1 | using System;
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2 | using System.Collections.Generic;
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3 | using System.Diagnostics;
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4 | using System.Diagnostics.Contracts;
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5 | using System.Linq;
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6 | using HeuristicLab.Common;
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7 | using HeuristicLab.Core;
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8 | using HeuristicLab.Problems.DataAnalysis;
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9 |
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10 | namespace GradientBoostedTrees {
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11 | public class RegressionTreeBuilder {
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12 | private readonly IRandom random;
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13 | private readonly IRegressionProblemData problemData;
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14 |
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15 | private readonly int nCols;
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16 | private readonly double[][] x; // all training data (original order from problemData)
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17 | private double[] y; // training labels (original order from problemData)
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18 |
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19 | private Dictionary<string, double> sumImprovements; // for variable relevance calculation
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20 |
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21 | private readonly string[] allowedVariables; // all variables in shuffled order
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22 | private Dictionary<string, int> varName2Index; // maps the variable names to column indexes
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23 | private int effectiveVars; // number of variables that are used from allowedVariables
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24 |
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25 | private int effectiveRows; // number of rows that are used from
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26 | private readonly int[][] sortedIdxAll;
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27 | private readonly int[][] sortedIdx; // random selection from sortedIdxAll (for r < 1.0)
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28 |
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29 |
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30 |
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31 | // helper arrays which are allocated to maximal necessary size only once in the ctor
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32 | private readonly int[] internalIdx, which, leftTmp, rightTmp;
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33 | private readonly double[] outx;
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34 | private readonly int[] outSortedIdx;
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35 | private readonly IList<RegressionTreeModel.TreeNode> nodeQueue;
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36 |
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37 | // prepare and allocate buffer variables in ctor
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38 | public RegressionTreeBuilder(IRegressionProblemData problemData, IRandom random) {
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39 | this.problemData = problemData;
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40 | this.random = random;
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41 |
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42 | var rows = problemData.TrainingIndices.Count();
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43 |
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44 | this.nCols = problemData.AllowedInputVariables.Count();
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45 |
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46 | allowedVariables = problemData.AllowedInputVariables.ToArray();
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47 | varName2Index = new Dictionary<string, int>(allowedVariables.Length);
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48 | for (int i = 0; i < allowedVariables.Length; i++) varName2Index.Add(allowedVariables[i], i);
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49 |
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50 | sortedIdxAll = new int[nCols][];
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51 | sortedIdx = new int[nCols][];
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52 | sumImprovements = new Dictionary<string, double>();
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53 | internalIdx = new int[rows];
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54 | which = new int[rows];
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55 | leftTmp = new int[rows];
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56 | rightTmp = new int[rows];
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57 | outx = new double[rows];
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58 | outSortedIdx = new int[rows];
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59 | nodeQueue = new List<RegressionTreeModel.TreeNode>();
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60 |
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61 | x = new double[nCols][];
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62 | y = problemData.Dataset.GetDoubleValues(problemData.TargetVariable, problemData.TrainingIndices).ToArray();
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63 |
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64 |
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65 | int col = 0;
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66 | foreach (var inputVariable in problemData.AllowedInputVariables) {
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67 | x[col] = problemData.Dataset.GetDoubleValues(inputVariable, problemData.TrainingIndices).ToArray();
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68 | sortedIdxAll[col] = Enumerable.Range(0, rows).OrderBy(r => x[col][r]).ToArray();
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69 | sortedIdx[col] = new int[rows];
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70 | col++;
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71 | }
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72 | }
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73 |
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74 | // r and m work in the same way as for alglib random forest
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75 | // r is fraction of rows to use for training
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76 | // m is fraction of variables to use for training
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77 | public IRegressionModel CreateRegressionTree(int maxDepth, double r = 0.5, double m = 0.5) {
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78 | // subtract mean of y first
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79 | var yAvg = y.Average();
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80 | for (int i = 0; i < y.Length; i++) y[i] -= yAvg;
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81 |
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82 | var seLoss = new SquaredErrorLoss();
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83 | var zeros = Enumerable.Repeat(0.0, y.Length);
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84 | var ones = Enumerable.Repeat(1.0, y.Length);
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85 |
