{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# GLM Model Selection\n", "\n", "\n", "**A fairly minimal reproducable example of Model Selection using DIC and WAIC.**\n", "\n", "+ This example creates two toy datasets under linear and quadratic models, and then tests the fit of a range of polynomial linear models upon those datasets by using the Deviance Information Criterion (DIC) and Watanabe - Akaike (or Widest Available) Information Criterion (WAIC).\n", "+ DIC (`stats.dic`) and WAIC (`stats.waic`) are new additions to PyMC3, so this example shows their usage in a more concrete fashion, also usage of the new `glm` submodule.\n", "+ The example was inspired by Jake Vanderplas' [recent blogpost](https://jakevdp.github.io/blog/2015/08/07/frequentism-and-bayesianism-5-model-selection/) on model selection, although in this first iteration, Cross-Validation and Bayes Factor comparison are not implemented.\n", "+ The datasets are tiny and generated within this Notebook. They contain errors in the measured value (y) only.\n", "\n", "\n", "For more information on Model Selection in PyMC3, and about DIC and WAIC, you could start with:\n", "\n", "+ Thomas Wiecki's [detailed response](https://stats.stackexchange.com/questions/161082/bayesian-model-selection-in-pymc3/166383#166383) to a question on Cross Validated\n", "+ The Deviance Information Criterion: 12 Years On [(Speigelhalter et al 2014)](http://onlinelibrary.wiley.com/doi/10.1111/rssb.12062/abstract)\n", "+ A Widely Applicable Bayesian Information Criterion [(Watanabe 2013)](http://www.jmlr.org/papers/volume14/watanabe13a/watanabe13a.pdf)\n", "+ Efficient Implementation of Leave-One-Out Cross-Validation and WAIC for Evaluating Fitted Bayesian Models [(Gelman et al 2015)](http://arxiv.org/abs/1507.04544)\n", "\n", "\n", "\n", "**Contents**\n", "\n", "+ [Setup](#Setup) \n", "+ [Generate Toy Datasets](#Generate-Toy-Datasets) \n", "+ [Demonstrate Simple Linear Model](#Demonstrate-Simple-Linear-Model)\n", "+ [Create Higher-Order Linear Models](#Create-Higher-Order-Linear-Models)\n", "+ [Compare Deviance Information Criterion (DIC)](#Compare-Deviance-Information-Criterion-[DIC])\n", "+ [Compare Watanabe-Akaike Information Criterion (WAIC)](#Compare-Watanabe---Akaike-Information-Criterion-[WAIC])\n", "\n", "\n", "\n", "**Note:**\n", "\n", "+ Python 3.4 project using latest available [PyMC3](https://github.com/pymc-devs/pymc3)\n", "+ Developed using [ContinuumIO Anaconda](https://www.continuum.io/downloads) distribution on a Macbook Pro 3GHz i7, 16GB RAM, OSX 10.10.5. \n", "+ Finally, if runs become unstable or Theano throws weird errors, try clearing the cache `$> theano-cache clear` and rerunning the notebook.\n", "\n", "\n", "**Package Requirements (shown as a conda-env YAML):**\n", "\n", "```\n", "$> less conda_env_pymc3_examples.yml\n", "\n", "name: pymc3_examples\n", " channels:\n", " - defaults\n", " dependencies:\n", " - python=3.4\n", " - ipython\n", " - ipython-notebook\n", " - ipython-qtconsole\n", " - numpy\n", " - scipy\n", " - matplotlib\n", " - pandas\n", " - seaborn\n", " - patsy \n", " - pip\n", "\n", "$> conda env create --file conda_env_pymc3_examples.yml\n", "\n", "$> source activate pymc3_examples\n", "\n", "$> pip install --process-dependency-links git+https://github.com/pymc-devs/pymc3\n", "\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setup" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "%qtconsole --colors=linux\n", "\n", "import warnings\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from collections import OrderedDict\n", "from time import time\n", "\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "from scipy.optimize import fmin_powell\n", "from scipy import integrate\n", "\n", "import pymc3 as pm\n", "import theano as thno\n", "import theano.tensor as T \n", "\n", "from IPython.html.widgets import interactive, fixed\n", "\n", "# configure some basic options\n", "sns.set(style=\"darkgrid\", palette=\"muted\")\n", "pd.set_option('display.notebook_repr_html', True)\n", "plt.rcParams['figure.figsize'] = 12, 8\n", "rndst = np.random.RandomState(0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Local Functions" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def generate_data(n=20, p=0, a=1, b=1, c=0, latent_sigma_y=20):\n", " ''' \n", " Create a toy dataset based on a very simple model that we might\n", " imagine is a noisy physical process:\n", " 1. random x values within a range\n", " 2. latent error aka inherent noise in y\n", " 3. optionally create labelled outliers with larger noise\n", "\n", " Model form: y ~ a + bx + cx^2 + e\n", " \n", " NOTE: latent_sigma_y is used to create a normally distributed,\n", " 'latent error' aka 'inherent noise' in the 'physical process' \n", " generating thses values, rather than experimental measurement error. \n", " Please don't use the returned `latent_error` values in inferential \n", " models, it's returned in e dataframe for interest only.\n", " '''\n", " \n", " df = pd.DataFrame({'x':rndst.choice(np.arange(100),n,replace=False)})\n", " \n", " ## create linear or quadratic model\n", " df['y'] = a + b*(df['x']) + c*(df['x'])**2 \n", "\n", " ## create latent noise and marked outliers\n", " df['latent_error'] = rndst.normal(0,latent_sigma_y,n)\n", " df['outlier_error'] = rndst.normal(0,latent_sigma_y*10,n)\n", " df['outlier'] = rndst.binomial(1,p,n)\n", " \n", " ## add noise, with extreme noise for marked outliers\n", " df['y'] += ((1-df['outlier']) * df['latent_error'])\n", " df['y'] += (df['outlier'] * df['outlier_error'])\n", " \n", " ## round\n", " for col in ['y','latent_error','outlier_error','x']:\n", " df[col] = np.round(df[col],3)\n", " \n", " ## add label\n", " df['source'] = 'linear' if c == 0 else 'quadratic'\n", " \n", " ## create simple linspace for plotting true model\n", " plotx = np.linspace(df['x'].min() - np.ptp(df['x'])*.1\n", " ,df['x'].max() + np.ptp(df['x'])*.1, 100)\n", " ploty = a + b*plotx + c*plotx**2\n", " dfp = pd.DataFrame({'x':plotx, 'y':ploty})\n", " \n", " return df, dfp\n", " \n", "\n", "def interact_dataset(n=20, p=0, a=-30, b=5, c=0, latent_sigma_y=20):\n", " ''' \n", " Convenience function:\n", " Interactively generate dataset and plot\n", " '''\n", " \n", " df, dfp = generate_data(n, p, a, b, c, latent_sigma_y)\n", "\n", " g = sns.FacetGrid(df, size=8, hue='outlier', hue_order=[True,False]\n", " ,palette=sns.color_palette('Set1'), legend_out=False)\n", "\n", " _ = g.map(plt.errorbar, 'x', 'y', 'latent_error', marker=\"o\"\n", " ,ms=10, mec='w', mew=2, ls='', elinewidth=0.7).add_legend()\n", "\n", " _ = plt.plot(dfp['x'], dfp['y'], '--', alpha=0.8)\n", "\n", " plt.subplots_adjust(top=0.92)\n", " _ = g.fig.suptitle('Sketch of Data Generation ({})'.format(df['source'][0])\n", " ,fontsize=16)\n", " \n", "\n", "def plot_datasets(df_lin, df_quad, dfp_lin, dfp_quad):\n", " '''\n", " Convenience function:\n", " Plot the two generated datasets in facets with generative model\n", " '''\n", " \n", " df = pd.concat((df_lin, df_quad), axis=0)\n", " dfp_lin, dfp_quad\n", " \n", " g = sns.FacetGrid(col='source', hue='source', data=df, size=6\n", " ,sharey=False, legend_out=False)\n", "\n", " _ = g.map(plt.scatter, 'x', 'y', alpha=0.7, s=100, lw=2, edgecolor='w')\n", "\n", " _ = g.axes[0][0].plot(dfp_lin['x'], dfp_lin['y'], '--', alpha=0.6)\n", " _ = g.axes[0][1].plot(dfp_quad['x'], dfp_quad['y'], '--', alpha=0.6)\n", " \n", " \n", "def plot_traces(traces, retain=1000):\n", " ''' \n", " Convenience function:\n", " Plot traces with overlaid means and values\n", " '''\n", " \n", " ax = pm.traceplot(traces[-retain:], figsize=(12,len(traces.varnames)*1.5),\n", " lines={k: v['mean'] for k, v in pm.df_summary(traces[-retain:]).iterrows()})\n", "\n", " for i, mn in enumerate(pm.df_summary(traces[-retain:])['mean']):\n", " ax[i,0].annotate('{:.2f}'.format(mn), xy=(mn,0), xycoords='data'\n", " ,xytext=(5,10), textcoords='offset points', rotation=90\n", " ,va='bottom', fontsize='large', color='#AA0022')\n", " \n", " \n", "def create_poly_modelspec(k=1):\n", " ''' \n", " Convenience function:\n", " Create a polynomial modelspec string for patsy\n", " '''\n", " return ('y ~ 1 + x ' + ' '.join(['+ np.power(x,{})'.format(j) \n", " for j in range(2,k+1)])).strip()\n", "\n", "\n", "def run_models(df, upper_order=5):\n", " ''' \n", " Convenience function:\n", " Fit a range of pymc3 models of increasing polynomial complexity. \n", " Suggest limit to max order 5 since calculation time is exponential.\n", " '''\n", " \n", " models, traces = OrderedDict(), OrderedDict()\n", "\n", " for k in range(1,upper_order+1):\n", "\n", " nm = 'k{}'.format(k)\n", " fml = create_poly_modelspec(k)\n", "\n", " with pm.Model() as models[nm]:\n", "\n", " print('\\nRunning: {}'.format(nm))\n", " pm.glm.glm(fml, df, family=pm.glm.families.Normal())\n", "\n", " start_MAP = pm.find_MAP(fmin=fmin_powell, disp=False)\n", " traces[nm] = pm.sample(2000, start=start_MAP, step=pm.NUTS(), progressbar=True) \n", " \n", " return models, traces\n", "\n", "\n", "def plot_posterior_cr(models, traces, rawdata, xlims,\n", " datamodelnm='linear', modelnm='k1'):\n", " '''\n", " Convenience function:\n", " Plot posterior predictions with credible regions shown as filled areas.\n", " '''\n", " \n", " ## Get traces and calc posterior prediction for npoints in x\n", " npoints = 100\n", " mdl = models[modelnm]\n", " trc = pm.trace_to_dataframe(traces[modelnm][-1000:])\n", " trc = trc[[str(v) for v in mdl.cont_vars[:-1]]]\n", "\n", " ordr = int(modelnm[-1:])\n", " x = np.linspace(xlims[0], xlims[1], npoints).reshape((npoints,1))\n", " pwrs = np.ones((npoints,ordr+1)) * np.arange(ordr+1)\n", " X = x ** pwrs\n", " cr = np.dot(X,trc.T)\n", "\n", " ## Calculate credible regions and plot over the datapoints\n", " dfp = pd.DataFrame(np.percentile(cr,[2.5, 25, 50, 75, 97.5], axis=1).T\n", " ,columns=['025','250','500','750','975'])\n", " dfp['x'] = x\n", "\n", " pal = sns.color_palette('Greens')\n", " f, ax1d = plt.subplots(1,1, figsize=(7,7))\n", " f.suptitle('Posterior Predictive Fit -- Data: {} -- Model: {}'.format(\n", " datamodelnm, modelnm), fontsize=16)\n", " plt.subplots_adjust(top=0.95)\n", "\n", " ax1d.fill_between(dfp['x'], dfp['025'], dfp['975'], alpha=0.5\n", " ,color=pal[1], label='CR 95%')\n", " ax1d.fill_between(dfp['x'], dfp['250'], dfp['750'], alpha=0.5\n", " ,color=pal[4], label='CR 50%')\n", " ax1d.plot(dfp['x'], dfp['500'], alpha=0.6, color=pal[5], label='Median')\n", " _ = plt.legend()\n", " _ = ax1d.set_xlim(xlims)\n", " _ = sns.regplot(x='x', y='y', data=rawdata, fit_reg=False\n", " ,scatter_kws={'alpha':0.7,'s':100, 'lw':2,'edgecolor':'w'}, ax=ax1d)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate Toy Datasets" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Interactively Draft Data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Throughout the rest of the Notebook, we'll use two toy datasets created by a linear and a quadratic model respectively, so that we can better evaluate the fit of the model selection.\n", "\n", "Right now, lets use an interactive session to play around with the data generation function in this Notebook, and get a feel for the possibilities of data we could generate.\n", "\n", "\n", "$$y_{i} = a + bx_{i} + cx_{i}^{2} + \\epsilon_{i}$$\n", "\n", "where: \n", "$i \\in n$ datapoints\n", "$\\epsilon \\sim \\mathcal{N}(0,latent\\_sigma\\_y)$\n", "\n", "\n", "**NOTE on outliers:** \n", "\n", "+ We can use value `p` to set the (approximate) proportion of 'outliers' under a bernoulli distribution.\n", "+ These outliers have a 10x larger `latent_sigma_y`\n", "+ These outliers are labelled in the returned datasets and may be useful for other modelling, see another example Notebook `GLM-robust-with-outlier-detection.ipynb`" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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KJiIiIg/jkpATHh6OsLAw+78DAwNx6NAh+/6KigoEBARAo9FAr9fX2U5ERNSS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\ndjpHfzpHfzpGbzrX40dygJ6kvVGXYCiqX/3XQe0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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "interactive(interact_dataset, n=[5,50,5], p=[0,.5,.05], a=[-50,50]\n", " ,b=[-10,10], c=[-3,3], latent_sigma_y=[0,1000,50])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Observe:**\n", "\n", "+ I've shown the `latent_error` in errorbars, but this is for interest only, since this shows the _inherent noise_ in whatever 'physical process' we imagine created the data.\n", "+ There is no _measurement error_.\n", "+ Datapoints created as outliers are shown in **red**, again for interest only." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Create Datasets for Modelling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use the above interactive plot to get a feel for the effect of the params. Now we'll create 2 fixed datasets to use for the remainder of the Notebook. \n", "\n", "1. For a start, we'll create a linear model with small noise. Keep it simple.