1 | #region License Information
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2 | /* HeuristicLab
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3 | * Copyright (C) 2002-2015 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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4 | * and the BEACON Center for the Study of Evolution in Action.
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5 | *
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6 | * This file is part of HeuristicLab.
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7 | *
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8 | * HeuristicLab is free software: you can redistribute it and/or modify
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9 | * it under the terms of the GNU General Public License as published by
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10 | * the Free Software Foundation, either version 3 of the License, or
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11 | * (at your option) any later version.
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12 | *
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13 | * HeuristicLab is distributed in the hope that it will be useful,
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14 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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15 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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16 | * GNU General Public License for more details.
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17 | *
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18 | * You should have received a copy of the GNU General Public License
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19 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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20 | */
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21 | #endregion
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22 |
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23 | using System;
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24 | using System.Collections;
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25 | using System.Collections.Generic;
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26 | using System.Diagnostics;
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27 | using System.Linq;
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28 | using HeuristicLab.Core;
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29 | using HeuristicLab.Problems.DataAnalysis;
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30 |
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31 | namespace HeuristicLab.Algorithms.DataAnalysis {
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32 | // This class implements a greedy decision tree learner which selects splits with the maximum reduction in sum of squared errors.
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33 | // The tree builder also tracks variable relevance metrics based on the splits and improvement after the split.
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34 | // The implementation is tuned for gradient boosting where multiple trees have to be calculated for the same training data
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35 | // each time with a different target vector. Vectors of idx to allow iteration of intput variables in sorted order are
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36 | // pre-calculated so that optimal thresholds for splits can be calculated in O(n) for each input variable.
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37 | // After each split the row idx are partitioned in a left an right part.
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38 | public class RegressionTreeBuilder {
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39 | private readonly IRandom random;
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40 | private readonly IRegressionProblemData problemData;
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41 |
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42 | private readonly int nCols;
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43 | private readonly double[][] x; // all training data (original order from problemData), x is constant
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44 | private double[] y; // training labels (original order from problemData), y can be changed
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45 |
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46 | private Dictionary<string, double> sumImprovements; // for variable relevance calculation
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47 |
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48 | private readonly string[] allowedVariables; // all variables in shuffled order
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49 | private Dictionary<string, int> varName2Index; // maps the variable names to column indexes
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50 | private int effectiveVars; // number of variables that are used from allowedVariables
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51 |
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52 | private int effectiveRows; // number of rows that are used from
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53 | private readonly int[][] sortedIdxAll;
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54 | private readonly int[][] sortedIdx; // random selection from sortedIdxAll (for r < 1.0)
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55 |
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56 | private int calls = 0;
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57 |
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58 | // helper arrays which are allocated to maximal necessary size only once in the ctor
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59 | private readonly int[] internalIdx, which, leftTmp, rightTmp;
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60 | private readonly double[] outx;
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61 | private readonly int[] outSortedIdx;
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62 |
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63 | private RegressionTreeModel.TreeNode[] tree; // tree is represented as a flat array of nodes
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64 | private int curTreeNodeIdx; // the index where the next tree node is stored
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65 |
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66 | private class Partition {
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67 | public int ParentNodeIdx { get; set; }
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68 | public int Depth { get; set; }
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69 | public int StartIdx { get; set; }
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70 | public int EndIndex { get; set; }
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71 | public bool Left { get; set; }
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72 | }
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73 | private readonly SortedList<double, Partition> queue;
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74 |
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75 | // prepare and allocate buffer variables in ctor
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76 | public RegressionTreeBuilder(IRegressionProblemData problemData, IRandom random) {
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77 | this.problemData = problemData;
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78 | this.random = random;
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79 |
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80 | var rows = problemData.TrainingIndices.Count();
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81 |
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82 | this.nCols = problemData.AllowedInputVariables.Count();
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83 |
