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  {
   "cells": [
    {
     "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()\n",
      "\n",
      "import numpy as np\n",
      "import pandas as pd"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "<matplotlib.figure.Figure at 0x10bce97d0>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "8. Regression Trees and Rule-Based Models"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Tree-based models consist of one or more nested **if-then** statements for the predictors that partition the data. Within these partitions, a model is used to predict the outcome. For example, a very simple tree could be defined as\n",
      "```\n",
      "if Predictor A >= 1.7 then\n",
      "    if Predictor B >= 202.1 then Outcome = 1.3\n",
      "    else Outcome = 5.6\n",
      "else Outcome = 2.5\n",
      "```\n",
      "In this case, two-dimensional predicotr space is cut into three regions, and, within each region, the outcome is predicted by a single number."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the terminology of tree models, there are two *splits* of the data into three *terminal nodes* or *leaves* of the tree. To obtain a prediction for a new sample, we would follow the **if-then** statements defined y the tree using values of that sample's predictors until we come to a terminal node. The model formula in the terminal node would then be used to generate the prediction.\n",
      "\n",
      "Notice that the **if-then** statements generated by a tree define a unique route to one terminal node for any sample. A *rule* is a set of **if-then** conditions that have been collapsed into independent conditions. For the example above, there would be three rules:\n",
      "```\n",
      "if Predictor A >= 1.7 and Predictor B >= 202.1 then Outcome = 1.3\n",
      "if Predictor A >= 1.7 and Predictor B < 202.1 then Outcome = 5.6\n",
      "if Predictor A < 1.7 then Outcome = 2.5\n",
      "```\n",
      "Rules can be simplified or pruned in a way that samples are covered by multiple rules. This approach can have some advantages over simple tree-based models.\n",
      "\n",
      "Tree-based and rule-based models are popular modeling tools for a number of reasons. First, they generate a set of conditions that are highly interpretable and are easy to implement. Because of the logic of their construction, they can effectively handle many types of predictors (sparse, skewed, continuous, categorical, etc.) without the need to pre-process them. In addtion, these models do not require the user to specify the form of the predictors' relationship to the response like, for example, a linear regression model requires. Furthermore, these models can effectively handle missing data and implicitly conduct feature selection, characteristics that are desirable for many real-life modeling problem.\n",
      "\n",
      "Models based on single trees or rules, however, do have particular weaknesses. Two well-known weaknesses are (1) model instability (i.e., slight changes in the data can drastically change to structure of the tree or rules and, hence, the interpretation) and (2) less-than-optimal predictive performance. The latter is due to the fact that these models define rectangular regions that contain more homogeneous outcome values. If the relationship between predictors and the response cannot be adequately defined by rectangular subspaces of the predictors, then tree-based or rule-based models will have larger prediction error than other kinds of models.\n",
      "\n",
      "To combat these problems, researchers developed ensemble methods that combine many trees into one model. Ensembles tend to have much better predictive performance than single trees."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "8.1 Basic Regression Trees"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Basic regression trees partition the data into smaller groups that are more homogenous with respect to the response. To achieve outcome homogeneity, regression trees determine:\n",
      "- The predictor to split on and value of the split\n",
      "- The depth or complexity of the tree\n",
      "- The prediction equation in the terminal nodes\n",
      "\n",
      "In this section, we focus on techniques where the model in the terminal nodes are simple constants."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There are many techniques for constructing regression trees. One of the oldest and most utilized is the classification and regression tree (CART). For regression, the model begins with the entire data set, $S$, and searches every distinct value of every predictor to find the predictor and split value that partitions the data into two groups ($S_1$ and $S_2$) such that the overall sums of squares error are minimized:\n",
      "$$\\text{SSE} = \\sum_{i \\in S_1}(y_i - \\bar{y}_1)^2 + \\sum_{i \\in S_2}(y_i - \\bar{y}_2)^2,$$\n",
      "when $\\bar{y}_1$ and $\\bar{y}_2$ are the averages of the training set outcomes within groups $S_1$ and $S_2$, respectively. Then within each of groups $S_1$ and $S_2$, this method searches for the predictor and split value that best reduces $SSE$. Because of the recursive splitting nature of regression trees, this method is also known as reursive partitioning."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# training (transformed)\n",
      "trainX = pd.read_csv(\"../datasets/solubility/solTrainXtrans.csv\").drop(\"Unnamed: 0\", axis=1)\n",
      "trainY = pd.read_csv(\"../datasets/solubility/solTrainY.csv\").drop(\"Unnamed: 0\", axis=1)\n",
      "\n",
      "# test (transformed)\n",
      "testX = pd.read_csv(\"../datasets/solubility/solTestXtrans.csv\").drop(\"Unnamed: 0\", axis=1)\n",
      "testY = pd.read_csv(\"../datasets/solubility/solTestY.csv\").drop(\"Unnamed: 0\", axis=1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# calculate the SSE for the continuum of splits\n",
      "def find_splits(values):\n",
      "    '''Find all splits points for a set of values.'''\n",
      "    uni_values = np.unique(values)\n",
      "    split_points = []\n",
      "    for i in range(len(uni_values)-1):\n",
      "        # insert split points in the middle of two unique values\n",
      "        split_points.append((uni_values[i] + uni_values[i+1])/2.0)\n",
      "    return split_points\n",
      "    \n",
      "def sse_split(X, y, split_point):\n",
      "    '''Calculate SSE for a given split point.'''\n",
      "    s1 = np.where(X <= split_point)[0]\n",
      "    s2 = np.where(X > split_point)[0]\n",
      "    sse = 0\n",
      "    \n",
      "    try:\n",
      "        y1 = np.mean(y[s1])\n",
      "        y2 = np.mean(y[s2])\n",
      "        for i in s1:\n",
      "            sse += (y[i] - y1)**2\n",
      "        for i in s2:\n",
      "            sse += (y[i] - y2)**2\n",
      "    except IndexError:\n",
      "        # if y is a pd.dataframe\n",
      "        y1 = np.mean(y.values[s1])\n",
      "        y2 = np.mean(y.values[s2])\n",
      "        for i in s1:\n",
      "            sse += (y.values[i][0] - y1)**2\n",
      "        for i in s2:\n",
      "            sse += (y.values[i][0] - y2)**2\n",
      "    \n",
      "    return sse\n",
      "\n",
      "# calculate SSE for continuum of splits for 'NumCarbon'\n",
      "split_points = find_splits(trainX['NumCarbon'])\n",
      "sse = []\n",
      "for i in split_points:\n",
      "    sse.append(sse_split(trainX['NumCarbon'], trainY, i))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plot the SSE for the continuum of splits\n",
      "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True)\n",
      "\n",
      "# number of carbon atoms\n",
      "ax1.scatter(trainX['NumCarbon'], trainY, alpha = 0.5)\n",
      "ax1.set_ylabel('Solubility')\n",
      "\n",
      "# SSEs\n",
      "ax2.plot(split_points, sse, 'o-')\n",
      "ax2.set_xlabel('Number of Carbon Atoms (transformed)')\n",
      "ax2.set_ylabel('SSE')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "<matplotlib.text.Text at 0x10f1eb250>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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sW/d2TH0mJtenjcLCBWRmlpCZWUJh4QKKi4f+hnHppZeiafWe0480vSx+BNZv\n69YPaGo6C3wO+BxNTWfZujW+2701NWfxeCRdXXV0ddXh8UhqamJzjnA6BVqssjv140q9LFpMwKXA\ng/pxKaHeC4Ndf1ZrOlp4j0n6sUAvCx+fLwu4FnhPP67VywbnH/+o1Od8rX6Y9LLB+clP1tHTswgp\n/Ujpp6dnET/5ybqQbcrKSnG7N1Ffv5f6+r36NtXg0XlffPFF1q7dwNq1G8LK8xlJHMZnnnmJzs4p\npKd/ifT0L9HZOYVnnnkpaF3QBLBw5rJlSwXd3VM4fbqK06er6O6eEjI+W7Q5V8MhkXHAwl2PZEbF\nUUs8yaJR68sDwB+GexKKwSkoKOCqq9Kpq9PicU2YMIGCgvA87uJJdrYRzT7oa3rJs2Rn54RoET0O\nRwd+/xTc7oAt0yU4HJHluByMurqADdxyAFyu56irq42pTymNaNuegdAVlyHl7qj7MxjS8fu/BARS\nW3VgMEQW+Dcjw0d39zFgll5yjIyMyJKyp6X5AS+9297VetngeL0WtPAggWtlIl5veDZy9fV2oA4p\nA3HkKvSygbHZbNx4Yz6rVmlbpCtXfm5QTUh1dTW//vWbSKlpVEM5BgQoKChg2jTvuRy8EyYUUFAQ\nfEu3vr4NIe7CYtG0VN3dp6ivXzfgXMLVktnt9ezceRifbzIARuMxZswI7lEbrp3VSLPHUt6qingx\nYgQ1IcRGIFgAoMellP+j1/k+4JZSDvhKt3z5coqKigDIzs5m5syZ5/bQA5J/sp8vX34bO3eu5/hx\nLXei1bqP5cvvj6n/G2+8Me7zbW8/xd69f2fUKM2mZe/eZygru5kAQ7Ve1dUOjMYvoT2wAZZQXf1S\nXMcLrJ/H04rfXwfMQ8p9wEekpVni+n0aG3uA69AsAgCuo7HxDzH1P3ZsFg0Nb6BproqA/WRm+vt5\ndEXSX1ZWGi0tH6Ep7ecB7aSlDdxfsOuvra0TWA8EsgE00dbWa6MWznxOnTqK9rsLoA7Yh93eHVZ7\nzR7OSa+w2d9GLlT7zEyrvnX6AmADLJjN7pDr+bOf/Ywf/ei3dHdrt8FvfvO/aGxs5Dvf+c6A473w\nwivU1Eg6Ow/h8ZwlJcXNhg2X8P3vf3PA+RUX57Fnz5O0tmoCa1OTgW9/+3tB648fn8HBg9twOGrx\n+Y4CjnPOMefXX7NmPQ7HBGbN0oS63bt3sWbNen760/+4oL7D4aCh4TQm0wwsllm43dXs2bNrwPV5\n/PE7WbPDpUTjAAAgAElEQVRmPQBf//r9/TIKBOqfOnWKRYsuOedYkZZ2CadOnTonGA3V/Saa9VDn\nn5zzwOfa2lrCRUgpw648nAghlgMrgEVSyqAWxUIImSzfJ1bKy8vPbXcuX35bgqLsx8batRvYvDm1\nT4iCVBYu7GbFiiVDOo85cz7PgQP3IqW2jSREBTNm/JEdO16J+1g33fRFNm++FCmz9bFaWbjwNJs2\nxU8JfPnlC6isLAKW6iUvM3VqLYcPvxd1n7NmLWLPnkK0bAIAv+fqq+vZvTu6dFv33PNlXnvtJPAl\nveQl7r57PK++Gn5Sdas1H7e7GPiUXvIhFksNLldozVRfLJbJeDwTgbF6yRnM5hO43ccGbZuSMhmX\n60EgsC3YiNX6PD09g7edNesmfT3v0kte19dz04Bt5s27jR07fEipOQcI8SJz5hjZtm1gs4abbvoC\n770HJpOmLfZ6n2XBAti06U8Dtnn00R/w7LMVeL2aptJk2s3XvlbK009f6OxQXl7OV76yhvZ2TTM1\natQb/O53Xw96v1m7dgMVFSV9bMT2UlpaFfTvfdmyx9i2bSFGoxaI2Ofbxbx5m3nhhZ8OOO9kI5L1\nUHxyEUIgB0liPGI0aqEQQtwKfBe4YSAh7ZPGokWL4iqc9X2TjSeRhihIBPfccx0VFc8jhGYILuXz\n3HPPTXEdI7B+zc12PV7bjfpYf6C5OXzBIhzy8jKByfQayE8mLy+2PKpnzrQDy4Dpeslizpz5VUx9\nQhPwcp/P4wesGez68/tT0bY9AwJpN35/ZLZ4QvQABfQKTK8gRHjXoJRe4CAQ8KrcqpcNjt9vxmgs\nxe/XtDkGQyl+f+h4egcOnETK7wCf1cf3c+DAz0K2cTi68PmuxWrVtlg9nlYcjt+GbLN58y7c7ssw\nGDThy+1uZ/PmXUHr1tQ4uP76R/oY8o8LasgPkW09lpRM4KOP7GRmalq9jg57QjI3hEOway8eYT5G\n2lZsokjUs0PRS1IIasAzaAGeNgohALZLKWOLR6FIOCMl/Ux29gTmz7+Zo0f/AsBll91MdnZi/FHO\nnGkD7kQITVsh5XHOnPldXMc4etSBZjsVYCJHj74VU59mswnooDeTQIdeFh3bth0CbiBgRwfr2LZt\ne0R9+P0WtPhns/WSOvz+jSFaXIiUKcDNQJle0o6U4aUxMxpT9LEDaz0bozG4QHM+eXnZgBchAvlS\nvXrZwPj9oHnKBozlR+llA1NUdCmVlW683kYALBYXRUWhHWVcLi9e73wMhsv1cefjch0O2SYcIgkF\nsXTpp/nww1VUV3frbY+ydOnIuKXHy7ZsKEJjKD4ZJIWgJqW8bPBailhI3BvRyEh1VVKyiBtu0Gx9\nEqHZC6xfamoGRmMuUmqv0QZDLqmp4eWHDJfWVgfwEb3ar4/0sugpKsrh1Kl36Q3P8S5FRdE7XHR2\netCEo6v0kjI6Owfemg12/VksHnp6KoFA4N1KLJaB84UGw+PxodmZBRTxTr1scPLysvX0X4HwHJZB\nha0AEyaMQcp9+P3ab2Qw7GPChOCelQEyMyWdnS8AgbAoL5CZGdqU4+6757Np0wZ8Ps2zWIiXuPvu\n0FtrublpQDVS1uol1XrZhRQX5/HDH/5fOjoW6HN8j4ceik9cwPR0C5dc4jz3ebg4/9qLZ5iPT0Jo\nDKVNSzxJIagpkpORkH4GhnYL4t57r+Opp9YBmnZAynXce+91cR3D63UCB4DX9ZIDeln0nDnTiKZN\nC9hQ1XHmTPT2ntnZFjo6DgPT9JLDZGdH9jBOSTHQ0/NXICCcvUNKiiHCmbjQhNpAPLeP9LLBGTdu\nNCdP/oVewekvjBs3Oqy2dXV2tC3XrXpJLnV1DWG0rAd+0+dzaFwuK9dcM4ejRzWbtMsum4PLFTrW\n25gxY0hPr8Lnex8Ao7GKMWOCC5FvvrmF1tYWvN6PAfD5WnjzzS1BzS4i0UQN570hGex7FYq+KEFN\nAVzcdgZDsQURWD+bbRbXXOOiqurnAJSUzMRmmzVI60gZhZZp4YB+XgLEFketoaEVzR4sIFh5aGiI\nPjzHlCk2Tp/eg9+vpZAyGPYwZcrAax7s+vN6QdNmBbZ1O/Wy8NEMdU8A2/SSE+jmE4OSn38JZvN+\nPJ61AJjNPvLzrxiklcbp06eR0gVoQWWl/B2nT4fWenZ2BmwbA0nVbXR2vjlwA7QwF8eOHaawUEuL\ndfbsBuz20ALe7NlXsXNnLW1t2t9DZmYes2cXBa27efMuvN4rsVgeAMDt/s2A9mzJEHC2vLycb3yj\nN8vBzp3r+drX9p7zrIXwX+xUuiqNi/nZMVJQgpoiYYwkY9qh3IK4+url3HZb4hwoxowxU19/Ai2k\nIMBvGDMm1gTqFrQsbXfo53+mVxCMnBtv/BRVVR10dmranfT0Um68ceAUUsHo6fGhbZ1eqZfso6fn\nw4j6yM620NLSQa8g2xG2Zq+724HHkw5oW4kezwa6u8PbYna7JVJeQyAunZTX4HaHtiNMSzPoWsiA\nHed60tJCaxClFLjdGTQ2anH7DIZsBnEgY8KEbFpaduF2a7HX/P5dTJgwc4DaRvz+BQQEeO3z4F6v\ngzFc94Z1697GZFpGfr6m9bPb4W9/W0sfOQ2bzcZ9913NunWah/Ly5bddcO+IJLG9QhErke4jKC5S\nEvFGFLjhdXb+ns7O33PffVdftDeywPpFG10+Em69dTFCjAM2AhsRYhy33ro4pj7Hjy8A3gf+WT/e\n18uiY+nST1NUdBiT6UNMpg8pKjrM0qWfHrB+sOtP8551ouXpPAw49bLwyckp0Ps4oh9OvWxwDh1y\nAA8gxByEmAM8oJeFgx/N07VbP5r0soH51KdmoqXael0/OvWygRFCYjZ76eg4S0fHWbzeKoQIvWW9\nfv1f8fkmYzTeitF4Kz7fZNav/2vQugsXXoPZfAS3+13c7ncxm4+wcOE1QetGcu0HtNylpVWUllbF\nLRBseXk5y5Y9xrJlj1FeHl5omcLC/t7I1dXVrF79LidOzOHEiTmsXv3uBVkFAontu7oW09W1mAMH\nBBs2hNZ+XqwobVriURq1JCUZ1O6BG57dPgeA1avfZeLEiSNyrvFiKLZZ582bx6FD9VRVadqakpJx\nzJsXLFZ0+Fx/vY3KyqNooQoB1nL99dH78Jw4cYIjRxppby8G4MiRmohzRGZlmWhuNgBf1EvWkJUV\n2S3L43Gj2acFxq3G4wk3wo8fOKRvnYImRIWX1UBznDkABISaTQzmTHP11aVs2ZJOW1sHAFlZU7j6\n6qkh2zgcDlpbu5BS06h6PF04HKGFyWPH7MAjmEyaEOX1dnLs2C+D1r399uv54x/X0N6ueb6OGrWH\n22//etC6kV778dZyB9vWXL2afjZogWDhdj1ijtf7AsuX9/dEf/nlt6ioSMfv10LenDyZzssvv8UP\nfvAv5+pUVp6ku/tqWlq0jlJSZlBZuSdu3+WTSjI814YDJaglIYlITZIIO4OXX36L/fuLycycD8D+\n/c4LbngXC33XL9HbrMXFebS0vMXYsdoDqaXlBYqLYwt7Ul5+CChF09IBXEl5+cC5FwfjJz95lubm\nsWg5T6G5+Y/85CfPDmi4Hez6y8+fSHPzErQsDAAt5Oc/H9E8NKFnAr2CWjttbQfDaltUlMGpUx/Q\nN+BuUVF4HrwWSzZwW5+S27BYgmutAjQ32+nuPoAQWnDe7u4DNDfnhmxz/PgZvF4PFouWPcHvt3P8\n+JmQbcaOHUVt7SG83kAcvkOMHRs8hZQWR21Zn6DVy6ipcQSNowaRXfvxfiivW/c2fv9CvF5NwPL7\nF7Ju3dv9rrlFixaxejV9nAnux2g09utn165/0NKSRVraLQB0da1n1662fnVMJg9nzpzAaNQE8ebm\nXZhMkXkkXyzE69mhUm4NTFSCmhDiNeB54O0+ydIVQ0QyGO0CVFXVYTTeSkaGpu3p6hpHVdXfhnlW\nyU9NjYPS0gf6BCF9YMAgpOFy8mQtmubpG3rJar0sOqqqTuH1fg2DQQtP4fffSFXVsxH1kZubgabF\n6tBLOvWy8OnpAbgEuF4vOUtPT3iCWkeHEc1DNLCFJujoCC8pvBbuop3eHKNHBgyBEWDHjt309PgJ\nWKT4fH527BjMocOI9v0CIUyK0YL0DkxGhgC20BsweQsZGcEFNYgsaHW4wlciHsodHS04HP8gLU17\naenqWk9HR9sF9SZOnMiCBdec+3zq1Knzahjw+Yrp7NRsGf3+YuAf/Wq0tDhJSQGDISAUNtDSEp3n\ntdIiaSTLc204iFajthr4KvCMEOKPwG+llEMfcl4RNxJhZzB16ng+/rgcp1MLjeD3lzN16sDR6ZOZ\nvus3FDferKwsSkq0nIvaw3PwUA6h8PutaI4Ega26M/j9+6Puz2IBqEfKgJahXi8LTnAbNRdC/Akp\nNScE7XNkNmqag+dsILCFOBshBk7j1JfTp6vRcp8GArGu0ssGR8tgsBEIbJseOfc9BqKm5jRauuPA\n9dKklw3MpEkFGAxV9PRosQpNpkNMmlQSss2RI20YjfciRKY+1y9w5Mgfg9aNxOg/0vAc3d1TaGzU\nHhsZGVNifigXF4/n73830t2tOTsYjTkUF/cXQAeaY/9+LqW83InPp4VTEcJJcXH/IMKZmTkUFFyB\nwVAHgN8/i8zMyP9eLgYtkrJRSzxRCWpSyo1oWQKy0fK7lAsh6oC1wO9l791ZkQBGkjdlKJYsuZ09\ne57Dbte204qKJEuW3D7Ms0osQ3HjTcTvn5OTjcMh6BUsBDk54QV3DcakSeM5fvw9pNS2zIT4mEmT\nIhPS/f50UlLG4/VqMcJMpmn4/Scj6sNqNeNy1dP7veqxWsPzkG1vNwJfJ5DSCfy0tz8eVtuGBjtg\nBVLOtdXKBkYLPWKj1/O2Ca93cAHcYMjCbNYC0goRWrADyMpK59SpfFJStG3pnp6/kJUVXFMYid1Z\nJBoRu72enTvr8Pm0+4HR+CYzZsSeQkpLE3eZ/vkY0BXxHEePzmHMmDp8PqnPrZHRo/vPLWDrFrCH\nC2brFg5Ki9RLsjzXhoOobdSEEKPRkgN+GdgNvATMRwscdGM8JqcITiIM1hNho2az2fjGNxb3Cy55\nsd6AAus3FDfeRPz+d91Vytq164EH9ZL13HVX9N6qWVlmpGwnkBFAynaysgbOdBDs+ps2bSwVFWcB\n7Wbt8fyVadPGXtg4BKmpFtrbdwABjcgOUlPDC88hhAHNeSAQvM2vlw1OW5sHTYsXSD/VRltbaI3L\nmDFjaGrKAdbrJTkDBqIN4HB0YzZLPJ5XAcjImITD0RyyzaOPLmHFiv/E6dRyuVoszTz66HcGrL9t\n2zaef15Lv2a1uuJyLTc1tdDUdCkWSxEAbvelNDW1DFg/HC11Tc1JzOYssrI0a5yurnpqai7c+jyf\nqqr+W8X5+YVcd90knE4tLVdGxg3k53f3q7No0SJWrNjNqlVaIvuVK2+POnBuW1sdp08HNIupg9Qe\necTr2aFSbg1MtDZqr6PdhV4APiulDAQpelkIEb0FsiJskiE1SXV1NS++uIf09C8D8OKLmy56r8+h\nIt6/v93uw2odhdutCdUWyyjs9vBSLQXj2LEWTKZ/wWDQQnL4/W9x7Ni6iPrIzs7FYhmH16vFUTOZ\nzpCd3TVIq/5MnjyJhgYb2rskwFQmTw7vtldQ4Keu7pdAwIvyZQoKwjPJNZsDBuoySFlwpk8fS2Xl\nJqBIL9nJ9OlTQrYxmbppa6vEbNYC3jocz2IyDS7MGgxjMRiW65/XDVhv/fr1PPLInzAavwbAI49o\ndob333+h9qisrJRXX32K8nLNu3XyZAuPPfbdoP02NjrJy5uJ0aj9nj5fMY2NHwStG66WOjMzR49F\n9yP9vJjMzP4vB1r+4ec4dEjT8ufnN3H99VcErdPWptmAWq1NlJU91K9OeXk5v/rVNlyuGwD41a+2\nMWtWecTCWnFxHk891V8z99BDQ58PeaSQDM+14SDaOGprpZSXSyl/HBDShKZzRkoZ36BRiiEhEXYG\nfbVLhYUzsVhuOve2dLExlHHUEkF9fRsWy6fJyfksOTmfxWL5NPX1g2sjBiIlJRWLpQmT6RVMplew\nWJpISRlYWxDs+mtsdFJYOIOJEwuZOLGQwsIZNDZGZrB97bVXYLWeRoiZCDETq/U0114bXnYBkykb\nLaTGNv1w62WDc8kluUAasEA/0vSygTlzxoEQl6BtSnwFIS7hzJnQoTZaWjykpa3Eai3Fai0lJeUL\ntLSEtjxZteovpKQ8zPjxSxg/fgkpKQ+zatVfBqwLX8ZgKMJgKAK+PGDdEydOUFnZjtP5GZzOz1BZ\n2c6JEyeC1p06dTxSbsblqsTlqkTKzQPar4Z7H7nyygLs9u10ddno6rJht2/nyisvjJnndDo5e9bO\n2bN2nE4n1113YYq38+uczzPPvERr6ySEuAsh7qK1dRLPPPNS0PmHoqbGwZQpN2My7cNk2seUKTdT\nUxNb3t6hRtmoJZ5oBbUngpRtj2Ui4SCE+I4Qwi+ECH3HUyiGiUQF8kw006aNpavrbdrajtDWdoSu\nrrcj3mbsyz33XIfb/ToeTzYeTzZu9+vcc09kOU+nTh2P2fw+o0adYdSoM5jN70fsjCKEEbN5Fmlp\nc0lLm4vZPAshQmu2ArjdJrTsD1/Sjwf0ssGZMKGYlJT5mEyXYjJdSkrKfCZMKA7Z5uzZLgyGz2Mw\nFOjH5zl7NrQGMTNzFLm5JlJSqklJqSY310Rm5sAenJHS09NJd/dhOjs/pLPzQ7q7D9PT0xm07rp1\nb2M0LiEzs4TMzBKMxiXnzB7OZ86cGfj9J3G79+N278fvP8mcOTNimuuHH1aSkjITi+U2LJbbSEmZ\nyYcfVvars2HDm9TWZpKVdR9ZWfdRW5t5QaDacOrU17chxEIslplYLDMRYmFULzZ2ez3V1QewWBZi\nsSykuvrAoCnAFJ88IhLUhBCXCCFKgVQhxCwhRKn+741or48JQwgxHlhMr1WwIo5s3bo17n0mq3Yp\nGvqun81mY8WKJaxYsSQphDTQvEjN5mw0D8nZmM3ZZGVlRd1fdvYESku/SFpaC2lpLZSWfpHs7IGN\nxYNdf0uW3M6MGZK0tI2kpW1kxozInVEaG53k5k4hPd1KerqV3NwpYWvl8vPTgUZgsn406mWDM3v2\nDPLynGRmNpCZ2UBenpPZs0MLIjk5Vny+evz+XPz+XHy+enJyQidYX7z4Suz2p2lvP0N7+xmamn7H\n4sVXhmyzcuXn8HhW09DwKg0Nr+LxrGblys8FrWuzjcHnq8DlGofLNQ6frwKbLbjdXEdHG01N9Tid\neTideTQ11QcNjwGaJmnu3G8xe/YXmD37C8yd+60BNUnh3kfq69swm2+hoOAGCgpuwGy+5QLhqbLy\nJB7P9bS3j6W9fSwez/Vs3bpt0DqVlf2dWObNm4Hff4TOzho6O2vw+48wb96Fv291dTVr125g7doN\nF2Q3AC0FmJQlaN6+hUhZMmgKsJFGIp4div5EaqN2C5pe/lLgZ33KO4Dw3KGi52ng/0NLQqhIApRx\naPJw/HgDBkMZZvMkAAyGMo4fD24zFA4NDQ3Y7RaysrRtRrt9Pw0N7RH1EQ9nlLy8VFpb38Ji0YSL\n1ta3yMvLH6SVhhYi8ji9oU+OE27YyLlzp7N69Sq8Xu2h6/eXM3fuypBtcnOzMBj24fdrsecMhn3k\n5oYWluvqWsnIuByf7zAA6enXUVfXGrLNvHnzKCr6DdXV/wlAUVE28+bNC1rX603Bav0sXq8mMJpM\nn8XrDZ6UfdKkQrZs2YPHowmKUu5h0qTYMmZA+PeRefNmsH//Ic6enaDP9dAFwtOYMRk4HJVYLFq4\nFre7klmzUi+oY7cfREpNoyzEQcaM6R+/b+XKL7Nr11NUVr4CwFVXHWPlyv72eOHY1hUUFDBrViFO\npyakXnbZJAoK6i/oR8VZ+2QTkaAmpVwHrBNC3COlfDUxU7oQIcQdwCkp5T4hkuttI1lIlJ3BJ8U4\ndKjjqMUbp7Mdt7sBs1nziHS7G3A6IxOs+tLcbKexsQopta1KIcppbh44vlew6y8ezih5eXmMGnWC\nzs7XARg1qpu8vLyw2p482QTcBOzTSyZz8mRwIeV8tm8/iMVyLTk52qaFwXAt27cfHMTY3IwWsPYj\n/byY3kC2wamqqsNs/hQul7bd6fO1U1VVGbLNqlXrOHasG69XW4djxzpYtWodTz/9oyC1JQaDG5Np\nvP49KunrINGXadNmMGtWG0ePakGtZ8woZdq04IJmcXEeTzyxCpdLy95gtb7NQw/904BzDuc+MnNm\nMR7Pc3raMJDy78yc2d8JYPToHEaPPobPpzmXZGbWMnPm1ef15MXvfw+vVxPOTKb3gKsuGC8/PwcQ\nfT73JxwP8EBIiqwsTZhzuz/uF5IiGeKsKRu1xBORoCaEWCalfAEoEkI82ve/ACmlfDraiQghNqLp\nf8/n+8C/AjefN15Qli9fTlFREQDZ2dnMnDnz3IUUUNGqc3WeqPPTp09TXn4Wi+UmzpzZxWuv/Yxn\nnvkONpttRMxvoPOMjHRMpo14vWcwGqdgte6np6e9n+t9JP3V1NjxePLw+zdiMEzBaJzDRx9tiai/\nNWvWc/hwKp2dWvyx9HQPa9as56c//Y+w51NTcxSzOY3MzHx6eo7h9fZqmwZr73Q2AH8F/o/e4j/0\nssHbV1XV4fdfQk5OCdnZN2K3b+Ldd9cyf/6VA4539uxR/P4q4J8B8Puf4ezZXuuUYOPV1e2lvn4f\nQjyMlPvp6HiD7u6SkPP785//Rk/PGDQnB/D53uPPf/4bn/vcTRfUd7macLnex+/PQMpKDIad5OZe\nEbT/9vZTHD36d0aN0jRLR48+RXt77227b/0dOw7Q3l5HZ+cqjMZcsrJMvPTS6xiNxqiv5//6rzV4\nPOMQQhNaPZ5C/uu/1pzzUN26dSstLU1MmzadurodOJ0nKSi4lPz8wn791dQ0YDBcg8l0FACD4Rpq\nak72G2/LlgrcbhvFxTaKim6kvn4va9as5zOfWXhuPlVVBzlzpuOcoHbmzC4yMuouWI/LL5esWvUt\nurtbufPOOeeEsK1bt/LXv27GYrmbwsKZ1NZupbk5+5ywN5LuH+o8/PPA59raWsJFSBn87ShoZSG+\nJqV8VgjxQ/q/VgUEtX8Pu7Pwx5yBlsMlYFU7DjgNXCultJ9XV0byfRS99H2AKiInsH5r126goqKk\nz1v0XkpLq1ixYskwzzA03/72/+a5544ipfYQFmI/Dz10Gf/93/8ZVX833bSUrVsnYjBomhi//yQ3\n3niCTZteDlo/2PX36KM/ZO3aFKS8Tp/TTlas6OHpp38Y9jx+9KNf8Pzz3fj9mremwdDKgw+mhpVv\ntrBwNg0Ns4GAF6WZgoJd1NcPrlV74omf8/zzx/D5NGHIaHyPBx+czPe//80B21x++fVUVnYDAc/S\nVqZOTeXw4fcHbDNz5u3s3z8Zs1lbI6+3mRkz/sbevW8O2CYn52paWx8ERuslTWRnP09Ly4VJxW+6\n6V7efVcihHY9S7mXG24QbNp0YSaDtWs3sHlzap+8oKksXNgd9Nq/6aYv8O67ToS4Vu/3I264IYNN\nm/4UdM7l5eX9tsCDaSbz8mbT1PRtjEZN++Xz/YPRo/8bh2NXv34efPA5XK7PA2C1vsI///NsvvOd\n3jhyd975T5SXT8dg0H4Hv7+VRYsO8sYbv+73XQf7O6+uruZ731uP3a5tBefn7+PJJ+/vpw1bv349\nK1duwOd7AACj8TesWrXknHCZDPcT9eyIDSEEchDDxEi3Pp/V//1hDPOKCCnlAeCcj7UQ4jhQKqUM\nHdVRoVCEzejRY8jOvoTOTi2FVHp6DqNHewdpFQofcAifT3tICfEOvVH6w2PfvoO4XGAyzQbA661g\n375BGp2HEBIh7ARSYwnxJkKEFwF//vxpvPZaLVJ+Xm/7CvPnTwur7Zw5M1i7ditutxbk1mo9yZw5\nd4Rs43b70KLqz9dLPsDtDu07pYVBySct7U69j00hw6AA5Oam0tp6CC0LIMD75OYGb+N0+rFar0dK\nLaaeEPNxOgcWHMPNC3r6dCM+33SMRs2JwedzcPp08Byl5eXlfOMbvbHGdu5cz+rVXCCsZWUZaWp6\nFZ8v4OzwKllZ/T18t28/iM93OS6XZtNnMl3OoUO1/eoUF+ezcePfcLtn6XV2U1zc33kh/Cj6bjQ7\nx8Dn/jz99AZcrq+SkqJlv+jpkTz99G/PCWoqWr8CIt/6fCbEf0sp5eCvqbGjVGYJQL0RxUZg/ZL5\nxur1nqGnRzM9tVpN9CbtjgYTMJdeZ/C5wMCR+YNdf06nJCXlZsxmLfG1x7MYp/PvEc1CSoHZfAW5\nuZqA1dFRp2dMGJyZM2fz7rvVtLVpgklW1hRmzgzPNqimxsGMGZ+nrk7bKp0w4fPU1DgYPB7qFHrf\nS6cwmJP7ypWf45FH/oTfvwUAIZ5j5covhGyzYME1eg7RwJZu+rkk5edz+eUFVFRsPRfw1ud7lssv\nDx62JZJr32pNx2BYgJQB55UFWK21QeuuW/c2JtMy8vO1rVm7XSs7X1BbsGAOtbUd+P1/1PvMZsGC\n/uFcdu36B62taRgMdwHQ2vo6TU39Q6BIKTAYxmI2awKzEPUXeGKG4+CwZUsFeXlLmTGjV3A930at\nra0TIcwYjRZ9LDNtbb3hT8IZZ7htYtWzI/FE6vVZgSYoBVPTDYkAJaUMHYxIoRhGktXTtaamEofj\nOLAcAIdjHTU1k2LqU4g0DIbAllnkUXXmzZvB4cNODIab9P7eCBoCIRTheNUNhBCSzEwzaWlfAbR8\nlEKEd5uz2+s5dOgwPt9kAA4dep+5cy8P2cbj8QLNwE69pEcvG5iA5mXVqnUArFz5haBZA/oihAeD\noRO/XzO0NxieQ4jgQXInTy6hsHAsnZ0Br9LZTJ4cPLm8zWbjvvuuZt263wOhvXSvvtrGwYPH+my1\nH4yjC5cAACAASURBVOPqq2P7O7HZisnPr6K9XRPgRo0qx2br/7hwOjvp6ZmK2VwEgMczAaezf/Bc\nh6ObnJy59PScAiAlZS4Ox4UOGuE4OAyWHqqsbBovvPBreno0zZ+Uv6asrL/WNtQ44TgbDLcgp4id\naLw+FRchys4gNvquXzJ6uu7efRy4GYNhHAB+/83s3h2Z9qovGRlpWCwH8fs1rZzBcJCMjIFDLQa7\n/rQQCD+mslIz6r7qKhcrV0YWBWgwr7pQxKKNczgcNDVJLJZP6eNW43CEjjjf0eEADqMF2QX4jV4W\nmgkTJrBjxythzQtg9+4TGAwPkpbWu922e/dvg9YtKChg/vyrcDo1e7aMjKYBBd1IvHRttmIKC/fT\n2fkuAOnpNdhswTNGBBKg23WL5IESoEspSEmZiMWirZnBMPECTVhGxihSUvIwGDTLGaMxj56e/nH1\n8vJSaWv7GItFE9Db2n4XNKTLYAJQOOmhHn/8UY4e/QFVVb8EoKQkm8cff5RwGcyzdCi8RtWzI/FE\nuvX5cynlN4UQ/xPkv6WUMnjURIXiE0RyvsEagPFYLNoWWE/PWaJPXAKTJo0FduP3a6EaDIYmJk2a\nFXE/+fnjgF5j7EiJRcNZUFDA2LFtHD26CoDLLhtHQcGFKYmC4XB0k5d3B0ajNpbPdwcOx+aQbTye\nFGARvdvFi/B4zgw61unTp1m7dgMQ3vWWkpKK1Srw+7VtWatVDGjXFomgG044igD5+YXMnz+pj+PB\n5y5IfB5g0aJFrF5NH2eC+4M6E4Rjj3jNNdPZt+8APt9EAIzGA5SUFPWrM3r0GEaPnoDPpzkTZGbO\nZvTo/nMLRwCqqXFQWvpAHyH3AWpq6vttf9tsNn74wxUxxQoMRSS/iWLkEunW53r9358F+T9lO5bE\nqDei2AisXzLEPQpGWdksjh17Bym17GwpKe9QVha5YNUXzc7niwAI8YeQdYNdf5qNz919bHxsUT1k\notVwWq0uKir+55x9VkXFs3z1q6HtvwKUlEzgo4/sZGZqAXI7OuyUlIR2YkhNtdLZCX1vpampoTMT\nVFdX8/rr+7HbNWHgnXf28OSTD4X8vvfccx0VFb9GCO32L+Wvueeem4LWTdRWfjiJz/uyaNGiQROe\nh6MBXbLkdvbseQ67Xfs++flm/vVfv9GvTkFBAdddV4jTqf12GRlTLtAihi8AtdEbMPlCYTjWWIEj\nwSZWPTsST6RbnxX6v1v1JOxTAT9QJaW80KVFofiEkaxvsA8//BV27fohVVWa9qikJIWHH/5K1P05\nHN3k59+F0ajZlPl8dw2qUQrGYDY+4RCthnPjxn2MGfMgRmMRAD7fg2zc+AGDmIABsHTpp9m7dz12\nu5bdoaiohqVLQzccMyYFh6Oc3rAZ5YwZE9pTdsOGNzlwQJCRsRiAAwc2sGHDmyHDgGRnT2D+/Js5\nelRLrn7ZZTeTnT1uwPrhCroB4evQoY0A5OeHFr60xOeaN2laWnBtWiSEY49os9l48smH+lwPd13w\n3WLZLu+LFtT3l7hcmkbYat3HQw890q9OrPeLwQTpkSDIKWInUo0aAEKI24E1QI1eVKzHWHsrbjNT\nDCnKziA2hnr9ErG9WlBQjBDRbzP2JVKNUrD1C8fGZzBi1XBarRnk52vCZiTJsjWB4P4+v9H9g44p\npRVt2/NDvSQNKUM7E1RWnqS7+5JzD/quLgeVlX8bdH7p6Rnk5uac+xw/LEDACaVjwFq9ic+1eGC1\ntYMLmIMRrpbufMHz/GsvHC1iOALQjh0HMBiKsVhuAMBgcLJjx4FBNYPxZCicm9SzI/FEJaih5d0s\nk1JWAwghJgNv6YdC8YllKN5gE7G9Gq9txgDRaJTOp6bGwZQpN1NXpwmNxcU3hxniopdYNBbhGrEP\nRHRbrieBQPR6AYTO9VlSMoGtW8/gdGoXnM93atAtVqvVxXvv/fXclm5t7bPce+/AW7rhvhREcg1V\nVp7EYLiVjIzwBMzwX0zCExQHY7DfLhwBqLLyJD5fAd3d2mMxNbXgguTusd4vwrkXJKNzk6I/0Qpq\n7QEhTacGiD4xoGLYUW9EsdHX4zPRb7DJsL0aqUYp2PVnt9dTXV1PRoamdamu3oDdHnuS73AJ14g9\nXnR12YGxwMN6ya/o6grtTBCNQLxx4z7S0+fidGrfKyNjLhs37gu6pZsom0tN43oqLAHz/Aj/77yz\n/oII/xD9y0a0977BBCCTqZszZ7afE4hbWp7FZOofgy7W+8VIuBeoZ0fiidTr8x794y4hxFtAII/I\nF4DwshUrFBc5yfgGmwhNYKzrIKVAyhICKYClLAk7PEaAZLLRaWwUwDeAQAYDP42N/ydEi+i2WM+e\nPfH/2Lvz+Kjqs///r4tAWASJFmVTFhGpaDUaFeldQ1ABLbYutVVraWkt1votePfW24pApbfgUq29\nkVar2NalavFurVpRCCKB+quKIFQLVQwaWSpuqKiAZLl+f5wJhDBJJjkzc84k7+fjkYfnnDkzc+Vy\nEq58Vt5//03atw8KiPffv4O33kp+b3MKgebkujkF5h//+AQvvtiH6ureAGzc+B5//OMTSbcB27jx\nef7+92Adt379BlNUVLDXPdnywQeVdOr0ddq1C3Y1qKn5Oh98ULbXfbn4+0Kyq7ktal9h95Skd4AR\nieN3ae7+MBIrGmcQTjbzl6miKsqFepPlL8xitbWaswhrfaluXZQuHTvms3071J312bFjfpPP27hx\nYzP3fszHfTQQFBDuZwAtXzOvVnM+Q80pMJcvf5ktW4ro0iVYPPijj15m+fK9d7lobpdurWSfvXSM\nAe3WbV8OPLCAvLzg/2d1dQHduu3b7NdpTCq/CzK9XJD+7ci85s76HJ+hOEQkRZkqquL2l31zl3BI\npry8nNtvX8g77wTrn91++8KUlz+4++4nqa4+m9oWverqs5NuXZQuF188mptuuh1P1Glmt3PxxaPT\n/j69e/emT58CduwIFn3t1KmA3r17J723uX8UNOczlPq9NcBadi9zsTZxbU8LF75EQcGZiTUAoVu3\nMxvs0m1Murp7a8c4tm9fW2zPbdYYx1Q09bsgV5cLkj21dNZn/WWsHcDdv5fkdskB+osonGznL25F\nVVgN5y/c4PCWLF9R6+OPP+L99zfTpcuJAGzb9gwff/xRyu/d3JaMG2+8EfgJv/3t9QBcdNEpiWuN\na+5nr7aA2GeffQCoqnq4wQIiTItkuhx33NEsX76BbdvuBKBr13047rij97rv448/YOvWNXTpEnwv\nW7fem9L/r/r5S9e4r2yNcWzsd0E2xrDp347Ma+lkgnnsbp/vDJwNNL2EtohIitIxE7W5swvrGjiw\nF4sXr6SyMhjE7r6SgQNTm8zQ0paMCRMmcOihwULDI0cWpfRezdWcAiLsgqzpMHz4Edx117N07Hgu\nAO3b/4nhw0/b675DDjmYxYv3pbIy6F50P4hDDklvV2NzpbJQr0hTWlSoufseG8uZ2QPsXvwn7cxs\nInApUA3Mc/efZOq92iqNMwhH+QsnU/lrzuzC+oYOPZKTTqpi/frnAOjXr5ihQ1P7ldmSloyWFnct\nyV2qBcTixSvYvv0w3n23dtHhw7I+q/D1199j+PBL6mzFdMleWzEBHH744Zx00j6sXx8sSNCv32Ec\nfvinTb5+/fzl0gSUpmTje9HvvsxraYtafYcBB6TptfZgZiOBrwJHuXulmWXkfUQkXtLxj0yY9dxq\n3/+gg2pXqM/sP9iLF6/gnXd6s359sINDv369M1YUpdot+847m1m5cvcSKZ98Mpcjj2y4VTFTA9e7\nd+/OkCHBwsObN69i93i13dL1/yvqiTXp1Jq+l7bM3Ju/RaeZfcLurk8H3gaucvc/pzG22vd6CPiN\nuze5/4yZeUu+HxGJp3T8wx/mNVr63PqtYzt3PtVk69iPfzyNu+76N+5BF5/Zn/j+9/vwy19em3K8\nqcZ21VV37dof9MAD329wf9AZM27lvvv2pVu3oKvx44/nM27c1qRLY7Tke0413lRfN9MzHEXSzcxw\nd2vsnpZ2faZzz5GmDAaKzew6YAdwhbtrzTaRNiAdkybCvEZLn9uSloyXX36Nbdv2BR5JXMnj5Zdf\na/Z7N6U5Eyyas0RK0E16PO++G/yz0rXr8WlpEWzOhIbWNslGBJq/4G0RdRf5qcfdX2xJEGa2kNo5\n8HuaQhDjfu5+opkdT7DI7iENvdb48eMZMGAAAAUFBRQWFu7qPy8rKwPQeZLz2uO4xJNr58pf68zf\npk2b2LYt+DXZpUsVffv2Tfn5GzduZPDgninfv3btampq9gX+K5GJW1i7dvcCvw09v/Zaqt9f7QSL\nqqoPAWjX7hReeWV+0vu7dKmic+cX6N79VP797+V8+OEKRo68POnrP/fcMzzzzD707PmfALz99h/o\n0uXTXWu8tfT/x0EHHcT996/ko48+D8D996+kf//+bNy4sUWvl0r+ysvL+c1v7gXgkkuCNd7i8HmM\n43nttbjEE/fz2uOKigpS1ayuTzMro/FCbWTKL5b6ez4J3ODuSxLn5cAwd38