\n", "2. Secondly, a quadratic model with small noise" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "n = 12\n", "df_lin, dfp_lin = generate_data(n=n, p=0, a=-30, b=5, c=0, latent_sigma_y=40)\n", "df_quad, dfp_quad = generate_data(n=n, p=0, a=-200, b=2, c=3, latent_sigma_y=500)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Scatterplot against model line" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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v5tFHH+VXv/oVtbW1bNu2LcuViohkX0NznP2HExgw4AMWKGSJiEiOmjJlCvfeey8An376\nKfn5+WzdupXKykoAJk2axLp166itrWXcuHE4HA78fj8jRoxg27ZtbNy4kUmTJmXuXb9+PaFQiEQi\nQXFxMQCXXnop69aty06BIiJ9hGVZ1H7cCkDFCG+WW9M3KGSJiEjOstlszJ8/n/vuu49vfvObWNZn\n6wV8Ph+hUIhwOEwgEMhc93q9met+vz9zb0tLS4drR14XERnIGg8k2HcoycgiDwV+rUYCrckSEZEc\nt2TJEvbv38+1115LLBbLXA+Hw+Tl5eH3+wmFQke9Hg6HM9cCgUAmmH3+3uMJBgPHvae/ybWacq0e\nUE39Qa7Us2b7XtweJ+PPCRAsdGW7OX2CQpaIiOSkl19+maamJm688UZcLhc2m42xY8eyYcMGLr74\nYt58802qqqooLy9n6dKlxONxYrEY9fX1lJWVceGFF7J69WrKy8tZvXo1lZWV+P1+TNNk586dFBcX\ns2bNmhPa+KK5ObdGu4LBQE7VlGv1gGrqD3KlnrRl4SBF0G8wpNCVEzW1O5UQnLWQ9fd///eZKRfF\nxcXMnj37hHd8EhEROZ6vfe1rLFiwgBkzZpBMJlm4cCEjR45k4cKFJBIJSktLmTp1KoZhMHPmTGpq\narAsi7lz52KaJtXV1cybN4+amhpM0+SRRx4BYPHixdx+++2k02kmTJhARUVFlisVEckem2FQdY6/\nw3RsAcPKwr+ReDzOd77zHV566aXMte9///vMmjWLyspKFi1axMSJE7ngggv43ve+x8qVK4lGo1RX\nV/PSSy/hdDq/8P1zLUHnUj2gmvqDXKsHcq+mXKsHcmfazNHk4meVSzXlWj2gmvqDXKsHcq+mfjeS\ntW3bNlpbW5k1axapVIrbbrut045Pa9euxWazddrxafv27YwdOzYbzRYRERERETmurIQst9vNrFmz\nmD59Oh9//DH/9E//dMI7PmkXJxERERER6cuyErJGjBjB8OHDM/9cUFDA1q1bM68fb8en48m1KSe5\nVg+opv4g1+qB3Ksp1+oREZH+oyWSIuCxZ7sZfVZWQtZvf/tb6urqWLRoEU1NTYRCISZMmHDCOz4d\nT67NBc2lekA19Qe5Vg/kXk25Vg8oNIqI9BfhaIqX1v2V0iI3l56nv91Hk5WQde2117JgwQJqamqw\n2WwsWbKEgoKCE97xSUREREREsmPzJxHSaRicr9OgjiUr/2acTic//elPO11fvnx5p2vTp09n+vTp\nvdEsERERERH5ApF4mu27InjdNkqL3NluTp9ly3YDRERERESkf9jySSupNFSM8GK3GdluTp+lkCUi\nIiIiIscVS6T5YGcUt2lQdoZGsb6IJlKKiIiIiMhx2QyDirM8uJ02HHaNYn0RhSwRERERETkup8Pg\n/LN82W5Gv6DpgiIiIiIiIt1IIUtERERERKQbKWSJiOSA+j1RUmkr280QERERFLJERPq9tGVRvyfG\nO3WhbDdFRERyTDJl0dAcw7L0IO9kKGSJiPRzNsPgsoo8Ks7yZrspIiKSY+p2R/i/mw6zpSGS7ab0\nKwpZIiI5wG4z8Lrs2W6GiIjkkGTK4v2PI9jtUFqkc7FOhkKWiIiIiIh08uGnUVpjaUYXe/CYig0n\nQ/+2RET6mQ8/jRJPprPdDBERyWGptEXtx63YbTB2uKajnywdRiwi0o+8Wx9m045WQgkbFw43s90c\nERHJUfV7YrRG04wZ7sHj0rjMyVLIEhHpJ9oDlt9j48vn5RMNaxGyiIj0jJFDXaQti5JBrmw3pV9S\nLBUR6QeODFjTxhUQ8OoZmYiI9By7zeCcMzWK1VX6tyYi0sd91BTrELD8Hu0iKCIi0pfpUaiISB83\nPGgyusTD2BKPApaIiEg/oJAlItLH2WwGVef4s90MEREROUGaLigiIiIiInzUFGP7rgiptJXtpvR7\nGskSEeljUmkLu83IdjNERGQASaUt/vJhiNZYmuJBJj63pqefCo1kiYj0Ie/Wh/n9Xw7qsGEREekV\nTqcdn8/Fp4fSxFIG55cGKAjoHMZTpZAlItJHtG/THomnSSQ1VUNERHqOYRj4/S4MV4p9yWZWb2sk\nRpgRZ8UwXKm21wzNqugqTRcUETmC02nHNB3Y7W0dSyplEY8nSSRSPfp7jzwHa+q4Ak3TEBGRHuXz\nmYSsQ+yJNrJ6WwPb9tk5fehBalucjLKNYqi7CL8vn1Aolu2m9ksKWSIitD3R8/lMogmLvYeTRONt\n0/Xcpo18rx2/30E4HMeyun+EadPnAlZA27SLiEgPcjrtxImxJ9rIW01v8dGeIBg+Ti/ax67WFE3R\nJiYOmUiJx43Tae/xB425SCFLRIS2J3oHwykammPU7mihYW8UgJLBbipKA5QEXRT4zG5/omdZFgfD\nKQUsERHpNabp4EDqIHWH6kikEwwb9SmxiInDbAtTiXSCukN1nG4OosAcpJDVBQpZIjLgOZ12ogmL\nhuYYr65vJn7Eeqj6xgi7mqNcURXEbXq6/YmeYRhMGhsgFrfwuLRMVkREep7dbhBPxWiMNAJgGOD2\nxjvc0xhpJGbFMtPn5eSoRxeRAc80HRxqTVG7o6VDwGoXT1rU7mjhcGsK0+z+Z1M2w1DAEhGRPsVA\n4epUqFcXkQHPbjeIxtOZKYJH07A3SiSe1hM9ERHp91IpC9NwUeQpOuY9Qz1DcRkuUintdtsVClki\nIiegu6JV3e4IsYTOwBIRkeyJx5P4bH5G5Y/CaXN2et1pczIqfxQ+e4B4PJmFFvZ/ClkiMuClUhZu\n00bJYPcx7xk22I3HtJ3SE7336sOs3Rpi7QctXX4PERGRUxWOJPjtnw6zv7GQiUMmUuwtxm7YcRgO\nir3FTBwykaHuIkxc2vSii7TxhYgMePF4knyvnYrSALuao53WZZkOg4rSAHlee5ee6Dmddt7/JML7\nO2Oclm8y+fzTcDpQxyUiIlnxQUOE/YfijErmU+Ip4HRzEDGrbfdcl+HCZw9g4iIcjh/nneRYFLJE\nZMBLJFL4/Q5Kgi6uqApmtnA3aBvBat/C3e00CIVOPBi1n7319gctvP3BYdxOGxeWBYgkwTR79uwt\nERGRo4kl0mxuiGA6DEYOdmDF7BSYgzJrjlMpi3gsSSihQ4hPhUKWiAgQDscp8Jm4TQ9DC00ifzuM\n2GPayPPacTuNk36i5/OZvP9xmNc3HaAlksJrGvxuzd4eP3tL2iSTSX784x+ze/duEokEs2fPpqio\niJtuuokRI0YAUF1dzbRp03jhhRdYsWIFTqeT2bNnM3nyZGKxGHfccQf79+/H7/ezZMkSCgsL2bRp\nE/fffz8Oh4NLLrmEOXPmZLdQEZGTsPmTCPGExbgyH6bDRiKR0syKHqCQJSJC26HAoVAMp9NOMM/R\n8YlePHlSI1jw2dlbKQsOhRK4zbYlsMmU1eNnb0mbV155hcLCQh566CEOHTrEVVddxQ9/+ENuuOEG\nrr/++sx9+/btY/ny5axcuZJoNEp1dTUTJkzg+eefZ9SoUcyZM4dXX32VJ554gjvvvJO7776bZcuW\nUVxczI033si2bds499xzs1eoiMgJisTTbG2I4DYNRhd7st2cnKaNL0REjpBIpAiHYxw+HOXw4Sjh\ncKxLAaj97K3N9SH8HjuOz2393tNnbwlMmzaNW2+9FYB0Oo3D4WDLli288cYbzJgxg4ULFxIOh6mt\nrWXcuHE4HA78fj8jRoxg27ZtbNy4kUmTJgEwadIk1q9fTygUIpFIUFxcDMCll17KunXrslajiMjJ\nSCQtggUOzj/Lh9OhI0l6knp2EZEeoLO3ss/jaXtKGwqFuPXWW/nnf/5n4vE406dP57zzzuPJJ59k\n2bJljB49mkAgkPk5r9dLKBQiHA7j9/sB8Pl8tLS0dLjWfn3Xrl29W5iISBflee1MvahAa4F7gUKW\niEg3SqasTqNWx6Jo1fMaGxuZM2cOM2bM4Bvf+AYtLS2ZQDVlyhTuu+8+Lr74YkKhUOZnwuEweXl5\n+P1+wuFw5logEMDn8x313uMJBgPHvae/ybWacq0eUE39Qa7VA7lZU1coZImIdJP3PgrzUVOMaeMK\nOpy9Vd8YOer93XH2lhzbvn37mDVrFj/5yU+oqqoCYNasWdx1112Ul5fz9ttvM2bMGMrLy1m6dCnx\neJxYLEZ9fT1lZWVceOGFrF69mvLyclavXk1lZSV+vx/TNNm5cyfFxcWsWbPmhDa+aG7OrbPRgsFA\nTtWUa/WAauoPcq0eyL2aTiUwKmSJiHSD9z4K8//+txWf20Y8aZFOpxlaaHLNpCHsORDnr4cT1O0M\nU9/YSip96mdvyfE9+eSTHD58mCeeeILHH38cwzBYsGAB999/P06nk2AwyD333IPP52PmzJnU1NRg\nWRZz587FNE2qq6uZN28eNTU1mKbJI488AsDixYu5/fbbSafTTJgwgYqKiixXKiLSkdNpxzQ7b+Kk\nTZZ6j2Hl4KTMXEvQuVQPqKb+INfqgZ6t6ciAdUVlIUODHqIJi5ZImtZYmlTaAgswIBxJsq0hzDkl\nvr9t4W7v0hbuufoZ5apc/KxyqaZcqwdUU3/QE/W0n88YJ0Yo1ULcihFqTeO2uxjsy88cMNxTX/9z\n8TPqKo1kiYicgiMD1rTKAoYGPRwMp2hojlG7o4VP98dJWXDm6S7KR/oZNtjN6OE+ksl0l87eEhER\nORafzyRkHWJPtJG6Q3U0Rhr5pG4o6ZYgf/93hYwadAZ+X77OZ+wFClkiIl1kWRahSDoTsE7LM4km\nLBqaY7y6vpl4su1Joc0w2NkcZe/BGF8fP4h8rxenzSIUUsASEZHu4XTaiRNjT7SRt5reIpFO0Bpy\nc3C/D29gP5tCW8jzT6TE49b5jL1AIUtEpIsMw+CS0X6icQuPy4ZpOth7OEntjpZMwAJIWxakLFpT\n8N7/HmZIgZNgnv78iohI9zFNBwdSB6k7VEcinQBg785BAAwu3k/SSlB3qI7TzUEUmIMUsnqYDiMW\nETkFhmHgcbX9KdXZWCIiki12u0HcitEYaQQgdMhL6JAXf34r/vxWABojjcSsmPqgXqBHqSIi3cjr\ntjPt4kHk+dr+vB4MJTvsKqhuTUREesPeXacDMGRYc+aaoV6o12RtJGv//v1MnjyZjz76iIaGBmpq\napgxYwaLFy/O3PPCCy9wzTXX8J3vfIc//elP2WqqiAgA23dHiMTTR33NMAxsNhtel518n5NYwiKW\nsPB77Fw8Op9vfnkwXpdNZ2OJiEiPSKUsTMNFkacIgDNH7qFo+F48/s82uRjqGYrLcKkP6gVZGclK\nJpMsWrQIt9sNwAMPPMDcuXOprKxk0aJFrFq1igsuuIDly5ezcuVKotEo1dXVTJgwAafTmY0mi8gA\nV/txKxs/DPPJoDhfuzC/0+s+n8n+wwk+2Rtjw/ZDvLPtMGnLYtSZXr48poDBBSZfH982N15nY4mI\nSHeLx5P4XQFG5Y+iKdoEngQuz8HM606bk1H5o/DZA8Rj6oN6WlZGsh588EGqq6sZPHgwlmWxdetW\nKisrAZg0aRLr1q2jtraWcePG4XA48Pv9jBgxgu3bt2ejuSIywLUHLK/bxpfP9Xd63em0E01YfLI3\nyv95Zx+7m2MUBpw47Ta2NrTy7Ko9/LUlwbDBHkrP8OB2GlpwLCIi3SqRSGHiYqi7iIlDJlLsLcZu\n2HEYDoq9xUwcMpGh7iJMXOqDekGvj2S99NJLnH766UyYMIFf/OIXAKTTn02/8fl8hEIhwuEwgcBn\nB4B5vV5aWnLncDMR6R+ODFhXVBYQ8Ng73XPkroKtsRROuw2b247LaWs7iBio29nKyCIPwXyTgwcj\nvV2GiIgMAOFwHL8vnxKPm9PNQcSstqmCLsOFzx7IHEYsPS8rIcswDNauXcv27duZN28eBw4cyLwe\nDofJy8vD7/cTCoU6XT8Rp3I6c1+Ua/WAauoPcq0eOPmaGvZG2bIrzqDT3FwzcTD5vmP/yYz/Ncme\ng0lMs+0eG+A84va9hxLEEhYOh51BgzqPhnVFLn5GIiLSdZZlEQrFcDrtFJiDMrsIplIW8ViSUEKH\nEPeWXg9Zzz77bOafv/vd77J48WIeeugh3nnnHcaPH8+bb75JVVUV5eXlLF26lHg8TiwWo76+nrKy\nshP6Hc07+oQXAAAgAElEQVTNuTPiFQwGcqoeUE39Qa7VA12ryY3FuWc4ObvITbw1QnPr0e/Ly3OT\nTqeJx5Mkj7GY2LIbpNNpYrEEhw8fe4v3E5Wrn5GIiHRNLJHmz9tDVJzlpcCHpgRmWZ/Ywn3evHnc\nddddJBIJSktLmTp1KoZhMHPmTGpqarAsi7lz52KaZrabKiIDiGEYXDjSd9z7UikLt2mjZLCb+saj\nTwXUroIiItKTNn8SYUdjjAK/g4IvmHkhvSOrn8AzzzyT+efly5d3en369OlMnz69N5skInLS4vEk\n+V47FaUBdjVHiSc7BinTYVBRGtCugiIi0iPC0RRbPmnF67Jx3jBPtpsjZPGcLBGRviaR7NooUyKR\nwu00KAm6uKIqyMgiDw67gdNuMLLIwxVVQUqCLu0qKCIiPWJTfduB9xeM9OKw68DhvkBjiSIitO0i\n+OHuKNMq8/G6Ou8geDzhcJwCn4nb9DC00MwcWuwxbeR57bidhnZ0EhGRbncwlKTu0yj5PjtlZ7qz\n3Rz5G4UsERnwjtymPdnFgaYjd3QK5jk67ugUTxIKaQRLRES63/6WJHYDKst82AyNYvUVClkiMqAd\nGbCmjSsgz3vyo1hHSiRSmhIoIiK9prTIzRmnmbhNBay+RCFLRAas97s5YImIiPQkp9OOaXaeLSF9\nj0KWiAxY0XhaAUtERPo8wzDw+UzixDiQOkg81XaosGm48LsC+F0uwuE4lqVjQvoKhSwRGbAqy3yU\nj/DiNrXRqoiI9F0+n0nIOsSeaCN1h+pojDQCUOQpYlT+KIa6i/D78gmFYlluqbRTyBKRAcswDM1h\nFxGRPs3ptBMnxp5oI281vUUinSARc+Awk+xq3UVTtImJQyZS4nHjdNq1LriP0ONbEREREZE+yjQd\nhFIt1B2qI5FOkEra2LF5ODs/PAPLgkQ6Qd2hOsKpFkxT4yd9hT4JEekWx1qM21eeqG3+KITfkcLn\n1torERHpP+x2g3gqlpkiuK/xNJIJOx5flPYd2xsjjcSsWKYPluxTyBKRU9K+GDeasNh7OEn0b4fw\nuk0b+V47fr8j64tx3/+4lc274hS4YVplQdbaISIicioSMQf7GwtxmklOH3ogc91A4aqvUcgSkVPi\n85kcDKdoaI5Ru6OFhr1RAEoGu6koDVASdFHgM7O2GPf9j1v5y4dhTi90M+E8T1baICIi0lWplIVp\nuCjyFLH+f5Ok0wZFw/Zhs3/28HKoZyguw0Uqpd0F+wqFLBHpMqfTTjRh0dAc49X1zcSTn/1xr2+M\nsKs5yhVVQdymJyuLcdsDltdl45qJQRKRaK/+fhERkVMVjyfxuwIMNso4vK8Rjy9CwaDDmdedNiej\n8kfhsweIx3RmVl+hjS9EpMtM08Gh1hS1O1o6BKx28aRF7Y4WDremen0xbtOBRCZgTavMp8Dv7NXf\nLyIi0h0SiRQmLs4+vYivnl/E+efYcNjsOAwHxd5iJg6ZyFB3ESauPrMOWjSSJSKnwG43iMbTmSmC\nR9OwN0oknu71xbiDCxxUlvkYPtgkz6s/dSIi0n+Fw3EKfAV89TwP4VSQmFUBgMtw4bMHMGk7jFj6\nDn3zEJEela2luIZhUD7Cm6XfLiIi0n0syyIUiuF02ikwB3XcyTeWJJTQIcR9jUKWiHRZKmXhNm2U\nDHZT3xg56j3DBrvxmDYtxhURETlFiURKUwL7Ca3JEpEui8eT5HvtVJQGMB2dx6xMh0FFaYA8r514\nvGcX48aT6R59fxEREZETpZAlIl2WSKRwOw1Kgi6uqAoyssiDw27gtBuMLPJwRVWQkqALt9Po0Sdv\nmz9p5eX1B2iJ6OmeiIjkjvc/bqV+TzSrZ01K12i6oIickrbFuCZu08PQQpPI3w4j9pg28rx23E6j\nRxfjbv6klY3/20rA68Dnc5Hnd7TNUY8nNaVCRET6rcOtSTbuCONz2Rg+2EUv7x8lp0ghS0ROyZGL\ncYN5jo6LceNJQqGeCzpbGiK8+1EEr8fBl8fmcyCc4kA4hdu0ke+14/c7CIfjegIoIiL9zjsfhrHS\nUFnmx25TwupvFLJEpFv09mLczZ+08u5HERx2G+cM8/LnrYcyW8mXDHZTURqgJOiiwGcSCmnXJRER\n6T8+/Wuchr1xBhc4GDHYzHZzpAsUskSkfzIM3Kadc4Z5efO9v3Y4DLm+McKu5ihXVAVxmx6cTnsW\nGyoiInLi0pbFhroQGPClc/wYhkax+iNtfCEi/dKXRhfwlYsKqf+0tUPAahdPWtTuaOFwawrT1PMk\nERHpH1qjadJpOLvIxaA8Z7abI12kbx4i0i/Z7QaWRWaK4NE07I0Siacz68RERET6Or/HzlVVhSR1\nvmS/ppAlIjlL0WpgSyaT/PjHP2b37t0kEglmz57N2Wefzfz587HZbJSVlbFo0SIAXnjhBVasWIHT\n6WT27NlMnjyZWCzGHXfcwf79+/H7/SxZsoTCwkI2bdrE/fffj8Ph4JJLLmHOnDlZrlREco3NZmBq\ns4t+TdMFRaTP274rwuHWjocZp1IWbtNGyWD3MX9u2GA3HtNGSk8DB6RXXnmFwsJCnnvuOZ5++mnu\nvfdeHnjgAebOncuzzz5LOp1m1apV7Nu3j+XLl7NixQqefvppHnnkERKJBM8//zyjRo3iueee48or\nr+SJJ54A4O677+bRRx/lV7/6FbW1tWzbti3LlYqISF+jkCUifdqWhlbWfRBi9eaWDluxx+NJ8r12\nKkoDmI7OT/tMh0FFaYA8r514PNnpdcl906ZN49ZbbwUglUpht9vZunUrlZWVAEyaNIl169ZRW1vL\nuHHjcDgc+P1+RowYwbZt29i4cSOTJk3K3Lt+/XpCoRCJRILi4mIALr30UtatW5edAkVEpM9SyBKR\nPmtLQysbtofxuGxMGhPosMNSIpHC7TQoCbq4oirIyCIPDruB024wssjDFVVBSoIu3E5DhxIPUB6P\nB6/XSygU4tZbb+W2227rENR9Ph+hUIhwOEwgEMhcb/+ZcDiM3+/P3NvS0tLh2pHXRUROxcFwkngy\nne1mSDfSmiwR6ZOODFjTxuWT7+v85yocjlPgM3GbHoYWmkTibR2Ux7SR57XjdhqEw/Hebrr0IY2N\njcyZM4cZM2bwjW98g4cffjjzWjgcJi8vD7/fTygUOur1cDicuRYIBDLB7PP3Hk8wGDjuPf1NrtWU\na/WAauoPgsEAqbTFa5v2kEhZzJgyFNPRv8dAcu0z6iqFLBHpc/YdThw3YAFYlkUoFMPptBPMc2R2\nEUylLOLxJKGQRrAGsn379jFr1ix+8pOfUFVVBcDo0aN55513GD9+PG+++SZVVVWUl5ezdOlS4vE4\nsViM+vp6ysrKuPDCC1m9ejXl5eWsXr2ayspK/H4/pmmyc+dOiouLWbNmzQltfNHcnFujXcFgIKdq\nyrV6QDX1B+31bGlopbE5wjnFbg4dCGe7WackFz+jrlLIEpE+Z1Cek6pz/ZxxmvOYAetIiURKUwKl\nkyeffJLDhw/zxBNP8Pjjj2MYBnfeeSf33XcfiUSC0tJSpk6dimEYzJw5k5qaGizLYu7cuZimSXV1\nNfPmzaOmpgbTNHnkkUcAWLx4MbfffjvpdJoJEyZQUVGR5UpFpL+KxNO8u6MV02lwUakv282RbmRY\nR05QzxG5lqBzqR5QTf1Bez1Opx3T7DxC1B8DTa5+Rrkkl6eY5OJnlUs15Vo9oJr6g2AwwMrVn/Lh\n7ihV5/oZPcyT7Sadslz8jLpKI1kiclR+v4towmLv4STRv611cps28r12/H4H4XCcHHxGIyIi0isO\nhpJ8+GmUQr+dc4qPfRyJ9E8KWSJyVAfDKRqaY9TuaKFhbxSAksFuKkoDlARdFPhMQqFYt/yuWCKN\ny9m/F/qKiIicjAK/g6kX5WO3GdgMHTycaxSyRKQDp9NOKNIWsF5d30w8+dloVX1jhF3NUa6oCuI2\nPTid9lOeOri1oZX3Pmpl2rgCCvy9+ycpl6ZDiohI/1N0mpntJkgPUcgSkQ5M08H+UILaHS0dAla7\neNKidkcLQwtNgnmOUwokWxta+fPfdhHszYd4hmHg85maDikiIiI9QiFLRDqw2w0isXRmiuDRNOyN\nEomnMyNAXdEesNym8YXbtPcEn8/s1emQIiIiMrAoZInISTvVQaetDZFMwLqisqBXA5bTaSeasHpt\nOqSIiEi7tGVp/dUAoZXmItJBKmXhcdkoGXzsnY6GDXbjMW2kUl2fTudx2Xo9YEHbdMhDranjToc8\n3JrCNPUcSkREuodlWfyfdw+xoS5EWtPRc56+QYhIB/F4kkK/i4rSALuao52CiOkwqCgNkOe1E48n\nu/Q7zivxcHaRCzMLOwra7QbReM9PhxQRETlS/Z4YjfsTOLSb4ICgkSwR6SCRSOH32CkJuriiKsjI\nIg8Ou4HTbjCyyMMVVUFKgi7cTuOUptJlI2CdKHV9IiLSneKJNBvqQtht8KVz/NlujvQCjWSJyFEV\n+Oy4TQ9DC00if9t9z2PayPPacTsNwuF4llvYNamUhdtsmw5Z3xg56j3dMR1SRESk3bv1rUTjFheV\negl47NlujvQChSwROapQKIbTaSeY1/kcqVDoxEewtu+KEMx3clqgb/y5iceT5HvtPTodUkREpN1f\nW5J8sDNCwGtnzHBvtpsjvaRvfOsRkT4pkUid4jlYEf68PUSh386VVYUYfWAOeiKRwu93ZKZDtm/h\nbtA2gtW+hbvbaZxUmBQRETkat2lw1hAXpUVuHFrrO2BkJWSl02kWLlzIRx99hM1mY/HixZimyfz5\n87HZbJSVlbFo0SIAXnjhBVasWIHT6WT27NlMnjw5G00WkZPUHrDcpsHkirw+EbDahcNxCnxmTk6H\nFBGRvsXrsvN35XnZbob0sqyErNdffx3DMHj++efZsGEDjz76KJZlMXfuXCorK1m0aBGrVq3iggsu\nYPny5axcuZJoNEp1dTUTJkzA6XRmo9kicoKODFjTKgso6OVt2o/Hsqxumw4pIiIi8nlZ+eYzZcoU\nLr/8cgA+/fRT8vPzWbduHZWVlQBMmjSJtWvXYrPZGDduHA6HA7/fz4gRI9i+fTtjx47NRrNF5AQc\nCCX5c13fDVhHOtXpkCIiIiJHk7VvPzabjfnz57Nq1Sr+7d/+jbVr12Ze8/l8hEIhwuEwgUAgc93r\n9dLS0nLc9w4GA8e9pz/JtXpANfUHXa0nGIRv2kyGFpqclte3Rp31GYmIiEhvyOoj5iVLlrB//36u\nvfZaYrFY5no4HCYvLw+/308oFOp0/Xiam48fxPqLYDCQU/WAauoPTrWeoBdSsSjNzcc+8Le36TPq\n+xQaRSQXpC2Ltz8IcV6Jh0J/353NIT0rK6eBvvzyyzz11FMAuFwubDYbY8eOZcOGDQC8+eabjBs3\njvLycjZu3Eg8HqelpYX6+nrKysqy0WQRERERkePa2hChbneULQ1HP4tRBoasxOuvfe1rLFiwgBkz\nZpBMJlm4cCEjR45k4cKFJBIJSktLmTp1KoZhMHPmTGpqajIbY5immY0mi8gxxBJpXM6sPK8RERHp\nU8LRFO/uaMV0GlSe7ct2cySLshKyPB4PP/vZzzpdX758eadr06dPZ/r06b3RLBE5SR/sjPD/doT5\n+kX5DOpj669ERER62/rtIZIpi0vPDeA29QByINOnLyJd8sHOCOu3hbAZ4LD1nTOwREREsqGhOUbD\n3jhDCp2cXeTKdnMkyxSyROSktQcst2kwbVwBBVrYKyIiA1w8YWE6DS45149h6OHjQKdvRiJyUhSw\nREREOjv7DDfDB7twOhSwRCFLRE6Sw27gcdmYelG+ApaIiMgRFLCknb4hichJKTvDzQg9qRMRERE5\nJq3JEpGTpoAlIiIicmwKWSIiIiIiJ6klkuLDT6NYlpXtpkgfpOmCInJM23dFOC3gIJivM7BERETa\nWZbF2x+0sHt/Ao9po3iQme0mSR+jkSwROaptuyKs+yDEm5tbSOspnYiISEb9nhi79yc483QnZ56u\nB5HSmUKWiHTy/kch3v6gbZv2r5yfh03nfYiIiAAQjaf5c10Iux2+PDqgM7HkqDRdUEQ62LYrwrsf\nx3CbBlN1DpaIiEgHf64LEYtbjB/lI+CxZ7s50kdpJEtEMg63pli/LdR2Dta4AgoVsERERDISSYsD\noSSD8h2cV+LJdnOkD9M3KBHJyPPamTQ2wNnDC0jHotlujoiISJ/idBj8fxcXEk2kNZVevpBGskSk\ng5FD3Zyep0W8IiIiR2OzGXhdmiYoX0whS0REREREpBspZIkMYJF4OttNEBEREck5ClkiA9S2XRF+\nu/avNB1MZLspIiIifVb9niixhB5KyslRyBIZgLbtivD2ByHsNjAdWrgrIiJyNHsPJli9uYX/+97h\nbDdF+hmFLJEBpj1gtZ+DpW3aJZe99957zJw5E4APPviASZMm8d3vfpfvfve7/P73vwfghRde4Jpr\nruE73/kOf/rTnwCIxWLccsstXHfdddx0000cOHAAgE2bNvHtb3+bmpoali1blpWaRKR3JFMWa7a2\ngAUXlXqz3RzpZ/TtSmQA2a6AJQPI008/zcsvv4zP5wNg8+bN3HDDDVx//fWZe/bt28fy5ctZuXIl\n0WiU6upqJkyYwPPPP8+oUaOYM2cOr776Kk888QR33nknd999N8uWLaO4uJgbb7yRbdu2ce6552ap\nQhHpSe/WhzkUTjF6mJuhhWa2myP9zHFHsmpra3ujHSLSC1xOG14dNCwDxPDhw3n88ccz/3vLli38\n6U9/YsaMGSxcuJBwOExtbS3jxo3D4XDg9/sZMWIE27ZtY+PGjUyaNAmASZMmsX79ekKhEIlEguLi\nYgAuvfRS1q1bl5XaRKRnNR9KsPmTCH6PjXFn+7PdHOmHjhuyfvrTn/Ktb32Lp59+mubm5t5ok4j0\nkBFDXFwz4TQFLBkQvvrVr2K3f3aWzfnnn8+PfvQjnn32WYYNG8ayZcsIhUIEAoHMPV6vl1AoRDgc\nxu9v+2Ll8/loaWnpcO3I6yKSexr/2rYp1KVjAji1dlm64LjftJ555hl2797Nyy+/zKxZsygqKuLq\nq6/mK1/5Ck6nDiwV6W8cdnUWMjBNmTIlE6imTJnCfffdx8UXX0woFMrcEw6HycvLw+/3Ew6HM9cC\ngQA+n++o956IYDBw/Jv6mVyrKdfqAdV0Kr4SDDDuvAQF/p79rqvPKHed0OPsM888k6uuugqHw8Gv\nf/1rnnnmGZYuXcrtt9/OV7/61Z5uo4iIyCmbNWsWd911F+Xl5bz99tuMGTOG8vJyli5dSjweJxaL\nUV9fT1lZGRdeeCGrV6+mvLyc1atXU1lZid/vxzRNdu7cSXFxMWvWrGHOnDkn9Lubm3NrxCsYDORU\nTblWD6im7tIcifbYe+sz6vtOJTAeN2S9+OKLvPzyyzQ3N3PVVVfxq1/9iqFDh9LU1MTVV1+tkCXS\nR9XtjhDw2inSYl0RAO6++27uvfdenE4nwWCQe+65B5/Px8yZM6mpqcGyLObOnYtpmlRXVzNv3jxq\namowTZNHHnkEgMWLF3P77beTTqeZMGECFRUVWa5KRET6IsOyLOuLbvjRj37ENddcw5e+9KVOr/3h\nD3/g61//eo81rqtyLUHnUj2gmnrD9l0R1n0Qwu+x8feXnIbddnJTBPtaPd0h12rKtXogt6eY5OJn\nlUs15Vo9oJo+z+m0Y5oO7H+bMp9KWcTjSRKJVHc28aToM+r7enQk66GHHjrma30xYIkMdO0By2Ua\nfOX8/JMOWCIiIrnCMAx8PpM4MQ6kDhJPxQAwDRd+VwC/y0U4HKfpQByAwQXab0C6h7YYE8khRwas\nqRcVcFpA/xcXEZGBy+czCVmH2BNtpO5QHY2RRgCKPEWMyh/FUHcRpivA6s37CMfSTJ9wGj63/Tjv\nKnJ8+gYmkiPC0RTrtytgiYiIQNsUwTgx9kQbeavpLRLpROa1Xa27aIo2MXHIRD7+