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84 | allowedVariables = problemData.AllowedInputVariables.ToArray();
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85 | varName2Index = new Dictionary<string, int>(allowedVariables.Length);
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86 | for (int i = 0; i < allowedVariables.Length; i++) varName2Index.Add(allowedVariables[i], i);
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87 |
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88 | sortedIdxAll = new int[nCols][];
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89 | sortedIdx = new int[nCols][];
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90 | sumImprovements = new Dictionary<string, double>();
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91 | internalIdx = new int[rows];
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92 | which = new int[rows];
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93 | leftTmp = new int[rows];
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94 | rightTmp = new int[rows];
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95 | outx = new double[rows];
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96 | outSortedIdx = new int[rows];
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97 | queue = new SortedList<double, Partition>();
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98 |
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99 | x = new double[nCols][];
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100 | y = problemData.Dataset.GetDoubleValues(problemData.TargetVariable, problemData.TrainingIndices).ToArray();
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101 |
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102 |
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103 | int col = 0;
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104 | foreach (var inputVariable in problemData.AllowedInputVariables) {
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105 | x[col] = problemData.Dataset.GetDoubleValues(inputVariable, problemData.TrainingIndices).ToArray();
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106 | sortedIdxAll[col] = Enumerable.Range(0, rows).OrderBy(r => x[col][r]).ToArray();
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107 | sortedIdx[col] = new int[rows];
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108 | col++;
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109 | }
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110 | }
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111 |
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112 | // simple API produces a single regression tree optimizing sum of squared errors
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113 | // this can be used if only a simple regression tree should be produced
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114 | // for a set of trees use the method CreateRegressionTreeForGradientBoosting below
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115 | //
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116 | // r and m work in the same way as for alglib random forest
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117 | // r is fraction of rows to use for training
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118 | // m is fraction of variables to use for training
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119 | public IRegressionModel CreateRegressionTree(int maxDepth, double r = 0.5, double m = 0.5) {
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120 | // subtract mean of y first
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121 | var yAvg = y.Average();
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122 | for (int i = 0; i < y.Length; i++) y[i] -= yAvg;
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123 |
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124 | var seLoss = new SquaredErrorLoss();
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125 | var zeros = Enumerable.Repeat(0.0, y.Length);
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126 | var ones = Enumerable.Repeat(1.0, y.Length);
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127 |
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128 | var model = CreateRegressionTreeForGradientBoosting(y, maxDepth, problemData.TrainingIndices.ToArray(), seLoss.GetLineSearchFunc(y, zeros, ones), r, m);
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129 |
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130 | return new GradientBoostedTreesModel(new[] { new ConstantRegressionModel(yAvg), model }, new[] { 1.0, 1.0 });
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131 | }
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132 |
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133 | // specific interface that allows to specify the target labels and the training rows which is necessary when for gradient boosted trees
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134 | public IRegressionModel CreateRegressionTreeForGradientBoosting(double[] y, int maxDepth, int[] idx, LineSearchFunc lineSearch, double r = 0.5, double m = 0.5) {
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135 | Debug.Assert(maxDepth > 0);
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136 | Debug.Assert(r > 0);
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137 | Debug.Assert(r <= 1.0);
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138 | Debug.Assert(y.Count() == this.y.Length);
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139 | Debug.Assert(m > 0);
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140 | Debug.Assert(m <= 1.0);
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141 |
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142 | this.y = y; // y is changed in gradient boosting
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143 |
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144 | // shuffle row idx
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145 | HeuristicLab.Random.ListExtensions.ShuffleInPlace(idx, random);
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146 |
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147 | int nRows = idx.Count();
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148 |
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149 | // shuffle variable idx
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150 | HeuristicLab.Random.ListExtensions.ShuffleInPlace(allowedVariables, random);
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151 |
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152 | // only select a part of the rows and columns randomly
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153 | effectiveRows = (int)Math.Ceiling(nRows * r);
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154 | effectiveVars = (int)Math.Ceiling(nCols * m);
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155 |
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156 | // the which array is used for partining row idxs
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157 | Array.Clear(which, 0, which.Length);
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158 |
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159 | // mark selected rows
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160 | for (int row = 0; row < effectiveRows; row++) {
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161 | which[idx[row]] = 1; // we use the which vector as a temporary variable here
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162 | internalIdx[row] = idx[row];
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163 | }
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164 |
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165 | for (int col = 0; col < nCols; col++) {
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166 | int i = 0;
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167 | for (int row = 0; row < nRows; row++) {
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168 | if (which[sortedIdxAll[col][row]] > 0) {
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169 | Debug.Assert(i < effectiveRows);
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170 | sortedIdx[col][i] = sortedIdxAll[col][row];
