{ "metadata": { "name": "", "signature": "sha256:2f100891f7d9603a07ea9342b506fcd29e7c26c1e4c1b02dd56f5c4d37b42c90" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "2. A Short Tour of the Predictive Modeling Process" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Introduce the broad concepts of modeling building, i.e. building candidate models and selecting the optimal model." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "2.1 Case Study: Predicting Fuel Economy" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check if data exists:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "!ls -l ../datasets/FuelEconomy/" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "total 280\r\n", "-rw-r--r-- 1 leigong staff 106388 Nov 18 16:08 cars2010.csv\r\n", "-rw-r--r-- 1 leigong staff 23219 Nov 18 16:08 cars2011.csv\r\n", "-rw-r--r-- 1 leigong staff 8969 Nov 18 16:08 cars2012.csv\r\n" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this study, we are only interested in data from 2010 and 2011. Use the DataFrame data type from **pandas** to store the files. It is very similar to the statistical package **R**'s data frame." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import numpy as np\n", "import pandas as pd\n", "\n", "cars10 = pd.read_csv(\"../datasets/FuelEconomy/cars2010.csv\")\n", "cars11 = pd.read_csv(\"../datasets/FuelEconomy/cars2011.csv\")" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "cars10.head(5)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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Unnamed: 0EngDisplNumCylTransmissionFEAirAspirationMethodNumGearsTransLockupTransCreeperGearDriveDescIntakeValvePerCylExhaustValvesPerCylCarlineClassDescVarValveTimingVarValveLift
0 1088 4.7 8 AM6 28.0198 NaturallyAspirated 6 1 0 TwoWheelDriveRear 2 2 2Seaters 1 0
1 1089 4.7 8 M6 25.6094 NaturallyAspirated 6 1 0 TwoWheelDriveRear 2 2 2Seaters 1 0
2 1090 4.2 8 M6 26.8000 NaturallyAspirated 6 1 0 AllWheelDrive 2 2 2Seaters 1 0
3 1091 4.2 8 AM6 25.0451 NaturallyAspirated 6 1 0 AllWheelDrive 2 2 2Seaters 1 0
4 1092 5.2 10 AM6 24.8000 NaturallyAspirated 6 0 0 AllWheelDrive 2 2 2Seaters 1 0
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" ], "metadata": {}, "output_type": "pyout", "prompt_number": 3, "text": [ " Unnamed: 0 EngDispl NumCyl Transmission FE AirAspirationMethod \\\n", "0 1088 4.7 8 AM6 28.0198 NaturallyAspirated \n", "1 1089 4.7 8 M6 25.6094 NaturallyAspirated \n", "2 1090 4.2 8 M6 26.8000 NaturallyAspirated \n", "3 1091 4.2 8 AM6 25.0451 NaturallyAspirated \n", "4 1092 5.2 10 AM6 24.8000 NaturallyAspirated \n", "\n", " NumGears TransLockup TransCreeperGear DriveDesc \\\n", "0 6 1 0 TwoWheelDriveRear \n", "1 6 1 0 TwoWheelDriveRear \n", "2 6 1 0 AllWheelDrive \n", "3 6 1 0 AllWheelDrive \n", "4 6 0 0 AllWheelDrive \n", "\n", " IntakeValvePerCyl ExhaustValvesPerCyl CarlineClassDesc VarValveTiming \\\n", "0 2 2 2Seaters 1 \n", "1 2 2 2Seaters 1 \n", "2 2 2 2Seaters 1 \n", "3 2 2 2Seaters 1 \n", "4 2 2 2Seaters 1 \n", "\n", " VarValveLift \n", "0 0 \n", "1 0 \n", "2 0 \n", "3 0 \n", "4 0 " ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check if there is any missing values 'NAN' in this dataset." ] }, { "cell_type": "code", "collapsed": false, "input": [ "cars10.count()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ "Unnamed: 0 1107\n", "EngDispl 1107\n", "NumCyl 1107\n", "Transmission 1107\n", "FE 1107\n", "AirAspirationMethod 1107\n", "NumGears 1107\n", "TransLockup 1107\n", "TransCreeperGear 1107\n", "DriveDesc 1107\n", "IntakeValvePerCyl 1107\n", "ExhaustValvesPerCyl 1107\n", "CarlineClassDesc 1107\n", "VarValveTiming 1107\n", "VarValveLift 1107\n", "dtype: int64" ] } ], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "print cars10.shape\n", "print cars11.shape" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(1107, 15)\n", "(245, 15)\n" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We only restrict ourselves to a single predictor 'EngDispl' and the response 'FE' in this introductory illustration." ] }, { "cell_type": "code", "collapsed": false, "input": [ "cars10_feature = cars10.get(['EngDispl'])\n", "cars10_target = cars10.get(['FE'])\n", "cars11_feature = cars11.get(['EngDispl'])\n", "cars11_target = cars11.get(['FE'])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "cars10_feature.head(5)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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EngDispl
0 4.7
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2 4.2
3 4.2
4 5.2
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" ], "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ " EngDispl\n", "0 4.7\n", "1 4.7\n", "2 4.2\n", "3 4.2\n", "4 5.2" ] } ], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "cars10_target.head(5)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "
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FE