MEFrzKJ8uFcB\nS7qNvoWJ5Aif285lFXn43XYFLBERGfBM08GB1EHqDtV1CFjtEukEb9d/zF8/MSkqCHDBSG8WWim5\n6riHEYtI/1ESdClgiYiIAHa7QdyKZaYIfl4yYee9D2xYRpqvjivUGmbpVgpZIiIiIjLgxKNOLMug\nYpSD0/O04YV0L4UskX6qNZa9bWdFRET6ulTKwjRcFHmKjvq6NxBl4peinD/SRyr1hScaiZw0hSyR\nfqhud4TfrPkru/fHs90UERGRPikeT+K3BxiVPwqnrfNIldPmZGywjIAjj3g8mYUWSi7T4g2RbtQb\nhx3W7Y6wdmvbLoIeU89JREREjiaRSOF3uRjqLmLikImZLdwNDIZ6hn62hTsuQolYtpsrOUYhS6Sb\n+P0uogmLvYeTRONpANymjXyvHb/fQTgcx7JObTrCkQFL27SLiIh8sXA4jt+XT4nHzenmIGJWW5hy\nGS589gAmbYcRi3Q3fUMT6SYHwykammPU7mihYW8UgJLBbipKA5QEXRT4TEKhrj8paw9YplMBS0RE\n5ERYlkUoFGs7M6s1j6YDCc4f6cOyIB5LagRLeoy+pYmcIqfTTijSFrBeXd9MPPnZaFV9Y4RdzVGu\nqAriNj04nfYuTx30uux4XTa+emG+ApaIiAxYXZma3xpJ8vsNB2hpTZHnsgjmazdB6Vn6piZyikzT\nwf5QgtodLR0CVrt40qJ2RwtDC02CeY4uh6ziQSbXTDgNh13neIiIyMDk97uIE+NA6iDxVNsolGm4\n8LsC+F2uY07N31AXoqU1xdjhHgUs6RUKWSKnyG43iMTSmSmCR9OwN0okns48desqBSwRERnIQtYh\n9kQbM5tYABR5ijKbWPh9+Z2m5n/cFKNud5TTAg4uOtuXjWbLAKSQJdILFI1ERES6zum005psZU+0\nkbea3iKRTmRe29W6i6ZoExOHTKTE4+4wNT8cTbH2gxbsNvi7sQHsNvXI0ju0/7PIKUqlLDwuGyWD\n3ce8Z9hgNx7TdsKHHX74aZSGZi3GFRERgbap+S3Jw9QdqusQsNol0gnqDtURTrVgmh3HEAr9Dr50\njp8Cv8YWpPfovzaRUxSPJyn0u6goDbCrOdppXZbpMKgoDZDntZ/QYYd1uyOs/SCE17RxxmmmpgiK\niMiAZ7cbRJPRzBTBo2mMNBKzYh2m5vvcdqaOy9eMEul1GskSOUWJRAq/x05J0MUVVUFGFnlw2A2c\ndoORRR6uqApSEnThdhrH3fSiPWCZDoOvXpivgCUiInKCjGNEKZthYBjqT6V39fpIVjKZ5Mc//jG7\nd+8mkUgwe/Zszj77bObPn4/NZqOsrIxFixYB8MILL7BixQqcTiezZ89m8uTJvd1ckRNW4LPjNj0M\nLTSJ/O0wYo9pI89rx+00jnvY4ZEBa9o4nYMlIiLSLpWycNvdFHmK2NW666j3DPUMxWW4TnhqvkhP\n6vVvca+88gqFhYU89NBDHD58mCuvvJJzzz2XuXPnUllZyaJFi1i1ahUXXHABy5cvZ+XKlUSjUaqr\nq5kwYQJOp7bdlL6p/bDDYF7nsztCoS8ewYrE0/x5e1gBS0RE5Cji8SQBfx6j8kfRFG3qtC7LaXMy\nKn8UXpufWKzzmi2R3tbr3+SmTZvG1KlTAUilUtjtdrZu3UplZSUAkyZNYu3atdhsNsaNG4fD4cDv\n9zNixAi2b9/O2LFje7vJIicskUh16Rwsj2njKxfk4XbaFLBEREQ+J5FIUeAIMNRdxMQhEzNbuBsY\nDPUMzWzh/uEnKeoaDjFxbB4eU6tiJHt6/ducx+MBIBQKceutt3Lbbbfx4IMPZl73+XyEQiHC4TCB\nQCBz3ev10tLS0tvNFek1Z5xmZrsJIiIifZrfyKfE4+Z0cxAxq20XXpfhwmcPcPiQjdXv7cVhh3Ra\nUwYlu7LyyLyxsZE5c+YwY8YMvvGNb/Dwww9nXguHw+Tl5eH3+wmFQp2un4hgMHD8m/qRXKsHVFN/\nkGv1QO7VlGv1iIgcT/vU/AJzUIep+aFwnP9ev4902mJSRR4+tz3LLZWBrtdD1r59+5g1axY/+clP\nqKqqAmD06NG88847jB8/njfffJOqqirKy8tZunQp8XicWCxGfX09ZWVlJ/Q7mptzZ8QrGAzkVD2g\nmqDtcMS+3AHoM+r7cq0eUGgUkRPz+an5lmXx5uYWWlpTjB3uYVjQlcXWibTp9ZD15JNPcvjwYZ54\n4gkef/xxDMPgzjvv5L777iORSFBaWsrU/7+9+4+Oqr7zP/668+POTGYmkwQCCUSIImnFAkKwy1cM\nX7otlXb123aLW2WldY+nLW7paWVx0foDPVvF7Wo9pyv21PWc3S5WxbXd737/6Nnvlq0FAV2VLuSL\nAqlS5YchBAxJZsjMnR+f7x8pIyERAkwyMzfPxzk9p7lzg583Q/KZ172f+/4sWSLLsrR8+XItW7ZM\nxhitWrVKts1yKpS/372f1PY9vVo0s1JTJzARAABwMQ50Otp/JKXamE/Nl4eLPRxAUhFC1j333KN7\n7rln0PENGzYMOnbjjTfqxhtvHI1hAaPid+8ntfWtXtk+S5FQ6d7JAgCgXFxSa+uqyyp0+aSgPB72\nw0JpoI0ZMEpOD1hLmqs0ji6CAABcNI9lac407mChtNDbEhgFbxOwAAAAxgw+6QGjIBLyKBzw6NNX\nxQhYAAAUmN/vlW37BnQcdJzMBe1dCRQCn/aAUVBXbevLC2rkZa04AAAX5YPejEIBj0K2R5ZlKRy2\n5SilruwJOdn+vbNsK6BIIKpIIKBEwpEx7JuF0UXIAkYJAQsAgIvT5+T0q53dsiR96X/UqLoqoLjp\n1pFku9q629Te1y5Jqg/VqynWpLpgvSLhmOLxVHEHjjGHkAUAAICSl8sZbd7do5PJnOZeXqGKkE+O\nUjqSbNfLHS8rnUvnzz108pA6kh1qmdiiKaGg/H4vSwcxqmh8ARTY2+8ntf9IstjDAADAVV7d0632\n44gSgVMAACAASURBVGldUmtrVmOFbNuneLZXbd1tAwLWKelcWm3dbUpke2Xb3FfA6OJfHFBAb7+f\n1Mtv9Srot9Qw3pbt4zoGAAAX60BnSm+09Sla4VHLlVFZliWv15KTTeWXCA6lva9dKZPKN8QARgsh\nCyiQUwHL9llaPCdGwAIAoEBOxLPyey398SdiCviHP79aIlyhOAhZQAHsOZDIB6zr5sY0vtJf7CEB\nAOAasy6t0PxZFTrZezJ/LJs1sq2A6kP1OnTy0JDfVxeqU8AKKJuluyBGF5fagYuUSue0pfUEAQsA\ngBEUDnoHfO04GUW8UTXFmuT3DJ57/R6/mmJNCnujcpzMaA0TkMSdLOCiBfwe/a9rxutEV4KABQDA\nKEmns4oEAqoL1qtlYku+hbslS3WhunwLd1sBxdO0cMfoImQBBVBfE5Av6xR7GADOsGvXLj366KPa\nsGGDDhw4oLvuuksej0fTp0/X2rVrJUkvvPCCNm7cKL/frxUrVmjRokVKpVK68847dfz4cUUiET3y\nyCOqrq7Wzp079fDDD8vn8+maa67RypUri1wh4E45Y+Sxzv08VSLhKBKOaUooqHH2eKVMf5gKWAGF\nvVHZ6t+MGBhtLBcEALjS008/rXvvvVfpdH9r53Xr1mnVqlV65plnlMvltGnTJh07dkwbNmzQxo0b\n9fTTT+uxxx5TOp3Wc889p6amJv3sZz/TF77wBT355JOSpAceeEA//OEP9eyzz6q1tVV79+4tZomA\nK3UnMvrfr3Spo2twW/YzGWMUj6dkUl5VecZrkt2gSXaDqjzjZVLe/tcMz2Nh9BGygPPU28dmhkA5\nmDp1qtavX5//+s0339S8efMkSQsXLtT27dvV2tqq5uZm+Xw+RSIRNTY2au/evdqxY4cWLlyYP/fV\nV19VPB5XOp1WQ0ODJOnaa6/V9u3bR78wwMWcdE7/uatH3Ynsec236XRWiURKPT1J9fQklUik2HwY\nRUXIAs7DO+1J/XzbB3qnnc2GgVK3ePFieb0fPih/+tXscDiseDyuRCKhaDSaP15RUZE/HolE8uf2\n9vYOOHb6cQCFkTNGm3f3qjuR1ZVTQ7p8UrDYQwIuGM9kAcP0TntSW97sb9MeC3vP/Q0ASorH8+F1\nxUQiocrKSkUiEcXj8SGPJxKJ/LFoNJoPZmeeOxy1tdFzn1Rm3FaT2+qRyq+m7W+e0LGEUdPUqD73\nP8bL4xn8TFa51XQubqtHcmdNF4KQBQzD6QGLNu1AeZoxY4Zef/11XX311dqyZYvmz5+vmTNn6vHH\nH5fjOEqlUtq/f7+mT5+uOXPmaPPmzZo5c6Y2b96sefPmKRKJyLZtHTx4UA0NDdq6deuwG190drrr\njldtbdRVNbmtHqn8ajqRyGhra5eiIa/mXWrr+PH4oHPKraZzcVs9kvtqupjASMgCzmH/EQIW4AZr\n1qzRfffdp3Q6rWnTpmnJkiWyLEvLly/XsmXLZIzRqlWrZNu2br75Zq1Zs0bLli2Tbdt67LHHJEkP\nPvigVq9erVwupwULFmjWrFlFrgpwh6qwT5+ZXalohVcBP0+zoPxZxoUtV9yWoN1Uj1R+NR3rSeul\n1h59alblRwascqvpXNxWj+S+mtxWj+TuJSZufK/cVJPb6pGoqRy4rR7JfTVxJwsYQeMr/fryNTVD\nrg0HAAAAzsT9WGAYCFgAAAAYLkIWAAAARtV/70/o8HGn2MMARgwhCzjNO+1J7TvUV+xhAADgWvsO\n92nnOyf1WltcOfe1BgAk8UwWkHd6m/bGiQG6GwEAUGCHjzt6ZU9ctt/Sp2dXymOxHB/uxKdIQB8G\nLL+3v007AQsAgMLqimf0UmuPLEv6zFUxVVZwrR/uxSdJjHmnB6wlzeyDBQBAoeVyRv+5q0fpjFHL\nlVFNrGKuhbtxCQFjmpPJ6bW2OAELAIAR5PFYuuaKiD7ozeiyumD+uN/vlW375PX2LxvMZo0cJ6N0\nOlusoQIFQcjCmGb7PLpubpVyxhCwAAAYQZNqbE2qsSVJlmUpHLblKKWu7Ak52ZQkybYCigSiigQC\nSiQcGRpjoEwRsjDm1UT5MQAAYDSFw7bipltHku1q625Te1+7JKk+VK+mWJPqgvWKhGOKx1NFHilw\nYfh0CQAAgFHj93vlKKUjyXa93PGy0rl0/rVDJw+pI9mhloktmhIKyu/3snQQZYnGFxhTek5mij0E\nAABcb9/hPr13dOi7ULbtUzzbq7butgEB65R0Lq227jYlsr2ybe4HoDwRsjBm7D+S1C+2d2kvmw0D\nADBiDnSmtH1PXNv39CqdGfxMlddryTGp/BLBobT3tStlUvmGGEC5IWRhTNh/JKnNu3vl81oaxzNY\nAACMiCNdjn7T2iOvp38vLL/vwkKSJcIVyhshC653KmCd2mi4NkYXQQAACu2D3ow27exRzkh/POuj\n59ts1si2AqoP1X/kn1UXqlPACiibpbsgyhMhC672+44UAQsAgBGWyxn9urVb6azRwk9E1TDe/shz\nHSejiDeqpliT/J7B87Lf41dTrElhb1SOw7PUKE+sm4KrVYe9qgx5tfATUQIWAAAjxOOxtPDKSnXF\nB242PJR0OqtIIKC6YL1aJrbkW7hbslQXqsu3cLcVUDxNC3eUJ0IWXK0q4tOXrqmWx2JtNwAAI2lC\nlV8TqoZ3QTORcBQJxzQlFNQ4e7xSpj9MBayAwt6obPVvRgyUK0IWXI+ABQBAaTHGKB5Pye/3qsoe\nn+8imM0aOakMd7BQ9ghZAAAAkN/vlW37BgYeJzPkZsDGGFkFuIiZTmfZbBiuRMiCa+w/ktTJVE6f\nmFpR7KEAAFA2LMtSOGzLUUpd2RNysv13kWwroEggqkigf+meMf2d/rI5o5dae3TpxICm1Z/9+Stg\nrCJkwRVOb9M+rS6oUIDGmQAADEc4bCtuunUk2Z5vQiFJ9aH6fBOKSDimeDylnDHavLtHBzsdGSNd\nVhcoyB0twG0IWSh7Z+6DRcACAGB4/H6vHKV0JNmulzteVjqXzr926OQhdSQ71DKxRVNCQXl9Hm3+\n7xN6r8NRXbVfn5pVScACPgKfRlHW2GgYAIALZ9s+xbO9autuGxCwTknn0mrrblM806NX9ia0/0hK\nE6p8+vRVlfJ5CVjAR+FOFspWJmv0+u8SBCwAAC6Q12vJyabySwSH0t7XruOJpN7tyGp8zKfFV8Vk\n+7hOD5xN0X5Cdu3apeXLl0uSDhw4oGXLlumWW27Rgw8+mD/nhRde0Je//GXddNNN+s1vflOkkaJU\n+byWlsyNEbAAABhBlixFwx598Zrx+uycmGw/AQs4l6L8lDz99NO69957lU7335Zet26dVq1apWee\neUa5XE6bNm3SsWPHtGHDBm3cuFFPP/20Hnvssfz5wCmxsI+ABQDABcpmjWwroPpQ/UeeUxeqU8AK\nqDriU4CABQxLUX5Spk6dqvXr1+e/fvPNNzVv3jxJ0sKFC7V9+3a1traqublZPp9PkUhEjY2N2rdv\nXzGGCwAA4EqOk1HEG1VTrEl+z+CLln6PX02xJoW9UTlOpggjBMpTUULW4sWL5fV681+f2ndBksLh\nsOLxuBKJhKLRaP54RUWFent7R3WcKC0nEvxyBwCgkNLprGwFVBesV8vEFjVUNMgjr5K9ETVUNKhl\nYovqgvWyFWDTYOA8lETjC4/nw6yXSCRUWVmpSCSieDw+6Phw1NZGz31SGXFbPdL519R26KT+784T\numZGTM1Nw/t3MNrc9j65rR7JfTW5rR4AxZFIOIqEY5oSCqraP04vt8a1/3BWk8aHNSVUI1v9mxED\nGL6SCFkzZszQ66+/rquvvlpbtmzR/PnzNXPmTD3++ONyHEepVEr79+/X9OnTh/XndXa6545XbW3U\nVfVI51/T/iNJbdndK5/XUtDKlOTfh9veJ7fVI7mvJrfVIxEagWIxxigeT8nr8+i/9/h0pD2oxhq/\nPl5bI5PKKZ5OFXuIQNkpiZC1Zs0a3XfffUqn05o2bZqWLFkiy7K0fPlyLVu2TMYYrVq1SrZtF3uo\nGGW/70jlA9Zn58Q0oYomFwAAFFo2Z/TrHV1676ij2phPi2aElXFoOAZcqKKFrMmTJ+v555+XJDU2\nNmrDhg2Dzrnxxht14403jvbQUCLeO5rS5v/XQ8ACAGCEbXurV+8ddVRX49dnZsfk97HRMHAxSuJO\nFjCUmqhPsbBXC66IErAAABhBV06tUM5I186IyuclYAEXi5CFkhUNefXF+dWyLH7ZAwAwksZFfVo0\nszQbSwHliJCFovH7vbJtn7x/uGKWzRo5TmZAi1gCFgAAAMoNIQtFEYkElEwbHe3JKOnkJElB26NY\nhVeRiE+JhDNg/zQAAFAYqXROAX9RtkoFxgxCForiRCKrA50ptb7TqwNHk0oks6qK+HXd1eM0pTag\nqrCteJyWsQAAFFJnd1q/2tmtudPC+nhDqNjDAVyLkIVR5fd7Fe/rD1i/fLVTTsboZCqn4z0ZdXZn\nlHKO6n8tmKCgHZLf72V3eQAF96d/+qeKRCKSpIaGBq1YsUJ33XWXPB6Ppk+frrVr10qSXnjhBW3c\nuFF+v18rVqzQokWLlEqldOedd+r48eOKRCJ65JFHVF1dXcxygGE7dMzRS609yuSMWIwPjCxCFkaV\nbft0PJ5W6zu9AwKWZUm1MZ9yRmp9p1d11bZqK32ELAAF5TiOJOmf//mf88duv/12rVq1SvPmzdPa\ntWu1adMmXXXVVdqwYYP+9V//VclkUjfffLMWLFig5557Tk1NTVq5cqV++ctf6sknn9Q999xTrHKA\nYfvd+0lte6tXliV9alalGicEij0kwNVYkItR5fVa6kvldOBoclDAOrU+/MDRpPqcXL4hBgAUyt69\ne3Xy5EnddtttuvXWW7Vr1y699dZbmjdvniRp4cKF2r59u1pbW9Xc3Cyfz6dIJKLGxkbt3btXO3bs\n0MKFC/PnvvLKK8UsBxiWPQf7tPXNXvl9lpbMrSJgAaOAO1koCmOMuhODA5YkljAAGDHBYFC33Xab\nbrzxRr377rv6+te/PqDJTjgcVjweVyKRUDQazR+vqKjIHz+11PDUuUCpm1Tj17hKnxZeGVVVhI9+\nwGjgJ63MDacNeinJZo1CAY+mTgwplTbK5sygDkeXTAgqZHuUzdJdEEBhNTY2aurUqfn/X1VVpbfe\neiv/eiKRUGVlpSKRyIAAdfrxRCKRP3Z6EDub2trhnVdO3FaT2+qRPqyptlaaNrXKFduiuO19cls9\nkjtruhCErDJlWZbCYbvs2qA7TkbVkYBmTYvqUGdSTmbg+GyfpVnToqqs8MpxMkUaJQC3+vnPf662\ntjatXbtWHR0disfjWrBggV577TV98pOf1JYtWzR//nzNnDlTjz/+uBzHUSqV0v79+zV9+nTNmTNH\nmzdv1syZM7V58+b8MsNz6ezsHeHKRldtbdRVNbmtHomayoHb6pHcV9PFBEZCVpkKh+1BbdAlacqE\noGZNi5ZsG/R0OquqKq+m1Ab0+fm1+bFb6r+DdWrsQb+leLw078YBKF9Lly7V3XffrWXLlsnj8eiR\nRx5RVVWV7r33XqXTaU2bNk1LliyRZVlavny5li1bJmOMVq1aJdu2dfPNN2vNmjVatmyZbNvWY489\nVuySgAF6TmYVDfHIPVBslim1Wx0F4LYEfWY9fr9XxuNV2+G+fBv009k+S5+fX6umySFZuWxJLB38\noDej6ohXlmWptjaqvj5HybRRz8ms+v5wFy5ke1RZ4VXQb5XkXbizceOVGzfVI7mvJrfVI7l7iYkb\n3ys31eSWevYfSerlN3vVfHlYn5o30RU1nc4t79MpbqtHcl9N3MkaY2zbp6M9mXwb9DM5GVNSbdDf\n7UjpN/+vR7MvrdCcaWFJUjyekt/vVW3l4OfJuIMFAMDwGWP023dOqvX3J+X3WaoK8/EOKDZ+CsuQ\n12sp6eTySwSHUipt0E8FLK/H0qRx9oDX0unSuMsGAEC5cjI5bdndq4OdjqIVHn1mdowOgkAJ4KfQ\npUqhf9DpAeuzc2OaWOUv9pAAAHCV7XviOtjpqL7Gr0/NqhzUsRdAcRCyylA2axS0PZoyIaj97X1D\nnlPsNugHOwlYAACMtObLw4qGvJozrUIeF7RoB9yCyx1lyHEyilV4NWtaVLZv8C/UUmiDXhP1qSbq\nI2ABADCCoiGvmi8PE7CAEsOdrDKUTmcVifhKug16OOjVDZ90x8aHAAAAwPkgZJWpRMJRVdhW0A6p\nrtr+yDboxUTAAgCgMI71pPX2+0n90ccizK9AGSBklSljDG3QAQBwOWOM9hxM6rXfxWWMdGldkGX4\nQBkgZJW5UmiD/u7RlI6eSOvq6WGurgEAUCCpdE7b9vTqvQ5HQdvSwk9UErCAMkHIwkV592hKv2nt\n7yL48YaQKiu8xR4SAABlr+dkVv/3tycU78tpYrVf//MTUYWDzLFAuSBk4YKdHrA+OydGwAIAoEDC\nQY9CtkeX1wc1+zLaswPlhpCFC3JmwJpYzfIFAADOxu/3yrYHP0c91LJ/r8fS5+dVyeMhXAHliJCF\n85YzRjv3JwhYAAAMg2VZCodtOUqpK3tCTjYlSbKtgCKBqCKBgBIJR8aYAd9HwALKFyEL581jWbpu\nTpV6+7KawAO4AACcVThsK266dSTZrrbuNrX3tUuS6kP1mhqarsPvVWnhxycq46SLPFIAhULIwgUJ\nBTwKBTzFHgYAACXN7/fKUUpHku16ueNlpXMfBqk9h7v00u8PabzPKBoMaO7UyqJ3DAZQGIQsAACA\nEWLbPnVlT6ituy0fsDIZj468O0EnjlXK4zGqbjyspstqZXt9hCzAJQhZOKfjvRnVRLzsgQUAwHny\nei052VR+iWA269E7rY1KOz6FIklNvuyIvOGs0pqRb4gBoPwRsnBW7x1N6aXWHs2YEtInmyLFHg4A\nAGXN680pNr5HPl9W4+q7ZFmSxccxwHX4qcZHOhWwvB5LU2rtYg8HAICSNlSLdmP6uwjWh+p16OQh\nSVLdlGMDvq8uVKeAFVA2awb9mQDKEyELQzo9YC2eU6m6akIWAABD+agW7emkX5MraxSzK9UUa1JH\nsmNA4wtJ8nv8aoo1KeyNykllijF8ACOAkIVBDh93CFgAAAzTmS3aD/Z0qOPgOCU/qNcXFnygP5oy\nXZMqJqtlYku+hbslS3WhOjXFmlQXrJetgOLpVLFLAVAghCwMMi7qU23Mp+bLwwQsAADO4vQW7VuO\nvKyjRyrUcXCKshmvAqEuvX78bU2o8WpadLqmVlymcfZ4pUx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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_datasets(df_lin, df_quad, dfp_lin, dfp_quad)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Observe:**\n", "\n", "+ We now have two datasets `df_lin` and `df_quad` created by a linear model and quadratic model respectively.\n", "+ You can see this raw data, the ideal model fit and the effect of the latent noise in the scatterplots above\n", "+ In the folowing plots in this Notebook, the linear-generated data will be shown in Blue and the quadratic in Green.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Standardize" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "dfs_lin = df_lin.copy()\n", "dfs_lin['x'] = (df_lin['x'] - df_lin['x'].mean()) / df_lin['x'].std()\n", "\n", "dfs_quad = df_quad.copy()\n", "dfs_quad['x'] = (df_quad['x'] - df_quad['x'].mean()) / df_quad['x'].std()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Create ranges for later ylim xim" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "dfs_lin_xlims = (dfs_lin['x'].min() - np.ptp(dfs_lin['x'])/10\n", " ,dfs_lin['x'].max() + np.ptp(dfs_lin['x'])/10)\n", "\n", "dfs_lin_ylims = (dfs_lin['y'].min() - np.ptp(dfs_lin['y'])/10\n", " ,dfs_lin['y'].max() + np.ptp(dfs_lin['y'])/10)\n", "\n", "dfs_quad_ylims = (dfs_quad['y'].min() - np.ptp(dfs_quad['y'])/10\n", " ,dfs_quad['y'].max() + np.ptp(dfs_quad['y'])/10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Demonstrate Simple Linear Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This *linear model* is really simple and conventional, an OLS with L2 constraints (Ridge Regression):\n", "\n", "$$y = a + bx + \\epsilon$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define model using ordinary pymc3 method" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 75.099693\n", " Iterations: 8\n", " Function evaluations: 303\n", " [-----------------100%-----------------] 2000 of 2000 complete in 2.5 sec" ] } ], "source": [ "with pm.Model() as mdl_ols:\n", " \n", " ## define Normal priors to give Ridge regression\n", " b0 = pm.Normal('b0', mu=0, sd=100)\n", " b1 = pm.Normal('b1', mu=0, sd=100)\n", " \n", " ## define Linear model\n", " yest = b0 + b1 * df_lin['x']\n", "\n", " ## define Normal likelihood with HalfCauchy noise (fat tails, equiv to HalfT 1DoF)\n", " sigma_y = pm.HalfCauchy('sigma_y', beta=10)\n", " likelihood = pm.Normal('likelihood', mu=yest, sd=sigma_y, observed=df_lin['y'])\n", "\n", " ## sample using NUTS (starting from MAP found using powell)\n", " start_MAP = pm.find_MAP(fmin=fmin_powell, disp=True)\n", " traces_ols = pm.sample(2000, start=start_MAP, step=pm.NUTS(), progressbar=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### View Traces after burn-in" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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a9H1/xkR7DxeLwJfp4Fvl+U0A4OxLfy8FAaBz3FrvCUTGXCq0hlVYdpXUiDUh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lIlKDjXopfkBHVQMg3wTmK3H7JgMrRP3EkoQlkZGltFoiVQCQ4cc4+scPKcg7NVLkYPNAbdn5ON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\nllDRHVUwqUKCwDFZst5zJjtNqXaBZ4GcgWbuwNOQTzcw2l3pFxCOKkOWCDf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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_traces(traces_ols, retain=1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Observe:**\n", "\n", "+ This simple OLS manages to make fairly good guesses on the model parameters - the data has been generated fairly simply after all - but it does appear to have been fooled slightly by the inherent noise.