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86 | var model = CreateRegressionTreeForGradientBoosting(y, maxDepth, problemData.TrainingIndices.ToArray(), seLoss.GetLineSearchFunc(y, zeros, ones), r, m);
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87 | return new GradientBoostedTreesModel(new[] { new ConstantRegressionModel(yAvg), model }, new[] { 1.0, 1.0 });
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88 | }
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89 |
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90 | // specific interface that allows to specify the target labels and the training rows which is necessary when this functionality is called by the gradient boosting routine
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91 | public IRegressionModel CreateRegressionTreeForGradientBoosting(double[] y, int maxDepth, int[] idx, LineSearchFunc lineSearch, double r = 0.5, double m = 0.5) {
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92 | Contract.Assert(maxDepth > 0);
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93 | Contract.Assert(r > 0);
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94 | Contract.Assert(r <= 1.0);
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95 | Contract.Assert(y.Count() == this.y.Length);
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96 | Contract.Assert(m > 0);
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97 | Contract.Assert(m <= 1.0);
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98 |
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99 | this.y = y; // y is changed in gradient boosting
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100 |
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101 | // shuffle row idx
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102 | HeuristicLab.Random.ListExtensions.ShuffleInPlace(idx, random);
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103 |
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104 | int nRows = idx.Count();
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105 |
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106 | // shuffle variable idx
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107 | HeuristicLab.Random.ListExtensions.ShuffleInPlace(allowedVariables, random);
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108 |
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109 | effectiveRows = (int)Math.Ceiling(nRows * r);
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110 | effectiveVars = (int)Math.Ceiling(nCols * m);
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111 |
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112 | Array.Clear(which, 0, which.Length);
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113 |
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114 | // mark selected rows
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115 | for (int row = 0; row < effectiveRows; row++) {
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116 | which[idx[row]] = 1;
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117 | internalIdx[row] = idx[row];
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118 | }
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119 |
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120 | for (int col = 0; col < nCols; col++) {
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121 | int i = 0;
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122 | for (int row = 0; row < nRows; row++) {
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123 | if (which[sortedIdxAll[col][row]] > 0) {
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124 | Trace.Assert(i < effectiveRows);
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125 | sortedIdx[col][i] = sortedIdxAll[col][row];
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126 | i++;
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127 | }
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128 | }
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129 | }
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130 | // start and end idx are inclusive
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131 | var tree = CreateRegressionTreeForIdx(maxDepth, 0, effectiveRows - 1, lineSearch);
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132 | return new RegressionTreeModel(tree);
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133 | }
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134 |
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135 | // startIdx and endIdx are inclusive
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136 | private RegressionTreeModel.TreeNode CreateRegressionTreeForIdx(int maxDepth, int startIdx, int endIdx, LineSearchFunc lineSearch) {
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137 | Contract.Assert(endIdx - startIdx >= 0);
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138 | Contract.Assert(startIdx >= 0);
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139 | Contract.Assert(endIdx < internalIdx.Length);
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140 |
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141 | RegressionTreeModel.TreeNode t;
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142 | // TODO: stop when y is constant
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143 | // TODO: use priority queue of nodes to be expanded (sorted by improvement) instead of the recursion to maximum depth
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144 | if (maxDepth <= 1 || endIdx - startIdx == 0) {
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145 | // max depth reached or only one element
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146 | t = new RegressionTreeModel.TreeNode(RegressionTreeModel.TreeNode.NO_VARIABLE, lineSearch(internalIdx, startIdx, endIdx));
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147 | return t;
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148 | } else {
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149 | int i, j;
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150 | double threshold;
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151 | string bestVariableName;
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152 | FindBestVariableAndThreshold(startIdx, endIdx, out threshold, out bestVariableName);
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153 |
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154 | // if bestVariableName is NO_VARIABLE then no split was possible anymore
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155 | if (bestVariableName == RegressionTreeModel.TreeNode.NO_VARIABLE) {
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156 | return new RegressionTreeModel.TreeNode(RegressionTreeModel.TreeNode.NO_VARIABLE, lineSearch(internalIdx, startIdx, endIdx));
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157 | } else {
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158 |
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159 |
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160 | int bestVarIdx = varName2Index[bestVariableName];
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161 | // split - two pass
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162 |
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163 | // store which index goes where
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164 | for (int k = startIdx; k <= endIdx; k++) {
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165 | if (x[bestVarIdx][internalIdx[k]] <= threshold)
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166 | which[internalIdx[k]] = -1; // left partition
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167 | else
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168 | which[internalIdx[k]] = 1; // right partition
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169 | }
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170 |