0 28.0198
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" ], "metadata": {}, "output_type": "pyout", "prompt_number": 8, "text": [ " FE\n", "0 28.0198\n", "1 25.6094\n", "2 26.8000\n", "3 25.0451\n", "4 24.8000" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generally, we want to first visulize the datasets to get a better understanding before doing anything crazy. Since there is one predicator, a simple scatter plot would do the trick. The characteristics from the visulization may suggest important and necessary pre-processing steps." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "\n", "# Some nice default configuration for plots\n", "plt.rcParams['figure.figsize'] = 10, 7.5\n", "plt.rcParams['axes.grid'] = True\n", "plt.gray()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "fig, (ax1, ax2) = plt.subplots(1, 2, sharey = True)\n", "\n", "ax1.scatter(cars10_feature, cars10_target)\n", "ax1.set_title('2010 Model Year')\n", "ax2.scatter(cars11_feature, cars11_target)\n", "ax2.set_title('2011 Model Year')\n", "\n", "fig.text(0.5, 0.04, 'Engine Displacement', ha='center', va='center')\n", "fig.text(0.06, 0.5, 'Fuel Efficiency (MPG)', ha='center', va='center', rotation='vertical')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 10, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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qSnRFSJ7BdYLUNd6efXabeyu5pw6UZyIihUnePYaJ3WPidYnf1pwTkexy5cj1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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because of the nature of this problem, i.e. predict the MPG for a new car line, we take the 2010 data as *training set* and the 2011 data as *test set*. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Define the evaluation metric: root mean squared error (RMSE)\n", "from sklearn.metrics import mean_squared_error\n", "\n", "def rmse(y_actual, y_predicted):\n", " '''calculate Root Mean Squared Error'''\n", " return np.sqrt(mean_squared_error(y_actual, y_predicted))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "A good starting point is the simple linear model \n", "$$y = \\beta_0 + \\beta_1x,$$\n", "where $y$ is the Fuel Efficiency (MPG) and $x$ is the Engine Displacement." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# simple linear model\n", "from sklearn.linear_model import LinearRegression\n", "\n", "reg = LinearRegression()\n", "reg.fit(cars10_feature, cars10_target)\n", "print \"Least square estimate: intercept = {0}, coefficient ={1}\".format(reg.intercept_, reg.coef_[0])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Least square estimate: intercept = [ 50.56322991], coefficient =[-4.52092928]\n" ] } ], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "X = np.linspace(np.min(cars10_feature)[0], np.max(cars10_feature)[0])[:, np.newaxis]\n", "y = reg.predict(X)\n", "cars10_target_pred = reg.predict(cars10_feature)\n", "y_range = np.linspace(np.min(cars10_target)[0], np.max(cars10_target)[0])[:, np.newaxis]\n", "\n", "fig, (ax1, ax2) = plt.subplots(1, 2)\n", "\n", "ax1.scatter(cars10_feature, cars10_target)\n", "ax1.plot(X, y, 'r')\n", "ax1.set_title('2010 Model Year')\n", "ax1.set_xlabel('Engine Displacement')\n", "ax1.set_ylabel('Fuel Efficiency (MPG)')\n", "\n", "ax2.scatter(cars10_target, cars10_target_pred)\n", "ax2.plot(y_range, y_range, 'r--')\n", "ax2.set_xlabel('Observed')\n", "ax2.set_ylabel('Predicted')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 13, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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TapCoqYGiIrj99nRHklSJ1mF6F2QcLS0tzJxZQ3v79QA88UQNy5c3aSNMKaWUGohly+BP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\nV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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The left-hand panel shows the training set data with a linear model fit defined by the estimated slope and intercept. The right-hand panel plots the observed and predicted MPG. These plots demonstrate that this model misses some of the patterns in the data, such as under-predicting fuel efficiency when the displacement is less than 2L or above 6L" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# calculate root mean square error (RMSE)\n", "from sklearn.cross_validation import cross_val_score\n", "\n", "scores = np.sqrt(np.abs(cross_val_score(reg, cars10_feature, cars10_target, cv=10, scoring='mean_squared_error')))\n", "print \"RMSE: {0}\".format(np.mean(scores))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "RMSE: 4.7277409602\n" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Notice** that simply re-predict the training set data is like to result in overly optimistic estimation of RMSE. An alternative approach for quantifying how well the model operates is to use *resampling* techniques, e.g. 10-fold cross-validation. We will cover that in Chapter 4." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking at the previous figure, it is conceivable that the problem might be solved by introducing some non-linearity in the model. The most basic approach is to supplement the simple linear model with additional complexity, e.g.\n", "$$y = \\beta_0 + \\beta_1 x + \\beta_2 x^2,$$\n", "which is referred to as *quadratic model*." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# quadratic model\n", "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.pipeline import make_pipeline\n", "\n", "quad = make_pipeline(PolynomialFeatures(2), LinearRegression())\n", "quad.fit(cars10_feature, cars10_target)\n", "\n", "scores = np.sqrt(np.abs(cross_val_score(quad, cars10_feature, cars10_target, cv=10, scoring='mean_squared_error')))\n", "print \"RMSE: {0}\".format(np.mean(scores))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "RMSE: 4.34528462825\n" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Reduce in the RMSE may suggest that this model is a better fit to the data." ] }, { "cell_type": "code", "collapsed": false, "input": [ "X = np.linspace(np.min(cars10_feature)[0], np.max(cars10_feature)[0])[:, np.newaxis]\n", "y = quad.predict(X)\n", "cars10_target_pred = quad.predict(cars10_feature)\n", "y_range = np.linspace(np.min(cars10_target)[0], np.max(cars10_target)[0])[:, np.newaxis]\n", "\n", "fig, (ax1, ax2) = plt.subplots(1, 2)\n", "\n", "ax1.scatter(cars10_feature, cars10_target)\n", "ax1.plot(X, y, 'r')\n", "ax1.set_title('2010 Model Year')\n", "ax1.set_xlabel('Engine Displacement')\n", "ax1.set_ylabel('Fuel Efficiency (MPG)')\n", "\n", "ax2.scatter(cars10_target, cars10_target_pred)\n", "ax2.plot(y_range, y_range, 'r--')\n", "ax2.set_xlabel('Observed')\n", "ax2.set_ylabel('Predicted')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 16, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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gQPDk44kn5jsSybBUXZBvdc69GluA4+Ne78lVgLnS0Zc8ahRceCFcd12P+8Z3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\njdkoK67MrHxG/eXbf1Rm/sWkeFLzLR4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uru72R1tdXd1r7lhNTWJlNc5qak7J2eckg5Ma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"text": [ "" ] } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "One issue with quadratic models is that they can perform poorly on the extremes of the predictor. From the above figure, one might notice that predicting new vehicles with large displacement values may produce inaccurate results." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are other approaches for creating sophisticated relationships between the predictors and outcome. One particular technique is the multivariate adaptive regression spline (MARS) model (Friedman (1991)). When used with a single predictor, MARS can fit separate linear regression lines for different ranges of engine displacement. This model, like many machine learning algorithms, has a *tuning parameter* which cannot be directly estimated from the data. While the MARS model has internal algorithms for making this dtermination, the user can try different values and use resampling to determin the appropriate value. Once the value is found, a final MARS model would be fit using all the training set data and used for prediction." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A Python module *py-earth* on Github implemented the MARS and is likely to be merged into *sklearn* in the near future (see [this](https://github.com/scikit-learn/scikit-learn/issues/845) issue)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# MARS\n", "from pyearth import Earth\n", "\n", "mars = Earth()\n", "mars.fit(cars10_feature, cars10_target)\n", "scores = np.sqrt(np.abs(cross_val_score(mars, cars10_feature, cars10_target, cv=10, scoring='mean_squared_error')))\n", "print \"RMSE: {0}\".format(np.mean(scores))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "RMSE: 4.38261607106\n" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "RMSE of MARS is similar to that of quadratic regression." ] }, { "cell_type": "code", "collapsed": false, "input": [ "X = np.linspace(np.min(cars10_feature)[0], np.max(cars10_feature)[0])[:, np.newaxis]\n", "y = mars.predict(X)\n", "cars10_target_pred = mars.predict(cars10_feature)\n", "y_range = np.linspace(np.min(cars10_target)[0], np.max(cars10_target)[0])[:, np.newaxis]\n", "\n", "fig, (ax1, ax2) = plt.subplots(1, 2)\n", "\n", "ax1.scatter(cars10_feature, cars10_target)\n", "ax1.plot(X, y, 'r')\n", "ax1.set_title('2010 Model Year')\n", "ax1.set_xlabel('Engine Displacement')\n", "ax1.set_ylabel('Fuel Efficiency (MPG)')\n", "\n", "ax2.scatter(cars10_target, cars10_target_pred)\n", "ax2.plot(y_range, y_range, 'r--')\n", "ax2.set_xlabel('Observed')\n", "ax2.set_ylabel('Predicted')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 18, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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eSy+9FHa45gBzGDNmGC+99FLqbyKBZPUWmaQaMMUTf/hyLOvrz6KsbB6wHLiQ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\nggWq9+y2QHX8YtOJ28ZZ4WtmxTxW38P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MDjazaWa2NRs5+ONdgpqBG8Pfu1q8eGlYE/Ey\nnfUKtWzlamYxgmu4gUOZCezRseZkJLKSSGQld9+9vMsakbff/hMGDTqfYNbkJgYNOp/bb/8J0H0G\n/ViTJ0+muLiMoBbjqxQXlzF58uT0fxQieUJtWOaUlg6luLgIuABYF97GE7Q/sWveOuBHBLW0W4Br\ngfeF2/ujguAi13gHAZ8CDgNeDWMliuHC59UAHyBor7cCrxBMNTS6h7gl4c8a4KvsscfIjKztK3mg\np54ZXa96jL+tTKWX158bnn2DTIfgm17X0+DDh3edzbhzWDFRHdZMq+Mme4IxtsegYD2x+OHDeIlm\nTu7tzFmQQ9e6hd7qE0R2Fx6fAUv1VojtVzr0NJQW1LwmH0acNGmSxQ8XFhfvEbZxqQ5Bxg4hxl/t\nGB3yjL3CclCCfRKzrd66D2XWh7P5JxqCTG0oUUOQ+SHVNixZAzIlye2EVIL051aIDVhxcffT4MXF\ne3d5TtchyGgdQmX4e73BMvsJJfbQuHHWdN99STtSVVVV3f5oq6qqeq0dmzSpe73EpEnHZe1zkoHp\n/7N37vFx1WX+f5+ZyWVCkiaT9JLSCxAEKVRIQa1bsVWTBrxUS111F920unZdwCIJUrTFRUlEkFa8\nIAi6bURWl7VbLK4kpGvbtb91XYEW63IRy0URKJdQKBJI0zy/P77nzJwzc2Ymk2RmTtLn/XqdVyZn\nzvl+n7mcZ57z/X6+z6MB2NFBOjF5W1ubRCLT4lrT5P+dc6uqZkskMk0aG+fH/Z3xdeZGs6SkTEpK\nnFxdtXbw5J6+rJFWwjIjriGL2s9Psf+vEiiT5uZmz81t8s2syV82TyKRaRKNzpSGhjnxhQVNTYvi\n5yW/3tGK6VWEH3zGLQATrzOpAE7OpeGxboV2YIWYSzaaLGdk6WyBDl9NVk9Pj6Tmm6mwHUS9lBGR\nh6uq5KaT5mcMpNLlHcsegC1Oeb6paXFOr1U1YNpfrmgAlj+CppURKaJNTz0lUl8v8uCDwbAnDWpP\ndoJmU64+LFMeMAAsy1qGqYdTBhxnWVYT8CWx9RDKyHnllReBGzF5uV4CbuSVV1I/AqMHmEIih00v\nJgY26dde51JaDr3Kntd/z208zC8z9noLcBkwCJwKQEfHanbvbmNgwBwRja6lo6M7fkZ9fV1KK377\nent742WJOjpWq45BUZQR0dvby7p1XcRiU1m8eAG7dt3H88+/AAxRXz89vg8y+5be3l4uvPByHn/8\nTwwPD1BSUkVZWSknnjiHq6++gtbW1rifevTRR/nzn//IP7/+F16aMoXjn3gCnngi7sNmz67hK1/5\nVtY+FWXcyBahAfcBNXhLE/0ulyhvNBsBu4McD8zQdoUk8sZUSHJeLhFnBMy96sY/W/3XmpvlSSyZ\nwfXxKUZ3mohwODVrczgcjveRTjuWqscw5Yfcx/b09Ehp6dT4MdmWUStKNtARsKOC1Oz3qdqpRCb7\n9CXWenp6XCksktuJSWlpjXR2dnr6WkKFPE6dVPBdCYdrpbS0xvf80ZR1U5RcfdhIHMmv7b/uAOy3\nuXQymm0yOjD/XDLlnmP801CkLqsOh2slFmuUK/gr+S/qJMIH7SnNRld/I8sDlkw02iCpyQOnexzT\neExTKoobDcCODrwSCL+by/NcfyVFIjHydhZ60jeU8EH5P2bKB/l3zzHpzteFR0qu5OrDRpKG4v8s\nyzofiFiW9QbLsr6FqQkxqUgubZAfKkiklphrP67wHJFIQ7ERGMCU4bgXUxqj297WEI0KAJ0s5GUi\nXMPvfPoT1+OdPvv8GRh4HZgPbLG3+cAw0MbAwDVs2HAzTzzxZMp57n2FeT+9FLpP7U+ZKATzs9xZ\n0N4W8QKPMJ07+GCaIx4sqD3ZCNpnFjR7IJg25UJWDRimIOA6TNKqH2EESVfl06jJwGj1UUYHAeYt\njgInYeqGtWFqkQF8ilde2URb29vp7v4eH+cr3MOX+B++Q8X7Pxxvy7JeR8SpPfkgcCOWNTQCKwYx\nOXkcLsWdB+fRRx9l7twZ9Pd7j5k79+QRvUZFUY5eOjpWs2vXRxkcbMDcEG53PXspxtetwdR/7E7R\nqLrb2bHjfIaGAI4nUWcX4BIsa4ja2uN45ZXPMTgIO3kLu7gZ+AEA4fAlhMPC4GC3ff63MLVvU3Wx\nipIPLDNqFjwsy5Kg2paN3t5eli9vs0eyzMW8dWs355zzPhKjYGAcxquIHI6fu2DB29mz52FXa9dh\nErd2kigM2w1cQkvLO+nrWwa00cR99LKEy9/2Vk547xI2btxEf/9BTNaQvfZ5ZxCL7eWFF/6Q0f5w\nuIrh4cNAlb3nECb599XApVRWlvCTn2xi2bKPMjj4RgBKSx9i27Yfq3BVGTWWZSEio82qGSgmsv/K\nN729vSxb9nEGB78GQCRyMfPnn2E/O3YRfjhs8dprryDybQBKSz/Lqaeezssvv8Sf//xHhoYizJ07\nkxtu+CpA/EZ5pH0qSjpy9mHZ5iiBHT7bL3KZ5xzNxgTWUKRL82A0WSvElKlotB/HfM7tEFPOwmkj\nNQkflKb0s4pPyCMlZVJJlb0/uUbayJL3+ScdjIpTQNzRmbmF/G1tbZqjRhkTqAbsqCBbGpygt68o\n6cjVh41EA/Y513YFZjjl3hFHeBOE8Z9L3gessLd99r4jmNIVfwC+Zz8+4jmro2M10egP8ZaxWIdZ\niNpub2VEo/X2sWtxtGG3ld7JzsPDfJ8S+/yfAC1AB1VVX6Cz8zLWrVs3AttrcJdBMo9PBzYAT3Lw\n4LPU1Z3Iddddx7333s8vf7mT7u6t9PdfQX//Faxffy2f/OQnc3u7xoHJrpGa7P0p+SOYn+XOYhvg\nIWjvkdqTnSDalAtZAzARuce17RaRSzDzWkoaFi9egMm/tczebmHx4gU0NFSQENP3AGvsfQmc+o6h\n0KOuY9+OqTG20d5eJxp9zVMLsqlpE3CYi7iBE6jms/w1Rq73fmKxGrZtu22EwVc6ZuIEY8PDc+nv\nv4Lt2/+X/v7neO01SA7Y/u3fesbQl6Iok5XEjWMPCY3X6vjzXV1d1NWdSF3diXR1dXn2l5RMw7Lq\nsKwKWlpa6OrqoqJiKpZVT0XFTLq6ujw3prPYCFzMzJlVyWZkJJ0NijKuZBsiw4h/nK0eOAd4OJdh\nttFsTOAh/HRD4KYUkTe9Q3IpIgfvsX51If2mLs0xc3lMnqFa3s48gTKJRmeOeGqws7NTwuHkdBn1\nAj2uvhtdj52cZl773OkwFGUkoFOQRw3p8hCmq3not9/UVCyT5BqPTm3JE6iS54hIjAtGLL/IZIOi\nZCNXHzYSR/I48Ji9PQL0AW/PpZPRbBPZgWUOwDLXgnQwubicY1PPcwIwx5G5892ASCvtdpLWqJhc\nNwsFKjI6koTj6RCwJFFLzV2Utl5MYVt3MKYOSxk7GoApyX7MuZnz25/p5i9We4L8jDfJWq7O+aYw\nnQ2Kko1xC8CAObk0NN5boR3YeNaU8mZ6TiQv9WaYXyvJmevdNDbOd93ZLUoJcMrLKzJmlI5Gp8tV\nkQrZRUQifM/ur14qKxtEJLXwrYjb8Rznc7f5xngQ52SoNvvn2fZVugK9Y+TEE08reCbpyV4rcbL3\npwFY/ghCzbzOzk4pL48J1Ek0OlM+8YlPiIjYha7niBnpr7VvOM8TaLP31dj+pc72NY32cTGBEoHZ\n9vE9tm+qlQ9QIQ8QlhKutG8QnULbNfZWLg0NDXZ93phAlSxYsEBEghOAOZ9ZpqolxbAnSATNpvEM\nwNyZ77fk0uh4bBM5ABNJf9E0NzfbjqRampub057f2HiGeKcr59mOIiYwNd6295gVEos1xvssCU+V\n/+BNch3t4hTjdgKu1FJDx7mmPaf43G3W2MFVSdwGM/zvn6kfTil4OY/JHqBM9v40AMsfxf6hMqPr\nZUl+p0La2tokFEreX+1z0+mUKDrG59gVrsfVUsF35THq5J3x0m9O+/VJ5yWP7JdJc3NzYKYgd+zY\nkfZmvhgU+zvkR9BsylcAtieXRsdjC5oDGw9yuZhKSiqTnECZfWc4S6BMOjs7palpUZJTqZempkXx\nNqLRaVLLt2U/x8uHuN3uc5qEw+4UF07ANEsSjqlWUksRxVzHxpKmU9OXE9Hl38pI0QBs8mJGlVKn\nC40fqffxH36yi/PS3Ow5mlTz3Dquktv4G9fN4aw05y30+b9OREzAGIS0OppSY2KRqw8bSSZ8ZZxI\nlBlqA2BgwOzzS/h3+HAZZrHpVcCL9t7S+PObNv0L1dVTMYla21xnboo/Ghh4ngG+wF/TTg+f5HcM\n89DAAFDrY12Zq51PY1ZxuhPGHnYdW8HQUI3r/9XAx1z/O6kxnvHpR1EUJX98g4sp43XgP0bdxrp1\n68a4alxRspMpDcWbLMs6ZFnWIWC+89jeXi6UgYWi8PlEMvdXWirALkzqtSFMgNRpb2Xs3//YCPqY\nAnyK+/gtK5nOFso4hmoaGo4hubYkrHKdV44pA7