d5v7cSOSxwEQgOjGT5Ybz9Vu+S+VlZWldgRFGLFcRiyTXt4nWqXH\n+tPqedz+7wV32n1t/C7oSR13//dj1+qCdawOueuoy/N07t27F88//zzS09NRXl6O+Ph4nDx5Ejab\nDdu3b4efnx8AYNWqVVi/fj28vb2xZs0azJgxA0DTlElJSUmoqalBXFwc1q5d2+Z+tDx/HOfpJNIG\nLbcTesD6kw/nkGyi7O9H1rFa5G4rODm8G9jpJNIGLbcTesD6kw87nU3Y6TQmVSaHp55yqB1AdlqY\na8zXd5D0QTYlf3x9B6ld1B7RwrEi6in9nccOtQO4jXWsPP3VsbzY6STdahq0LmT+yWq1zvOD44mI\niIyHt9fdwNvr2uKZ4wHwmGiPltsJPWD9yYe315vw9rox8fY6EREREekOO50e4VA7gOyMOy7FoXYA\n2Rn3WFFvor/z2KF2ALexjpWnvzqWFzudRERERKQ4jul0A8d0agvHdPZeWm4n9ID1Jx+O6WzCMZ3G\nxDGdRERERKQ77HR6hEPtALIz7rgUh9oBZGfcY2UcxcXFuPHGGzF27FiMGzdO+sa28vJyxMTEYPTo\n0YiNjUVFRYX0mtTUVAQFBSE4OBh79uyR1ufk5CA0NBRBQUFYunSpx8uiFP2dxw61A7iNdaw8/dWx\nvNjpJCJSmY+PD1544QUcOXIE+/btw8svv4yjR4/CbrcjJiYG+fn5iI6Oht1uBwDk5eVh27ZtyMvL\nQ0ZGBpYsWSLdAktOTkZaWhoKCgpQUFCAjIwMNYtGRCThmE43cEyntnBMZ++l5XZCDvPmzcMDDzyA\nBx54AHv37oXZbMapU6cQFRWFL774AqmpqfDy8kJKSgoAYObMmXjqqacwfPhw3HTTTTh69CgAYOvW\nrXA4HHjllVdabN/o9edJHNPZhGM6jYljOomIDKyoqAgHDx7ElClTUFZWBrPZDAAwm80oKysDAJSU\nlMBqtUqvsVqtcLlcrdZbLBa4XC7PFoCIqB0ddjpra2sxZcoUhIeHIyQkBI8++igAjjNyn0PtALIz\n7rgUh9oBZGfcY2U858+fx2233YY1a9agf//+LR4zmUzfXU3qnfR3HjvUDuA21rHy9FfH8vLu6MG+\nffsiKyuce3FUAAAgAElEQVQL/fr1Q319PX7yk5/gww8/RHp6OmJiYvDII49g9erVsNvtsNvtLcYZ\nuVwuTJ8+HQUFBTCZTNI4o8jISMTFxSEjIwMzZ870VDmJiDTt22+/xW233YYFCxZg3rx5ACDdVg8I\nCEBpaSn8/f0BNF3BLC4ull7rdDphtVphsVjgdDpbrLdYLG3uLykpCTabDQDg5+eH8PBwREVFAfj+\nF6OWlnNzczWV59Ll7zs/ly7nXrZ8+eNdWYZHy9PT/V2yhXbK093l5nWXP97T/X23pLHzSc1lh8OB\njRs3AoDUPshKdNGFCxfEpEmTxP/+9z8xZswYcerUKSGEEKWlpWLMmDFCCCFWrVol7Ha79JoZM2aI\nTz75RJSUlIjg4GBp/RtvvCF++ctftrkfNyJ5HAABCIV/tFt+rfHM8eAx0SKjHZPGxkaxYMECsWzZ\nshbrly9fLrWpqampIiUlRQghxJEjR0RYWJi4ePGiOH78uBg5cqRobGwUQggRGRkp9u3bJxobG8Ws\nWbPE7t27W+3PaPWnJuXaIX0dI2XbY9axWuSuow6vdAJAY2MjJkyYgK+++grJyckYO3Zsh+OMpk6d\nKr22eZyRj48PxxkREbXjo48+wmuvvYbx48cjIiICQNNQpRUrViA+Ph5paWmw2WzYvn07ACAkJATx\n8fEICQmBt7c31q1bJ916X7duHZKSklBTU4O4uDjeUSIizei00+nl5YXc3FycO3cOM2bMQFZWVovH\ne/s4o65xoOVtAv1zOByX3FoyEgd4rMjTfvKTn6CxsbHNxzIzM9tcv3LlSqxcubLV+okTJ+Lw4cOy\n5tMC/Z3HDuitLWEdK09/dSyvTjudzQYMGIDZs2cjJydH0XFGgLbHGnVv7Ig7Y3tanpRql1epsT/q\nHo+OlnPbeRyK5PfEspbHwrlzvjkcDhQVFYGIiPSpw3k6z5w5A29vb/j5+aGmpgYzZszA7373O7z9\n9tu45pprkJKSArvdjoqKCumDRHfccQeys7OlDxIdO3YMJpMJU6ZMwdq1axEZGYnZs2fjwQcfbPO2\nj5bnj+M8ndrCeTp7Ly23E3rA+pMP5+lswnk6jUnutqLDK52lpaVITExEY2MjGhsbsWDBAkRHRyMi\nIoLjjIiIiIioy/iNRG7o/l9yDnR93Il2y38pLYxLUeYvawdaHyt9HJP2aOFYyU3L7YQe6LH+tHoe\nt98OOdCz8YaeP0Y9qWN1rnQ60JvqWA38RiIiIiIi0h1e6XQDx3RqC8d09l5abif0gPUnH47pbMIx\nncbk0TGdRERERMbkrciUj/37D0RlZbns2zUC3l73CIfaAWR3+dRJxuFQO4DsjHusqDfR33nsUDuA\n23pfHdej6QqqvD9VVWfbT6y7OpYXO51EREREpDiO6XQDx3RqC8d09l5abif0gPUnH47pbKLXMZ08\ndh3jp9eJiIiISHfY6fQIh9oBZGfccSkOtQPIzrjHinoT/Z3HDrUDuI11rDz91bG82OkkIiIiIsVx\nTKcbOKZTWzims/fScjuhB6w/+XBMZxOO6Wy5XT0du45wTCcRERER6Q47nR7hUDuA7Iw7LsWhdgDZ\nGfdYUW+iv/PYoXYAt7GOlae/OpYXv5GIiIgMzdd3UIcTdhORZ3Q6prO4uBgLFy7E119/DZPJhPvu\nuw8PPvggysvLMX/+fJw4cQI2mw3bt2+Hn58fACA1NRXr169Hnz59sHbtWsTGxgIAcnJykJSUhNra\nWsTFxWHNmjWtA2l4rBHHdGoLx3T2XlpuJ/Sgt9WfXscb6ukY6bWOeew65vExnT4+PnjhhRdw5MgR\n7Nu3Dy+//DKOHj0Ku92OmJgY5OfnIzo6Gna7HQCQl5eHbdu2IS8vDxkZGViyZIkUODk5GWlpaSgo\nKEBBQQEyMjJkKwgRERERaVennc6AgACEh4cDAK6++mpcf/31cLlcSE9PR2JiIgAgMTERO3bsAADs\n3LkTCQkJ8PHxgc1mQ2BgIPbv34/S0lJUVVUhMjISALBw4ULpNcbnUDuA7Iw7LsWhdgDZGfdYUW+i\nv/PYoXYAt7GOlae/OpaXWx8kKioqwsGDBzFlyhSUlZXBbDYDAMxmM8rKygAAJSUlsFqt0musVitc\nLler9RaLBS6XS44yEBEREZHGdbnTef78edx2221Ys2YN+vfv3+Ixk8n03XgOaluU2gFkFxUVpXYE\nhUSpHUB2xj1W1Jvo7zyOUjuA21jHytNfHcurS59e//bbb3HbbbdhwYIFmDdvHoCmq5unTp1CQEAA\nSktL4e/vD6DpCmZxcbH0WqfTCavVCovFAqfT2WK9xWJpc39JSUmw2WwAAD8/P4SHh0sHqvnStFrL\n31/OV2q5aZ9aKa/Wl5U/Hs3LUCQ/l7u23Pz/oqIiEBGRTolONDY2igULFohly5a1WL98+XJht9uF\nEEKkpqaKlJQUIYQQR44cEWFhYeLixYvi+PHjYuTIkaKxsVEIIURkZKTYt2+faGxsFLNmzRK7d+9u\ntb8uRFINAAGIbvxkufFc7Zb/UllZWWpH6MHxcPdY6eOYtEcLx0puej8matNj/fXkPFamrfi+feh5\nu9/Wj/d325b3p3//gazjTrfb87xK1LEa5G4rOr3S+dFHH+G1117D+PHjERERAaBpSqQVK1YgPj4e\naWlp0pRJABASEoL4+HiEhITA29sb69atk269r1u3DklJSaipqUFcXBxmzpzZ3b4yERGRgdUDCkzn\nU1XFoXCkHn73uhs4T6e2cJ7O3kvL7UR3LVq0