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define model using pymc3 GLM method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "PyMC3 has a quite recently developed method - `glm` - for defining models using a `patsy`-style formula syntax. This seems really useful, especially for defining simple regression models in fewer lines of code. \n", "\n", "I couldn't find a direct comparison in the the examples, so before I launch into using `glm` for the rest of the Notebook, here's the same OLS model as above, defined using `glm`." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 93.518364\n", " Iterations: 7\n", " Function evaluations: 273\n", " [-----------------100%-----------------] 2000 of 2000 complete in 4.7 sec" ] } ], "source": [ "with pm.Model() as mdl_ols_glm:\n", "\n", " # setup model with Normal likelihood (which uses HalfCauchy for error prior)\n", " pm.glm.glm('y ~ 1 + x', df_lin, family=pm.glm.families.Normal())\n", " \n", " ## sample using NUTS (starting from MAP found using powell)\n", " start_MAP = pm.find_MAP(fmin=fmin_powell, disp=True)\n", " traces_ols_glm = pm.sample(2000, start=start_MAP, step=pm.NUTS(), progressbar=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### View Traces after burn-in" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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uw3XXXQeWZfHYY48hNzcXS5Ys6VTMsIwseHoTUreLEiC2C3WZXNr2HA0pSgLQ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\nO1rbAgjFZFhMDGrMJiiK2vfbDRHpUieP6lK1DtnYUqHXuZhWa0U6Jp7J6Lg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_traces(traces_ols_glm, retain=1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Observe:**\n", "\n", "+ The output parameters are of course named differently to the custom naming before. Now we have:\n", "\n", " `b0 == Intercept` \n", " `b1 == x` \n", " `sigma_y_log == sd_log` \n", " `sigma_y == sd` \n", " \n", " \n", "+ However, naming aside, this `glm`-defined model appears to behave in a very similar way, and finds the same parameter values as the conventionally-defined model - any differences are due to the random nature of the sampling.\n", "+ We can quite happily use the `glm` syntax for further models below, since it allows us to create a small model factory very easily." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Create Higher-Order Linear Models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Back to the real purpose of this Notebook: demonstrate model selection.\n", "\n", "First, let's create and run a set of polynomial models on each of our toy datasets. By default this is for models of order 1 to 5." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Create and run polynomial models\n", "\n", "Please see `run_models()` above for details. Generally, we're creating 5 polynomial models and fitting each to the chosen dataset" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Running: k1\n", " [-----------------100%-----------------] 2000 of 2000 complete in 2.6 sec\n", "Running: k2\n", " [-----------------100%-----------------] 2000 of 2000 complete in 4.7 sec\n", "Running: k3\n", " [-----------------100%-----------------] 2000 of 2000 complete in 6.3 sec\n", "Running: k4\n", " [-----------------100%-----------------] 2000 of 2000 complete in 13.3 sec\n", "Running: k5\n", " [-----------------100%-----------------] 2000 of 2000 complete in 26.4 sec" ] } ], "source": [ "models_lin, traces_lin = run_models(dfs_lin, 5)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Running: k1\n", " [-----------------100%-----------------] 2000 of 2000 complete in 36.6 sec\n", "Running: k2\n", " [-----------------100%-----------------] 2000 of 2000 complete in 9.8 sec\n", "Running: k3\n", " [-----------------100%-----------------] 2000 of 2000 complete in 16.6 sec\n", "Running: k4\n", " [-----------------100%-----------------] 2000 of 2000 complete in 64.1 sec\n", "Running: k5\n", " [-----------------100%-----------------] 2000 of 2000 complete in 74.4 sec" ] } ], "source": [ "models_quad, traces_quad = run_models(dfs_quad, 5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A really bad method for model selection: compare likelihoods" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Evaluate log likelihoods straight from model.logp" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "dfll = pd.DataFrame(index=['k1','k2','k3','k4','k5'], columns=['lin','quad'])\n", "dfll.index.name = 'model'\n", "\n", "for nm in dfll.index:\n", " dfll.loc[nm,'lin'] =-models_lin[nm].logp(pm.df_summary(traces_lin[nm])['mean'].to_dict())\n", " dfll.loc[nm,'quad'] =-models_quad[nm].logp(pm.df_summary(traces_quad[nm])['mean'].to_dict())\n", "\n", "dfll = pd.melt(dfll.reset_index(), id_vars=['model'], var_name='poly'\n", " ,value_name='log_likelihood')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Plot log-likelihoods" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "g = sns.factorplot(x='model', y='log_likelihood', col='poly', hue='poly'\n", " ,data=dfll, kind='bar', size=6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Observe:**\n", "\n", "+ Again we're showing the linear-generated data at left (Blue) and the quadratic-generated data on the right (Green)\n", "+ For both datasets, as the models get more complex, the likelhood increases monotonically\n", "+ This is expected, since the models are more flexible and thus able to (over)fit more easily.\n", "+ This overfitting makes it a terrible idea to simply use the likelihood to evaluate the model fits." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### View posterior predictive fit\n", "\n", "Just for the linear, generated data, lets take an interactive look at the posterior predictive fit for the models k1 through k5.\n", "\n", "As indicated by the likelhood plots above, the higher-order polynomial models exhibit some quite wild swings in the function in order to (over)fit the data" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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yktWr1/PAA3cxbtw1bN68kVtuub118owMgpIkSVKQPv10B4MHX0JqaifAN4vL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "interactive(plot_posterior_cr, models=fixed(models_lin), traces=fixed(traces_lin)\n", " ,rawdata=fixed(dfs_lin), xlims=fixed(dfs_lin_xlims), datamodelnm=fixed('linear')\n", " ,modelnm = ['k1','k2','k3','k4','k5'])" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Compare Deviance Information Criterion [DIC]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Deviance Information Criterion (DIC) is a fairly unsophisticated method for comparing the deviance of likelhood across the the sample traces of a model run. However, this simplicity apparently yields quite good results in a variety of cases, see the discussion worth reading in [(Speigelhalter et al 2014)](http://onlinelibrary.wiley.com/doi/10.1111/rssb.12062/abstract)\n", "\n", "DIC has recently been added to PyMC3, so lets see what it tells us about our model fits for both datasets." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "##### Manual calculation, probably error-prone" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "191.16310801115768" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dftrc_lin = pm.trace_to_dataframe(traces_lin['k1'])\n", "trc_lin_logp = dftrc_lin.apply(lambda x: models_lin['k1'].logp(x.to_dict()), axis=1)\n", "mean_deviance = -2 * trc_lin_logp.mean(0)\n", "mean_deviance" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "188.03386766667467" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "deviance_at_mean = -2 * models_lin['k1'].logp(dftrc_lin.mean(0).to_dict())\n", "deviance_at_mean" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "194.29234835564068" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dic_k1 = 2 * mean_deviance - deviance_at_mean\n", "dic_k1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Or we could use the newly created function in `stats.py`, much better!" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "194.29234835564063" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pm.stats.dic(model=models_lin['k1'], trace=traces_lin['k1'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Observe:**\n", "\n", "+ It's good to see the manual method agrees with the implemented package method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Now loop through all the models and calculate the DIC" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dfdic = pd.DataFrame(index=['k1','k2','k3','k4','k5'], columns=['lin','quad'])\n", "dfdic.index.name = 'model'\n", "\n", "for nm in dfdic.index:\n", " dfdic.loc[nm, 'lin'] = pm.stats.dic(traces_lin[nm],models_lin[nm])\n", " dfdic.loc[nm, 'quad'] = pm.stats.dic(traces_quad[nm],models_quad[nm])\n", "\n", "dfdic = pd.melt(dfdic.reset_index(), id_vars=['model'], var_name='poly', value_name='dic')\n", "\n", "g = sns.factorplot(x='model', y='dic', col='poly', hue='poly', data=dfdic, kind='bar', size=6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Observe**\n", "\n", "+ We should prefer the model(s) with lower DIC, which (happily) directly opposes the increasing likelihood we see above.\n", "\n", "\n", "+ Linear-generated data (lhs):\n", " + The DIC increases monotonically with model complexity, this is great too see!\n", " + The more complicated the model, the more it would appear we are overfitting.\n", "\n", "\n", "+ Quadratic-generated data (rhs):\n", " + The DIC dips slightly for the correct model k2\n", " + The difference is slight though!\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compare Watanabe - Akaike Information Criterion [WAIC]\n", "\n", "The Widely Applicable Bayesian Information Criterion (WBIC), a.k.a the Watanabe - Akaike Information Criterion (WAIC) is another simple option for calculating the goodness-of-fit of amodel using numerical techniques. See [(Watanabe 2013)](http://www.jmlr.org/papers/volume14/watanabe13a/watanabe13a.pdf) for details.\n", "\n", "WAIC has also recently been added to PyMC3, so lets see what it tells us about our model fits for both datasets." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### This time go straight for the implementation in pymc3" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "130.93585669884246" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pm.stats.waic(model=models_lin['k1'], trace=traces_lin['k1'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Observe:**\n", "\n", "+ Well, we get a number... not much to tell from just one though, so lets compare all models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Now loop through all the models and calculate the WAIC" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dfwaic = pd.DataFrame(index=['k1','k2','k3','k4','k5'], columns=['lin','quad'])\n", "dfwaic.index.name = 'model'\n", "\n", "for nm in dfwaic.index:\n", " dfwaic.loc[nm, 'lin'] = pm.stats.waic(traces_lin[nm],models_lin[nm])\n", " dfwaic.loc[nm, 'quad'] = pm.stats.waic(traces_quad[nm],models_quad[nm])\n", "\n", "dfwaic = pd.melt(dfwaic.reset_index(), id_vars=['model'], var_name='poly', value_name='waic')\n", "\n", "g = sns.factorplot(x='model', y='waic', col='poly', hue='poly', data=dfwaic, kind='bar', size=6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Observe**\n", "\n", "+ We should prefer the model(s) with lower WAIC\n", "\n", "\n", "+ Linear-generated data (lhs):\n", " + The WAIC seems quite flat across models\n", " + The WAIC seems best (lowest) for simpler models, but **k1** doesn't stand out as much as it did when using DIC\n", "\n", "\n", "+ Quadratic-generated data (rhs):\n", " + The WAIC is certainly wrong for **k1**, but otherwise also quite flat across the models\n", " + There does appear to be a slight dip in the right place at **k2**\n", " \n", " \n", "For these particular models and data, I would prefer to use the DIC scores in order to choose models.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## TODO" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### K-Fold Cross Validation and/or Leave-One-Out (LOO)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Left for future development - should be easy enough" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "http://www.stat.columbia.edu/~gelman/research/unpublished/waic_stan.pdf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bayes Factor" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Will be left for future development - scipy only useful for 2D and 3D. Beyond that, dragons." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Following text lifted directly from [JakeVDP blogpost](https://jakevdp.github.io/blog/2015/08/07/frequentism-and-bayesianism-5-model-selection/)\n", "\n", "The Bayesian approach proceeds very differently. Recall that the Bayesian model involves computing the odds ratio between two models:\n", "\n", "$$O_{21}=\\frac{P(M_{2} \\;|\\; D)}{P(M_{1} \\;|\\; D)}=\\frac{P(D \\;|\\; M_{2})}{P(D \\;|\\; M_{1})}\\frac{P(M_{2})}{P(M_{1})}$$\n", "\n", "Here the ratio $\\frac{P(M2)}{P(M1)}$ is the prior odds ratio, and is often assumed to be equal to 1 if no compelling prior evidence favors one model over another. The ratio $\\frac{P(D \\;|\\; M2)}{P(D \\;|\\; M1)}$ is the **Bayes factor**, and is the key to Bayesian model selection.\n", "\n", "\n", "The Bayes factor can be computed by evaluating the integral over the parameter likelihood:\n", "\n", "$$P(D \\;|\\; M)=\\int_{\\Omega}P(D \\;|\\; \\theta,M) \\; P(\\theta \\;|\\; M) \\;d\\theta$$\n", "\n", "This integral is over the entire parameter space of the model, and thus can be extremely computationally intensive, especially as the dimension of the model grows beyond a few. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Example originally contributed by Jonathan Sedar 2016-01-09 [github.com/jonsedar](https://github.com/jonsedar)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }