[12332] | 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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[12349] | 35 | private readonly IList<RegressionTreeModel.TreeNode> nodeQueue; //TODO
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[12332] | 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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