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171 | // partition sortedIdx for each variable
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172 | for (int col = 0; col < nCols; col++) {
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173 | i = 0;
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174 | j = 0;
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175 | int k;
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176 | for (k = startIdx; k <= endIdx; k++) {
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177 | Debug.Assert(Math.Abs(which[sortedIdx[col][k]]) == 1);
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178 |
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179 | if (which[sortedIdx[col][k]] < 0) {
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180 | leftTmp[i++] = sortedIdx[col][k];
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181 | } else {
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182 | rightTmp[j++] = sortedIdx[col][k];
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183 | }
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184 | }
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185 | Debug.Assert(i > 0); // at least on element in the left partition
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186 | Debug.Assert(j > 0); // at least one element in the right partition
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187 | Debug.Assert(i + j == endIdx - startIdx + 1);
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188 | k = startIdx;
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189 | for (int l = 0; l < i; l++) sortedIdx[col][k++] = leftTmp[l];
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190 | for (int l = 0; l < j; l++) sortedIdx[col][k++] = rightTmp[l];
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191 | }
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192 |
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193 | // partition row indices
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194 | i = startIdx;
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195 | j = endIdx;
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196 | while (i <= j) {
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197 | Debug.Assert(Math.Abs(which[internalIdx[i]]) == 1);
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198 | Debug.Assert(Math.Abs(which[internalIdx[j]]) == 1);
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199 | if (which[internalIdx[i]] < 0) i++;
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200 | else if (which[internalIdx[j]] > 0) j--;
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201 | else {
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202 | Trace.Assert(which[internalIdx[i]] > 0);
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203 | Trace.Assert(which[internalIdx[j]] < 0);
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204 | // swap
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205 | int tmp = internalIdx[i];
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206 | internalIdx[i] = internalIdx[j];
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207 | internalIdx[j] = tmp;
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208 | i++;
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209 | j--;
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210 | }
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211 | }
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212 | Debug.Assert(j < i);
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213 | Debug.Assert(i >= startIdx);
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214 | Debug.Assert(j <= endIdx);
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215 |
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216 | t = new RegressionTreeModel.TreeNode(bestVariableName,
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217 | threshold,
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218 | CreateRegressionTreeForIdx(maxDepth - 1, startIdx, j, lineSearch),
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219 | CreateRegressionTreeForIdx(maxDepth - 1, i, endIdx, lineSearch));
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220 |
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221 | return t;
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222 | }
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223 | }
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224 | }
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225 |
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226 | private void FindBestVariableAndThreshold(int startIdx, int endIdx, out double threshold, out string bestVar) {
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227 | Contract.Assert(startIdx < endIdx + 1); // at least 2 elements
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228 |
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229 | int rows = endIdx - startIdx + 1;
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230 | Contract.Assert(rows >= 2);
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231 |
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232 | double sumY = 0.0;
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233 | for (int i = startIdx; i <= endIdx; i++) {
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234 | sumY += y[internalIdx[i]];
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235 | }
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236 |
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237 | double bestImprovement = 0.0;
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238 | double bestThreshold = double.PositiveInfinity;
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239 | bestVar = string.Empty;
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240 |
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241 | for (int col = 0; col < effectiveVars; col++) {
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242 | // sort values for variable to prepare for threshold selection
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243 | var curVariable = allowedVariables[col];
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244 | var curVariableIdx = varName2Index[curVariable];
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245 | for (int i = startIdx; i <= endIdx; i++) {
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246 | var sortedI = sortedIdx[curVariableIdx][i];
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247 | outSortedIdx[i - startIdx] = sortedI;
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248 | outx[i - startIdx] = x[curVariableIdx][sortedI];
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249 | }
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250 |
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251 | double curImprovement;
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252 | double curThreshold;
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253 | FindBestThreshold(outx, outSortedIdx, rows, y, sumY, out curThreshold, out curImprovement);
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254 |
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255 | if (curImprovement > bestImprovement) {
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256 | bestImprovement = curImprovement;
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257 | bestThreshold = curThreshold;
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258 | bestVar = allowedVariables[col];
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259 | }
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260 | }
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261 |
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262 | UpdateVariableRelevance(bestVar, sumY, bestImprovement, rows);
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263 |
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264 | threshold = bestThreshold;
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265 |
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266 | // Contract.Assert(bestImprovement > 0);
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267 | // Contract.Assert(bestImprovement < double.PositiveInfinity);
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268 | // Contract.Assert(bestVar != string.Empty);
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269 | // Contract.Assert(allowedVariables.Contains(bestVar));
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270 | }
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271 |
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272 | // assumption is that the Average(y) = 0
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273 | private void UpdateVariableRelevance(string bestVar, double sumY, double bestImprovement, int rows) {
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274 | // update variable relevance
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275 | double err = sumY * sumY / rows;
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276 | double errAfterSplit = bestImprovement;
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277 |
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278 | double delta = (errAfterSplit - err); // relative reduction in squared error
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279 | double v;
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280 | if (!sumImprovements.TryGetValue(bestVar, out v)) {
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281 | sumImprovements[bestVar] = delta;
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282 | }
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283 | sumImprovements[bestVar] = v + delta;
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284 | }
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285 |
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286 | // x [0..N-1] contains rows sorted values in the range from [0..rows-1]
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287 | // sortedIdx [0..N-1] contains the idx of the values in x in the original dataset in the range from [0..rows-1]
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288 | // rows specifies the number of valid entries in x and sortedIdx
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289 | // y [0..N-1] contains the target values in original sorting order
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290 | // sumY is y.Sum()
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291 | //
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292 | // the routine returns the best threshold (x[i] + x[i+1]) / 2 for i = [0 .. rows-2] by calculating the reduction in squared error
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293 | // additionally the reduction in squared error is returned in bestImprovement
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294 | // if all elements of x are equal the routing fails to produce a threshold
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295 | private static void FindBestThreshold(double[] x, int[] sortedIdx, int rows, double[] y, double sumY, out double bestThreshold, out double bestImprovement) {
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296 | Contract.Assert(rows >= 2);
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297 |
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298 | double sl = 0.0;
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299 | double sr = sumY;
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300 | double nl = 0.0;
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301 | double nr = rows;
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302 |
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303 | bestImprovement = 0.0;
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304 | bestThreshold = double.NegativeInfinity;
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305 | // for all thresholds
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306 | // if we have n rows there are n-1 possible splits
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307 | for (int i = 0; i < rows - 1; i++) {
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308 | sl += y[sortedIdx[i]];
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309 | sr -= y[sortedIdx[i]];
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310 |
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311 | nl++;
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312 | nr--;
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313 | Debug.Assert(nl > 0);
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314 | Debug.Assert(nr > 0);
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315 |
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316 | if (x[i] < x[i + 1]) { // don't try to split when two elements are equal
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317 | double curQuality = sl * sl / nl + sr * sr / nr;
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318 | // curQuality = nl*nr / (nl+nr) * Sqr(sl / nl - sr / nr) // greedy function approximation page 12 eqn (35)
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319 |
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320 | if (curQuality > bestImprovement) {
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321 | bestThreshold = (x[i] + x[i + 1]) / 2.0;
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322 | bestImprovement = curQuality;
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323 | }
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324 | }
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325 | }
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326 |
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327 | // if all elements where the same then no split can be found
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328 | }
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329 |
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330 |
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331 | public IEnumerable<KeyValuePair<string, double>> GetVariableRelevance() {
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332 | double scaling = 100 / sumImprovements.Max(t => t.Value);
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333 | return
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334 | sumImprovements
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335 | .Select(t => new KeyValuePair<string, double>(t.Key, t.Value * scaling))
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336 | .OrderByDescending(t => t.Value);
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337 | }
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338 | }
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339 | }
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340 |
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341 |
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342 |
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343 |
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344 |
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345 |
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346 |
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347 |
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348 |
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349 |
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350 |
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351 |
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352 |
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353 |
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354 |
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355 |
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356 |
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357 |
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358 |
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