/yb3q+myhsjINCA1D\n+QsnjvnLVFdeQ/r1G8aGDROALyeuPMHBB89h/frnG31ec3M3Y8at/OY3G9i2LRho36XLPlxyycFJ\nuzMh9e7EmTNncd99e45nGzeuV6iN1gHmzJnLihVD6kzMWEVR0avNXOS3YfXzl+3/77kujj+7uSTt\nXZ/uXhIqopZ5BDgZWGJmhwH5yYo0CUc/aOEof+HEMX/Z3kdx584agk1eanfm25641rjm5q5fvwK2\nbHmYysoTANixYxn9+n2hwftT7U488MBeHHPMQD75pHaG6HAOPHB7s2KLQv38xWH/zFwSx5/d1qZd\nS55kZvlmdpmZ/TnxNdHMOqQ7uITfAYeY2cvAg0B6l3YWEYmB/PztwCKgd+JrUeJaej388BLy8o6m\nS5ez6dLlbPLyjubhh5eEft2RI4vo3HktffsOoW/fIXTuvDYta8GNHFnEzp1PsXnzKjZvXpWYzZmZ\nNeZE4qhFhRpwO3As8GvgNoJN425PV1B1uXulu49z9y+4e5G7l2Xifdq6uv3n0nzKXzhxzF/2C4Qu\nwH8AeYmv/0hca1xzc7d580eYHUH79utp3349ZkeweXPqOy40pHYCRVHRqxQVvdpkd2F5eTlz5sxl\nzpy5lJeXp+11m6t+/kaOLOK99/7I00/fxNNP38R77/1RhWEj4viz29q0dB214939qDrni8zspXQE\nJCISB9leg8q9A3Bo4gtge+Jaeg0d2ocVK/4/du68CIDq6icYOrRPWl471W7S+O9BmU+YrctE0qml\nhVqVmR3q7uUAZjYIqEpfWJJtGmcQjvIXjvIHBx/cnU2bHsY9WNPb7GEOPrh7k89rbu4OOeRQevSo\nZuvWYEbpfvsVcsghec2ON5lFixbV2Zrq9AZ3P2jOOLBMF3XJxqiF3bqsLdHPbua1tFD7b+BpM3sj\ncd4f+F56QhIRiV62W31OPPEE/vGP7VRV/QuA9u0P48QTO2fkvTp37kp+/iEA5OW9BYQfC7do0SJ+\n+MN7ad9+HADPP38vt99O6L0uNbhf2rpmjVEzsxPMrLe7LyLYNurPBPtvLgRWZSA+yRKNMwhH+Qsn\njvmrWyD06lVIfv6pu7pBM+Hwww9n5MiTGDLkCIYMOYKRI0/i8MMPb/J5zc2dmZOf/zoHHLCTAw7Y\nSX7+65iFX9bo7rufpH37cRx44KkceOCptG8/blfrWn1xmiCQbIxaXGLLBXH82W1tmtuidgdQ++fR\nCcBk4EfAMcCdwLnpC01EpO0YObKIBQvuoqAg2NqpU6f3GTny+2l/nzgso9Gc8X+1eVmzZiEQbHmV\niby0JDaRbGhuodbO3bckjs8D7kjs7/lnM/tHekOTbNI4g3CUv3DimL90bArfXO+88wGvvLJ/4uyD\nlJ7T3NzVfl/du6d3s/nx40/nb3/7Fa+++jcAOnZ8ifHjf9Tg/c3b7ilzg/uT5U9bUaUujj+7rU1z\nC7U8M+vg7pXAqcDFIV5LRCS2st2yctttf2Dlys/hHizJsXLl57jttj9wyy3T0/o+mfq++vfvz+GH\nD6S8vFfifT6mf//+oV9Xg/vD0Ub1ua+5xdWDBDsEvAdsA/4GYGaDgQ/THJtkkbYBCUf5Cyeu+ctm\ny8rTTz/H9u19qakJxkO1a7eSp5/e1OTzWpK7THxfixevoH//bzNs2O6tnuJYUNUvXDZu3BjLz146\nZGNCTFx/dluT5m4hNdPMnibYQL3U3Wv3NzFgYrqDExFpK7ZseZfq6i8BRwBQXf0vtmzRHK10dkEn\nK1xOOaV3ukKNHc2YbR2a3V3p7s8mubY2PeFIVPQXUTjKXzjKH+zc2R7oB3yWuNIvca1xccldpsb0\npbOrNlnhsm3bq6FjbMvi8vlrzTSuTEQkBnr12o93311ATU2wnVO7ds/Rq9d+EUeVukyO6dPg/paJ\nYkKMpJ8KNQE0ziAs5S8c5Q/GjDmaf/xjIVAJQE1NOWPGjGryeXHKXdwLqmRLfXTp8oWIo8qcbEyI\nidPnr7XKiULNzE4AfgV0INiq6lJ3fyHaqERE0ufVV9+jQ4f9qKwMVkDq0GE/Xn31vYijao2aXuqj\nNc2UjHvxLE0z9/ArUmeamZUB17v7AjM7HbjS3Ucmuc9z4fsREalv0KDjeP31/YBvJK48xCGHfMC6\ndcujDKtVmTNnLk8/3YtPPgkWFe7a9X1OPnkzEyact+ue+hMOdu58KmYbxktrYma4uzV2T060qAFv\nAbW7ExcATc9ZFxHJIVu3VgNfBb6cuLKDrVt/l5H3ikOLUXNiSFe8b7/9Ni++uJ1u3YYA8PHHyzni\niK173KOZkhI3zdrrM0JXAb8ws/XATQRbV0kaab+2cJS/cJQ/6NSpC9AHsx6Y9QD6JK41rrm5q20x\nWrFiCCtWDOG66x6hvLy8RTG3VHNiSGe8Zk5l5Yu8++4zvPvuM1RWvsgbb2jRgjD0s5t5sWlRM7OF\nBOuz1TcFmARMcve/mNnXgd8BSUfZjh8/ngEDBgBQUFBAYWHhroGOtR8onetc5zqP2/mRR/bk3/++\ng3btgpmeNTV3cOSRPanV0POberz++WuvvU1+/qns2BGsUd6pU7DZ/MaNG7P2/S5evIL33itg//0/\nZMCAEjZvht/85l7OOOPkjMb7+uuvEQxzfoMdO9bRrt2/CZZE2X1/7UzJF18Mupx79PiQkSPPivzz\nEdfzWnGJJ+7ntccVFRWkKlfGqG11930TxwZ86O7dk9ynMWoikpPKy8u54IKreOWVYB21z3++Iw8+\neEPau9zmzJnLihVD6nTtraKo6NU9xmllWnNiSGe8M2bcyn337Uu3bqcB8PHH8xk3bitTp07a475U\nulrj0H0sua81jVErN7MR7r4EOBlQW7WItDqf+1wvevXqnDjenpH3iMPaWs2JIZ3x9uzZk8GDq1i/\n/gEABg/uSc+ePfe6r6mZktnYmkmkVq6MUbsY+LmZrQJmsOdm8JIG9ZuxpXmUv3CUP5g7dx6rV7fj\n/feLef/9YlavbsfcufOafF5zc1e7tlZR0asUFb0aSYHRnBgOPfRQLrzwGD799A98+ukfuPDCY1oc\n7yGH9GDt2lKqqo6iquoo1q4tZevWjc1+nboTDnr1KiQ//9RdrWttjX52My8nWtTcfTkwLOo4REQy\nZfHiZbz11tG0a/cuAFu3HsTixcuYMiX97xWHtbVSjaG8vJz771/JPvt8C4D773+K/v37tyj+119/\nj6Ki79VZnuN7vPXWoma/jkg25UShJplXO+BRWkb5C0f5g02bNlBTk09NzbjElb+xadOGJp/X2nOX\n7uUyunfvzpAhRyZeaxVDhhzR7NeIQ/dxXLT2z18cqFATEYmFPNwPw2x/ANwPAyoijai1CbaQupc1\na4LlPQ488CVGjvx2s18nG1szidTKlTFqkmEaZxCO8heO8gd9+/ahffv9ad9+Z+Jrf/r27dPk81p7\n7kaOLGLnzqfYvHkVmzevSrReFYV4xZ3AG4mvnTz//PMtepVDDz2UCRPOY8KE89p0kdbaP39xoBY1\nEZEYGDnyBF59dTWffhoUZ/vss5qRI0+IOKropbP1avHiFfTocT5HHrl7qY+VKx/mwgvTFq5I2uXE\nOmqp0jpqIpKrysvL+e53p/Lqq8HCrkOGFPD7389o06016RaHNeRE6kplHTV1fYqIxMCbb77Jhg1G\nXt4E8vImsGGD8eabb0YdVquS/m5UkcxToSaAxhmEpfyFo/zB3Xc/SZcuFzFkyNcYMuRrdOlyEXff\n/WSTz1PuUpds/bbaraikZfT5yzyNURMRkTaj/vptKtQk7jRGTUQkBhYtWsQPf3gv7dsH66hVVd3H\n7bd/m1NOOSXiyEQkU1IZo6ZCTUQkJhYtWrSru3P8+NNVpIm0cppMICnTOINwlL9wlL/AKaecwn33\n3cx9992ccpGm3IWj/IWj/GWeCjURERGRmIpN16eZfR2YDnweON7dX6zz2GTge0A1MMndSxt4DXV9\nioiISE5IpeszTrM+XwbOBu6oe9HMhgLnAUOBvsBTZnaYu9dkP0QRERGR7IlN16e7v+Lua5M8dCbw\noLtXunsFUA5oX5U00ziDcJS/cJS/llPuwlH+wlH+Mi82hVoj+gB1F7rZSNCyJiIiItKqZbXr08wW\nAr2SPHS1u/+1GS/V4EC08ePHM2DAAAAKCgooLCykpKQE2F3563zv85KSkljFk2vnyp/yl47zTZs2\nsW1b8Gu5S5cq+vbtG6v4dK5znYc7rz2uqKggVbGZTFDLzBYDl9dOJjCzqwDc/YbE+XzgGnd/Pslz\nNZlARHJSeXk51133CPn5pwKwc+dTXH31WdqUXaQVy+V11OoG/Rhwvpnlm9lAYDCwLJqwWq+61b40\nn/IXjvIHixevID//VHr1KqRXr0Ly809l8eIVTT5PuQtH+QtH+cu82BRqZna2mW0ATgTmmdmTAO6+\nBngIWAM8CVyqZjMRERFpC2LX9RmGuj5FJFep61Ok7dFenyIiOaS8vHxXd+fIkUUq0kRauVweoyZZ\npnEG4Sh/4Sh/gUMPPZQJE85jwoTzUi7SlLtwlL9wlL/MU6EmIiIiElPq+hQRERGJgLo+RURERHKY\nCjUBNM4gLOUvHOWv5ZS7cJS/cJS/zFOhJiIiIhJTGqMmIiIiEgGNURMRERHJYSrUBNA4g7CUv3CU\nv0B5eTlz5sxlzpy5lJeXp/Qc5S4c5S8c5S/z2kcdgIiI7L2F1LPPPqItpEREY9REROJgzpy5rFgx\nhF69CgHYvHkVRUWvMmHCeRFHJiKZknNj1Mzs62a22syqzayozvVRZrbczF5K/HdklHGKiIiIZEOs\nCjXgZeBsYClQt2nsXeAMdz8K+A5wXwSxtWoaZxCO8heO8hdswr5z51Ns3ryKzZtXsXPnU4wcWdTk\n85S7cJS/cJS/zIvVGDV3fwWCpsB611fVOV0DdDazDu5emcXwREQy5tBDD+Xqq89i8eIVAIwcqfFp\nIhLTMWpmthi43N1fTPLYucDF7j46yWMaoyYiIiI5IZUxallvUTOzhUCvJA9d7e5/beK5RwA3AKMa\numf8+PEMGDAAgIKCAgoLCykpKQF2N9HqXOc617nOda5znWf7vPa4oqKCVOVMi5qZHQQsAsa7+7MN\nPE8tai1UVla26wMlzaf8haP8tZxyF47yF47yF07OzfqsZ1fgZlYAzAN+0lCRJiIiItLaxKpFzczO\nBm4FegAfASvd/XQzmwpcBbxW5/ZR7v5eveerRU1ERERyQiotarEq1MJSoSYiIiK5Ite7PiWL6g50\nlOZT/sJR/lpOuQtH+QtH+cs8FWoiIiIiMaWuTxEREZEIqOtTREREJIepUBNA4wzCUv7CUf5aTrkL\nR/kLR/nLPBVqIiIiIjGlMWoiIiIiEdAYNREREZEcpkJNAI0zCEv5C0f5aznlLhzlLxzlL/NUqImI\niIjElMaoiYiIiERAY9REREREclhsCjUz+7qZrTazajM7Nsnj/czsEzO7PIr4WjuNMwhH+QtH+Ws5\n5S4c5S8c5S/zYlOoAS8DZwNLG3j8FmBe9sJpW1atWhV1CDlN+QtH+Ws55S4c5S8c5S/z2kcdQC13\nfwWC/tr6zOws4HXg0yyH1WZ8+OGHUYeQ05S/cJS/llPuwlH+wlH+Mi9OLWpJmVlX4EpgesShiIiI\niGRVVlvUzGwh0CvJQ1e7+18beNp04Jfuvs2SNbdJWlRUVEQdQk5T/sJR/lpOuQtH+QtH+cu82C3P\nYWaLgcvd/cXE+VLg4MTDBUANMM3db0vy3Hh9MyIiIiKNaGp5jtiMUatnV9DuXrzrotk1wMfJirTE\nvWpxExERkVYjNmPUzOxsM9sAnAjMM7Mno45JREREJEqx6/oUERERkUBsWtREREREZE8q1ERERERi\nSoWaiIiISEypUBMRERGJKRVqIiIiIjGlQk1EREQkplSoiYiIiMSUCjURERGRmFKhJiIiIhJTKtRE\nREREYkqFmoiIiEhMqVATERERiSkVaiIiIiIxpUJNREREJKZUqImIiIjElAo1ERERkZhSoSYiIiIS\nUyrURERERGJKhZqIiIhITKlQExEREYkpFWoiIiIiMaVCTURERCSmVKiJiIiIxJQKNREREZGYUqEm\nIiIiElMq1ERERERiSoWaiIiISEypUBMRERGJKRVqIiIiIjGV8ULNzPLMbKWZ/TVxvr+ZLTSztWZW\namYFde6dbGavmdkrZja6zvUiM3s58disTMcsIiIiEgfZaFG7DFgDeOL8KmChux8GLEqcY2ZDgfOA\nocBpwG1mZonn3A5c5O6DgcFmdloW4hYRERGJVEYLNTM7CPgycBdQW3R9FbgncXwPcFbi+EzgQXev\ndPcKoBwYZma9gW7uvixx3711niMiIiLSamW6Re2XwH8DNXWu9XT3txPHbwM9E8d9gI117tsI03sk\nFAAAIABJREFU9E1yfVPiuoiIiEirlrFCzczOAN5x95Xsbk3bg7s7u7tERURERKSO9hl87S8CXzWz\nLwOdgH3N7D7gbTPr5e6bE92a7yTu3wQcXOf5BxG0pG1KHNe9vinZG5qZij4RERHJGe6etDGrVsZa\n1Nz9anc/2N0HAucDT7v7OOAx4DuJ274DPJI4fgw438zyzWwgMBhY5u6bga1mNiwxuWBcnecke199\nteDrO9/5TuQx5PKX8qf8KXe5+dXa8vf440sYPXoKI0Zcw+jRU3j88SWhX3PbNmfjRufll53jj59C\n0BFW+/UdwBkzZmrk33sufqUiky1q9dVGdAPwkJldBFQA3wBw9zVm9hDBDNEq4FLf/V1cCtwNdAae\ncPf5WYxbREQkK+bNW8qtt5by2Wft6dixikmTRjN2bHFKj8+bt5TLLlvAunUzd92/bt0UAEaNKuaD\nD+CDD2DLFpo8rnsOsP/+sN9+sHFj8rJhx468DGVEslKoufsSYEnieAtwagP3XQdcl+T6CuALmYyx\nrRswYEDUIeQ05S8c5a/llLtw4pS/xgqtsWOLG3z8nXdgwIBirryydI/Hgsdn8tWvTqNdu2L2249d\nX7WFV+1x//5QWLj39f32g86dd7/emDFVlJbWfYcBAHTqVJ3udEhCNlvUJMZKSkqa/EtOGlZSUhJ1\nCDlN+Ws55S6cbOavqd+xt96avNCaNGkaZWXFzJ1byoYNez/+wx9O44QTinn//eT/pA8fnsff/gbW\n6Eio1EyaNJp166bUibOEQYOuZuJELW+aKSrUBIBnn/0Hv/3tOw3+JSciIi2XrDWsvHwK//wnQDHP\nPguLFyf/J7m6Oo8ePSA/P/njJ56YR1lZstauQNeu1Wkp0mD3vwezZ09jx448tm1bxzXXTNC/Exmk\nvT4FgIcfXp70L7nZsxdGFJGISOuRrLXs9ddncv31C3nrLbjgAjjxxKqkz/3856v5yU9g0KDkj9d2\nO06aNJpBg6bs8VjQ2jUqDd/BbmPHFjN//rWUlU3n5z+/SEVahqlFTQDYZ59BSa8//XQeX/kKHHdc\n8FVUBL16ZTm4HKDup3CUv5ZT7sJJZ/6SdW1++cvFLF8Oq1cn/+e2sDCP//3f4Lhr19H8+99T9ijo\n6nYr7t3tuOfj9Vu7OnWqZuLE0zJaSOnzl3kq1ASAjh2T/6U2fHg148fDihUwaxYsXw5duuwu3GqL\ntwMOyG68IiLZlMpszPpdmy+8MIWOHaFr1+IGf8fWHYTfVKGVSiE2dmyxWrham6jXEEnzeiQuLXPd\ndf/rgwZd7eC7vgYNmuyPP75kj/tqatzXrXOfO9f9yivdTz7ZvXt393793M85x/2669xLS93ffz+i\nbyQiixcvjjqEnKb8tZxyF04q+Xv88SVJfj9e7Y8/vsS3b3d/9VX3oqIpezxe+zV8+FSvqWnoNfb+\nHZtr9PkLJ1G3NFrbqEVNABg+/GiOOqpdk03mZnDIIcHXN74RXKupgXXrgla35cth5kx48UXo0WPP\nVreiIigoiOCbExEJoaHZmOecMw0o5qCDaHDGZX5+HmbRdEtK62Ce4sq4ucDMvDV9P7mspgbWrt1d\nvC1fDqtWBePb6hZvxx4L++4bdbQiIg076aTpPPPM9L2un3hicD0vD8aMmUpp6Yy97hkzZhrz51+b\n8RglN5kZ3sQWUmpRk4xo1w4+//ng68ILg2vV1fDqq7sLtz//Gf7xDzj44N2F23HHwTHHQNeuu19L\n67uJSFSeeQZWrEg+vqx792ryEgvyNzXQX6Sl1KImAJSVlUUye6eqCtas2bPl7eWXYeDAoHDr3Hkp\n8+YtYNOmur/8pjBr1phYFWtR5a+1UP5aTrkLp6H8bd8OU6fCgw/CRRct5cEHF+xVhM2addpeEwpm\nz15Yp2tzVKx+T2WCPn/hqEVNYq99ezjqqODru98NrlVWwurVQdH2s5+V7lGkQe36btNa/S9AEcmO\n+q32o0eP5q67ijnqKHjpJejRo5gTT2x6fJlmXEomqEVNYq2kZDpLlkzf6/rRR09n5crpaVttW0Ta\npmTLarRrN4UrrhjDjTeq6JLMSqVFTTsTSKw1tPbQ2rXVnHQSzJ8fTHQXEWmJZDM6a2pm8o9/aFcW\niQcVagIE4wziqKEtUf74x1FceilccQUcfzw88kgw0zQqcc1frlD+Wk65C+fttzcmvb5jR16WI8lN\n+vxlnsaoSaw1tfbQ+efDo4/CjBnBwN8pU4L13fL0O1ZEUpCXV530et0dA0SilLExambWCVgCdATy\ngUfdfbKZnQD8CugAVAGXuvsLiedMBr4HVAOT3L00cb0IuBvoBDzh7pc18J4ao9ZGucOCBXDttfDu\nu3DVVfCtb0F+ftSRiUhcuUNJyVJefHEBn3zS+IxOkUxIZYxaRicTmFkXd99mZu2BZ4ArgGuBG9x9\ngZmdDlzp7iPNbCjwAHA80Bd4Chjs7m5my4AfufsyM3sCuNXd5yd5PxVqbZw7LFkStLC99hr85Cfw\nve9Bp05RRyYicfOLX8ADD8CUKUu58862tayGxEPkkwncfVviMB/IAz4ANgPdE9cLgE2J4zOBB929\n0t0rgHJgmJn1Brq5+7LEffcCZ2Uy7raotYwzMIOSEnjqKZg7F558Mtju6he/gE8+ydz7tpb8RUX5\naznlrmWeegpuvhmuvLKMc84pZv78aykrm878+deqSGsGff4yL6OFmpm1M7NVwNvAYndfDVwF/MLM\n1gM3AZMTt/cB6o7q3EjQslb/+qbEdZFGnXgi/PWv8MQT8PzzQcE2cyZ8+GHUkYlIlCoqgqERDzwA\nPXtGHY1I4zI6mcDda4BCM+sOLDCzEmAqwfizv5jZ14HfAaPS9Z7jx49nwIABABQUFFBYWLhr1eTa\nyl/ne5+XlJTEKp50nz/0ENxzTxn33w+33FLCD38Ixx9fRvfuyl8czpU/nWfr/IQTSjj7bDj33LJE\nC3y84tN56z6vPa6oqCBVWVvw1symAduBn7r7volrBnzo7t3N7CoAd78h8dh84BrgTYLWuMMT1y8A\nRrj7JUneQ2PUpEmvvw433gj/93/B+LXLL4fevaOOSkQyzR3GjQuO77sPLZgtkYt0jJqZ9TCzgsRx\nZ4JWs1VAuZmNSNx2MrA2cfwYcL6Z5ZvZQGAwsMzdNwNbzWxYorAbBzySqbjbqrrVfmt3yCFwxx3B\n1jCVlXDEEfD//h+8+WbLX7Mt5S8TlL+WU+5SN2tWsD3dnXfuLtKUv3CUv8zLZNdnb+AeM2tHUBDe\n5+5PmdnFwK/NrCNBC9vFAO6+xsweAtawe9mO2uaxSwmW5+hMsDzHXjM+RZrroIOCX9xXXw2//CUc\neyyceSZMngyDB++9/9+kSaM1yFgkh9T9Gf700ypee200q1YV06VL1JGJpE57fYokbNkCs2fDr34F\nQ4cu5Y03FrBhQ921laYwa9YYFWsiOSDZHp69e09hzhz9DEt8RL6OWrapUJN02LoVjjtuKq+9NmOv\nx8aMmcb8+ddGEJWINMeYMVMpLdXPsMRb5OuoSe7QOIPd9t0X+vRJPiqgof3/lL9wlL+WU+6S2749\ntZ9h5S8c5S/ztNenSBIdO1Ylva79/0TizT1Y7PqFF/QzLK2Duj5Fkkg2viUv72rmzDmN735X41tE\n4uiZZ4Lldqqq4Nxzl/Lb3+75M6w9PCVuNEZNJIR585Yye/bu/f/69BnF8uXFPPNM0D0qItGpO6Oz\nqqqKmprRbNpUzMyZ8M1vQrt2e/8Maw9PiRsVapKysrKyXSsoS3LucOmlwYK5jz8OHTrsfkz5C0f5\na7m2mLtkLd777x/M6DznnOYVYm0xf+mk/IWjyQQiaWQWLN+RlxcUbPqbQCQat95aukeRBrBly0zu\nvHNhRBGJZI5a1ESa6eOPobgYzjsPrroq6mhE2p7hw6fz3HPT97o+YsR0ysr2vi4SV6m0qGnWp0gz\ndesWdH0OHw4DBsD550cdkUjb8cknsHq1ZnRK26GuTwG0Fk5z9e0Lf/0rTJwYzDRT/sJR/lquLeWu\nqgq+8Q0YPnw0gwZN2eOxQYOuZuLEUc1+zbaUv0xQ/jJPLWoiLXT00XDffXDuuXDzzVFHI9K61U7m\ncYfHHy+mtBRmz55WZ0anlt2Q1klj1ERCuvNOuOkmePZZ6NEj6mhEWqfrr4eHHoKlS4PhByKtgWZ9\nimTBxRfD174GZ54JO3ZEHY1I63P//fCb38C8eSrSpO1RoSaAxhmENXp0GQcdBOPHQ01N1NHkHn3+\nWq61527xYvjxj+GJJ6BPn/S/fmvPX6Ypf5mnQk0kDdq1g7vvhg0bYMqUJm8XkRSsXh0sg/PHP8IR\nR0QdjUg0MjZGzcw6AUuAjkA+8Ki7T048NhG4FKgG5rn7TxLXJwPfS1yf5O6lietFwN1AJ+AJd7+s\ngffUGDWJ1HvvwYknwk9+AhMmRB2NSG6puy0UVLFmzWhuuaWYb30r6shEMiPSddTcfYeZjXT3bWbW\nHnjGzL4EdAC+Chzl7pVmdkAi2KHAecBQoC/wlJkNTlRetwMXufsyM3vCzE5z9/mZil2kpXr0CLpo\niouhXz8YMybqiERyQ0PbQu23H4Bmc0rbldGuT3ffljjMB/KAD4BLgOvdvTJxz7uJe84EHnT3Snev\nAMqBYWbWG+jm7ssS990LnJXJuNsijTMIp27+DjsM/vQnGDcOXnopuphyiT5/LddactfQtlCzZ2d2\nW6jWkr+oKH+Zl9FCzczamdkq4G1gsbuvBg4Dis3sOTMrM7PjErf3ATbWefpGgpa1+tc3Ja6LxNaX\nvgS33gpnnAH//nfU0YjE3yefJO/g2bEjL8uRiMRLRhe8dfcaoNDMugMLzKwk8Z77ufuJZnY88BBw\nSLrec/z48QwYMACAgoICCgsLKSkpAXZX/jrf+7ykpCRW8eTaebL89epVxpgxMHZsCUuXwooV8Yk3\nbuf6/LXd8yOPLOGXv4TnnlsHlAHB48Hx7m2h4hKvznUe5rz2uKKiglRlbcFbM5sGbAdOAW5w9yWJ\n6+XAicD3Adz9hsT1+cA1wJsErXGHJ65fAIxw90uSvIcmE0isuAeTCt56Cx59FNprLxBpg+pOEujY\nsYpJk0Zz3HHF3Hwz/Pa38PWvwwknLOX66/ccozZo0NXMmqUdB6T1inTBWzPrYWYFiePOwChgJfAI\ncHLi+mFAvru/BzwGnG9m+WY2EBgMLHP3zcBWMxtmZgaMS7yGpFHdal+ar6H8mcHtt0NlJUyaFBRu\nsjd9/lou7rmrnSRQWjqDJUumU1o6gwsvXMCgQUvZsQP+8Q+44w646KJiZs0aw5gx0xgxYjpjxkzL\nSpEW9/zFnfKXeZn8+743cI+ZtSMoCO9z90VmthT4nZm9DOwEvg3g7mvM7CFgDVAFXFqneexSguU5\nOhMsz6EZn5IzOnSA//u/YNzaLbfA5ZdHHZFI9iSbJPDRRzMpKZnG7Nl7FmFjxxar9UykHu31KZIl\n69fDF78Is2YFW06JtAUlJdNZsmT6XtdHjJhOWdne10XakkjXURORPfXrB489Fqyt1rdvsDCuSGtW\nUwObNlUlfax2koCINC5jY9Qkt2icQTip5u/YY+H3v4ezz4bXX89sTLlEn7+Wi2vutm4NWo7btx9N\n//577qs2aNDVTJw4KqLI9hTX/OUK5S/z1KImkmVnnAFTp8KXvwx//zvsv3/UEYmk1yuvBH+MlJTA\n3LnFLFwIs2dPY8eOPDp1qmbiRM3kFEmVxqiJROTyy2HFCliwADp2jDoakfR49NFgSZrrr4eLLoo6\nGpF4S2WMmgo1kYjU1MC558I++8B55y1l9uw915lSi4PkkpoamD4d7r472ELthBOijkgk/jSZQFJW\nVla2awVlab6W5K9dO/jDH6CwcCnz5i3ggw92L2Gwbl0wpqetFGv6/LVcunKXbFHaxj5/de/Py6ti\n69bRdOlSzAsvQM+eocPJGn32wlH+Mk+FmkiEunSBPn1Kee21PdeZWrduJrNnT2szhZpEq3ZR2rrr\nnTX2x0Ky+7t3n8I990DPnvrMiqSTuj5FIqZ1piRqY8ZMpbR0xl7X+/Wbxte+di15eezx9cADU1m3\nbu/7x4yZxvz512YjZJFWQV2fIjmgY0etMyXR+uyz5P8UdOiQR9++UF2951dlZfL7d+zIy2SYIm2S\n1lETQGvhhBUmf5MmjWbQoD3XmRo4MD7rTGWDPn8tl47cNfTHwqGHVnP55XDllTB5crCszDXXwOc/\n33r+uNBnLxzlL/PUoiYSsdoxQLNnT2P79jxef72az33uNE47TWN9JDtOOWU0Tz01hZqa3WPOgkVp\nT0t6/6RJo1m3bsoeY9Qau19EWk5j1ERiZudOGD062GLqhhuijkZau3ffhaIi+O53l/L88wvrLEo7\nqslZn7Nnp36/iOxN66iJ5Kj33oNhw4J1qcaNizoaaa1qaoIdMgoL9UeBSBRSKdQ0Rk0AjTMIK935\n69Ej2MD98svhuefS+tKxpM9fy4XJ3XXXwbZtMGPvCZxthj574Sh/madCTSSmjjgCfve7YGPrDRui\njkZam6efhttugz/+EdprtLJIbGWs69PMOgFLgI5APvCou0+u8/jlwE1AD3ffkrg2GfgeUA1McvfS\nxPUi4G6gE/CEu1/WwHuq61NanZtuggcfhL/9LdhuSiSst94KxqXdey+cemrU0Yi0XZF2fbr7DmCk\nuxcCRwEjzexLicAOBkYBb9YJdihwHjAUOA24zcxqg78duMjdBwODzUxTi6TNuOIKOPJIGD8+GFMk\nEkZVFVxwAVxyiYo0kVyQ0a5Pd9+WOMwH8oAtifNbgCvr3X4m8KC7V7p7BVAODDOz3kA3d1+WuO9e\n4KxMxt0WaZxBOJnMnxnceSds3AjXttJF3/X5a7nm5u6nP4X8fJgypel72wJ99sJR/jIvoyMTzKwd\n8CIwCLjd3deY2ZnARnd/aXeDGQB9gLrDpjcCfYHKxHGtTYnrIm1Gp07wl7/ACSfA0KHw9a9HHZHk\noieegPvugxUrgq2gRCT+MlqouXsNUGhm3YEFZvZlYDIwus5tjfbNNtf48eMZMGAAAAUFBRQWFlJS\nUgLsrvx1vvd5SUlJrOLJtfNs5O+VV8qYNg0uvbSEQw+Fjz6Kz/cf9lyfv6bPr79+Fg8/vJx99hlE\nx45VlJQcwPDhR6f8/Llzy7jkEvjrX0s48MDovx+d67wtntceV1RUkKqsraNmZtMAByYCtV2iBxG0\nkA0Dvgvg7jck7p8PXEMwjm2xux+euH4BMMLdL0nyHppMIK3en/4E//VfsGwZ9OoVdTSSDfPmLeWy\nyxbU2wlgCrNmjUlpkdmdO6G4OJhB/N//nclIRaQ5Ip1MYGY9zKwgcdyZYPLAs+7e090HuvtAgi7N\nY939beAx4HwzyzezgcBgYJm7bwa2mtmwxOSCccAjmYq7rapb7UvzZTN/554L3/8+nH027NiRtbfN\nKH3+GnfrraV7FGkA69bNZPbshQ3mbt68pYwZM5WSkukMHjyVmpqlXHFFFoLNMfrshaP8ZV4muz57\nA/ckxqm1A+5z90X17tnV/JUYv/YQsAaoAi6t0zx2KcHyHJ0JlueYn8G4RWJv2jRYvRouvhjuuSeY\ncCCt12efJf9VvWhRHm+8AV/4AvTvDwMGBP9dv34pt9yygDfe2F3c5eVN4Ykn0DZPIjlGW0iJ5Kht\n2+Ckk+C88+DK+nOopVUZM2YqpaV7bx9QUjKNG2+8looKePNNdv23rGwqn3669/1jxkxj/vxWOnVY\nJAel0vWp9ahFclSXLvDoo8GeoIcfDl/5StQRSaZMmjSadeum1BujdjVXXHEaJ5wQzAauq6SkPUuW\n7P06O3ZoqqdIrsnYGDXJLRpnEE5U+TvoIHj4YbjoIvjnPyMJIS30+Wvc2LHF/PSnY8jPn8aIEdMZ\nM2Yas2adxtixxUlz17FjVdLX6dSpOsOR5h599sJR/jJPLWoiOW7YMLjlFjjzTHj++WBDd2l9Bg0q\n5phjiknl38WGWuAmTtSmLiK5RmPURFqJyZPh2WehtDRYeV5al/vvh8cfD/Z9TcW8eUuZPXshO3bk\n0alTNRMnjtJEApGYSWWMmgo1kVaipgbOOitYW+2OOzQTtLWZMQM+/RSuvz7qSEQkXSJdR01yi8YZ\nhBOH/LVrF7S6PPss/OpXUUfTPHHIX9xVVMDAgXtfV+7CUf7CUf4yT4WaSCvSrRs89hhcdx0sXBh1\nNJJOb7wRrJMmIm2Luj5FWqGlS4ON2//2NzjssKijkXQYNAjmz4fBg6OORETSRWPURNqwu+6Ca65Z\nypAhpdTUtKdjxyomTRqtAeU5qLo6WDdv61bo2DHqaEQkXTRGTVKmcQbhxDF/vXsv5dNPF7B48QyW\nLJlOaekMLrtsAfPmLY06tL3EMX9xsmkTHHBA8iJNuQtH+QtH+cs8FWoirdStt5by0UfJN/KW3KLx\naSJtV4OFmpl1b+SxfpkJR6JSUlISdQg5LY75a2gj7zhuIxTH/MVJQzM+QbkLS/kLR/nLvMZa1Mpq\nD8xsUb3HHs1INCKSNtpGqPVQi5pI25Vq1+f+GY1CIqdxBuHEMX+TJo1m0KApe1zLz7+aH/xgVEQR\nNSyO+YuTxlrUlLtwlL9wlL/M016fIq1U7ezO2bOn7dpGaOvW01i8uJizz444OGmWN96Ab3876ihE\nJAoNLs9hZhuBWwADflznGODH7n5Qoy9s1glYAnQE8oFH3X2ymd0EnAHsBNYB33X3jxLPmQx8D6gG\nJrl7aeJ6EXA30Al4wt0va+A9tTyHSCM+/BCOPRZuvhnOOSfqaCRV/ftDWVnDrWoikptCraNmZtOB\n2get/rG7/yyFALq4+zYzaw88A1wBdAYWuXuNmd1A8GJXmdlQ4AHgeKAv8BQw2N3dzJYBP3L3ZWb2\nBHCru89P8n4q1ESasGwZnHEGPP+8/uHPBZWV0LUrfPIJdOgQdTQikk6h1lFz9+nu/rPE117HqQTg\n7tsSh/lAHrDF3Re6e03i+vNAbcvcmcCD7l7p7hVAOTDMzHoD3dx9WeK+e4GzUnl/SZ3GGYSTS/k7\n4QSYPBnOPx927ow6mkAu5S/bNmyA3r0bLtKUu3CUv3CUv8xrbHmOi83ssMSxmdnvzWyrmb1kZsem\n8uJm1s7MVgFvA4vdfU29W74HPJE47gNsrPPYRoKWtfrXNyWui0gL/ed/Qs+eQcEm8aYZnyJtW2OT\nCS4Dfp84vgA4GhgIHAPMAk5q6sUTLWeFiTXZFphZibuXAZjZFGCnuz/Q8vD3Nn78eAYkfqsVFBRQ\nWFi4a52X2spf53ufl5SUxCqeXDvPtfyZwfe/X8aECcH5V76i/MX1vKKihIED4xOPznWu85af1x5X\nVFSQqsbGqK1y98LE8QPAMnf/38T5Snc/JuV3CZ4zDdju7jeb2XhgAnCKu+9IPH4VgLvfkDifD1wD\nvEnQGnd44voFwAh3vyTJe2iMmkgz/P3vcPbZ8MIL0E/LWMfS1KlBt+c110QdiYikW9i9PmvMrE9i\n9uYpBIP7a3VO4c17mFlB4rgzMApYaWanAf8NnFlbpCU8BpxvZvlmNhAYTFAcbga2mtkwMzNgHPBI\nU+8vzVO32pfmy9X8ffGLcPnlwXi1ysro4sjV/GVDY2uogXIXlvIXjvKXeY0Vaj8FXiBo0XrM3f8J\nYGYjCJbVaEpv4OnEGLXngb+6+yJgNtAVWGhmK83sNoDE+LWHgDXAk8CldZrHLgXuAl4DypPN+BSR\nlrniCigoCFpuJH40Rk2kbWus6/MEgkkAH7v7FjP7DvA1YDPwP+6+MekTI6SuT5GWee89OOYYuPNO\nOP30qKORuvr2heeeg4MPjjoSEUm3sOuorSQYQ7bFzIqBucCPCCYTfN7dz013wGGpUBNpuaVL4Rvf\ngBUrguJAordjB3TvDtu2QV5e1NGISLqFHaPWzt23JI7PA+5w9z+7+1SC8WPSimicQTitIX/FxTBx\nIlxwAVQl3889Y1pD/jJh/fqgJa2xIk25C0f5C0f5y7zGCrU8M6tdYvFUYHGdx7RHqEgrNHkydOoE\n06dHHYmAxqeJSONdn1OAscB7wMFAUWLbp8HA3e7+H9kLMzXq+hQJ7+23g/1A774bRo2KOpq27Y47\nYPlymDMn6khEJBNS6fpssGXM3Wea2dNAL6C0zrZPBkxMX5giEic9e8If/gAXXhiMV+vdO+qI2i61\nqIlIY12fuPuz7v4Xd/+0zrW17v5i5kOTbNI4g3BaW/5GjoQf/CAo1qqrM/9+rS1/6dLUGmqg3IWl\n/IWj/GVeo4WaiLRdteuqzZgRbRxtmVrURKTBMWq5SGPURNLrrbegqAjuvz9oZZPs6tkTVq1S97NI\naxV2eQ4RaeN694Z77oFvfSuYZCDZ8+mnsHVrUKyJSNulQk0AjTMIqzXnb9Qo+O53Ydw4qKlp+v6W\naM35a6k334T+/aFdE7+llbtwlL9wlL/MU6EmIk2aPj1YJf/666OOpO3Q+DQRAY1RE5EUbdoUjFd7\n6KFgFwPJrF//Gv75T7j99qgjEZFMCbWOmohIXX37wu9/D+ecs5QvfKEU9/Z07FjFpEmjGTtWlVu6\nqUVNREBdn5KgcQbhtJX81dQspbp6AWVlM1iyZDqlpTO47LIFzJu3NNTrtpX8NUcqa6iBcheW8heO\n8pd5GSvUzKyTmT1vZqvMbI2ZXZ+4vr+ZLTSztWZWamYFdZ4z2cxeM7NXzGx0netFZvZy4rFZmYpZ\nRBp3662lfPjhzD2urVs3k9mzF0YUUeulFjURgQyPUTOzLu6+zczaA88AVwBfBd5z95+b2U+A/dz9\nKjMbCjwAHA/0BZ4CBru7m9ky4EfuvszMngBudff5Sd5PY9REMqikZDpLlkzf6/qIEdMpK9v7urTc\n5z4Hr7wCBxwQdSQikimRr6Pm7tsSh/lAHvABQaF2T+L6PcBZieMzgQfdvdLdK4ByYJioMY1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R/PP9+xhxCK1Wvd1QrXX3lcf+VpS6LmPmpmZh3U0hhuBTvuCGeckX1eegkOO2zmRkkaFB5CmORW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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e768290>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Use the regression tree approach, the optimal split point for this variable is 3.78. The reduction in the $SSE$ associated with this split is compared to the optimal valeus for all the other predictors and the split corresponding to the absolute minimum error is used to form subsets $S_1$ and $S_2$. After considering all other variables, this variable was chosen to be the best.\n",
      "\n",
      "If the process were stopped at this point, all samples with values for this predictor less than 3.78 would be predicted to be 1.84 (the average of the solubility results for these samples) and samples above the splits all have a predicted value for -4.49:\n",
      "```\n",
      "if the number of carbon atoms >= 3.78 then Solubility = -4.49\n",
      "else Solubility = -1.84\n",
      "```"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "s1 = np.where(trainX['NumCarbon'] <= 3.7768)[0]\n",
      "s2 = np.where(trainX['NumCarbon'] > 3.7768)[0]\n",
      "y = [trainY.values[s1, 0], trainY.values[s2, 0]]\n",
      "\n",
      "plt.boxplot(y)\n",
      "plt.ylabel('Solubility')\n",
      "plt.xticks([1, 2], ['<= 3.7768', '> 3.7768'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "([<matplotlib.axis.XTick at 0x10e289210>,\n",
        "  <matplotlib.axis.XTick at 0x10e292e10>],\n",
        " <a list of 2 Text xticklabel objects>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Aa+2nd73+RUle0lq7dDG+Mtv/rvzUYvxZrbX3V9WJJK9trT2zqr4gyctba3c/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\nAICBaMQAAAaiEQMAGIhGDABgIP8fjKRaCjNo1vkAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10f21a410>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In practice, the process then continues within sets $S_1$ and $S_2$ until the number of samples in the splits falls below some threshold. This would conclude the *tree growing step*."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "When the predictor is continuous, the process for finding the optimal split point is straightforward since the data can be ordered in a natural way. Binary predictors are also easy to split, because there is only one possible split point. However, when a predictor has more than two categories, the process for finding the optimal split point can take a couple of justifiable paths.\n",
      "\n",
      "Once the full tree has been grown, the tree may be very large and is likely to over-fit the training set. The tree is then *pruned* back to a potentially smaller depth. The goal of this process is to find a \"right-sized tree\" that has the smallest error rate. To do this, we penalize the error rate using the size of tree:\n",
      "$$\\text{SSE}_{C_p} = \\text{SSE} + C_p \\times (\\# \\text{Terminal Nodes}),$$\n",
      "where $C_p$ is called the *complexity parameter*. For a specific value of the complexity parameter, we find the smallest pruned tree that has the lowest penalized error rate. As with other regularization methods previously discussed, smaller penalties tend to produce more complex models, which, in this ccase, result in larger trees.\n",
      "\n",
      "To find the best pruned tree, we use cross-validation approaches to evaluate the data across a sequence of $C_p$ values. One can also consider one-standard-error rule to optimize criteria for identifying the simplest tree: find the smallest error tree that is within one standard error of the tree with smallest absolute error."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that, unfortunately, sklearn current does not support pruning methods such as the complexity parameter. Instead, a couple of optional parameters, i.e.,\n",
      "- 'max_depth': the maximum depth of the tree.\n",
      "- 'min_samples_split': the minimum number of samples required to split an internal node.\n",
      "- 'min_samples_leaf': the minimum number of samples required to be at a leaf node.\n",
      "\n",
      "A preferred parameter to specify is the 'min_samples_split' since it directly prevents overfitting."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.tree import DecisionTreeRegressor\n",
      "from sklearn.grid_search import GridSearchCV\n",
      "from sklearn.cross_validation import ShuffleSplit\n",
      "\n",
      "cv = ShuffleSplit(trainX.shape[0], n_iter=10, random_state=3)\n",
      "treg = DecisionTreeRegressor()\n",
      "gs_param = {\n",
      "    'min_samples_split': range(2, 100),\n",
      "}\n",
      "gs_treg = GridSearchCV(treg, gs_param, cv=cv, scoring=\"mean_squared_error\", n_jobs=-1)\n",
      "gs_treg.fit(trainX.values, trainY.values[:, 0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "GridSearchCV(cv=ShuffleSplit(951, n_iter=10, test_size=0.1, random_state=3),\n",
        "       estimator=DecisionTreeRegressor(compute_importances=None, criterion='mse',\n",
        "           max_depth=None, max_features=None, max_leaf_nodes=None,\n",
        "           min_density=None, min_samples_leaf=1, min_samples_split=2,\n",
        "           random_state=None, splitter='best'),\n",
        "       fit_params={}, iid=True, loss_func=None, n_jobs=-1,\n",
        "       param_grid={'min_samples_split': [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]},\n",
        "       pre_dispatch='2*n_jobs', refit=True, score_func=None,\n",
        "       scoring='mean_squared_error', verbose=0)"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# calculate RMSE for all candidates\n",
      "def gs_rmse(scores):\n",
      "    '''Calcuate RMSE for a GridSearchCV grid_scores_ object.'''\n",
      "    rmse = []\n",
      "    for dx, v in enumerate(scores):\n",
      "        rmse.append([v[0]['min_samples_split'], np.sqrt(-v[1]), np.std(np.sqrt(-v[2]))])\n",
      "    return np.array(rmse)\n",
      "\n",
      "gs_treg_rmse = gs_rmse(gs_treg.grid_scores_)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(gs_treg_rmse[:,0], gs_treg_rmse[:,1], c='b')\n",
      "plt.xlabel('\\'min_samples_split\\'')\n",
      "plt.ylabel('RMSE')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "<matplotlib.text.Text at 0x110e61b10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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K2JF0lNQU4KQY47D2fmA5WbRJqmVvvQVbbgn//W8aEZNU3Sq2TxuwZoyxf+nk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\nkS9zlzfzlzfzV7ss2jpgvvng4ouhT5/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       "text": [
        "<matplotlib.figure.Figure at 0x10e7492d0>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# use the one-standard-error rule\n",
      "thres_rmse = np.min(gs_treg_rmse[:,1]) + gs_treg_rmse[np.argmin(gs_treg_rmse[:,1]), 2]\n",
      "\n",
      "for idx, i in reversed(list(enumerate(gs_treg_rmse))):\n",
      "    if i[1] < thres_rmse:\n",
      "        best_param = i[0]\n",
      "        break\n",
      "        \n",
      "print \"The best parameter: 'min_samples_split' = {0}.\".format(best_param)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The best parameter: 'min_samples_split' = 51.0.\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This particular tree methodology can also handle missing data. When building the tree, missing data are ignored. For each split, a variety of alternatives (called *surrogate splits*) are evaluated. A surrogate split is one whose results are similar to the original split actually used in the tree. If a surrogate split approximates the original split well, it can be used when the predictor data associated with the original split are not available.\n",
      "\n",
      "Once the tree has been finalized, we begin to assess the relative importance of the predictors to the outcome. One way to compute an aggregate measure of importance is to keep track of the overall reduction in the optimization criteria, e.g., *SSE*. Intuitively, predictors that appear higher in the tree or those that appear multiple times in the tree will be more important than predictors that occur lower in the tree or not at all. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# the important values for the 16 predictors\n",
      "treg_best = DecisionTreeRegressor(min_samples_split=53)\n",
      "treg_best.fit(trainX.values, trainY.values[:, 0])\n",
      "\n",
      "def viz_importance(scores, num_predictors = 16, predictor_names = trainX.columns):\n",
      "    '''Visualize the relative importance of predictors.'''\n",
      "    idx = np.argsort(scores)[-num_predictors:]\n",
      "    names = predictor_names[idx]\n",
      "    importances = scores[idx]\n",
      "    \n",
      "    y_pos = np.arange(num_predictors)\n",
      "    plt.barh(y_pos, importances, align='center', alpha=0.4)\n",
      "    plt.yticks(y_pos, names)\n",
      "    plt.xlabel('Importance')\n",
      "    \n",
      "viz_importance(treg_best.feature_importances_)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Oy9c7H/hpRMxrGqMb+ATwdxHxZCohmBMRN5eOWeWbkMzMzKzTddyD6CW9TFL5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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11211f990>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "An advantage of tree-based models is that, when the tree is not large, the model is simple and interpretable. Tree models intrinsically conduct feature selection; if a predictor is never used in a split, the prediction equation is independent of these data. This advantage is weakened when there are highly correlated predictors. If two predictors are extremely correlated, the choice of which to use in a split is somewhat random. For example, the two surface area predictors have an extremely high correlation (0.96) and each is used in the tree shown in the above figure. It is possible that the difference between these predictors is strongly driving the choice between the two, but it is more likely to be due to small, random differences in the variables. Because of this, more predictors may be selected than actually needed. In addition, the variable importance value for each variable decreases.\n",
      "\n",
      "While trees are highly interpretable and easy to compute, they do have some noteworthy disadvantages. First, single regression trees are more likely to have sub-optimal predictive performance compared to other modeling approaches. This partly due to the simplicity of the model. By construction, tree models partition the data into rectangular regions of the predictor space. If the relationship between predictors and the outcome is not adequately described by these rectangles, then the predictive performance of a tree will not be optimal. Also, the number of possible predicted outcomes from a tree is finite and is determiend by the number of terminal nodes. This limitation is unlikely to capture all of the nuances of the data.\n",
      "\n",
      "An additional disadvantage is that an individual tree tends to be *unstable*. If the data are slightly altered, a completely different set of splits might be found (i.e., the model variance is high). While this is a disadvantage, ensemble methods exploit this characteristic to create models that tend to have extremely good performance.\n",
      "\n",
      "Finally, these trees suffer from *selecion bias*: predictors with a higher number of distinct values are favored over more granular predictors. Also, as the number of missing values increases, the selection of predictors becomes more biased.\n",
      "\n",
      "It is worth noting that the variable importance scores in the above example show that the model tends to rely more on continuous (i.e., less granular) predictors than the binary fingerprints. This could be due to the selection bias or the content of the variables."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "8.2 Regression Model Trees"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One limitation of simple regression trees is that each terminal node uses the average of the training set outcomes in that node for prediction. As a consequence, these models may not do a good job predicting samples whose true outcomes are extremely high or low.\n",
      "\n",
      "One approach to dealing with this issue is to use a different estimator in the terminal nodes. Here we focus on the *model tree* approach called M5, which is similar to regression trees except:\n",
      "- The splitting criterion is different.\n",
      "- The terminal nodes predict the outcome using a linear model (as opposed to the simple average).\n",
      "- When a sample is predicted, it is often a combination of the predictions from different models along the same path through the tree.\n",
      "\n",
      "The main implementation of this technique is a \"rational reconstruction\" of this model called M5, which is included in the *Weka* software package."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Like simple regression trees, the initial split is found using an exhaustive search over the predictors and training set samples, but, unlike those models, the expected reduction in the node's error rate is used. Let $S$ denote the entire set of data and let $S_1, \\cdots, S_p$ represent the $P$ subsets of the data after splitting. The split criterion would be $$\\text{reduction} = \\text{SD}(S) - \\sum_{i=1}^p {n_i \\over n} \\times \\text{SD}(S_i),$$ where $\\text{SD}$ is the standard deviation and $n_i$ is the number of samples in partition $i$. This metric determines if the total variation in the splits, weighted by sample size, is lower than in the presplit data. The split that is associated with the largest reduction in error is chosen and a linear model is created within the partitions using the split variable in the model. For subsequent splitting iterations, this process is repeated: an initial split is determined and a linear model is created for the partition using the current split variable and all others that preceded it. The error associated with each linear model is used in place of $\\text{SD}(S)$ to determine the expected reduction in the error rate for the next split. The tree growing process continues along the branches of the tree until there are no further improvements in the error rate or there are not enough samples to continue the process. Once the tree is fully grown, there is a linear model for every node in the tree.\n",
      "\n",
      "Once the complete set of linear models have been created, each undergoes a simplification procedure to potentially drop some of the terms. For a given model, an adjusted error rate is computed. First, the absolute differences between the observed and predicted data are calculated then multiplied by a term that penalizes models with large number of parameters: $$\\text{Adjusted Error Rate} = {n^{*}+p \\over n^{*}-p} \\sum_{i=1}^{n^{*}} | y_i - \\hat{y}_i|,$$ where $n^{*}$ is the number of training set data points that were used to build the model and $p$ is the number of parameters. Each model term is dropped and the adjusted error rate is computed. Terms are dropped from the model as long as the adjusted error rate decreases. In some cases, the linear model may be simplified to having only an intercept.  This procedure is independently applied to each linear model."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Model trees also incorporate a type of *smoothing* to decrease the potential for over-fitting. The technique is based on the \"recursive shrinking\" methodology. When predicting, the new sample goes down the appropriate path of the tree, and moving from the bottom up, the linear models along that path are combined. That is, $$\\hat{y}_{(p)} = {n_{(k)} \\hat{y}_{(k)} + c\\hat{y}_{(p)} \\over n_{(k)} + c}$$,\n",
      "where $\\hat{y}_{(k)}$ is the prediction from the child note, $n_{(k)}$ is the number of training set data points in the child node, $\\hat{y}_{(p)}$ is the prediction from the parent node, and $c$ is a constant with a default value of 15. Once this combined prediction is calculated, it is similarly combined with the next mode along the tree (the next parent node) and so on. Note that the smoothing equation is a relatively simple linear combination of models. \n",
      "\n",
      "This type of smoothing can have a significant positive effect on the model tree when the linear models across nodes are very different. There are several possible reasons that the linear models may produce very different predictions. First, the number of training set samples that are available in a node will decrease as new splits are added. This can lead to nodes which model very different regions of the training set and, thus, produce very different linear models. This is especially true for small training sets. Secondly, the linear models derived by the splitting process may suffer from significant collinearity. Suppose two predictors in the training set have an extremely high correlation with one another. In this case, the algorithm may choose between the two predictors randomly. If both predictors are eventually used in splits and become candidates for the linear models, there would be two terms in the linear model for effectively one piece of information, which can lead to substantial instability in the model coefficients. Smoothing using several models can help reduce the impact of any unstable linear models."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Once the tree is fully grown, it is pruned back by finding inadequate sub-trees and removing them. Starting at the terminal nodes, the adjusted error rate with and without the sub-tree is computed. If the sub-tree does not decrease the adjusted error-rate, it is pruned from the model. This process is continued until no more sub-trees can be removed."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "8.3 Rule-Based Models"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A rule is defined as a distinct path through a tree. For the tree, a new sample can only travel down a single path through the tree defined by these rules. The number of samples affected by a rule is called its *coverage*.\n",
      "\n",
      "In addition to the pruning algorithms described before, the complexity of the model tree can be further reduced by either removing entire rules or removing some of the conditions that define the rule.\n",
      "\n",
      "One approach to creating rules from model trees uses the \"separate and conquer\" strategy. This procedure derives rules from many different model trees instead of from a single tree. First, an initial model tree is created (it is recommneded to use unsmoothed model trees). However, only the rule with the largest coverage is saved from this model. The samples covered by the rule are removed from the training set and another model tree is created with the remaining data. Again, only the rule with the maximum coverage is retained. This process repeats until all the training set data have been covered by at least one rule. A new sample is preducted by determining which rule(s) it falls under then applies the linear model associated with the largest coverage."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "8.4 Bagged Trees"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the 1990s, ensemble techniques (methods that combine many models' predictions) began to appear. Bagging, short for *bootstrap aggregation*, was one of the earliest developed ensemble techniques. Bagging is a general approach that uses bootstrapping in conjunction with any regression or classification model to construct a ensemble. The model is fairly simple in structure and consists of the steps outlined below.\n",
      "```\n",
      "for i = 1 to m do\n",
      "    Generate a bootstrap sample of the original data\n",
      "    Train an unprunned tree model on this sample\n",
      "end\n",
      "```\n",
      "Each model in the ensemble is then used to generate a prediction for a new sample and these $m$ predictions are averaged to give the bagged model's prediction.\n",
      "\n",
      "Bagging models provide several advantages over models that are not bagged. First, bagging effectively reduces the variance of a prediction through its aggregation process. For models that produce an unstable prediction, like regression tree, aggregating over many versions of the training data actually reduces the variance in the prediction and, hence, makes the prediction more stable. If the goal of the modeling effort is to find the best prediction, then bagging has a distinct advantage.\n",
      "\n",
      "Bagging stable, lower variance models like linear regression and MARS, on the other hand, offers less imrpovement in the predictive performance."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# use two datasets to illustrate the performance of bagging\n",
      "solu_trainX = pd.read_csv('../datasets/solubility/solTrainXtrans.csv').values[:, 1:]\n",
      "solu_trainY = pd.read_csv('../datasets/solubility/solTrainY.csv').values[:, 1]\n",
      "solu_testX = pd.read_csv('../datasets/solubility/solTestXtrans.csv').values[:, 1:]\n",
      "solu_testY = pd.read_csv('../datasets/solubility/solTestY.csv').values[:, 1]\n",
      "\n",
      "concre = pd.read_csv('../datasets/concrete/concrete.csv').drop('Unnamed: 0', 1)\n",
      "concreX = concre.drop('CompressiveStrength', 1)\n",
      "concreY = concre['CompressiveStrength']\n",
      "\n",
      "from sklearn.cross_validation import train_test_split\n",
      "concre_trainX, concre_testX, concre_trainY, concre_testY = train_test_split(concreX, concreY, test_size = 0.2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# some basic setups\n",
      "def boostrap_sample(X, Y):\n",
      "    '''Generate a boostrap sample of the original data.'''\n",
      "    bsample = np.random.choice(range(len(Y)), len(Y), replace=True)\n",
      "    bs_X = X[bsample]\n",
      "    bs_Y = Y[bsample]\n",
      "    return bs_X, bs_Y\n",
      "\n",
      "def test_pred(trainX, trainY, testX, model):\n",
      "    '''Generate a test set prediction based on the given model.'''\n",
      "    reg = model\n",
      "    reg.fit(trainX, trainY)\n",
      "    return reg.predict(testX)\n",
      "\n",
      "def test_rmse(Y, pred_Y):\n",
      "    '''Calculate RMSE based on the test set prediction.'''\n",
      "    return np.sqrt(np.mean((Y - pred_Y)**2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# bagging: tree vs linear regression vs MARS\n",
      "from sklearn.tree import DecisionTreeRegressor\n",
      "from sklearn.linear_model import LinearRegression\n",
      "from pyearth import Earth\n",
      "\n",
      "np.random.seed(3)\n",
      "\n",
      "tree_solu_rmse = []\n",
      "tree_concre_rmse = []\n",
      "lm_solu_rmse = []\n",
      "lm_concre_rmse = []\n",
      "mars_solu_rmse = []\n",
      "mars_concre_rmse = []\n",
      "\n",
      "for i in range(0, 50, 2):\n",
      "    # generate a boostrap sample\n",
      "    bs_solu_trainX, bs_solu_trainY = boostrap_sample(solu_trainX, solu_trainY)\n",
      "    bs_concre_trainX, bs_concre_trainY = boostrap_sample(concre_trainX, concre_trainY)\n",
      "    \n",
      "    # train a model\n",
      "    tree_solu = test_pred(bs_solu_trainX, bs_solu_trainY, solu_testX, DecisionTreeRegressor())\n",
      "    lm_solu = test_pred(bs_solu_trainX, bs_solu_trainY, solu_testX, LinearRegression())\n",
      "    mars_solu = test_pred(bs_solu_trainX, bs_solu_trainY, solu_testX, Earth())\n",
      "    tree_concre = test_pred(bs_concre_trainX, bs_concre_trainY, concre_testX, DecisionTreeRegressor())\n",
      "    lm_concre = test_pred(bs_concre_trainX, bs_concre_trainY, concre_testX, LinearRegression())\n",
      "    mars_concre = test_pred(bs_concre_trainX, bs_concre_trainY, concre_testX, Earth())\n",
      "    \n",
      "    # aggregate prediction\n",
      "    if i != 0:\n",
      "        tree_solu_agg = np.vstack([tree_solu_agg, tree_solu])\n",
      "        lm_solu_agg = np.vstack([lm_solu_agg, lm_solu])\n",
      "        mars_solu_agg = np.vstack([mars_solu_agg, mars_solu])\n",
      "        tree_concre_agg = np.vstack([tree_concre_agg, tree_concre])\n",
      "        lm_concre_agg = np.vstack([lm_concre_agg, lm_concre])\n",
      "        mars_concre_agg = np.vstack([mars_concre_agg, mars_concre])\n",
      "    else: # if agg not defined\n",
      "        tree_solu_agg = tree_solu\n",
      "        lm_solu_agg = lm_solu\n",
      "        mars_solu_agg = mars_solu\n",
      "        tree_concre_agg = tree_concre\n",
      "        lm_concre_agg = lm_concre\n",
      "        mars_concre_agg = mars_concre\n",
      "    \n",
      "    # calculate rmse\n",
      "    tree_solu_rmse.append(test_rmse(solu_testY, np.mean(tree_solu_agg, 0)))\n",
      "    lm_solu_rmse.append(test_rmse(solu_testY, np.mean(lm_solu_agg, 0)))\n",
      "    mars_solu_rmse.append(test_rmse(solu_testY, np.mean(mars_solu_agg, 0)))\n",
      "    tree_concre_rmse.append(test_rmse(concre_testY, np.mean(tree_concre_agg, 0)))\n",
      "    lm_concre_rmse.append(test_rmse(concre_testY, np.mean(lm_concre_agg, 0)))\n",
      "    mars_concre_rmse.append(test_rmse(concre_testY, np.mean(mars_concre_agg, 0)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The test set performance based on RMSE is plooted by number of bagging iterations."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, (ax1, ax2) = plt.subplots(nrows = 2, sharex = True)\n",
      "\n",
      "# solubility data\n",
      "l1, l2, l3 = ax1.plot(range(0, 50, 2)[1:], tree_solu_rmse[1:], '-o',\n",
      "                      range(0, 50, 2)[1:], lm_solu_rmse[1:], '-x',\n",
      "                      range(0, 50, 2)[1:], mars_solu_rmse[1:], '-^')\n",
      "ax1.set_title('Solubility')\n",
      "\n",
      "# concrete date \n",
      "ax2.plot(range(0, 50, 2)[1:], tree_concre_rmse[1:], '-o',\n",
      "         range(0, 50, 2)[1:], lm_concre_rmse[1:], '-x',\n",
      "         range(0, 50, 2)[1:], mars_concre_rmse[1:], '-^')\n",
      "ax2.set_title('Concrete')\n",
      "\n",
      "fig.legend((l1, l2, l3), ('Tree', 'Linear Regression', 'MARS'), loc='upper center', ncol=3, frameon=False)\n",
      "fig.text(0.5, 0.06, 'Number of Bagging Iterations', ha='center', va='center')\n",
      "fig.text(0.06, 0.5, 'RMSE', va='center', rotation='vertical')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "<matplotlib.text.Text at 0x103778c50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9cB6zZMuSUsFaQnwCU8+dWqWAqGlsU07pdAqndDqFX50IF18MJ2yBKVOL2LJ/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\nW665BbmRrmJQ4frDGVjOZ59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WUvX24JW+1S5b1ZliELjl5pZKa04OKbfdxrS1a51b+j35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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x111097550>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Linear regression and MARS are least improved throughout the ensemble, while the predictions for regression trees are dramatically improved."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As a further demonstration of bagging's ability to reduce the variance of a model's prediction, consider a set of simulated *sin* waves. For this illustration, 20 *sin* waves were simulated, and, for each data set, regression trees and MARS model, as well as bagged regressions and MARS models (each with 50 model iterations), were computed."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# simulated 20 sin waves\n",
      "np.random.seed(3)\n",
      "\n",
      "X = np.zeros([20, 100])\n",
      "Y = np.zeros([20, 100])\n",
      "for i in range(20):\n",
      "    X[i,:] = np.sort(np.random.uniform(2, 10, 100))\n",
      "    Y[i,:] = np.sin(X[i,:]) + np.random.normal(0, 0.2, 100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def model_pred(x, y, model):\n",
      "    '''Fit model and generate predictions.'''\n",
      "    reg = model\n",
      "    reg.fit(x, y)\n",
      "    return reg.predict(x)\n",
      "\n",
      "def bagg_model_pred(x, y, model, niter=50):\n",
      "    '''Fit bagging model with 50 iterations and generate predictions.'''\n",
      "    for i in range(niter):\n",
      "        bs_x, bs_y = boostrap_sample(x, y)\n",
      "        bs_order = np.argsort(bs_x, axis=0)[:,0]\n",
      "        pred = model_pred(bs_x[bs_order], bs_y[bs_order], model)\n",
      "        if i != 0:\n",
      "            pred_agg = np.vstack([pred_agg, pred])\n",
      "        else:\n",
      "            pred_agg = pred\n",
      "    return np.mean(pred_agg, 0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# build models for each sin wave and make predictions\n",
      "tree_pred = []\n",
      "mars_pred = []\n",
      "bagg_tree_pred = []\n",
      "bagg_mars_pred = []\n",
      "\n",
      "for i in range(20):\n",
      "    x = X[i,:][:,np.newaxis]\n",
      "    y = Y[i,:]\n",
      "    \n",
      "    tree_pred.append(model_pred(x, y, DecisionTreeRegressor(max_depth=3)))\n",
      "    mars_pred.append(model_pred(x, y, Earth()))\n",
      "    bagg_tree_pred.append(bagg_model_pred(x, y, DecisionTreeRegressor(max_depth=3), 50))\n",
      "    bagg_mars_pred.append(bagg_model_pred(x, y, Earth(), 50))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, axarr = plt.subplots(2, 2)\n",
      "\n",
      "x_test = np.arange(2.0, 10.0, 0.01)\n",
      "\n",
      "# tree\n",
      "axarr[0, 0].plot(x_test, np.sin(x_test), 'r')\n",
      "for i in range(20):\n",
      "    axarr[0, 0].plot(X[i,:], tree_pred[i], 'black', alpha=0.3)\n",
      "axarr[0, 0].set_title('Tree')\n",
      "axarr[0, 0].set_ylim([-1.5, 1.5])\n",
      "    \n",
      "# bagged tree\n",
      "axarr[1, 0].plot(x_test, np.sin(x_test), 'r')\n",
      "for i in range(20):\n",
      "    axarr[1, 0].plot(X[i,:], bagg_tree_pred[i], 'black', alpha=0.3)\n",
      "axarr[1, 0].set_title('Bagged Tree')\n",
      "axarr[1, 0].set_ylim([-1.5, 1.5])\n",
      "\n",
      "# MARS\n",
      "axarr[0, 1].plot(x_test, np.sin(x_test), 'r')\n",
      "for i in range(20):\n",
      "    axarr[0, 1].plot(X[i,:], mars_pred[i], 'black', alpha=0.25)\n",
      "axarr[0, 1].set_title('MARS')\n",
      "axarr[0, 1].set_ylim([-1.5, 1.5])\n",
      "    \n",
      "# bagged MARS\n",
      "axarr[1, 1].plot(x_test, np.sin(x_test), 'r')\n",
      "for i in range(20):\n",
      "    axarr[1, 1].plot(X[i,:], bagg_mars_pred[i], 'black', alpha=0.25)\n",
      "axarr[1, 1].set_title('Bagged MARS')\n",
      "axarr[1, 1].set_ylim([-1.5, 1.5])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "(-1.5, 1.5)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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g+PHjpKenYzAY8PPzIzAwkLCwMMd5FEWhrKwMmAg38PDwID4+flYhB3q9noSE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yJcY2NjGAD12c/C179OizPHzW63Ex0djc1mm3RKUWt9wT/e4eHhi66jKPlbMwfXVLxSirCwMHp6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\nDRISEqipq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aWFiIgI+vv7SUhIkOiWEHBIDpcgCH5BcriCj5qaGpqamhgcHCQmJoaQkBAM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\nx94r+AMvKZ5f0PEnwEvjw+INwI2eDD6epIsAj9avKYp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       "text": [
        "<matplotlib.figure.Figure at 0x11108cc10>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The red lines in the panels show the true trend while the multiple black lines show the predictions for each model. Note that the Tree panel has more noise around the true *sin* curve than the MARS model, which only shows variation at the change of points of the pattern. This illustrates the high variance in the regression tree due to model instability. The bottom panels of the figure show the results for bagged models. The variation around the true curve is greatly reduced for regression trees, and, for MARS, the variation is only reduced around the curvilinear portions on the pattern. \n",
      "\n",
      "**Variance/bias tradeoff**: Bagging improves the RMSE of the fitted models by reducing the variance, but not the biases."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Another advantage of bagging models is that they can provide their own internal estimate of predictive performance that correlates well with either cross-validation estimates or test set estimates. Here's why: when constructing a bootstrap sample for each model in the ensemble, certain samples are left out. These samples are called *out-of-bag*, and they can be used to assess the predictive performance courtesy of that specific model since they were not used to build the model. Hence, every model in the ensemble generates a measure of predictive performance courtesy of the out-of-bag samples. The average of the out-of-bag performance metrics can then be used to gauge the predictive performance of the entire ensemble, and this value usually correlates well with the assessment of predictive performance we can get with either cross-validation or from a test set. This error estimate is usually referred to as the out-of-bag estimate."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In its basic form, the user has one choice to make for bagging: the number of bootstrap samples to aggregate, *m*. Often we see an exponential decrease in predictive improvement as the number of iterations increase; the most improvement in prediction performance is obtained with a small number of trees (m < 10)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# display cross-validated predictive performance (RMSE) for varing number of bootstraped samples\n",
      "def bagg_rmse(trainX, trainY, testX, testY, num_bagged, model):\n",
      "    '''Calculate RMSE on test set for bagged models.'''\n",
      "    for i in range(num_bagged):\n",
      "        bs_x, bs_y = boostrap_sample(trainX, trainY)\n",
      "        reg = model\n",
      "        reg.fit(bs_x, bs_y)\n",
      "        pred = reg.predict(testX)\n",
      "        if i != 0:\n",
      "            pred_agg = np.vstack([pred_agg, pred])\n",
      "        else:\n",
      "            pred_agg = pred\n",
      "    pred_avg = np.mean(pred_agg, 0)\n",
      "    return np.sqrt(np.mean((pred_avg - testY)**2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.cross_validation import ShuffleSplit\n",
      "\n",
      "cv = ShuffleSplit(solu_trainX.shape[0], n_iter=10, random_state=3)\n",
      "\n",
      "cv_rmse = []\n",
      "\n",
      "for num_bagged in np.logspace(0, 2, num=7).astype(int):\n",
      "    \n",
      "    temp_rmse = []\n",
      "    \n",
      "    for train_indices, test_indices in cv:\n",
      "        trainX = solu_trainX[train_indices]\n",
      "        trainY = solu_trainY[train_indices]\n",
      "        testX = solu_trainX[test_indices]\n",
      "        testY = solu_trainY[test_indices]\n",
      "        \n",
      "        temp_rmse.append(bagg_rmse(trainX, trainY, testX, testY, num_bagged, \n",
      "                                   DecisionTreeRegressor(max_depth=5)))\n",
      "    cv_rmse.append(temp_rmse)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.errorbar(np.logspace(0, 2, num=7).astype(int), \n",
      "             np.mean(cv_rmse, 1), yerr = np.std(cv_rmse, 1))\n",
      "plt.xlim(-2, 102)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x103713410>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Notice predictive performance improves through ten trees and then tails off with very limited improvment beyond that point. In our experience, if performance is not at an acceptable level after 50 bagging iterations, then we suggest trying other more powerfully predictive ensemble methods such as random forests and boosting.\n",
      "\n",
      "Although bagging usually improves predictive performance for unstable models, there are a few caveats. First, computational costs and memory requirements increase as the number of bootstrap samples increases. This disadvantage can be mostly mitigated if the modeler has access to parallel computing because the bagging process can be easily parallelized. Another disadvantage to this approach is that a bagged model is much less interpretable than a model that is not bagged. However, measures of variable importance can be constructed by combining measures of importrance from the individual models across the ensemble."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "8.5 Random Forests"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Bagging trees (or any high variance, low bias technique) improves predictive performance over a single tree by reducing variance of the prediction. Generating bootstrap samples introduces a random component into the tree building process, which induces a distribution of trees, and therefore also a distribution of predicted values for each sample. The trees in bagging, however, are not completely independent of each other since all of the original predictors are considered at every split of every tree. One can imagine that if we start with a sufficiently large number of original samples and a relationship between predictors and response that can be adequately modeled by a tree, then trees from different bootstrap samples may have similar structures to each other due to the underlying relationship. This characteristic is known as tree correlation and prevents bagging from optimally reducing variance of the predicted values. Reducing correlation among trees, known as de-correlating trees, is then the next logical step to improving the performance of bagging.\n",
      "\n",
      "From a statistical perspective, reducing correlation among predictors can be done by adding randomness to the tree construction process. A general *random forests* algorithm for a tree-based model can be implemented as below.\n",
      "```\n",
      "Select the number of models to build, m\n",
      "for i = 1 to m do\n",
      "    Generate a bootstrap sample of the original data\n",
      "    Train a tree model on this sample\n",
      "    for each split do\n",
      "        Randomly select k (<p) of the original predictors\n",
      "        Select the best predictor among the k predictors and partition the data\n",
      "    end\n",
      "    Use typical tree model stopping criteria to determine when a tree is complete (but do not prune)\n",
      "end\n",
      "```\n",
      "\n",
      "Random forests' tuning parameter is the number of randomly selected predictors, k, to choose from at each split, and is commonly referred to as $m_{try}$. In the regression context, it is suggested to set $m_{try}$ to be one-third of the number of predictors. For the purpose of tuning the $m_{try}$ parameter, since random forests is computationally intensive, we suggest starting with five values of k that are somewhat evenly spaced across the range from 2 to p. The practioner must also specify the number of trees for the forest. It is proved that random forests is protected from over-fitting. Practically speaking, the larger the forest, the more computational burden we will incur to train and build the model. As a starting point, we suggest using at least 1000 trees.\n",
      "\n",
      "It is shown that the linear combination of many independent learners reduces the variance of the overall ensemble relative to any individual learner in the ensemble. A random forest model achieves this variance reduction by selecting strong, complex learners that exhibit low bias. This ensemble of many independent, strong learners yields an improvement in error rates. Because each learner is selected independently of all previous learners, random forests is robust to a noisy response. At the same time, the independence of learners can underfit data when the response is not noisy.\n",
      "\n",
      "Compared to bagging, random forests is more computationally efficient on a tree-by-tree basis since the tree  building process only needs to evaluate a fraction of the original predictors at each split, although more trees are usually required by random forests. Combining this attribute with the ability to parallel process tree building makes random forests more computationally efficient than boosting."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Tree was used as the base learner in random forests, as well as 10-fold cross-validation and out-of-bag validation, to train models on the solubility data. The $m_{try}$ parameter was evaluated at ten values from 10 to 228."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.ensemble import RandomForestRegressor\n",
      "from sklearn.metrics import mean_squared_error\n",
      "\n",
      "cv = ShuffleSplit(solu_trainX.shape[0], n_iter=10, random_state=3)\n",
      "\n",
      "cv_rmse = []\n",
      "oob_rmse = []\n",
      "for m_try in range(10, 228, 22):\n",
      "    # out-of-bag score\n",
      "    rf = RandomForestRegressor(n_estimators=1000, max_features=m_try, oob_score=True)\n",
      "    rf.fit(solu_trainX, solu_trainY)\n",
      "    oob_rmse.append(np.sqrt(mean_squared_error(solu_trainY, rf.oob_prediction_)))\n",
      "    \n",
      "    # cross-validation score\n",
      "    cv_temp_rmse = []\n",
      "    for train_indices, test_indices in cv:\n",
      "        trainX = solu_trainX[train_indices]\n",
      "        trainY = solu_trainY[train_indices]\n",
      "        testX = solu_trainX[test_indices]\n",
      "        testY = solu_trainY[test_indices]\n",
      "        \n",
      "        rf = RandomForestRegressor(n_estimators=1000, max_features=m_try)\n",
      "        rf.fit(trainX, trainY)\n",
      "        cv_temp_rmse.append(np.sqrt(mean_squared_error(testY, rf.predict(testX))))\n",
      "    cv_rmse.append(cv_temp_rmse)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(range(10, 228, 22), np.mean(cv_rmse, 1), 'o-', label = 'CV score')\n",
      "plt.plot(range(10, 228, 22), oob_rmse, 'x-', label = 'OOB score')\n",
      "plt.legend()\n",
      "plt.xlim(0, 228)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KOanAE0ANYLe1NjX/+L3A1UAe8A3wG2vt0RKfDWhP1d3z7ubhTx5m882bSYpL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\nztNWowlTYT4Pa+Fh4VRXV3O85Dhxt8RxvPg4gzs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       "text": [
        "<matplotlib.figure.Figure at 0x11447d450>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Our experience is that the random forest tuning parameter does not have a drastic effect on performance. In these data, the only real difference in the RMSE comes when the smallest value is used (10 in this case). It is often the case that such a small value is not associated with optimal performance. However, we have seen rare examples where small tuning parameter values generate the best results. To get a quick assessment of how well the random forest model performs, the default tuning parameter value for regression ($m_{try} = p/3$) tends to work well. If there is a desire to maximize performance, tuning this value may result in a slight improvment. Also, note that, use the out-of-bag error rate would drastically decrease the computational time to tune random forest models.\n",
      "\n",
      "The ensemble nature of random forests makes it impossible to gain an understanding of the relationship between the predictors and the response. However, because trees are the typical base learner for this method, it is possible to quantify the impact of predictors in the ensemble. One approach is to randomly permuting the values of each predictor for the out-of-bag sample of one predictor at a tiem for each tree. The difference in predictive performance between the non-permuted sample and the permuted sample for each predictor is recorded and aggregated across the entire forest. Another approach is to measure the improvement in the node purity based on the performance metric for each predictor at each occurence of that predictor across the forest. These individual improvement values for each predictor are then aggregated across the forest to determine the overall importance for the predictor.\n",
      "\n",
      "Although this strategy to determine the relative influence of a predictor is very different from the approach for single regression tree, it suffers from the same limitations related to bias. Also, the correlations between predictors can have a significant impact on the importance values. Also, the $m_{try}$ tuning parameter has a serious effect on the importance values.\n",
      "\n",
      "Another impact of between-predictor correlations is to dilute the importances of key predictors. For example, suppose a critical predictor had an importance of X. If another predictor is just as critical but is almost perfectly correlated as the first, the importance of these two predictors will be roughly X/2. If three such predictors were in the model, the values would further decrease to X/3 and so on."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rf = RandomForestRegressor(n_estimators=1000, max_features=120)\n",
      "rf.fit(solu_trainX, solu_trainY)\n",
      "viz_importance(rf.feature_importances_)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6HicCkyNij/TnncBuknanSJT7lfZ9kGI1FmAcxarpBkk3p22dVnkvBA7YxPla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\nnslPhRXwmao6GDgWeL6P2u8DvG9g3W1VdXBVvR6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       "text": [
        "<matplotlib.figure.Figure at 0x10e7a3a10>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Contrasting random forest importance results to a singe tree, we see many important predictors are in common. However, the importance ordering are much different. These differences should not be disconerning; rather they emphasize that a single tree's greediness prioritizes predictors differently than a random forest."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "8.6 Boosting"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Boosting models were originally developed for classification problems and were later extended to the regression setting. Boosting, especially in the form of AdaBoost algorithm, was shown to be a powerful predictive tool, usually outperforming any individual model. The AdaBoost algorithm clearly worked, and after its successful arrival, several reseachers connected the AdaBoost algorithm to statistical concepts of loss functions, additive modeling, and logistic regression and showed that boosting can be interpreted as a forward stagewise additive model that minimize exponential loss. This fundamental understanding of boosting led to a new view of boosting that facilitated several algorithmic generalizations to classification problems. Moreover, this new perspective also enabled the method to be extended to regression problem.\n",
      "\n",
      "The \"gradient boosting machines\" is a method stemmed from boosting's statistical framework, which emcompassed both classification and regression. The basic principles of gradient boosting are as follows: given a loss function (e.g., squared error for regression) and a weak learner (e.g., regression trees), the algorithm seeks to find an additive model that minimizes the loss function. The algorithm is typically initialized with the best guess of the response (e.g., the mean of the response in regression). The gradient (e.g., residual) is calculated, and a model is then fit to the residuals to minimize the loss function. The current model is added to the previous model, and the procedure continues for a use-specified number of iterations.\n",
      "\n",
      "As described throughout this text, any modeling technique with tuning parameters can produce a range of predictive ability -- from weak to strong. Because boosting requires a weak learner, almost any technique with tuning parameters can be made into a weak learner. Tree, as it turns out, make an excellent base learner for boosting for several reasons. First, they have the flexibility to be weak learners by simply restricting their depth. Second, separate trees can be easily added together, much like individual predictors can be added together in a regression model, to generate a prediction. And third, trees can be generated very quickly. Hence, results from individual trees can be directly aggregated, thus making them inherently suitable for an additive modeling process.\n",
      "\n",
      "When regression trees are used as the base learner, simple gradient boosting for regression has two tuning parameters: tree depth and number of iterations. Tree depth in this context is also known as *interaction depth*, since each subsequential split can be thought of as a higher-level interaction term with all of the other previous split predictors. If squared error is used as the loss function, then a simple boosting algorithm using these tuning parameters is listed below.\n",
      "```\n",
      "Select tree depth, D, and number of iterations, K\n",
      "Compute the average response, $\\bar{y}$, and use this as the initial predicted value for each sample\n",
      "for k = 1 to K do\n",
      "    Compute the residual, the difference between the observed value and the current predicted value, for each sample\n",
      "    Fit a regression tree of depth, D, using the residuals as the response\n",
      "    Predict each sample using the regression tree fit in the previous step\n",
      "    Update the predicted value of each sample by adding the previous iteration's predicted value to the predicted value \n",
      "    generated in the previous step\n",
      "end\n",
      "```\n",
      "Clearly, this version of boosting has similarities to random forests: the final prediction is based on an ensemble of models, and trees are used as the base learner. However, the way the ensembles are constructed differs substantially between each model. In random forests, all trees are created independently, each tree is created to have maximum depth, and each tree contributes equally to the final model. The trees in boosting, however, are dependent on past trees, have minimum depth, and contribute unequally to the final model. Despite these differences, both random forests and boosting offer competitive predictive performance. Computation time for boosting is often greater than for random forests, since random forests can be easily parallel processed given that the trees are created independently.\n",
      "\n",
      "The gradient boosting machine could be susceptible to over-fitting, since the learner employed -- even in its weakly defined learning capacity -- is tasked with optimally fitting the gradient. This means that boosting will select the optimal learner at each stage of the algorithm. Despite using weak learners, boosting still employs the greedy strategy of choosing the optimal weak learner at each stage. Although this strategy generates an optimal solution at the current stage, it has the drawbacks of not finding the optimal global model as well as over-fitting the training data. A remedy for greediness is to constrain the learning process by employing regularization, or shrinkage. In the above algorithm, instead of adding the predicted value for a sample to previous iteration's predicted value, only a fraction of the current predicted value is added to the previous iteration's predicted value. This fraction is commonly referred to as the *learning rate* and is parameterized by the symbol, $\\lambda$. THis parameter can take values between 0 and 1 and becomes another tuning parameter for the model. Small values of the learning parameter ($<$0.01) works best, but the value of the parameter is inversely proportional to the computation time required to find an optimal model, because more iterations are necessary. Having more iterations also implies that more memory is required for storing the model.\n",
      "\n",
      "A variation, *stochastic gradient boosting*, borrows some idea from bagging techniques. It inserts the following step before line within the loop: randomly select a fraction of the training data. The residuals and models in the remaining steps of the current iteration are based only on the sample of data. The fraction of training data used, knownas the bagging fraction, then becomes another tuning parameter for the model. It turns out that this simple modification improved the predictive accuracy of boosting while also reducing the required computational resources. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.ensemble import GradientBoostingRegressor\n",
      "from sklearn.grid_search import GridSearchCV\n",
      "from sklearn.cross_validation import ShuffleSplit\n",
      "\n",
      "cv = ShuffleSplit(solu_trainX.shape[0], n_iter=10, random_state=3)\n",
      "\n",
      "gs_param = {\n",
      "    'learning_rate': [0.01, 0.1],\n",
      "    'max_depth': range(1, 8, 2),\n",
      "    'n_estimators': range(100, 1001, 50),\n",
      "    'subsample': [0.5],\n",
      "}\n",
      "gbr = GradientBoostingRegressor()\n",
      "gs_gbr = GridSearchCV(gbr, gs_param, cv=cv, scoring='mean_squared_error', n_jobs=-1)\n",
      "gs_gbr.fit(solu_trainX, solu_trainY)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "GridSearchCV(cv=ShuffleSplit(951, n_iter=10, test_size=0.1, random_state=3),\n",
        "       estimator=GradientBoostingRegressor(alpha=0.9, init=None, learning_rate=0.1, loss='ls',\n",
        "             max_depth=3, max_features=None, max_leaf_nodes=None,\n",
        "             min_samples_leaf=1, min_samples_split=2, n_estimators=100,\n",
        "             random_state=None, subsample=1.0, verbose=0, warm_start=False),\n",
        "       fit_params={}, iid=True, loss_func=None, n_jobs=-1,\n",
        "       param_grid={'n_estimators': [100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950, 1000], 'subsample': [0.5], 'learning_rate': [0.01, 0.1], 'max_depth': [1, 3, 5, 7]},\n",
        "       pre_dispatch='2*n_jobs', refit=True, score_func=None,\n",
        "       scoring='mean_squared_error', verbose=0)"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "scores1 = np.zeros([len(range(100, 1001, 50)), len(range(1, 8, 2))])\n",
      "scores2 = np.zeros([len(range(100, 1001, 50)), len(range(1, 8, 2))])\n",
      "\n",
      "for score in gs_gbr.grid_scores_:\n",
      "    if score[0]['learning_rate'] == 0.01:\n",
      "        idx = (score[0]['n_estimators'] - 100)/50\n",
      "        jdx = score[0]['max_depth']/2\n",
      "        scores1[idx, jdx] = np.sqrt(-score[1])\n",
      "    else:\n",
      "        idx = (score[0]['n_estimators'] - 100)/50\n",
      "        jdx = score[0]['max_depth']/2\n",
      "        scores2[idx, jdx] = np.sqrt(-score[1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, (ax1, ax2) = plt.subplots(ncols=2, sharey=True)\n",
      "\n",
      "for i in range(4):\n",
      "    ax1.plot(range(100, 1001, 50), scores1[:, i], 'x-')\n",
      "ax1.set_title('shrinkage: 0.01')\n",
      "    \n",
      "for i in range(4):\n",
      "    ax2.plot(range(100, 1001, 50), scores2[:, i], 'x-', label = 'tree depth:' + str(2*i+1))\n",
      "ax2.set_title('shrinkage: 0.10')\n",
      "ax2.legend(loc='upper right')\n",
      "\n",
      "fig.text(0.5, 0.06, '# Trees', ha='center', va='center')\n",
      "fig.text(0.08, 0.5, 'RMESE (Cross-Validation)', ha='center', va='center', rotation=90)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "<matplotlib.text.Text at 0x114438490>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KWw03vdtuE/m//6vyO/KZNWvW+DeAxnNcTI3nW1ppqzunXxt2xPRVvGCutIWSlJSUCgMi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KmigCQSkItAooBcApxAgNzz2z9mEgIEOAnnJGdOvu/X67zOmWFmfvPMmfPkx8zzPMPw556DzMyD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\nExEREQmA/wckL4E9fCD9uQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1144f3890>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The cross-validated RMSE results is presented for boosted trees across tuning parameters of tree depth (1-7), number of trees (100-1000), and shrinkage (0.01 or 0.10); the bagging fraction was fixed at 0.5. The larger value of shrinkage has an impact on reducing RMSE for all choices of tree depth and number of trees. The same pattern holds true for RMSE when shrinkage is 0.1 and the number of trees is less than 300.\n",
      "\n",
      "Variable importance for boosting is a function of the reduction in squared error. Specifically, the improvement in squared error due to each predictor is summed within each tree in the ensemble (i.e., each predictor gets an improvement value for each tree). The improvement values for each predictor are then averaged across the entire ensemble to yield an overall importance value."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gbr = GradientBoostingRegressor(learning_rate=0.01, max_depth=5, n_estimators=500, subsample=0.5)\n",
      "gbr.fit(solu_trainX, solu_trainY)\n",
      "viz_importance(gbr.feature_importances_)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/ChwcEUskHQMcEBGflPQ48IaIeL50ri8AO0TE6XVj2BT4b+AF4EWKSfG2wOsoambL5zsX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\ndfPsR5IkaVWYuJKA1cCSgHZ+FDPMTNqZSztzaWc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BjwROrqovJbkY+DZwLHAw8Jqq+psk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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e7a9510>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The importance profile for boosting has a much steeper importance slope than the one for random forests. This is due to the fact that the trees from boosting are dependent on each other and hence will have correlated structures as the method follows by the gradient. Therefore, many of the same predictors will be selected across the trees, increasing their contribution to the importance metric. Differences between variable importance ordering and magnitude between random forests and boosting should not be disconcerning. Instead, one should consider these as two different perspectives of the data and use each view to provide some understanding of the gross relationships between predictors and the response."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}