LN3j5l9+8c+2m77UtJBFqDRKOXEwp1YIKxHSnL\ny/NNMfNk9fb2snTpCpYuXUFvb2/e+ysEEz3HjpKg2J9le/sq4Dm8fucCzj//XEKhQ6T6ozck7bsU\nUy5on8+xZ9iPfwu08wr/zgv8ByZn4m/tfh8g4a+c836b1P4empub8vo+5MLOnTtTcj0W2qcm2xM0\ngmhTTuQyXFbIjQmuAfPDOwW5NuMUpNGAOUPP/mkoGhpOSJmCbGg4IT58bqYSV9jn7JDvcbb8mBLp\nuesuW3dRb7ddFm/D2FeZ0q7ZFxOY45p29Gb1d7RnLS3nyZlnnn3UiPALpdNQDdjE2Qrtv7IRBK3M\nSET4llUnpaXVUlU1W2Kx6WJZjmi+UhJCeux9tWI0qVWux8fYj2uksrIhnsIiEnHayC7CDwoqws9O\n0GzK1YdpLcgCM9Ii3QsWLGHPnlWYacFjga/grQXZTiQSYWjobNy1Hi3rLkQieKcPW4D3U85n+H8c\nYsHXv07vKaekrYH23vf+LUeObEzq7yrMaNwaYD4wA5ORJNHPyDPtTy6WLl0Rr8lpMMlx7757SzHN\nmnBoLUhFUSYyufow1YAFliFMsHMTZqZ4jeu5NTQ3v4Xdu+9jaMgbBImESGSlBzNkvwn4Na9xhBWU\n89jVV9O6ZQutrgDBHTcd8VZHcuG02Q48mNQPbNp0PY888gi33XYXAOeffy6bN2/O7WVPWJzSU2Cm\nShRFKRgiYE2K2F05ihhJLcijgkLMJff29rJs2cfp61tGX98bWLbs42n1Qi+//DIQxuitOoHXgUuA\nDpqb30JfXx/HHjuH1JqNpa5WejGjVxuB84EKHicCmzbBRz8KzzwTt8urXzqMCfjeZm9rMCNeDifZ\nm5f9+x+ku3srQ0PXMjS0iu7uraxcuXI0b9WoKJZGKl3pqXz1VygmvL5CiROUz9Ip8VNWNg3LOgbL\nqmfmzLkeP+inp8yosdy3D5Ysobenh5kz52JZ9UQi09L6nnRtBeU9clB7shNEm3Iil/nKQm5MQg1Y\nU9Nil5Zrh8BmaWpa7HtsNDojRfcVjc7wHOO3RDkUirn0WwtT+oNac/IXvyjyjndI789+lqJfKi9P\nToHh5OXZbOslFtlbLEknFkvpL12m/3xQLI1UoZaKqwZs4myF9l/ZCIJWxr+ckEkgHQqVSU9Pj6+e\nsrOzM73GcnhY5O1vl9995jO++cSSE11n0msG4T1yo/ZkJ2g25erDiu6o0hoWMAc2HlRVzUn5oa6q\nmpNynHFUsZRjk4MZP2diMug7Obz8yndUmZOHhkRaW+X2uW/wCeL88vI4SWCTHaiToLXC97xCBmDF\nQnP1jA8agE1u/MsJOddOvSu5dGoW+rTX1+bNImedJa3Ny8Uvn1iy/9FrVcknufownYIsIENDr2L0\nU87S53Z7X4Kuri7Wr78WkxYiedn0K55h89bWVrZuNYLvlpZtbN3azQ03fI3S0h9gpsLKSF2yfch0\nFA7Dbbdx9oE/s4LfeGwYHh5O8wr8pjyHgd/T2NjAxz/+3pT+zj//XKAwaRrGg5UrV1JSMp2Skukj\nnj4N0lJxRZls9Pcf9N3/nz/5CS+s/gcuDFXx7AvPAjKq9p9//sCE8E3KJCSXaK2QG5NwCtIswa6w\nR4xOEaiQ8vKY5xjv3V6PfWyjPao1I3UI3gdn2bJZjr1ITFbpGvtxrefY//7Wt+RZLDmZr8TbhpDP\nSFckzYhaIoN+c3NzvMZkKFQTH/6fKGka/Eo0pavVmdxfITJn6xTkxNkK7b+yEYSpmtFMQSZKDdV7\n/EdnZ6fcFI7Kd3inPdJVJyYNRW5TkKWlNVJa6lQGyZwaqNAE4TNzEzR7RIJnU64+rOiOKq1hkzAA\n805B7hC/KciqqtmuYzrtAGea7YScIrUdGYfNE/Umy10Oaa39uDzl+H0XXyyPH1Ml73/nMunp6ZHU\nUkQrxEw/1klq/bT5rmCsLt6m+/3Mddh/tHlvxvoZessrie8Uhl9/EyXADHp/GoDlj6D8UDk3Kibo\nqRCok4aGOZ7rxbn+E7VpJX4zGolMiz+/ggullhdc/meh7TNN2aOGhuN8bXD7Fz9dblCmJIPymTkE\nzR6R4NmkAViAMRe7t8ZisgjfaLjq7aAn+W7RCeDqpbFxvm8fJvgqswO3Gp8Rqxp/4z7xCZGPfERk\neFi8xbh7JLWIrVNbrTopAJvi23QuAVhPT499N7s5fmdbqDvSXAMwB9WVjA8agClu/LRfsVijiPhf\nc8m1HUdyDeq1q4wnGoAFGL8h+OTpKuMQnOLXyQ5mavxxVdVs3z4g6urDr+h2mgDs1VdFmppErr9e\nTDZpv5WUThuJkbjEFGS9RCL+becyQuStAGD6a2w8Y+Rv8hjIdQrSQZ34+KABmOImk79MnUqcKqWl\nNa5jp8Qz4WciuZ1IpE4qKxuKXoRbmZhoADZKCjGU6f2h3uH7Q51wCH4BWF3KnWAy3vPcDsyZgiyJ\n95Myzbd/v8i0afJXVElCO+ZXBikRdEFDPBiLRhvidiS/nyOdVhztKJRfn6PB0bBFItOyBl/uKUjj\n/BcKLJTS0ppxHbUrVnknnYKcOP4rG0GbqhEZmU2ZtJXJPqWnp8e+gauxbw79b3KTcdqZObNRvBKL\n7Ofmk6B9ZkGzRyR4NmkANkqCEoCJGIdQUuKXi6s+q2OIRJJHvZx8XSb4ikQqMo9I/exn8ieQ6VTa\nz3f42OFMQVa4HF29RKP1cTtG+35Go1PFaNCc/molGp06onPH4zPMRX/mDcCmxm0uLZ06boFSLvVD\nxxsNwCaO/8pG0H6oRPJjU6Zpy2xUVc0c9bn5IGifWdDsEQmeTRqABRijbzrGDmBmSSRyTNof04aG\nBkmsmHSCnXDWoXHvsH1HUhvVEosdm3XK7MuUy05OljCH7eedKdFZEgqVSVPTYnukaoW49Wzj4axi\nsakCYUnkHQtLLDayAGysjFZMn88pyKNpelMDsIlBupsUZ39T02JpbJxnj1xNl3B4qoTDU6WhYY40\nNS2SWGyGfW3XCpRLSUmlRKPOSu1K22dNEaiVcLjEPrZcFlIpq4mKWe1Y6zqu2n7s7Cu3H1fb7bkL\ndVdKKFQnDQ0nSVPTImloOElCoSliWbWSkF40iBn5j0k4nLpoSVHSkasP0zxgBeSee+5haCiMKS3U\nydBQmHvuucf32Keffh34DvAre/sOMIUXXvhDxoLX69ato7PzMmKxq4DvAhWYckafBko5ePCVrHZe\nSZTXKOFqPm/vmW//fQvDwxdRX1/HlVeuAe4CnrK3G2lvX5W17Wz0978MHIMpn7QROMbelyhjUld3\nIl1dXWPuK5kNG25mYOAanDxnAwPXxAuWK4pi8vktX95ml1NbxvLlbfT29nr279mziv37n6S/v4z+\n/gGOHPkaR458jaefPsiePf9Lf/+rmGv760CIw4dDDAxcC1yPKaUWAb4BfJ0jR6LAKYQp4UZqeZk2\nIArMw/i2b2DyEVYAn7D/huzH3wTK7cdR4AhQzvDwBp5++gvs2fMwTz/9foaHSxBxjjkZ+AuwAdjI\nkSOltLS0FOKtVY5GconWCrkxCacgvcPjOzIOcftrwGK+x6YjFKpL6S8UqssqPIVSiVEpj1En53Gh\nJHLxJMStsdixkjw12dzcHO97tO9nutc9kgUMufaZfCef62hTIdJQ6BTkxNwK7b+yMV6fZbprxH9V\nop9+1J2tfof4L/JZmPT/NPkM58t23iUwHN+Xet55rvPP89k/K8M554nRyfq1W5f9jckDQZteC5o9\nIsGzKVcfFilm8Kf409vbS3n5IK+9tsa19wIgQknJdM4//1w2b96ctR3LGgb2ASuA54C3YFnD8Qz6\nGzbczKOPPsr+/QO88soGANavXwNE6GeYvybMz7mR31HK7/kU0ArAK6+0Y4pxfxozWmTYvr1jzK89\nFAqRnIg/FAqxceMmEln4DRs3XsW6devo7e1lw4ab6e9/jq6udbS2tmbtx7ljNyNesHt3G+vWfYbd\nu9cyMGCOMRntu7O25X4/ATo6ukdkw0hwt21e3/i1rSgTgRkc4Yv8lLfzG8AqtjmKMn7kEq0VcwDz\nKAAAIABJREFUciNgd5DjwUhGcbwjHvNs/UKqIN+dZT6daNybksIR0Ec9x/jXZ0uMQn2K78o+jpUK\nliU973/HO9okqg7pUkGkE9fmoqtzk+5Ofqz2K6MHHQELPAn/1GGPNNVKW1ubz/5jxKTBca9IrJBE\n/djkfYn0EcbfvVHgNIEa+SHVcjWlktC11ojRacVc59Xbz9VL8uKgxEKicvHmNHSf4/xdlOJ/3CP7\nipKJXH1Y0R1VWsMmqQPLVrJmpEP5TkboTFNfI5nG9A/Aal37huWfOVVuIyrwVkkIW3vsx4lFAk1N\nTeMyFeeXCiJd8NrYOC9lf2PjvKx9HE3i9omCBmATA7+bpM7OTuns7JRQyKmi4U3ebFmOYN59M1gp\nJmm0E6idJonyROb8Um6RH1AiFdRJ6o2oE7xV2207wVeZ7cOm2IGcs4ipXKBKoFZisbnS1LTIFv9X\numyoFUCcyh8afCm5oAHYKAlKmZdcArB0QYQT5Hkz2u8QM2o019OfX2BjsuknVlKWUyX3MUcu4nx7\n/1RJTk9hWVOkqWlRSn/jGdT4Ba/evGE74u9NNsYjd1dQvjOTpT8NwPLHeH6W6UajE/4o1S/5nRMK\nOYlTpyWd5+cDzxN/vZifzqwuzbHTJPlmy89/QH0gbsaCpm8Kmj0iwbMpVx+mGrCA0dGxmt2722wd\n0j5Coc3U1FTS33+B66g1nH/+cp566lDK+Y8++ih9fdsxeql9gKMjexD4LnPnngoQ100BtLUt5847\nrwKgvf0yHnnkEeB1YD3wGq/xLVZwNr/ibdzLZ3g49mMGBm5jYCChyRKBhx66fFzeg66uLlvzBe3t\nq+KrPtetW5eyAjQaLedQ0tsQjZaPsKcSjI4N4HOjN1hRFEVRciWXaK2QGwG5gyyGJqinp0eamhbZ\nw/lmhCkcrpVQaIpnWs5vCrKysiHpzm+FfUfYKLAi/joyTRWGQlXiV4rovdwpf6JW/vod7/HNWB8O\nTx3zFGS28iPJn8VIdHV+JEo+JfKYBeGu92gGHQELHN7C1U22L0nVpFZWTrOnGb1TiM7zkUilp8Zr\nQpNVLQndVbIeK1mrlawXqxYo9dk3zz42uYbtohS/5DedGgqVqf5TGRW5+rCiO6q0hgXAgeUzvUC2\nfv2G7CORaSnaseSgxHteaiHttra2rPqn9OWMNsuXKZWdoYiEqRSvCDYmlZUNYw5Yq6rmSKIM0jSB\nRVJVNSdttvnRivDNdKnXyTc1Lcqq0VPyhwZgwSJ1QZBXfxUO14rRTCXK/pjgbKHAXPv/mKQK7mdL\nouRPhxipRIkd3DmarqjdlpOctUoaGo6zAy6n3xWufqfYx061A7sKMfqvWfZzYWlsPMPXL7W1tUk4\nPFWgThoa5mjwpYwaDcBGid9ccj6F2unmrhPaJL+cNafFHU66USHviJBbB7FDUrUa6QKwatfz3pGi\nEJdID1PkGqokOVN/U1NT1teXDSOgTb6jNdn3k21ualo84vJOyfi119BwUkrfmYKwya7JUg3YxPFf\n2RjNZ+m9tvy0VsmLfNz+Jp1ma5YkNF87fM4TOZN/ktlMsY9NnGtuLhem8Y3O/vPEm2vMPD8SXWjQ\n9ERqT3aCZlOuPkwz4QeMz3/+KgYHI8BHgEuBbnu7FJiC0Vx9k2uu+a5vVuqzzjrLlQn/ERJ5wL5o\nPzY6s2h0bbxtk+9qtcuKQYx2rBuT5X4+sAXYwjCncz4lfJi/sJxm3Jn69+37c9rXtXLlSkpKplNS\nMp2WlhaWLl3B0qUr6O3tTTryGBL5vtrsx8fwxBNPprTpt28sPPvsiyl9O1o0RVGSGQS+CswE5gKP\n4fiY9LxqbzcB/2vvO2j/v4Iy7uRH3MSpHLaPOxl4O3ATBw++mKbNfcCTwGvAfwHDKUeICAsWvJ26\nuhNZsGCJj99RlCKQS7RWyI0A3EEWYwoydQpxoX336dRdTNzRZdMxGX2Dd5RqZPnDYnZ/jWLy7VSI\nd0RqnpzFF+VZLDmJWzw2+bXrp7Pw02OIiIRCqXevoVC9PWXonfJsalo06s/IbwoyFJqS0ncxi/Ee\nbaAjYIEi2xRkYkoxWWvVIQnNVra8Wys87V5BhWwhnORzal3tuft1pjD9fEvyvhKPLY6EQVHGk1x9\nWNEdVVrDAuLACi3C95sacwppJzQP9dLYOD+tjsmhoeGElOcbGk7IakOq44zZTs0J+Mxy7tW0yT6i\nUsF3xUlf4RcM+Qn2/ZaEG5vnpDjPhoY5ow4m0+EXvPrlFFMdWOHQACx4+Ivw6yQWm+u6Fv2mJhcK\ntEkiYepCMTeUzjHnuY415x/PfnmOSplN8kIi9/H1YrRdMdfmd2ynJKY7Z/naqYtulPEmVx+mU5A2\nO3fu9N3f2trK3Xdv4e67t4xLCZje3l6WLl3BWWe9w3cY/OqrP09p6edITD2uBa7ETI39GriJSOQw\nN9zwNUzR2utITJldZ+8zPP30S67n5wLX2fuyUZrU7kZgOmYacn78qJup4x6OcAufofndb8ayql3F\nrOeOqpj1aaedZfdxmb3N57TTzuLOO3eTXJzc7EvQ3//ciPsx07A/BJYBy4hGf8gNN2yMT9/GYlfR\n2XlZxsLn6b4z+WKy96fkj9F+lm7/d9999yHyPCLPc+aZZ2Y4qxaT3mUzRsLglC1L9p8PEovV2o+F\nb7KG6ziHP1GRoe1y4HLgBXs7Kc1x64BOzPTlrAztJQja913tyU4QbcqJXKK1Qm4EQIQ/3oy0sHJi\nNaP3rtER0DvnZBPTh8OpxbjD4eyFZf2mARN3kM4Qvxn6j/Jd2cNsuaSkKm0iVm9iV/dS8c0SiRwj\nVVVz4qsO000pZipFlFgduTanqYWxrnic7KJ4FeFPHP+VjfH+LBOLhZKnIB35QvJ0Za3rfzMFGYlM\nkc7OTolGp8vJfEX2MltK4nIL9/nOFGS1pI7OV4hXmuDMFLjLIdXKSKYggyboVnuyEzSbcvVhRXdU\naQ0LmAMbD3JZVTkSbVO2Y9LVVXTOTTdt56/ZqrQdWIkklneb13ICf5ADVMmHjn1DynmdnZ326/am\nlojFGtNO+eWS7yvd6shsFCvFiJIeDcAmFk6+wsrKBqmqmiONjWdIU9OieDWOpqbF8eu8sXG+VFXN\nlmi0QSorG6SpaXH8enOu99kz3iCh0BSxrJidN2yaXSqoSqBOGhsbJRqtt32RKTXU2NgolZUNdg7C\nGdLQMEcsy6k16dWmNTSYGz1334oynmgAFmByTWsxEm1TtmP86iqOJHdWY2OjJDQW88Q7GpaqvXgv\nn5UnQ2GZyj9K8qKAdK/bjGp5dViZRO9mJM1oUJwabelGxrIxlhQjRgtj3gN36g1lbGgApoyVbOWQ\nFCWf5OrDVANmU4i55MWLF5BI73A5sMbe50+u+rN77rknJb3D5s2bOXz4AH19/8rmzZsBuPDCdoaG\nwhiNRCdDQ2EuvLA93s7KlSvZv/85jPZrI/AM4NarnQSscr2Wbn4R/RF3TW3gx+wkzL8Cn8HRi6VL\nezE4+Kq9b5m9dTM4+GpcJ+d+HV1dXWzf/r/ABmAD27f/L11dXcydOwNod72n7fa+BF1dXdTVnUhd\n3YmsXLmSpUtXcO+995N9yXwqCxYsYM+eB4AKIMSePQ+wYEH6z3A8UQ2YMlqC+FkGzSa1JzNBsweC\naVNO5BKt5bJh1JK/BvYCDwBX2/tjQB/we+BuoCbN+fkLU33IlBh1vFZBelfenS25lL/x0yt5p9G8\ny7GTp9Tcr89kffbeHYbDU13P16WMTCWSwNZLQpfWIRCLvzc9//Ef0mdF5GpmCpziKXDt9z42Np6R\n0k9Dw0k5acC8qyNPEffqSOd9S51OdWfQ7shpCjJRPsVozpySKoVANWAFH8UatQ8rtP/Kxmg/SzPN\nuNieunMqRUyNjwCHQmX2tGGtva9cTOb5Ka7HJqN9KBST8vKYVFbWCtRJKDRFmpub7RWWi+KJlTP5\nDDd+o/udnZ12CbfUKchsOs+g6YnUnuwEzaZcfVi+HViF/TcC/A9mScq1wGX2/rXAV9Ocm6/3aMSM\nt05otNNe6fRP3vZG3na2AAyfMkNG0OoEZonz3Bmme3p6ZKoVlccJyweok1CoIuP75ZdGI7WWpXu6\nMjUAyzYF6fe8yW+WODaX4Np/2XtsXAL0ich4lm4KWgAmY/BhQfBfYyW5/Je5VkOSKrCfIm7f5C1N\ntCIlEHJyfNXzTUksyEkcE41Oj4vzc9G3JtLgdIi5IauUaLRBy4opBSNQAVi8EzNf8xvgVOAhYLq9\nfwbwUJpz8vQWjZzxLkU02oAuXZAxkgDM7wfST/ze2Dgv3p+pqZYcZNT4OL0KaWg4KR58OO2+mS/K\nAarkDRzjaTcZPwF9VdVs8Usumy4IHVsA1jGKAKzWp72anD7PycJoC6GnI4gBmLPl6sOC4L/Gip//\ny1x+yDnmPPFea6krqqt4Sf7EsfJGviJ+ZY78rlu37/XPLZjajub6UgpJrj4srxowy7JClmXtBQ4A\nO0Tk/2zHdcA+5AAmwVTRKcRccmtrK1u3dtPSso0zz/w+W7d2jym3mFdbdTxuTVY0upaZM6tYv/5a\n+vuvoL//Q6xffy1dXV3ccMNGLOt1THmjS7Gs17nhho3xdsPhkpS+wuES/vznPwMD9nlrgAhPP/2F\neBmkxx57Fvgmv+FL/D1/zxZqefaxZ9PaX19fl7Jv2rQa4BYSurBbWLx4AevWrfPN0dXevgq4AHgb\nMA+4wN5nMI8T74t5fIb9Gm6hv/+KuP0jKU/S3HwmyTo+OAtoG1Xes1wImgbMlGma3KWbJpIPy0TQ\ntDJXciXf4jQeYmaxTYkTtPdI7clOEG3KhUj2Q0aPiAwDZ1iWNQXotSzrnUnPi2VZku78lStXctxx\nxwFQU1PDGWecwZIlS4DEGz9e/+/duzfl+ebmt7J791oGBgAepLT0Zjo6fjSm/lpbW2ltbeX666+n\nrKws/loznd/evor16y8AHgROAdbwwQ9+iLKyMrZu7WbDhpvp73+O00//EH/60zYAmpvb6ez8Bokf\nyOuBf2Tjxk20t4NIGPgkcAoia7j99tspKytjyZIlTJtWxdNPr/H0Z1khtm//NSbguA54B/BXdtsw\nMPAgJlGq4U5mM48abpRHQISdu3ZlfX8jkW/z7LN1ts1z7Za+ya5d21i0aCeLFi2KJ0bduXOn6+KL\nAIuBPwJ/9rx/zvHXXPMFAM47bzlPPXWI//mfH3Ho0D967F+3riseEKf7PPr6+mhpaWH79jXAYUzg\n2wfstN+v7J/naP/fu3dv3r7/o+nv8OEBEuT++vfu3cvBgwcBePzxxwkiY/FhhfRfo/Fv2f5vbn4r\nu3Z9jsFBMJ/tjcArGB/gfNa/BS52/X8j8CnMzcm3gHMxNzuJ509jkOO5nys4x25rlqvNU4hG1/LB\nD76XH/7wErtvKC29hObmy3F497ub6O29gAQXsGDBG3nwwdH760JfX2rP2P93KGb/O3fuHL3/ymW4\nbCwbcAXmSnwImGHvayDAU5AihS9FlI7RaG2i0ZkpQ/LR6Mys03ZGm1VtTy+8MWmayRHhL06ZKiwt\nneI5NkqVPFBaJvLtb6d9H53XVVnZIJFIne+URqZphJGkofB778ZjevlozyV2NE1BSo4+LCj+a6yM\ntwg/WlYr/x0Kyz9wjITDU8ddhB8Uf60cneTqw/LprOqxVwcBUUyZ+ndjBKxr7f2XE2AR/kSnvDyW\n8gNZXh7LGrR4V2v6azhMDjFv27HYdIEycfKLQZl8+5JL5LUpU+QdZYlM2E6g4g1gnMCrRyAR1GTL\nbJ/ttaQLEsYreDjaHf5kFuGPxYep/0rDbbeJnHWWyNBQsS1RlHEnSAHYfOA+zBLu3wKfs/fHgO1M\nkDQUE7k/E5yssIOomQIr4j+UmYIP7/Ppiu2mrgY0qyu9aTaamhbLFacvlD8Sk6kc8Iw2pV9E0Bzv\nw7JKMgY2XlvXprwW8x6UuWwui9/Nm9VYTrBY4SlkPhIm43emmP0FMAAbtQ8LWgA2tjQUTuWKRKZ7\nv1HsqqrZ0tg43/dmxLlRef+7lsnOzZvjNjn7GxrmSDg81TOalcmmfNz0BC2lgdqTnaDZlKsPy5sG\nTET2ASkZKkWkH2jOV79KAqMduxajqTIajvb2RIHpjRuvso/zFp3etes+jI5jGxDGJDo1lJZ+jlNP\nPYWHHnrU1lokEDmSYsMTTzzJ/5x5OuXU8698hFZ6Oexr7WrgYxgB/j7bZhBZw6pVq3nqqSfo7e2N\ni9w7OlbT2trqeS2HDw+wdq33tfT37weqMQllAdbQ37/fTgJbgUlGC3ApjzzyaJp3UjkaOdp9WG9v\nL8uWfZTBwQhwHf39YHzBQnbvbmPr1m7uuecel4+BQ4cuZf/+pfHnW1tb6e3tZflys0gFYPuv1rJ1\nxgzuv/9+rrxyIwMDJwIH4210d68BiCeOTrbJ3Za7H0WZcOQSrRVyI2B3kBOV0UwRpdZunBevoWZK\nGC0Uk5i1wjWKFpOSksqUkbXGxnnS09Mjx5RPkztoks0skmj5NJ8pyM12cV+/PFt1o9ZbpcvbVVU1\nJ2V/VdWcsb7dyhggYCNgY9kmg/8yfiBdmon0+fnczyfaSdVbJvanppRw5xdMtUlTTSjBJFcfpqWI\nJjnr1q3jhRf+wAsv/MEzMpQJkZcxo1DX2tuTLFhwPDDE0FAp8GmMFrkU+DxmpGwVkUglyWkJoJTW\n1la23PEDvveu2by1+gH2LX93fDWok5ajpWUb27b9mHA4nGJPOBxiw4ab7bte0/ZYUz6ceOLxI9qn\nKEc3z6V95vnnD/Dyy4eS9t4J7ALa2b69h66urnwapygTm1yitUJuqAasaP35JTmMRKZJNDrD527X\nyWBdLZGIO8P+DnFWXXo4cECksVHk5pt9+zYFt71CfmelVLY7X7/XWFmZOipXWVmZkuU7m9jfD3d/\nfoXCx5sgf2fGA3QELG+M9LN0j5ibovMV9jXuZJevFVghpaU1EolMEaMvjYlZLb0o5VqDMmn7u7/z\nZKi3rFppbJwvsdgsMRU2nEobiQz66a6hfK48DpqeSO3JTtBsytWH5TUPmDK5GBxM1XjBMHAV0MLQ\n0M8w+XzA0ZwNDAx6D582De66C84+G2bNgnPP9Tz92GNPAWUktFlreOyxp7jhhkvZvbstrjszBb27\ns9p86NAhqqqqeOUVo2OrrBzm0CFz175t260uTdmto9aRmLxg/4ujYdm+fQ0tLS309fWNqj1FKQZd\nXV0ePVd//xpMHq8mYAPwdQBCoUuoq6vh6adfxmTmADMi/kcgkVsPoJ7P84//cjtvXLeWL3x5AyKn\nIXIy+/c/AJwD/MI+vhuTQ6wEmI9lVfva6IyaJ65b1X8pExfLBG3Bw7IsCaptk53kgAIuIBabyksv\nvcKRI4dd+y+1/15nPz4M/D3wmL3/eOD7iLyY2smvfgXvfz+0tMB73gPnnANTp1JSMp2hoWtJOPFu\noIOWlsUsXrzAXiCQEOEHAcuqx/xAeW0Web54Rk1ALMtCRKxi2zEeTDT/1dvby/ve93c+19564C2Y\nazlxXYfDP+DIka8lHXsVMBX4FdALXMr3+D0vM0w75RjJwgzMopjf248vw0gYlmF8yLDd3iu0tf0N\nmzdvZsGCBezZ84S9/yDhcB3HHXcsN9zw1cD4AEWB3H2YasCUFMzd53yMc7wYKKW//0scObLBPuKr\nwE3Aq8BnMU74OsCyz9tib/OB1B+hrq4u6t73cU49Usl/vPYabN0KJ54Ib30r/8QAZ/EoVtwRA4Tp\n61tGV9e36OhYzd13b8nJ8ba0tGBZ9VhWPS0tLTm+G4oyuXFWFhp9J0AXphLFpcDzmIwb3STKg33P\nvhFL5nngXvu8v+VtfIBzqOCfqMb81KwCngQWYVYl/xmjNQWz+nnQPuYkoILu7h8SjUbZs+dxzIrl\ndwKVHDnyDvbv/yzve9/5IyofpiiBJZf5ykJuqAasaP15i2T7FeStt7cVSfsdvYiTk6teIOpp2y8H\nWXl5TKbXniC3rlolt0yJyf8Rkmeols0skg8TlRpOHtGKJ7/XaLRZ3v7GS6Pl9JfPPvz6KxSqAZs4\n/isbmT7LhL6y09ZfJuu4pvj4gDe6rnXHJ1SLyXofkzDflz2cLh/lXySRT9DpxynWvdbWf3W4/k5P\n6rsi6X8nr2F2fzCe71ExUHuyEzSbcvVhqgFTfBgiMb34lM/zUzD12/owd8ZGkzUwUIapyXgVpmj3\nYmAHQDyH144du4EW+xiAFl577de89toX+fimNTQ2nsD+l97JcfyGc3mYjzGFW9jP/ZzNz5nBi4cO\nGt9rjWyUd/v2PSRWZjr7Okb+VoyARH1I025z81tU/6VMQNZh6rl+Bff1kvAFbuZhcvddCTwC3AY8\ng8kTFuICfkE/MX7MR4EfZOjzCLAJM1LeCzgrnR1uSvp/PUYjqiiTgFyitUJuBOwO8mjC3BE7d5qp\n5YzMcyafVig0xZVdv9zn2PKklUvVPsfE4ne0lZUNnlVOUC1lXCxL6ZBvh6Pyl4YGkZkzRT75SZEt\nW0ReeinjazErE1Pzio03ueZbO9pLGPmBjoAVBe/1mW6ls189WOf5aa7Hpwl0yHuJysl8Jen8Dtdf\n59qvdLVb49P3wqT/a+P+JxKp02tHCRS5+rCiO6q0hk0gBzbZSC1F5C26nZhCcBzuZtuBV/s40Oqk\nFBKpBcLNPhHokEhkmqcwb2dnZ2qg8vvfi1x/vUhLi0hlpTx/+uny3TecJp98W7P03HWX57WM1/Rg\npoDJb1q1sXFe2uDqaC/inQ4NwIqH+Q7XiZnyS00lYYKe8wTmSuq04KL4DVkiMOuwg6VaO8iqtJ+f\n5/Ilb0zyBR1Jfdf59IWEw1OlsfEMvWaUwKEB2CiZ7PqaXPpLX6PRCZjcAdhi12O3VmRHfJ+3Pb/M\n2bOSnG+HhEJ10tS0OKuT7bvjDllRWiPf4Z3yI6rlcSskT7zvfSJ33inyyisi4s3R1dDQIJHItLQ1\n59ra2lKeTxcwOe+pfzbwWWmDq9Fm8w7yd2Y80AAsf7jrLibfGLS1tdnXbrWYUagVAnPEjGzNkoTW\ny/m+zpNEbdWQfU6tfQ27r4GYNDY2SigUdh2PGK2Zc9Myy37snFMvMFXMjV+P/dwsu615eX+PgoTa\nk52g2ZSrD1MNmJIFp0ajwxpMnchu+3E5sAKzTP2Ive8m4CXMKqdhOjpWs2PHRxgaugl4nUSuMNNe\neXmEoaFbGRr6JmZp+ucYHt7Anj2wbNnH2bbt1nhNueRakNfe8AP6Bq9nC23ADubJr7j44R+xeuNG\n+Ju/gUWL6Hv/++HGG1nZ2Ul391bS1ZxbuXKl7/NPPXXIlYUfBgZgw4ab+cIXPgPA4cN+K8LKMBn7\nzbG6XF4pFr29vVx00VoeffRJhodXAvP5z//8G04/fR5vetOJnu88XIDJzXUyZrXiJuAQRtt1k73v\nWcxqxe9hrv9TgT0YnzDfbuezwCfZv38DybVYjY6rGpMz7BR73x6MpnQQs+LxIfv/+cDLhEKvc8MN\nThuKMknIJVor5EbA7iCPJvxqNJqVkXWSmIpYJIk6i2Z6IBSqTtoXk0ikxmeKrkyi0ZkevVRiVGix\nJPRnjQIrpKpqtjQ1LfJkrndGltKNJvX09MgH3vl++dKb3ip/WrpUpKFBfk9YrqdFltIjZQyI0ZEk\nas6lqwBg+nBPw66QWKwx3k9j4zxJnbbplHSjWzoF6Q86AjbuJH/XzCrDHknIC9y1UnvEu7KxQszU\nYa193gpJ6LYaJKHfcq6bHvv6WGiPqImkq8Wauq9WLCua5D9q7D5WjKpShaIUmlx9WNEdVVrDAuLA\njlb8pisqKxtsB7xQnCk2txO1rFQRbWnpVN8pulis0dNPU9Niuxj3MT7BTLlvf45tycFMZ2enZ59l\nlQjUyulUy+dZIb9kkbxElWzjdLkwVCny2GMikj4A8waQXp1KNDpdmpoWuYLGmWI0Mwn7/UT5KsJP\nRQOw8cfvBsWbDsJ9XbmP7bGDn2oxOs8ZrsBrrv0dr7X3V8gsNkgHX3P14QjzRxqAxcRfnpBIX+Hc\n9DQ3N2eUEShKsdAAbJRMdn3NePRntCJO8HFaFse6Ix7ApAvAUkfapor/Sqha8VsM4IwsOcHMmWee\n7TMq5hbhJ2rV1fJt+QhR2X3CCSJTp4rMmyc/P/VUWUKFlPC9ePDU1taWQRNnXmMieHQC0xW+do6V\nifidyQUNwMafxHd3R1JQ44yErXBdHwuTvudvFO+IlLOasUKSxfE/IST/xAfi/xsd12YBJPWGytm3\n1rWvIs21784ftjDJ3sQ1Oh4ETU+k9mQnaDbl6sNUA6aMmKeeOkQip9YtePMDXUokMsjQkLcW5NSp\nMS68cBXr13t1X7W1c/nbv72QgYGPYUqRwODg32E0J8lYwPuARJ06WMPixZcBpj5ca2srO3fuZMmS\nJXGdmMGdB6wNeDvQzqFIhPLzP8yizZtheBjuuYdzf/5zTjpwA3XPf4pfWKUcfNuZfKKri6Wr3Lan\nowT4dPy9gB8CrRhdzGMjOF9Rxp+OjtV2DdWVwBMYvdURYDZGp/WMfeRnMfor57v+FPAKRrvV5mrx\nJtdjs7+V33IG37CVotswGtFNQDtNTU3s2bMHoyEDeBmjGb0DuAFTnugVTG7BTwBrXe1fjMkPtojE\nNXUhyXn9brvtMmwZp6JMLHKJ1gq5EZA7SCWR48pM0TkrnRanjEiVlk5L2dfYeIanjaqq2RKJOKsl\nU7Nph0J+ucRmCJyRcnfstJ2Md2TNb7ojfR6wzs5OOalmrnz6mGnyu/nzRWpr5aUTTpBrIxWyiC9I\nmEs89oVCFXYfJZJY6TUnPpqg+q6Rg46A5QVnVNhcv/X2d/Q0n+usQsx0f8w+Lt2IlLOJlDEgjzBN\nzqEu6bh6zwh1Y+MZEolMk/JyZyWk36iYV0cWCk2RpqZF9gi643dSR9PdOk5FKSa5+rDnDQl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fxXepbzp9ai+yH/8i/dlJWVsWTJkpztnXRUVsK7311sK5SxcvrpJj1JdXXeumhvX8X69U7euweB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\nnT3ozTrja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"text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Both quadratic model and MARS are evaluated on the test set." ] }, { "cell_type": "code", "collapsed": false, "input": [ "X = np.linspace(np.min(cars11_feature)[0], np.max(cars11_feature)[0])[:, np.newaxis]\n", "\n", "fig, (ax1, ax2) = plt.subplots(1, 2)\n", "\n", "ax1.scatter(cars11_feature, cars11_target)\n", "ax1.plot(X, quad.predict(X), 'r')\n", "ax1.set_xlabel('Engine Displacement')\n", "ax1.set_ylabel('Fuel Efficiency (MPG)')\n", "ax1.set_title('Quadratic model')\n", "\n", "ax2.scatter(cars11_feature, cars11_target)\n", "ax2.plot(X, mars.predict(X), 'r')\n", "ax2.set_xlabel('Engine Displacement')\n", "ax2.set_ylabel('Fuel Efficiency (MPG)')\n", "ax2.set_title('MARS')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 19, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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Hvffey2mnnaZ6PK3n3nvv5eWXXwbgqaeewkMVyS+ABQsWcN55l7Ju3TcAuOOOz3DxxWfF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\n+yxsUns0TpcMFqph9UnjdEnNKjTGTVtbG+vXP8X69U9VtFilNQZOuWO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"text": [ "" ] } ], "prompt_number": 19 }, { "cell_type": "code", "collapsed": false, "input": [ "# RMSE\n", "quad_scores = np.sqrt(np.abs(cross_val_score(quad, cars11_feature, cars11_target, cv=10, scoring='mean_squared_error')))\n", "mars_scores = np.sqrt(np.abs(cross_val_score(mars, cars11_feature, cars11_target, cv=10, scoring='mean_squared_error')))\n", "\n", "print \"Quadratic model RMSE: {0} and MARS RMSE: {1}\".format(np.mean(quad_scores), np.mean(mars_scores))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Quadratic model RMSE: 4.79365661288 and MARS RMSE: 4.83734524679\n" ] } ], "prompt_number": 20 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first thing to notice is that both scores are very similar, which indicates that either model is appropriate for this task. Also, both scores are lower than their previous values (fitted to 2010 data) as we would expect." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "2.2 Themes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are several aspects of the model building process that are worth discussing further." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Data Splitting" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- How we allocate data to certain tasks, e.g. model building, evaluating performance?\n", " - extrapolation: order matters\n", " - interpolation: a simple random sample of the data\n", "- How much data should be allocated to the training and test sets?\n", " - small data sets: resampling techniques, i.e. no test set\n", " - large data sets" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Predictor Data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Feature selection: the process of determining the minimum set of relevant predictors needed by the model." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Estimating Performance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Quantitative assessments of statistics (using resampling techniques)\n", "- Visualization" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Evaluating Several Models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"No Free Lunch\" Theorem - Try a wide variety of techniques then determine which model to focus on." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Model Selection" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- between models\n", "- within the same model\n", "\n", "Rely on cross-validation and the test set to produce quantitative assessments of the models to make the choice." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "2.3 Summary" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To get a reliable, trustworthy model for predicting new samples, we must first understand the data and the objective of the modeling." ] } ], "metadata": {} } ] }