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171 | i++;
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172 | }
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173 | }
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174 | }
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175 |
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176 | // prepare array for the tree nodes (a tree of maxDepth=1 has 1 node, a tree of maxDepth=d has 2^d - 1 nodes)
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177 | int numNodes = (int)Math.Pow(2, maxDepth) - 1;
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178 | this.tree = new RegressionTreeModel.TreeNode[numNodes];
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179 | this.curTreeNodeIdx = 0;
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180 |
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181 | // start and end idx are inclusive
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182 | queue.Add(calls++, new Partition() { ParentNodeIdx = -1, Depth = maxDepth, StartIdx = 0, EndIndex = effectiveRows - 1 });
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183 | CreateRegressionTreeForIdx(lineSearch);
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184 |
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185 | return new RegressionTreeModel(tree);
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186 | }
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187 |
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188 | private void CreateRegressionTreeForIdx(LineSearchFunc lineSearch) {
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189 | while (queue.Any()) {
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190 | var f = queue.First().Value; // actually a stack
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191 | queue.RemoveAt(0);
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192 |
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193 | var depth = f.Depth;
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194 | var startIdx = f.StartIdx;
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195 | var endIdx = f.EndIndex;
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196 |
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197 | Debug.Assert(endIdx - startIdx >= 0);
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198 | Debug.Assert(startIdx >= 0);
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199 | Debug.Assert(endIdx < internalIdx.Length);
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200 |
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201 | double threshold;
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202 | string bestVariableName;
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203 |
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204 | // stop when only one row is left or no split is possible
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205 | if (depth <= 1 || endIdx - startIdx == 0 || !FindBestVariableAndThreshold(startIdx, endIdx, out threshold, out bestVariableName)) {
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206 | CreateLeafNode(startIdx, endIdx, lineSearch);
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207 | if (f.ParentNodeIdx >= 0) if (f.Left) {
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208 | tree[f.ParentNodeIdx].leftIdx = curTreeNodeIdx;
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209 | } else {
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210 | tree[f.ParentNodeIdx].rightIdx = curTreeNodeIdx;
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211 | }
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212 | curTreeNodeIdx++;
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213 | } else {
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214 | int splitIdx;
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215 | CreateInternalNode(f.StartIdx, f.EndIndex, bestVariableName, threshold, out splitIdx);
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216 |
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217 | // connect to parent tree
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218 | if (f.ParentNodeIdx >= 0) if (f.Left) {
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219 | tree[f.ParentNodeIdx].leftIdx = curTreeNodeIdx;
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220 | } else {
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221 | tree[f.ParentNodeIdx].rightIdx = curTreeNodeIdx;
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222 | }
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223 |
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224 | Debug.Assert(splitIdx + 1 <= endIdx);
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225 | Debug.Assert(startIdx <= splitIdx);
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226 |
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227 | queue.Add(calls++, new Partition() { ParentNodeIdx = curTreeNodeIdx, Left = true, Depth = depth - 1, StartIdx = startIdx, EndIndex = splitIdx }); // left part before right part (stack organization)
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228 | queue.Add(calls++, new Partition() { ParentNodeIdx = curTreeNodeIdx, Left = false, Depth = depth - 1, StartIdx = splitIdx + 1, EndIndex = endIdx });
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229 | curTreeNodeIdx++;
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230 |
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231 | }
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232 | }
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233 | }
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234 |
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235 |
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236 | private void CreateLeafNode(int startIdx, int endIdx, LineSearchFunc lineSearch) {
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237 | // max depth reached or only one element
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238 | tree[curTreeNodeIdx].varName = RegressionTreeModel.TreeNode.NO_VARIABLE;
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239 | tree[curTreeNodeIdx].val = lineSearch(internalIdx, startIdx, endIdx);
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240 | }
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241 |
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242 | // routine for building the tree for the partition of rows stored in internalIdx between startIdx and endIdx
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243 | // the lineSearch function calculates the optimal prediction value for tree leaf nodes
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244 | // (in the case of squared errors it is the average of target values for the rows represented by the node)
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245 | // startIdx and endIdx are inclusive
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246 | private void CreateInternalNode(int startIdx, int endIdx, string splittingVar, double threshold, out int splitIdx) {
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247 | int bestVarIdx = varName2Index[splittingVar];
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248 | // split - two pass
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249 |
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250 | // store which index goes into which partition
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251 | for (int k = startIdx; k <= endIdx; k++) {
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252 | if (x[bestVarIdx][internalIdx[k]] <= threshold)
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253 | which[internalIdx[k]] = -1; // left partition
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254 | else
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255 | which[internalIdx[k]] = 1; // right partition
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256 | }
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257 |
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258 | // partition sortedIdx for each variable
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259 | int i;
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260 | int j;
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261 | for (int col = 0; col < nCols; col++) {
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262 | i = 0;
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263 | j = 0;
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264 | int k;
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265 | for (k = startIdx; k <= endIdx; k++) {
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266 | Debug.Assert(Math.Abs(which[sortedIdx[col][k]]) == 1);
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267 |
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268 | if (which[sortedIdx[col][k]] < 0) {
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269 | leftTmp[i++] = sortedIdx[col][k];
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270 | } else {
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271 | rightTmp[j++] = sortedIdx[col][k];
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272 | }
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273 | }
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274 | Debug.Assert(i > 0); // at least on element in the left partition
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275 | Debug.Assert(j > 0); // at least one element in the right partition
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276 | Debug.Assert(i + j == endIdx - startIdx + 1);
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277 | k = startIdx;
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278 | for (int l = 0; l < i; l++) sortedIdx[col][k++] = leftTmp[l];
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279 | for (int l = 0; l < j; l++) sortedIdx[col][k++] = rightTmp[l];
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280 | }
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281 |
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282 | // partition row indices
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283 | i = startIdx;
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284 | j = endIdx;
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285 | while (i <= j) {
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286 | Debug.Assert(Math.Abs(which[internalIdx[i]]) == 1);
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287 | Debug.Assert(Math.Abs(which[internalIdx[j]]) == 1);
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288 | if (which[internalIdx[i]] < 0) i++;
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289 | else if (which[internalIdx[j]] > 0) j--;
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290 | else {
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291 | Debug.Assert(which[internalIdx[i]] > 0);
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292 | Debug.Assert(which[internalIdx[j]] < 0);
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293 | // swap
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294 | int tmp = internalIdx[i];
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295 | internalIdx[i] = internalIdx[j];
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296 | internalIdx[j] = tmp;
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297 | i++;
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298 | j--;
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299 | }
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300 | }
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301 | Debug.Assert(j + 1 == i);
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302 | Debug.Assert(i <= endIdx);
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303 | Debug.Assert(startIdx <= j);
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304 |
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305 | tree[curTreeNodeIdx].varName = splittingVar;
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306 | tree[curTreeNodeIdx].val = threshold;
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307 | splitIdx = j;
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308 | }
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309 |
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310 | private bool FindBestVariableAndThreshold(int startIdx, int endIdx, out double threshold, out string bestVar) {
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311 | Debug.Assert(startIdx < endIdx + 1); // at least 2 elements
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312 |
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313 | int rows = endIdx - startIdx + 1;
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314 | Debug.Assert(rows >= 2);
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315 |
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316 | double sumY = 0.0;
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317 | for (int i = startIdx; i <= endIdx; i++) {
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318 | sumY += y[internalIdx[i]];
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319 | }
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320 |
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321 | // see description of calculation in FindBestThreshold
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322 | double bestImprovement = 1.0 / rows * sumY * sumY; // any improvement must be larger than this baseline
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323 | double bestThreshold = double.PositiveInfinity;
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324 | bestVar = RegressionTreeModel.TreeNode.NO_VARIABLE;
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325 |
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326 | for (int col = 0; col < effectiveVars; col++) {
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327 | // sort values for variable to prepare for threshold selection
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328 | var curVariable = allowedVariables[col];
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329 | var curVariableIdx = varName2Index[curVariable];
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330 | for (int i = startIdx; i <= endIdx; i++) {
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331 | var sortedI = sortedIdx[curVariableIdx][i];
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332 | outSortedIdx[i - startIdx] = sortedI;
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333 | outx[i - startIdx] = x[curVariableIdx][sortedI];
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334 | }
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335 |
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336 | double curImprovement;
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337 | double curThreshold;
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338 | FindBestThreshold(outx, outSortedIdx, rows, y, sumY, out curThreshold, out curImprovement);
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339 |
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340 | if (curImprovement > bestImprovement) {
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341 | bestImprovement = curImprovement;
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342 | bestThreshold = curThreshold;
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343 | bestVar = allowedVariables[col];
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344 | }
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345 | }
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346 | if (bestVar == RegressionTreeModel.TreeNode.NO_VARIABLE) {
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347 | threshold = bestThreshold;
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348 | return false;
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349 | } else {
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350 | UpdateVariableRelevance(bestVar, sumY, bestImprovement, rows);
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351 | threshold = bestThreshold;
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352 | return true;
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353 | }
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354 | }
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355 |
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356 | private void UpdateVariableRelevance(string bestVar, double sumY, double bestImprovement, int rows) {
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357 | if (string.IsNullOrEmpty(bestVar)) return;
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358 | // update variable relevance
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359 | double baseLine = 1.0 / rows * sumY * sumY; // if best improvement is equal to baseline then the split had no effect
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360 |
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361 | double delta = (bestImprovement - baseLine);
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362 | double v;
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363 | if (!sumImprovements.TryGetValue(bestVar, out v)) {
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364 | sumImprovements[bestVar] = delta;
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365 | }
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366 | sumImprovements[bestVar] = v + delta;
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367 | }
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368 |
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369 | // x [0..N-1] contains rows sorted values in the range from [0..rows-1]
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370 | // 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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371 | // rows specifies the number of valid entries in x and sortedIdx
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372 | // y [0..N-1] contains the target values in original sorting order
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373 | // sumY is y.Sum()
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374 | //
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375 | // 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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376 | // additionally the reduction in squared error is returned in bestImprovement
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377 | // if all elements of x are equal the routing fails to produce a threshold
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378 | private static void FindBestThreshold(double[] x, int[] sortedIdx, int rows, double[] y, double sumY, out double bestThreshold, out double bestImprovement) {
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379 | Debug.Assert(rows >= 2);
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380 |
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381 | double sl = 0.0;
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382 | double sr = sumY;
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383 | double nl = 0.0;
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384 | double nr = rows;
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385 |
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386 | bestImprovement = 1.0 / rows * sumY * sumY; // this is the baseline for the improvement
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387 | bestThreshold = double.NegativeInfinity;
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388 | // for all thresholds
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389 | // if we have n rows there are n-1 possible splits
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390 | for (int i = 0; i < rows - 1; i++) {
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391 | sl += y[sortedIdx[i]];
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392 | sr -= y[sortedIdx[i]];
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393 |
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394 | nl++;
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395 | nr--;
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396 | Debug.Assert(nl > 0);
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397 | Debug.Assert(nr > 0);
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398 |
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399 | if (x[i] < x[i + 1]) { // don't try to split when two elements are equal
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400 |
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401 | // goal is to find the split with leading to minimal total variance of left and right parts
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402 | // without partitioning the variance is var(y) = E(y²) - E(y)²
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403 | // = 1/n * sum(y²) - (1/n * sum(y))²
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404 | // ------------- ---------------
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405 | // constant baseline for improvement
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406 | //
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407 | // if we split into right and left part the overall variance is the weigthed combination nl/n * var(y_l) + nr/n * var(y_r)
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408 | // = nl/n * (1/nl * sum(y_l²) - (1/nl * sum(y_l))²) + nr/n * (1/nr * sum(y_r²) - (1/nr * sum(y_r))²)
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409 | // = 1/n * sum(y_l²) - 1/nl * 1/n * sum(y_l)² + 1/n * sum(y_r²) - 1/nr * 1/n * sum(y_r)²
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410 | // = 1/n * (sum(y_l²) + sum(y_r²)) - 1/n * (sum(y_l)² / nl + sum(y_r)² / nr)
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411 | // = 1/n * sum(y²) - 1/n * (sum(y_l)² / nl + sum(y_r)² / nr)
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412 | // -------------
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413 | // not changed by split (and the same for total variance without partitioning)
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414 | //
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415 | // therefore we need to find the maximum value (sum(y_l)² / nl + sum(y_r)² / nr) (ignoring the factor 1/n)
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416 | // and this value must be larger than 1/n * sum(y)² to be an improvement over no split
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417 |
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418 | double curQuality = sl * sl / nl + sr * sr / nr;
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419 |
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420 | if (curQuality > bestImprovement) {
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421 | bestThreshold = (x[i] + x[i + 1]) / 2.0;
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422 | bestImprovement = curQuality;
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423 | }
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424 | }
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425 | }
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426 |
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427 | // if all elements where the same then no split can be found
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428 | }
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429 |
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430 |
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431 | public IEnumerable<KeyValuePair<string, double>> GetVariableRelevance() {
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432 | // values are scaled: the most important variable has relevance = 100
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433 | double scaling = 100 / sumImprovements.Max(t => t.Value);
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434 | return
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435 | sumImprovements
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436 | .Select(t => new KeyValuePair<string, double>(t.Key, t.Value * scaling))
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437 | .OrderByDescending(t => t.Value);
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438 | }
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439 | }
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440 | }
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441 |
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