CP/973/h7++Pw4cPA0CvnA9ZCZxDsuV2lTj2rOOW\n2zXK+4vfvU5EZEB33313q7mLOR8yERkJO50e4VA7gOyMO9eYQ+0AsjPusTKWadOmYeDAgS3WcT7k\n7+nvPHaoHcBtrGPl6a+O5cVOJxGRRnE+ZCIyEnY6PSJK7QCyM+5cY1FqB5CdcY9V79Lb50PW33kc\npXYAt7GOlae/OpZXl+bpJCIiz+ut8yHLP58v0HQrNuqS/0MHy+jk8e4tKzmfrhJ5v18n1/aal9HJ\n491d1u982w6HAxs3bgQAqX2QlawTMMlAg5Ek6PacXu7MJabd8l9KC3ONdf94uHus9HFM2qOFYyU3\nvR+T9hQWFopx48ZJy71xPuT2cA5J+fKyjvVZx2qQu60wxJXOTz75BLt27VY7BhFRtyUkJGDv3r04\nc+YMhg4dimeeeYbzIRORoRhins577nkA69cXApiiTCgAwAcAMgHO06kZnKez9+pt80zKrbfVH+eQ\nbLldJY4967jldo3y/pK7rTDElc4mswA8oOD2V6Op00lERKRX3r36A2mkLn563SMcageQnXHnGnO0\nsc5b+uSwUj++voOUK5FhjxX1Jvo7jx1qB2hH89drtvWT1cFjnf2owaHSfrtPf+exvAx0pZNIKcp8\nB/Kl+H3IRERkdAYa0xkM5W+vrwDHdGqHJ8d08rhrS28bkyi33lZ/HG+o5+0quW2O6eyMx797fdGi\nRTCbzQgNDZXWlZeXIyYmBqNHj0ZsbCwqKiqkx1JTUxEUFITg4GDs2bNHWp+Tk4PQ0FAEBQVh6dKl\nshWAiIiIiLSv007n3XffjYyMjBbr7HY7YmJikJ+fj+joaNjtdgBAXl4etm3bhry8PGRkZGDJkiVS\nDzk5ORlpaWkoKChAQUFBq20am0PtALIz7rgUh9oBZGfcY0W9if7OY4faAbrBoXYANznUDuA2/Z3H\n8uq00zlt2jQMHDiwxbr09HQkJiYCABITE7Fjxw4AwM6dO5GQkAAfHx/YbDYEBgZi//79KC0tRVVV\nFSIjIwEACxculF5DRERERMbXrU+vl5WVwWw2A2j6mraysjIAQElJCaxWq/Q8q9UKl8vVar3FYoHL\n5epJbp2JUjuA7Iz7/bFRageQnXGPFfUm+juPo9QO0A1RagdwU5TaAdymv/NYXj3+9HrzlC9El/L1\nHYSqqrNqxyAiIiKN6Fan02w249SpUwgICEBpaSn8/f0BNF3BLC4ulp7ndDphtVphsVjgdDpbrLdY\nLO1uPykpSfqieT8/P4SHh3f4RfWlpS4Awd+92vHdv1EyL6OTxztazgWwrIvPbypTR+XVwnLzuvYe\nb+pwii6UtyfLJgW2/yKA8DYex2XLcu2v5faVOF65ublYtmyZYtv3xHLz/4uKikC906Xtoj44oL8r\ncQ7oK7MD+sqrx/NYZl35gvbCwkIxbtw4aXn58uXCbrcLIYRITU0VKSkpQgghjhw5IsLCwsTFixfF\n8ePHxciRI0VjY6MQQojIyEixb98+0djYKGbNmiV2797d5r66GKmFRYt+JYCXBCAU/LF/NwNud16b\n5cZz3S+/GrKysjp8vPt15c6PEvto61h5pixqHSs90sv7RKv0WH89OY+VfQ+3t2132n1PtW+dbbcn\nmVnHl25XifNYDXK3FZ3O05mQkIC9e/fizJkzMJvNeOaZZ3DzzTcjPj4eJ0+ehM1mw/bt2+Hn5wcA\nWLVqFdavXw9vb2+sWbMGM2bMANA0ZVJSUhJqamoQFxeHtWvXtrk/ztNpjPm9PDOHJufp7K162zyT\ncutt9cd5OvW8XSW3zXk6OyN3W8HJ4buMnU53sNPp/j6McNw9pbd1muTW2+qPnU49b1fJbbPT2RmP\nTw5PcnCoHUB2xp1rzKF2ANkZ91hRb6K/89ihdoBucKgdwE0OtQO4TX/nsbzY6SQiIiIixfH2epfx\n9ro7eHvd/X0Y4bh7Sm+7PSy33lZ/vL2u5+0quW3eXu8Mb68TERERke6w0+kRDrUDyM6441IcageQ\nnXGPFfUm+juPHWoH6AaH2gHc5FA7gNv0dx7Lq8ffSERy81b8G5769x+IyspyRfdBREREdCmO6ewy\nz43pNML4QY7pdH8fGnsralpvG5Mot95WfxzTqeftKrltjunsDMd0EhEREZHusNPpEQ61A8jOuONS\nHGoHkJ1xjxX1Jvo7jx1qB+gGh9oB3ORQO4Db9Hcey4tjOnsl5ceNkrs4lpeIiIyNnU6PiFI7wGXq\n4ZnxlnoUpdJ+lT8mVVV6PSZEQFRUlNoR3BSldoBuiFI7gJui1A7gNv2dx/Jip5Oo1+DVVNIup9OJ\n++//LerqGtSOQkQK8XinMyMjA8uWLUNDQwMWL16MlJQUT0dQgQN6/IusYw4Yr0yAMcvlQFOZeDW1\nt9BjO3vs2DFkZf0P1dVPt/OMIwDGdmPLFwG82f1g3eaA/toSB/SV2QFt5lXmD3wj/FHv0U5nQ0MD\nHnjgAWRmZsJisWDy5MmYO3curr/+ek/GUEEutPnG6AkjlgkwZrmMWCZqj57bWR+fwQBub+dRZweP\ndaSm+4F6RI/vO71l1mrejv7AfxHAsm5t1Qh/1Hv00+vZ2dkIDAyEzWaDj48PfvGLX2Dnzp2ejKCS\nCrUDKMCIZQKMWS4jlonaY9x2Vm/nsd7yAvrLrLe8gD4zy8ejnU6Xy4WhQ4dKy1arFS6Xy5MRiIgM\nje0sEWmVR2+vK/shhj0AqhTc/t4evLZIrhAaUqR2AIUUqR1AAUUe3JdnPqxE7dPzdGgXL54AkNrO\no+kAftCNrX7b/UA9UqTSfnuiSO0AbipSO0A3FPXgtfofK+rRTqfFYkFxcbG0XFxcDKvV2uI5o0aN\n6kGlvtWDdF3V3WybPLAPd8ixj87KpJdyXK6tcum1LM2ay6TfDkmzqqqzGDVqlNoxNEv5dlZpKzt4\n7GAPtqtkedvbtjvtvjvb7amOttuTzKzjrm23p5nlVVV1tt32QO621qPfvV5fX48xY8bg3XffxZAh\nQxAZGYk33nhDFwPciYj0gO0sEWmVR690ent7489//jNmzJiBhoYG3HPPPWwIiYhkxHaWiLTKo1c6\niYiIiKh38uin1y9VW1uLKVOmIDw8HCEhIXj00UcBAMuXL8f111+PsLAw3HrrrTh37pxaEd3WXpma\nPf/88/Dy8kJ5ub4md+2oXC+99BKuv/56jBs3ThcTUDdrr0zZ2dmIjIxEREQEJk+ejE8//VTlpO5r\naGhAREQE5syZAwAoLy9HTEwMRo8ejdjYWFRU6HPKjsvLpee2wpP++c9/YuzYsejTpw9ycnKk9e+8\n8w4mTZqE8ePHY9KkScjKypIeq6urw3333YcxY8bg+uuvx7/+9S9N5202d+5chIaGeixrM3cz19TU\nYPbs2VLbefnvCq3lBYCcnByEhoYiKCgIS5cu9WjeyzMfOHBAWl9eXo4bb7wR/fv3x69//esWr9mw\nYQNCQ0MRFhaGWbNm4ZtvvtF0Xq2877qat5lb7zuhogsXLgghhPj222/FlClTxAcffCD27NkjGhoa\nhBBCpKSkiJSUFDUjuq2tMgkhxMmTJ8WMGTOEzWYT33zzjZoRu6Wtcr333nti+vTpoq6uTgghxNdf\nf61mRLe1VaaoqCiRkZEhhBBi165dIioqSs2I3fL888+LO+64Q8yZM0cIIcTy5cvF6tWrhRBC2O12\n3b2nml1eLr23FZ5y9OhR8eWXX4qoqCiRk5MjrT948KAoLS0VQgjxv//9T1gsFumxJ598UjzxxBPS\n8pkzZzSdVwgh3nzzTXHHHXeI0NBQj2Vt5m7m6upq4XA4hBBC1NXViWnTpondu3drNq8QQkyePFns\n379fCCHErFmzPJq3o8wXLlwQH374oXjllVfEAw88IK2/ePGiGDRokPT79pFHHhFPPfWUZvMKoc33\nXUd5hXD/fafalU4A6NevH4Cm3n1DQwMGDRqEmJgYeHk1xZoyZQqcTqeaEd3WVpkA4De/+Q3++Mc/\nqhmtRy4v18CBA/HKK6/g0UcfhY+PDwBg8ODBakZ0W1tlCggIkK6YVVRUwGKxqBnRbU6nE7t27cLi\nxYshvhs5k56ejsTERABAYmIiduzYoWbEbmmrXHpvKzwlODgYo0ePbrU+PDwcAQEBAICQkBDU1NTg\n22+bphfasGFDi6tv11xzjWfCont5z58/jxdeeAGPP/64dH54kruZr7zyStxwww0AAB8fH0yYMMGj\nc6m6m7e0tBRVVVWIjIwEACxcuNDj7Uh7mfv164cf//jH+MEPWk6n5e3tjYEDB+L8+fMQQqCystKj\n7bm7eQFtvu86ytud952qnc7GxkaEh4fDbDbjxhtvREhISIvH169fj7i4OJXSdU9bZdq5cyesVivG\njx+vdrxuu7xcY8eORX5+Pt5//31MnToVUVFR+Oyzz9SO6Za2ymS32/Hb3/4Ww4YNw/Lly5Ga2t6c\ngdr00EMP4bnnnpM6YwBQVlYGs9kMADCbzSgrK1MrXre1Va5L6bGt0JI333wTEydOhI+PjzT84vHH\nH8fEiRMRHx+Pr7/+WuWELV2aFwCeeOIJPPzww9Ifklp0eeZmFRUVeOuttxAdHa1SsrZdmtflcrWY\ndstisWjuCwcun/LHy8sLa9aswbhx42CxWHD06FEsWrRIpXStXZ5X6++7tqZU6s77TtVOp5eXF3Jz\nc+F0OvH+++/D4XBIjz377LO44oorcMcdd6gXsBsuL9OuXbuQmpqKp59+WnqOGn+J91Rbx6q+vh5n\nz57Fvn378NxzzyE+Pl7tmG5pq0z33HMP1q5di5MnT+KFF17QVCPVmf/85z/w9/dHREREu+eYyWTS\n8PyMbeusXHptK+QUExOD0NDQVj9vvdX53MVHjhzBihUr8OqrrwJomnLJ6XTixz/+MXJycvDDH/4Q\nDz/8sGbz5ubm4vjx47j55psVbVvlzNysvr4eCQkJWLp0KWw2m+bzKq0nmS9XWVmJBx98EJ9//jlK\nSkoQGhoq+0UEOfNq/X13ue6+7zw6ZVJ7BgwYgNmzZ+Ozzz5DVFQUNm7ciF27duHdd99VO1q3NZfp\nwIEDKCwsRFhYGICm24QTJ05EdnY2/P39VU7pvkuPldVqxa233goAmDx5Mry8vPDNN9949JaAHC4t\nU3Z2NjIzMwEAt99+OxYvXqxyuq77+OOPkZ6ejl27dqG2thaVlZVYsGABzGYzTp06hYCAAJSWluru\nvGurXAsXLsTmzZsN0VbI4Z133unW65xOJ2699VZs2bIFI0aMANB0S69fv37Se/v2229HWlqabFkB\nefPu27cPn332GUaMGIH6+np8/fXXuOmmm/Dee+/JGVnWzM2aPzTy4IMPyhGxBTnzWiyWFsNXnE6n\nIrequ5u5LUePHsWIESOkMvz85z/H6tWrZds+IG9eLb/v2tLd951qVzrPnDkjXU6uqanBO++8g4iI\nCGRkZOC5557Dzp070bdvX7XidUtbZfrhD3+IsrIyFBYWorCwEFarFQcOHNDVL/72jtW8efOkEyw/\nPx91dXW66XC2Vabw8HAEBgZi796mrzx977332hzjolWrVq1CcXExCgsLsXXrVtx0003YsmUL5s6d\ni02bmr4BY9OmTZg3b57KSd3TVrk2b96s67ZCLZdekaioqMDs2bOxevVq/PCHP5TWm0wmzJkzR/rk\n8rvvvouxY8d6PCvQtbz3338/XC4XCgsL8eGHH2L06NGydzjd0ZXMQNNt1MrKSrzwwguejthCV/Je\nd9118PX1xf79+yGEwJYtW1RtR9q6snb5upEjR+KLL77AmTNnADR1uC4fwucpXcmr1fdde+u6/b7r\nzqec5HDo0CEREREhwsLCRGhoqPjjH/8ohBAiMDBQDBs2TISHh4vw8HCRnJysVkS3tVemS40YMUJ3\nn15vr1x1dXXirrvuEuPGjRMTJkwQWVlZ6gZ1Q3tl+vTTT0VkZKQICwsTU6dOFQcOHFA5afc4HA7p\nU97ffPONiI6OFkFBQSImJkacPXtW5XTdl5WVJZVLz22FJ/3rX/8SVqtV9O3bV5jNZjFz5kwhhBC/\n//3vxVVXXSXVX3h4uDh9+rQQQogTJ06In/70p2L8+PFi+vTpori4WNN5mxUWFqry6XV3MxcXFwuT\nySRCQkKk9WlpaZrNK4QQn332mRg3bpwYNWqU+PWvf+2xrJ1lFkKI4cOHi0GDBomrr75aWK1WcfTo\nUSGEEJs2bRLjxo0T48ePF3PnzhXl5eWayzt06FAprxbfdx3lbebO+46TwxMRERGR4lT9IBERERER\n9Q7sdBIRERGR4tjpJCIiIiLFsdNJRERERIpjp5OIiIiIFMdOJxEREREpjp1OIiIiIlIcO51ERERE\npDh2OomIiIhIcex0EhEREZHi2OkkIiIiIsWx00lEREREimOnk4iIiIgUx04nERERESmOnU4iIiIi\nUhw7nURERESkOHY6iYiIiEhx7HQSERERkeLY6SQiIiIixbHTSURERESKY6eTiIiIiBTHTicRERER\nKY6dTiIiIiJSHDudpBgvLy8cP35c7RiKKCoqgpeXFxobG9WOQkQkCyO32aQN7HQSAMBms+EHP/gB\nvvnmmxbrIyIi4OXlhZMnT/Zo+0lJSXjiiSdarFO74xYcHIwNGza0Wr9mzRpMnjxZhURERF2jRptN\n1FPsdBIAwGQyYeTIkXjjjTekdYcPH0ZNTQ1MJpMs25djO3JKSkrC5s2bW63fsmULkpKSPB+IiKiL\nemObTfrHTidJ7rrrrhadsE2bNmHhwoUQQgAALl68iIcffhjDhw9HQEAAkpOTUVtbKz3/ueeew5Ah\nQ2C1WrF+/Xq393/u3DksXLgQ/v7+sNlsePbZZ6V9P/XUU1iwYIH03Muvkm7cuBGjRo2Cr68vRo4c\niddff1167vr16xESEoJBgwZh5syZ0hWAu+66Cx9++GGLKwJ5eXk4fPgwEhIS8N///hcREREYMGAA\nhg0bhqefftrtMhERKUXpNrt5O83t7ebNmzF8+HAMHjwYq1atkp7X2NiIVatWITAwEL6+vpg0aRKc\nTqdSxSYdY6eTJFOnTkVlZSW++OILNDQ0YNu2bbjrrrsANDU+K1aswLFjx/D555/j2LFjcLlceOaZ\nZwAAGRkZeP7555GZmYn8/HxkZma22n5zA9aeX//616iqqkJhYSH27t2LzZs3S7e/O/qL+8KFC1i6\ndCkyMjJQWVmJTz75BOHh4QCAnTt3IjU1Ff/+979x5swZTJs2DQkJCQAAq9WKG2+8EVu2bJG2tWXL\nFsyePRuDBg3C1Vdfjddeew3nzp3Df//7X/zlL3/Bzp073ahRIiLlKN1mX+6jjz5Cfn4+3n33XTzz\nzDP48ssvAQDPP/88tm7dit27d6OyshIbNmxAv379lCs46ZcgEkLYbDaRmZkp/vCHP4hHH31U7N69\nW8TGxor6+nphMplEYWGhuOqqq8RXX30lvebjjz8WI0aMEEIIcffdd4tHH31Ueiw/P1+YTCbp+YmJ\niaJv377Cz89P+vH19RVeXl6ioaFB1NfXiyuuuEIcPXpU2sarr74qoqKihBBC/O53vxN33XWX9Fhh\nYaEwmUyioaFBnD9/Xvj5+Yk333xTVFdXtyjXzJkzRVpamrTc0NAg+vXrJ06ePCmEEOK1114TY8aM\nkR4bNmyY2LFjR5t1tHTpUvHQQw+12j8Rkacp3WYnJSWJxx9/XAjxfXvncrmk50dGRopt27YJIYQY\nPXq0SE9PV7zMpH+80kkSk8mEBQsW4B//+Eer2zSnT59GdXU1Jk6ciIEDB2LgwIGYNWsWzpw5AwAo\nLS3F0KFDpW0NGzas1baXL1+Os2fPSj+HDh2Stn/mzBl8++23GD58eIttuFyuTnNfddVV2LZtG155\n5RUMGTIEP/vZz6S/wE+cOIGlS5dKma+55hoAkLZ7yy23oLS0FPv374fD4UB1dTVmz54NANi/fz9u\nvPFG+Pv7w8/PD6+++mqrQftERGpRss1uS0BAgPT/fv364fz58wAAp9OJUaNGyVk0Mih2OqmFYcOG\nYeTIkdi9ezduvfVWaf21116LK6+8Enl5eVKnsaKiApWVlQCA6667rsXYyLY+OSkuu71+6fK1114L\nHx8fFBUVtdiG1WoF0NSxrK6ulh47depUi23FxsZiz549OHXqFIKDg3HvvfdK5fnrX//aorN74cIF\nTHTw6cMAACAASURBVJ06FUBTw3n77bdj8+bNeO2115CQkABvb28AwB133IF58+bB6XSioqIC999/\nP6dIIiJNUbLN7qqhQ4fi2LFj3S8E9RrsdFIraWlpeO+993DllVdK67y8vHDvvfdi2bJlOH36NICm\nq4V79uwBAMTHx2Pjxo04evQoqqurW33o5vIO5+X69OmD+Ph4PPbYYzh//jxOnDiBF154QRqfFBER\ngffffx/FxcU4d+4cUlNTpdd+/fXX2LlzJy5cuAAfHx9cddVV6NOnDwDg/vvvx6pVq5CXlweg6cNK\n//znP1vsOzExEVu3bsWbb76JxMREaf358+cxcOBAXHHFFcjOzsbrr7/OT3MSkeao0WZfavHixXji\niSdw7NgxCCFw6NAhlJeXy1AyMhp2OqmVkSNHYsKECdJy89QZq1evRmBgIKZOnYoBAwYgJiYG+fn5\nAICZM2di2bJluOmmmzB69GhER0e36KC1N/3GpeteeuklXHXVVRg5ciSmTZuGO++8E3fffTcAYPr0\n6Zg/fz7Gjx+PyZMnY86cOdJrGxsb8cILL8BiseCaa67BBx98gL/85S8AgHnz5iElJQW/+MUvMGDA\nAISGhuLtt99ukeGnP/0p/Pz8MHToUEycOFFav27dOjz55JPw9fXF73//e8yfP7/d7EREavFEm91R\ne/eb3/wG8fHxiI2NxYABA3Dvvfe2+JQ8UTOT6ODPmdraWtxwww24ePEi6urqcPPNNyM1NRVPPfUU\n/v73v2Pw4MEAgFWrVmHWrFkAgNTUVKxfvx59+vTB2rVrERsbCwDIyclBUlISamtrERcXhzVr1nig\neERE+lBRUYHFixfjyJEjMJlM2LBhA4KCgjB//nycOHECNpsN27dvh5+fHwC2tUSkPx1e6ezbty+y\nsrKQm5uLQ4cOISsrCx9++CFMJhN+85vf4ODBgzh48KDU4czLy8O2bduQl5eHjIwMLFmyRLpEn5yc\njLS0NBQUFKCgoAAZGRnKl46ISCeWLl2KuLg4HD16FIcOHUJwcDDsdrt0dSo6Ohp2ux0A21oi0qdO\nb683z7VVV1eHhoYGDBw4EEDb4z127tyJhIQE+Pj4wGazITAwEPv370dpaSmqqqoQGRkJAFi4cCF2\n7NghZzmIiHTr3Llz+OCDD7Bo0SIAgLe3NwYMGID09HRpnHFiYqLUbrKtJSI96rTT2djYiPDwcJjN\nZtx4440YO3YsgKbxd2FhYbjnnntQUVEBACgpKZE+bQw0Tb7tcrlarbdYLF2aCoeIqDcoLCzE4MGD\ncffdd2PChAm49957ceHCBZSVlcFsNgMAzGYzysrKALCtJSJ96rTT6eXlhdzcXDidTrz//vtwOBxI\nTk5GYWEhcnNzcd111+G3v/2tJ7ISERlSfX09Dhw4gCVLluDAgQO46qqrpFvpzfhd2ESkd95dfeKA\nAQMwe/ZsfPbZZ4iKipLWL168GHPmzAHQ9Fd1cXGx9JjT6YTVaoXFYmnxPaxOpxMWi6XN/VgsFpSU\nlLhbDiLqRUaNGmWoeQGtViusVismT54MALj99tuRmpqKgIAAnDp1CgEBASgtLYW/vz+Anre1bGeJ\nqCvkbms7vNJ55swZ6dZ5TU0N3nnnHURERLSYmPvf//43QkNDAQBz587F1q1bUVdXh8LCQhQUFCAy\nMhIBAQHw9fXF/v37IYTAli1bMG/evDb3WVJSAiGEbn4SExNVz2DkvHrMrLe8esz81VdfydUGakJA\nQACGDh0qTWeTmZmJsWPHYs6cOdi0aRMAYNOmTVK72dO2VivtrBbOOy1k0EoOZtBWDi1kkLut7fBK\nZ2lpKRITE9HY2IjGxkYsWLAA0dHRWLhwIXJzc2EymTBixAi8+uqrAICQkBDEx8cjJCQE3t7eWLdu\nnXQ7aN26dUhKSkJNTQ3i4uIwc+ZMWQtCRKRnL730Eu68807U1dVh1KhR2LBhAxoaGhAfH4+0tDRp\nyiTAGG2tr+8gVFWdlTrVcuvffyAqKzlBOZGWdNjpDA0NxYEDB1qt37x5c7uvWblyJVauXNlq/cSJ\nE3H48OFuRNQ2m82mdgS36C0voL/MessL6DOz0YSFheHTTz9ttT4zM7PN5+u9ra2qOgvgdwCeUmj7\nXRv/qpVzXws5mOF7WsihhQxy4zcS9dCl41v1QG95Af1l1lteQJ+ZyQii1A6gmXNfCzmY4XtayKGF\nDHJjp5OIiIiIFMdOJxEREREprsPvXleDyWSCxiIRkcawnegZLdRf0weflMygfhmJ9E7utoJXOomI\niIhIcex09pDD4VA7glv0lhfQX2a95QX0mZmMwKF2AM2c+1rIwQzf00IOLWSQGzudRERERKQ4julU\nQPOkx3LjZMdETYzQTqhJC/XHMZ1E2id3W8FOpwKUa0z1XzdEcjBCO6EmLdQfO51E2scPEmmM3sZc\n6C0voL/MessL6DMzGYFD7QCaOfe1kIMZvqeFHFrIIDd2OomIiIhIcby9rgDeXidSlhHaCTVpof54\ne51I+3h7nYiIiIh0h53OHtLbmAu95QX0l1lveQF9ZiYjcKgdQDPnvhZyMMP3tJBDCxnkxk4nERER\nESmuwzGdtbW1uOGGG3Dx4kXU1dXh5ptvRmpqKsrLyzF//nycOHECNpsN27dvh5+fHwAgNTUV69ev\nR58+fbB27VrExsYCAHJycpCUlITa2lrExcVhzZo1bQfSwFijnuKYTiJlGaGdUJMW6o9jOom0z6Nj\nOvv27YusrCzk5ubi0KFDyMrKwocffgi73Y6YmBjk5+cjOjoadrsdAJCXl4dt27YhLy8PGRkZWLJk\niRQ2OTkZaWlpKCgoQEFBATIyMmQrBBERERFpW6e31/v16wcAqKurQ0NDAwYOHIj09HQkJiYCABIT\nE7Hj/7d3t8FNXQfewP8Gu5NNeTFksEyltuLFvBgbyw0VPJ2hIxZsB2eTQsi4MQm2Q8hm4NkWNxnH\nm35ps/MUi2TS1qSh09nFQzrbofChBW+KvZSNb0JeDBuwJlmcHdxiF1t+ScA4mPBuneeDsIyxwb7S\nvTrniP9vxgP3Sjr3r6t7j4/vPTpn/34AwIEDB1BcXIyUlBS43W7MnTsXR48eRVdXF/r7++H1egEA\nJSUlkdfoTrc+F7rlBfTLrFteQM/MlAgM2QGUOfZVyMEMQ1TIoUIGq43Z6AyFQvB4PHA4HFixYgUW\nLVqEnp4eOBwOAIDD4UBPTw8AoLOzEy6XK/Jal8uFYDA4Yr3T6UQwGLT6vRARERGRosZsdE6YMAGB\nQAAdHR1499130dDQMOzxpKSkm31z7k0+ny+OW0uO7O9of1asWDFsecqU6XHMH5347uPY6ZYX0DNz\nInK73Vi8eDFyc3Mjd4Z6e3uRl5eHefPmIT8/H319fZHnV1VVISMjAwsWLMChQ4ci648fP47s7Gxk\nZGRg69atcX8f4+eTHUCZY1+FHMwwRIUcKmSwWvJ4nzh16lQ8/PDDOH78OBwOB7q7u5Geno6uri6k\npaUBCF/BbG9vj7ymo6MDLpcLTqcTHR0dw9Y7nc47bqusrAxutxsAkJqaCo/HE9n5g5ebVV8eMrjs\ns2D5BoAGE88fe7m/PwmGYUjfX1zm8t2WB//f1taGRJaUFD4fp08f+mNwsA/9iy++iO3bt8Pv98Pv\n9w/rQx8MBrFq1Sq0tLQgKSkp0ofe6/WisLAQ9fX1eOihhyS+MyIiAOIuPv/8c3H+/HkhhBCXLl0S\ny5cvF4cPHxYVFRXC7/cLIYSoqqoSlZWVQgghTp48KXJycsTVq1fF6dOnxezZs0UoFBJCCOH1ekVj\nY6MIhUJi9erVoq6ubtRtjhFJOQ0NDSPWARCAsOHHinIbRpSputH2scp0yyuEfpl1OG6j4Xa7xdmz\nZ4etmz9/vuju7hZCCNHV1SXmz58vhBBi27ZtkXpYCCEKCgrEhx9+KDo7O8WCBQsi6/fs2SOee+65\nYWWqsP/C9dnt9ZG19eV4qHLsq5CDGYaokEOFDFbXFXe90tnV1YXS0lKEQiGEQiFs2LABK1euRG5u\nLoqKirBr167IkEkAkJmZiaKiImRmZiI5ORk7d+6M3HrfuXMnysrKcPnyZRQWFvKvbiKi2yQlJWHV\nqlWYOHEinnvuOTz77LN37UO/bNmyyGsH+9CnpKSwDz0RKYlzr9vAznE6rS9X//1N955EqCdG09XV\nhZkzZ+Lzzz9HXl4eXn/9dTz66KM4f/585DnTp09Hb28vfvCDH2DZsmV48sknAQCbNm3C6tWr4Xa7\n8c///M/485//DAA4cuQIXnnlFfzHf/xHpAwV9h/H6SRSn9V1xbj7dBIRkb1mzpwJAJgxYwbWrl2L\nY8eO2daHXoW+80MGl30WL8PW/FzmcqItG4aB3bt3A0CkfrCUpTfrLaBgpLtin077qdCvxQzd8gqh\nX2YdjluzvvzyS3HhwgUhhBAXL14U3/nOd8R//ud/2tKHXoX9B/bpHEaFHMwwRIUcKmSwuq7glU4i\nIgX09PRg7dq1AIAbN27gySefRH5+PpYsWcI+9ESUEO75Pp1TpkxHf//5sZ9oGvt0EtlFhT6JOlNh\n/9nfpzMF4WHm7DF58jRcuNBrW/lEKrC6rrjnG532VHz8IhGRnVRoNOlMhf0Xjy8S8YtKRLGxuq6Y\nYFlJ9yxDdgCTDNkBTBv5pQO16ZYX0DMzJQJDdgCokUGNc5AZhqiQQ4UMVmOjk4iIiIhsx9vrvL3O\nW0SkHRVuD+tMhf3H2+tE6uPtdSIiIiLSDhudMTNkBzDJkB3ANN36teiWF9AzMyUCQ3YAqJFBjXOQ\nGYaokEOFDFZjo5OIiIiIbMc+nezTyX5JpB0V+iTqTIX9xz6dROpjn04iIiIi0g4bnTEzZAcwyZAd\nwDTd+rXolhfQMzMlAkN2AKiRQY1zkBmGqJBDhQxWY6OTiIiIiGw3Zp/O9vZ2lJSU4LPPPkNSUhL+\n8R//ET/84Q/x05/+FP/2b/+GGTNmAAC2bduG1atXAwCqqqpQU1ODiRMnYseOHcjPzwcAHD9+HGVl\nZbhy5QoKCwtRXV09MhD7dMa5XPZLIv2o0CdRZyrsP/bpJFJf3Ode7+7uRnd3NzweDy5evIgHH3wQ\n+/fvx759+zB58mQ8//zzw57f3NyM9evX47//+78RDAaxatUqtLS0ICkpCV6vF7/61a/g9XpRWFiI\nH/7wh3jooYdsfYNjYaOTFSfpR4VGk85U2H9sdBKpL+5fJEpPT4fH4wEATJo0CQsXLkQwGASAUYMc\nOHAAxcXFSElJgdvtxty5c3H06FF0dXWhv78fXq8XAFBSUoL9+/db9kbkMWQHMMmQHcA03fq16JYX\n0DMzJQJDdgCokUGNc5AZhqiQQ4UMVjPVp7OtrQ1NTU1YtmwZAOD1119HTk4OnnnmGfT19QEAOjs7\n4XK5Iq9xuVwIBoMj1judzkjjlYiIiIgS27gbnRcvXsTjjz+O6upqTJo0CZs3b0ZraysCgQBmzpyJ\nF154wc6cCvPJDmCST3YA03w+n+wIpuiWF9AzMyUCn+wAUCODGucgMwxRIYcKGayWPJ4nXb9+HevW\nrcNTTz2FNWvWAADS0tIij2/atAmPPPIIgPAVzPb29shjHR0dcLlccDqd6OjoGLbe6XSOur2ysjK4\n3W4AQGpqKjweT2TnD15utmo5zMBQxWPc/DfWZYzxuCrL4X1i1/7lMpetWB78f1tbG4iISFNiDKFQ\nSGzYsEGUl5cPW9/Z2Rn5/89//nNRXFwshBDi5MmTIicnR1y9elWcPn1azJ49W4RCISGEEF6vVzQ2\nNopQKCRWr14t6urqRmxvHJEsBUAAIoafhlHWxVrmnX6sKPf2vPHd39FoaGiQHcEU3fIKoV9mHY5b\nlamw/8L12Wj1Z7zry2gzWLsPVTgHmWGICjlUyGD1cT7mlc73338f//7v/47FixcjNzcXQHh4pD17\n9iAQCCApKQmzZs3Cb37zGwBAZmYmioqKkJmZieTkZOzcufPmtxSBnTt3oqysDJcvX0ZhYeGIb64T\nERERUWLi3OscMonDfpB2VBjyR2cq7D8OmUSkPs69TkSUoAYGBpCbmxvpI9/b24u8vDzMmzcP+fn5\nkVFCgPAkHBkZGViwYAEOHToUWX/8+HFkZ2cjIyMDW7dujft7ICK6EzY6Y2bIDmCSITuAabqNVaZb\nXkDPzImouroamZmZkS5Jfr8feXl5OHXqFFauXAm/3w8gPAnH3r170dzcjPr6emzZsiVyNWLz5s3Y\ntWsXWlpa0NLSgvr6emnvZ2yG7ABQI4Ma5yAzDFEhhwoZrMZGJxGRAjo6OnDw4EFs2rQp0oCsra1F\naWkpAKC0tDQyoca9NwkHESUCNjpj5pMdwCSf7ACm6TZWmW55AT0zJ5of/ehHePXVVzFhwlC13NPT\nA4fDAQBwOBzo6ekBkEiTcPhkB4AaGdQ4B5lhiAo5VMhgNTY6iYgke+utt5CWlobc3Nw7dtpPSkqK\n3HYnItLRuAaHp7sxoMpfyuNjQK+8wwev14FueQE9MyeSDz74ALW1tTh48CCuXLmCCxcuYMOGDXA4\nHOju7kZ6ejq6uroik3LoNgnHnQf9NxCujwaXfbest2IZYzx+67ajL9+K/REIBFBeXm5ZedEsD66T\nOSnE7Vnivf3B5Xv18zAMA7t37waASP1gKUtH/bRAvCOBg8PHdX9HQ4UBcs3QLa8Q+mXW4biNlmEY\n4h/+4R+EEEJUVFQIv98vhBCiqqpKVFZWCiH0m4RjNODg8MOocA4ywxAVcqiQwerjnON0cpxOjjVH\n2lFhnEm7vPPOO3jttddQW1uL3t5eFBUV4cyZM3C73di3bx9SU1MBhCfpqKmpQXJyMqqrq1FQUAAg\nPGTSrZNw7NixY8Q2VNh/HKeTSH1W1xVsdLLRyYqTtKNCo0lnKuw/NjqJ1MfB4ZVjyA5gknHbcnLk\nCwpW/kyZMt26xJqNVaZbXkDPzJQIDNkBoEYGNc5BZhiiQg4VMliNXyS6592AHVcD+vv5LVsiIiIa\nwtvrvL1uQ5nhchU7tCiBqHB7WGcq7D/eXidSH2+vExEREZF22OiMmSE7gEmG7ACm6davRbe8gJ6Z\nKREYsgNAjQxqnIPMMESFHCpksBobnURERERkO/bpZJ9OG8oMl6vYoUUJRIU+iTpTYf+xTyeR+uLe\np7O9vR0rVqzAokWLkJWVFRlouLe3F3l5eZg3bx7y8/PR19cXeU1VVRUyMjKwYMECHDp0KLL++PHj\nyM7ORkZGBrZu3WrZmyAiIiIitY3Z6ExJScEvfvELnDx5Eo2NjXjjjTfw6aefwu/3Iy8vD6dOncLK\nlSvh9/sBAM3Nzdi7dy+am5tRX1+PLVu2RFrJmzdvxq5du9DS0oKWlhbU19fb++7iwpAdwCRDdgDT\ndOvXolteQM/MlAgM2QGgRgY1zkFmGKJCDhUyWG3MRmd6ejo8Hg8AYNKkSVi4cCGCwSBqa2tRWloK\nACgtLcX+/fsBAAcOHEBxcTFSUlLgdrsxd+5cHD16FF1dXejv74fX6wUAlJSURF5DRERERInN1BeJ\n2tra0NTUhKVLl6KnpwcOhwMA4HA40NPTAwDo7OyEy+WKvMblciEYDI5Y73Q6EQwGrXgPkvlkBzDJ\nJzuAaT6fT3YEU3TLC+iZmRKBT3YAqJFBjXOQGYaokEOFDFYbd6Pz4sWLWLduHaqrqzF58uRhjw1O\nfUhERERENJpxTYN5/fp1rFu3Dhs2bMCaNWsAhK9udnd3Iz09HV1dXUhLSwMQvoLZ3t4eeW1HRwdc\nLhecTic6OjqGrXc6naNur6ysDG63GwCQmpoKj8cTafEP9nGwajnMwNBfu8bNf8e7/EsAnlEex23L\n0ZZv9fLteQefY/X2bi5Z8HkFAgGUl5dbVp7dy7rlHeTz+ZTJM1o+wzDQ1tYGSiQG5F9pVCFD+PiW\nfWWLGdTKoUIGy4kxhEIhsWHDBlFeXj5sfUVFhfD7/UIIIaqqqkRlZaUQQoiTJ0+KnJwccfXqVXH6\n9Gkxe/ZsEQqFhBBCeL1e0djYKEKhkFi9erWoq6sbsb1xRLIUAAGIGH4aRlkXa5l3+rGi3Nvz2pfV\nKg0NDZaVFQ+65RVCv8zxricSjQr7L1z3jFZ/xru+jDaDtftQhXOQGYaokEOFDFYf52OO0/nee+/h\nu9/9LhYvXhy5hV5VVQWv14uioiKcOXMGbrcb+/btQ2pqKgBg27ZtqKmpQXJyMqqrq1FQUAAgPGRS\nWVkZLl++jMLCwsjwS7fiOJ3xLpfjdJJ+VBhnUmcq7D+O00mkPqvrCg4Oz0anDWWGy1Xs0KIEokKj\nSWcq7D82OonUF/fB4WkshuwAJhmyA5im21hluuUF9MxMicCQHQBqZFDjHGSGISrkUCGD1djoJCIi\nIiLb8fY6b6/bUGa4XMUOLUogKtwe1pkK+4+314nUx9vrREQJ5sqVK1i6dCk8Hg8yMzPx0ksvAQB6\ne3uRl5eHefPmIT8/H319fZHXVFVVISMjAwsWLMChQ4ci648fP47s7GxkZGRg69atcX8vRER3wkZn\nzAzZAUwyZAcwTbd+LbrlBfTMnEjuu+8+NDQ0IBAI4OOPP0ZDQwPee+89+P1+5OXl4dSpU1i5ciX8\nfj8AoLm5GXv37kVzczPq6+uxZcuWyNWIzZs3Y9euXWhpaUFLSwvq6+tlvrUxGLIDQI0MapyDzDBE\nhRwqZLAaG51ERAq4//77AQDXrl3DwMAApk2bhtraWpSWlgIASktLsX//fgDAgQMHUFxcjJSUFLjd\nbsydOxdHjx5FV1cX+vv74fV6AQAlJSWR1xARycZGZ8x8sgOY5JMdwDTdZmTQLS+gZ+ZEEwqF4PF4\n4HA4sGLFCixatAg9PT1wOBwAwrPA9fT0AAA6Ozvhcrkir3W5XAgGgyPWO51OBIPB+L4RU3yyA0CN\nDGqcg8wwRIUcKmSw2rimwSQiIntNmDABgUAAX3zxBQoKCtDQ0DDs8aSkpMgEHUREOmKjM2YGVPlL\neXwM6JVXv/lndcsL6Jk5UU2dOhUPP/wwjh8/DofDge7ubqSnp6OrqwtpaWkAwlcw29vbI6/p6OiA\ny+WC0+lER0fHsPVOp3PU7ZSVlcHtdgMAUlNT4fF4Rsx5b/fyUH00uOy7Zb0Vyxjj8Vu3HX35VuyP\nQCCA8vJyy8qLZnlwnazt37ptWdsfXL5XPw/DMLB7924AiNQPlrJ0Uk0LxDsSYp57fLR5ezn3upWf\nowrzz5qhW14h9MusYNUVk88//1ycP39eCCHEpUuXxPLly8Xhw4dFRUWF8Pv9QgghqqqqRGVlpRBC\niJMnT4qcnBxx9epVcfr0aTF79mwRCoWEEEJ4vV7R2NgoQqGQWL16tairqxuxPRX2X7juiXbecyvr\ny2gzWLsPVTgHmWGICjlUyGD1cc5xOjlOpw1lhstV7NCiBKLCOJNW+uSTT1BaWopQKIRQKIQNGzag\noqICvb29KCoqwpkzZ+B2u7Fv3z6kpqYCALZt24aamhokJyejuroaBQUFAMJDJpWVleHy5csoLCzE\njh07RmxPhf3HcTqJ1Me5123Ynk4NOZ2yKnZoUQJRodGkMxX2HxudROrj4PDKMWQHMMmQHcA03cYq\n0y0voGdmSgSG7ABQI4Ma5yAzDFEhhwoZrMZGJxERERHZjrfXeXvdhjLD5Sp2aFECUeH2sM5U2H+8\nvU6kvrjfXt+4cSMcDgeys7Mj637605/C5XIhNzcXubm5qKurizzG+YCJiIiI6HZjNjqffvrpEXP3\nJiUl4fnnn0dTUxOampqwevVqAIk0H7AZhuwAJhmyA5imW78W3fICemamRGDIDgA1MqhxDjLDEBVy\nqJDBamM2OpcvX45p06aNWD/a5VbOB0xEREREo4n6i0Svv/46cnJy8Mwzz6Cvrw9AIs0HbIZPdgCT\nfLIDmKbbTDm65QX0zEyJwCc7ANTIoMY5yAxDVMihQgarRdXo3Lx5M1pbWxEIBDBz5ky88MILVuci\nIiIiogQS1dzrg/P/AsCmTZvwyCOPALBmPmAgvnMChxmIfo7fXwLwjPI4bluOtnyrl2/PO/gcq7d3\ncylB5sBN5LyD4j3Hr9l8hmGgra0NlEgMyL/SqEKG8PEt+8oWM6iVQ4UMlhvPXJmtra0iKysrstzZ\n2Rn5/89//nNRXFwshIh9PuCbwzeNJ5JlEPPc46PN28u51638HFWYf9YM3fIKoV/meNcTiUaF/Reu\ne6Kd99zK+jLaDNbuQxXOQWYYokIOFTJYfZyPOU5ncXEx3nnnHZw9exYOhwMvv/xy5GpOUlISZs2a\nhd/85jdwOBwAYpsPGOA4nfEvl+N0kn5UGGdSZyrsP47TSaQ+zr1uw/Z0asjplFWxQ4sSiAqNJp2p\nsP/Y6CRSH+deV44hO4BJhuwApuk2VplueQE9M1MiMGQHgBoZ1DgHmWGICjlUyGC1qL5IRDS25JtX\nMqw1efI0XLjQa3m5RETm2FPH3Yr1HSUa3l7n7XUbyrS3XMUOWZJAhdvDOlNh/yXC7XV7yw9vQ/bn\nRPc23l4nIiIiIu2w0RkzQ3YAkwzZAaJgyA5gio79cHTMTInAkB0AamQAVMihQj2gQgZAjRwqZLAa\nG51EREREZDv26WSfThvKtLdcxQ5ZkkCFPok6U2H/sU/n+LYh+3Oiexv7dBIRJZj29nasWLECixYt\nQlZWVmTyjN7eXuTl5WHevHnIz89HX19f5DVVVVXIyMjAggULcOjQocj648ePIzs7GxkZGdi6dWvc\n3wsR0Z2w0RkzQ3YAkwzZAaJgyA5gio79cHTMnEhSUlLwi1/8AidPnkRjYyPeeOMNfPrpp/D7/cjL\ny8OpU6ewcuVK+P1+AEBzczP27t2L5uZm1NfXY8uWLZGrEZs3b8auXbvQ0tKClpYW1NfXy3xrYzBk\nB4AaGQAVcqhQD6iQAVAjhwoZrMZGJxGRZOnp6fB4PACASZMmYeHChQgGg6itrUVpaSkAoLS0RB9Y\nPAAAF79JREFUFPv37wcAHDhwAMXFxUhJSYHb7cbcuXNx9OhRdHV1ob+/H16vFwBQUlISeQ0RkWxs\ndMbMJzuAST7ZAaLgkx3AFJ/PJzuCaTpmTlRtbW1oamrC0qVL0dPTA4fDAQBwOBzo6ekBAHR2dsLl\nckVe43K5EAwGR6x3Op0IBoPxfQOm+GQHgBoZABVyqFAPqJABUCOHChmsxkYnEZEiLl68iHXr1qG6\nuhqTJ08e9lhSUpLtM+AQEdmJ02DGzIAKf6GOnwG98gK6ZTYMQ7u/UHXMnGiuX7+OdevWYcOGDViz\nZg2A8NXN7u5upKeno6urC2lpaQDCVzDb29sjr+3o6IDL5YLT6URHR8ew9U6nc9TtlZWVwe12AwBS\nU1Ph8Xgix8BgXzK7l4fO7cFl3y3rrVjGGI/fum27yh/vcgBA+ajlx+/zCK+L1/ZGW749S7y3P7gc\nCARQXl4ubfu37oN47//du3cDQKR+sJRQTLwjARCAiOGnYZR1sZZ5px8ryr09r8pZR8us3CE7QkND\ng+wIpumWWYfjwIxQKCQ2bNggysvLh62vqKgQfr9fCCFEVVWVqKysFEIIcfLkSZGTkyOuXr0qTp8+\nLWbPni1CoZAQQgiv1ysaGxtFKBQSq1evFnV1dSO2p8L+C9cRo9Wf8a6Dos1gdd05Wo74fk4q1AMq\nZBBCjRwqZLD6GOQ4nRyn04Yy7S1XsUOWJFBhnEkrvffee/jud7+LxYsXR26hV1VVwev1oqioCGfO\nnIHb7ca+ffuQmpoKANi2bRtqamqQnJyM6upqFBQUAAgPmVRWVobLly+jsLAwMvzSrVTYfxync3zb\nkP050b3N6rpizEbnxo0b8ac//QlpaWn45JNPAITHjvv+97+Pv/3tbyMqwqqqKtTU1GDixInYsWMH\n8vPzAQxVhFeuXEFhYSGqq6vj8gbHwkanTlnD5bISJhUaTTpTYf+x0Tm+bcj+nOjeFvfB4Z9++ukR\n47wl/thxZhiyA5hkyA4QBUN2AFN0HFtNx8yUCAzZAaBGBkCFHCrUAypkANTIoUIGq435RaLly5ej\nra1t2Lra2lq88847AMJjx/l8Pvj9/juOHffNb35z1LHjHnroIevfERERxeS9995DIBCQHYOIEkxU\n316/29hxy5YtizxvcOy4lJQUzcaOM8MnO4BJPtkBouCTHcAUHb8FrmN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"text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Evaluation\n", "\n", " * GBRT vs RandomForest vs SVM vs Ridge Regression" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import time\n", "from collections import defaultdict\n", "from sklearn.metrics import mean_absolute_error\n", "from sklearn.linear_model import Ridge\n", "from sklearn.ensemble import RandomForestRegressor\n", "from sklearn.pipeline import Pipeline\n", "from sklearn.preprocessing import StandardScaler\n", "from sklearn.dummy import DummyRegressor\n", "from sklearn.svm import SVR\n", "\n", "res = defaultdict(dict)\n", "\n", "def benchmark(est, name=None):\n", " if not name:\n", " name = est.__class__.__name__\n", " t0 = time.clock()\n", " est.fit(X_train, y_train)\n", " res[name]['train_time'] = time.clock() - t0\n", " t0 = time.clock()\n", " pred = est.predict(X_test)\n", " res[name]['test_time'] = time.clock() - t0\n", " res[name]['MAE'] = mean_absolute_error(y_test, pred)\n", " return est\n", " \n", "benchmark(DummyRegressor())\n", "benchmark(Ridge(alpha=0.0001, normalize=True))\n", "benchmark(Pipeline([('std', StandardScaler()), \n", " ('svr', SVR(kernel='rbf', C=10.0, gamma=0.1, tol=0.001))]), name='SVR')\n", "benchmark(RandomForestRegressor(n_estimators=100, max_features=5, random_state=0, \n", " bootstrap=False, n_jobs=4))\n", "est = benchmark(GradientBoostingRegressor(n_estimators=500, max_depth=4, learning_rate=0.1,\n", " loss='huber', min_samples_leaf=3, \n", " random_state=0))\n", "\n", "res_df = pd.DataFrame(data=res).T\n", "res_df[['train_time', 'test_time', 'MAE']].sort('MAE', ascending=False)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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train_timetest_timeMAE
DummyRegressor 0.00 0.00 0.909090
Ridge 0.02 0.00 0.532860
SVR 89.90 6.63 0.379575
RandomForestRegressor 74.73 0.50 0.318885
GradientBoostingRegressor 45.76 0.15 0.300638
\n", "
" ], "metadata": {}, "output_type": "pyout", "prompt_number": 25, "text": [ " train_time test_time MAE\n", "DummyRegressor 0.00 0.00 0.909090\n", "Ridge 0.02 0.00 0.532860\n", "SVR 89.90 6.63 0.379575\n", "RandomForestRegressor 74.73 0.50 0.318885\n", "GradientBoostingRegressor 45.76 0.15 0.300638" ] } ], "prompt_number": 25 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise\n", "\n", "The above ``GradientBoostingRegressor`` is not properly tuned for this dataset. Diagnose the current model and find more appropriate hyperparameter settings. \n", "\n", "Hint: check whether you are in the high-bias or high-variance regime" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# diagnose the model\n", "test_dev, ax = deviance_plot(est, X_test, y_test, ylim=(0, 1.0))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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xX/BkjicAAIArETwBAADgCPcGTx6nBAAA4CruC57c1Q4AAOBKrguehdFvLmru4K52AAAA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\nLZalSBiNBt3MaLDNiIXUWGD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"text": [ "" ] } ], "prompt_number": 19 }, { "cell_type": "code", "collapsed": false, "input": [ "## modify the hyperparameters\n", "#tuned_est = benchmark(GradientBoostingRegressor(n_estimators=500, max_depth=4, learning_rate=0.1,\n", "# loss='huber', random_state=0, verbose=1))\n", "\n", "## print results\n", "#res_df = pd.DataFrame(data=res).T\n", "#res_df[['train_time', 'test_time', 'MAE']].sort('MAE', ascending=False)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 27 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Feature importance\n", "\n", " * What are the important features and how do they contribute in predicting the target response?\n", " * Derived from the regression trees \n", " * Can be accessed via the attribute ``est.feature_importances_``" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fx_imp = pd.Series(est.feature_importances_, index=names)\n", "fx_imp /= fx_imp.max() # normalize\n", "fx_imp.sort()\n", "fx_imp.plot(kind='barh', figsize=FIGSIZE)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 21, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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BBYc+0FV3wfc/0ccCAAAg+rgWS+jdu7cWLlwoSZo2bZoGDx4c+ERcRUWFRowYoS5duigt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\nAogaZG4BNG6OZW5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"text": [ "" ] } ], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Partial dependence\n", "\n", " * Relationship between the response and a set of features, marginalizing over all other features\n", " * Intuitively: expected response as a function of the features we conditioned on" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from sklearn.ensemble.partial_dependence import plot_partial_dependence\n", "\n", "features = ['MedInc', 'AveOccup', 'HouseAge',\n", " ('AveOccup', 'HouseAge')]\n", "fig, axs = plot_partial_dependence(est, X_train, features, feature_names=names, \n", " n_cols=2, figsize=FIGSIZE)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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6khohrCW3OJcvD37Jon2LCPQM5K3Bb9E7uLe1YwkHIxeaETatsLyQ2xbfxuM9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"text": [ "" ] } ], "prompt_number": 22 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Scikit-learn provides a convenience function to create such plots and a low-level function that you can use to create custom partial dependence plots (e.g. map overlays or 3d plots). \n", "More detailed information can be found [here](http://scikit-learn.org/dev/modules/ensemble.html#partial-dependence).\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Performance\n", "\n", "Comparision of scikit-learn against R's [gbm](http://cran.r-project.org/web/packages/gbm/index.html) package.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tipps & Tricks\n", "\n", "### Categorical features\n", "\n", "Scikit-learn requires that categorical variables are encoded as numerics. For tree-based methods ordinal encoding is as effective as one-hot encoding but more efficient (less memory & faster runtime) given that you grow deep enough trees:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "df = pd.DataFrame(data={'icao': ['CRJ2', 'A380', 'B737', 'B737']})\n", "# ordinal encoding\n", "df_enc = pd.DataFrame(data={'icao': np.unique(df.icao,\n", " return_inverse=True)[1]})\n", "X = np.asfortranarray(df_enc.values, dtype=np.float32)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 23 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Feature interactions\n", "\n", "GBRT automatically detects feature interactions but often explicit interactions help.\n", "\n", "Trees required to approximate $X_1 - X_2$: 10 (left), 1000 (right)\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary\n", "\n", " - Flexible non-parametric classification and regression technique\n", " - Applicable to a variety of problems\n", " - Solid, battle-worn implementation in scikit-learn\n", " \n", "" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }