[13939] | 1 | #region License Information
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| 2 | /* HeuristicLab
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[14185] | 3 | * Copyright (C) 2002-2016 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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[13939] | 4 | *
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| 5 | * This file is part of HeuristicLab.
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| 6 | *
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| 7 | * HeuristicLab is free software: you can redistribute it and/or modify
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| 8 | * it under the terms of the GNU General Public License as published by
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| 9 | * the Free Software Foundation, either version 3 of the License, or
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| 10 | * (at your option) any later version.
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| 11 | *
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| 12 | * HeuristicLab is distributed in the hope that it will be useful,
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| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 15 | * GNU General Public License for more details.
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| 16 | *
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| 17 | * You should have received a copy of the GNU General Public License
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| 18 | * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
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| 19 | */
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| 20 | #endregion
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| 21 |
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| 22 | using System;
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| 23 | using System.Collections.Generic;
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[14271] | 24 | using System.Globalization;
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[13939] | 25 | using System.Linq;
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| 26 | using HeuristicLab.Common;
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| 27 | using HeuristicLab.Core;
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[14291] | 28 | using HeuristicLab.Problems.DataAnalysis;
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[13939] | 29 | using HeuristicLab.Random;
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| 30 |
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| 31 | namespace HeuristicLab.Problems.Instances.DataAnalysis {
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| 32 | public class VariableNetwork : ArtificialRegressionDataDescriptor {
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| 33 | private int nTrainingSamples;
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| 34 | private int nTestSamples;
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| 35 |
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| 36 | private int numberOfFeatures;
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| 37 | private double noiseRatio;
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| 38 | private IRandom random;
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| 39 |
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| 40 | public override string Name { get { return string.Format("VariableNetwork-{0:0%} ({1} dim)", noiseRatio, numberOfFeatures); } }
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| 41 | private string networkDefinition;
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| 42 | public string NetworkDefinition { get { return networkDefinition; } }
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| 43 | public override string Description {
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| 44 | get {
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| 45 | return "The data are generated specifically to test methods for variable network analysis.";
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| 46 | }
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| 47 | }
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| 48 |
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| 49 | public VariableNetwork(int numberOfFeatures, double noiseRatio,
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| 50 | IRandom rand)
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| 51 | : this(250, 250, numberOfFeatures, noiseRatio, rand) { }
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| 52 |
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| 53 | public VariableNetwork(int nTrainingSamples, int nTestSamples,
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| 54 | int numberOfFeatures, double noiseRatio, IRandom rand) {
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| 55 | this.nTrainingSamples = nTrainingSamples;
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| 56 | this.nTestSamples = nTestSamples;
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| 57 | this.noiseRatio = noiseRatio;
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| 58 | this.random = rand;
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| 59 | this.numberOfFeatures = numberOfFeatures;
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| 60 | // default variable names
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| 61 | variableNames = Enumerable.Range(1, numberOfFeatures)
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| 62 | .Select(i => string.Format("X{0:000}", i))
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| 63 | .ToArray();
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[14271] | 64 |
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| 65 | variableRelevances = new Dictionary<string, IEnumerable<KeyValuePair<string, double>>>();
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[13939] | 66 | }
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| 67 |
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| 68 | private string[] variableNames;
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| 69 | protected override string[] VariableNames {
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| 70 | get {
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| 71 | return variableNames;
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| 72 | }
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| 73 | }
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| 74 |
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| 75 | // there is no specific target variable in variable network analysis but we still need to specify one
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| 76 | protected override string TargetVariable { get { return VariableNames.Last(); } }
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| 77 |
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| 78 | protected override string[] AllowedInputVariables {
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| 79 | get {
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| 80 | return VariableNames.Take(numberOfFeatures - 1).ToArray();
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| 81 | }
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| 82 | }
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| 83 |
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| 84 | protected override int TrainingPartitionStart { get { return 0; } }
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| 85 | protected override int TrainingPartitionEnd { get { return nTrainingSamples; } }
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| 86 | protected override int TestPartitionStart { get { return nTrainingSamples; } }
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| 87 | protected override int TestPartitionEnd { get { return nTrainingSamples + nTestSamples; } }
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| 88 |
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[14271] | 89 | private Dictionary<string, IEnumerable<KeyValuePair<string, double>>> variableRelevances;
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| 90 | public IEnumerable<KeyValuePair<string, double>> GetVariableRelevance(string targetVar) {
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| 91 | return variableRelevances[targetVar];
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| 92 | }
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[13939] | 93 |
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| 94 | protected override List<List<double>> GenerateValues() {
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| 95 | // variable names are shuffled in the beginning (and sorted at the end)
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| 96 | variableNames = variableNames.Shuffle(random).ToArray();
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| 97 |
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[14110] | 98 | // a third of all variables are independent vars
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[13939] | 99 | List<List<double>> lvl0 = new List<List<double>>();
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| 100 | int numLvl0 = (int)Math.Ceiling(numberOfFeatures * 0.33);
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| 101 |
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| 102 | List<string> description = new List<string>(); // store information how the variable is actually produced
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[13963] | 103 | List<string[]> inputVarNames = new List<string[]>(); // store information to produce graphviz file
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[14271] | 104 | List<double[]> relevances = new List<double[]>(); // stores variable relevance information (same order as given in inputVarNames)
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[13939] | 105 |
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| 106 | var nrand = new NormalDistributedRandom(random, 0, 1);
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| 107 | for (int c = 0; c < numLvl0; c++) {
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[13963] | 108 | inputVarNames.Add(new string[] { });
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[14271] | 109 | relevances.Add(new double[] { });
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[14260] | 110 | description.Add(" ~ N(0, 1)");
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[14271] | 111 | lvl0.Add(Enumerable.Range(0, TestPartitionEnd).Select(_ => nrand.NextDouble()).ToList());
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[13939] | 112 | }
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| 113 |
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| 114 | // lvl1 contains variables which are functions of vars in lvl0 (+ noise)
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| 115 | int numLvl1 = (int)Math.Ceiling(numberOfFeatures * 0.33);
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[14271] | 116 | List<List<double>> lvl1 = CreateVariables(lvl0, numLvl1, inputVarNames, description, relevances);
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[13939] | 117 |
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| 118 | // lvl2 contains variables which are functions of vars in lvl0 and lvl1 (+ noise)
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| 119 | int numLvl2 = (int)Math.Ceiling(numberOfFeatures * 0.2);
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[14271] | 120 | List<List<double>> lvl2 = CreateVariables(lvl0.Concat(lvl1).ToList(), numLvl2, inputVarNames, description, relevances);
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[13939] | 121 |
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| 122 | // lvl3 contains variables which are functions of vars in lvl0, lvl1 and lvl2 (+ noise)
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| 123 | int numLvl3 = numberOfFeatures - numLvl0 - numLvl1 - numLvl2;
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[14271] | 124 | List<List<double>> lvl3 = CreateVariables(lvl0.Concat(lvl1).Concat(lvl2).ToList(), numLvl3, inputVarNames, description, relevances);
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| 125 |
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| 126 | this.variableRelevances.Clear();
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| 127 | for (int i = 0; i < variableNames.Length; i++) {
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| 128 | var targetVarName = variableNames[i];
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| 129 | var targetRelevantInputs =
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| 130 | inputVarNames[i].Zip(relevances[i], (inputVar, rel) => new KeyValuePair<string, double>(inputVar, rel))
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| 131 | .ToArray();
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| 132 | variableRelevances.Add(targetVarName, targetRelevantInputs);
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[13939] | 133 | }
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[14271] | 134 |
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[14260] | 135 | networkDefinition = string.Join(Environment.NewLine, variableNames.Zip(description, (n, d) => n + d).OrderBy(x => x));
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[13963] | 136 | // for graphviz
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| 137 | networkDefinition += Environment.NewLine + "digraph G {";
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[14271] | 138 | for (int i = 0; i < variableNames.Length; i++) {
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| 139 | var name = variableNames[i];
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| 140 | var selectedVarNames = inputVarNames[i];
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| 141 | var selectedRelevances = relevances[i];
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| 142 | for (int j = 0; j < selectedVarNames.Length; j++) {
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| 143 | var selectedVarName = selectedVarNames[j];
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| 144 | var selectedRelevance = selectedRelevances[j];
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| 145 | networkDefinition += Environment.NewLine + selectedVarName + " -> " + name +
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| 146 | string.Format(CultureInfo.InvariantCulture, " [label={0:N3}]", selectedRelevance);
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[13963] | 147 | }
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| 148 | }
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| 149 | networkDefinition += Environment.NewLine + "}";
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| 150 |
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[14271] | 151 | // return a random permutation of all variables (to mix lvl0, lvl1, ... variables)
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[13939] | 152 | var allVars = lvl0.Concat(lvl1).Concat(lvl2).Concat(lvl3).ToList();
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| 153 | var orderedVars = allVars.Zip(variableNames, Tuple.Create).OrderBy(t => t.Item2).Select(t => t.Item1).ToList();
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| 154 | variableNames = variableNames.OrderBy(n => n).ToArray();
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| 155 | return orderedVars;
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| 156 | }
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| 157 |
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[14271] | 158 | private List<List<double>> CreateVariables(List<List<double>> allowedInputs, int numVars, List<string[]> inputVarNames, List<string> description, List<double[]> relevances) {
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| 159 | var res = new List<List<double>>();
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| 160 | for (int c = 0; c < numVars; c++) {
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| 161 | string[] selectedVarNames;
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| 162 | double[] relevance;
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| 163 | var x = GenerateRandomFunction(random, allowedInputs, out selectedVarNames, out relevance);
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| 164 | var sigma = x.StandardDeviation();
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| 165 | var noisePrng = new NormalDistributedRandom(random, 0, sigma * Math.Sqrt(noiseRatio / (1.0 - noiseRatio)));
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| 166 | res.Add(x.Select(t => t + noisePrng.NextDouble()).ToList());
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| 167 | Array.Sort(selectedVarNames, relevance);
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| 168 | inputVarNames.Add(selectedVarNames);
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| 169 | relevances.Add(relevance);
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| 170 | var desc = string.Format("f({0})", string.Join(",", selectedVarNames));
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| 171 | // for the relevance information order variables by decreasing relevance
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| 172 | var relevanceStr = string.Join(", ",
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| 173 | selectedVarNames.Zip(relevance, Tuple.Create)
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| 174 | .OrderByDescending(t => t.Item2)
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| 175 | .Select(t => string.Format(CultureInfo.InvariantCulture, "{0}: {1:N3}", t.Item1, t.Item2)));
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| 176 | description.Add(string.Format(" ~ N({0}, {1:N3}) [Relevances: {2}]", desc, noisePrng.Sigma, relevanceStr));
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| 177 | }
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| 178 | return res;
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| 179 | }
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| 180 |
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[13939] | 181 | // sample the input variables that are actually used and sample from a Gaussian process
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[14271] | 182 | private IEnumerable<double> GenerateRandomFunction(IRandom rand, List<List<double>> xs, out string[] selectedVarNames, out double[] relevance) {
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[13939] | 183 | double r = -Math.Log(1.0 - rand.NextDouble()) * 2.0; // r is exponentially distributed with lambda = 2
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| 184 | int nl = (int)Math.Floor(1.5 + r); // number of selected vars is likely to be between three and four
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| 185 | if (nl > xs.Count) nl = xs.Count; // limit max
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| 186 |
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| 187 | var selectedIdx = Enumerable.Range(0, xs.Count).Shuffle(random)
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| 188 | .Take(nl).ToArray();
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| 189 |
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| 190 | var selectedVars = selectedIdx.Select(i => xs[i]).ToArray();
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[13963] | 191 | selectedVarNames = selectedIdx.Select(i => VariableNames[i]).ToArray();
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[14271] | 192 | return SampleGaussianProcess(random, selectedVars, out relevance);
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[13939] | 193 | }
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| 194 |
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[14271] | 195 | private IEnumerable<double> SampleGaussianProcess(IRandom random, List<double>[] xs, out double[] relevance) {
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[13939] | 196 | int nl = xs.Length;
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| 197 | int nRows = xs.First().Count;
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| 198 |
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[14291] | 199 | // sample u iid ~ N(0, 1)
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| 200 | var u = Enumerable.Range(0, nRows).Select(_ => NormalDistributedRandom.NextDouble(random, 0, 1)).ToArray();
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| 201 |
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| 202 | // sample actual length-scales
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[13939] | 203 | var l = Enumerable.Range(0, nl)
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[13963] | 204 | .Select(_ => random.NextDouble() * 2 + 0.5)
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[13939] | 205 | .ToArray();
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| 206 |
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[14291] | 207 | double[,] K = CalculateCovariance(xs, l);
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[13939] | 208 |
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| 209 | // decompose
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| 210 | alglib.trfac.spdmatrixcholesky(ref K, nRows, false);
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| 211 |
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| 212 |
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| 213 | // calc y = Lu
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| 214 | var y = new double[u.Length];
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| 215 | alglib.ablas.rmatrixmv(nRows, nRows, K, 0, 0, 0, u, 0, ref y, 0);
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| 216 |
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[14291] | 217 | // calculate relevance by removing dimensions
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| 218 | relevance = CalculateRelevance(y, u, xs, l);
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| 219 |
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[13939] | 220 | return y;
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| 221 | }
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[14291] | 222 |
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| 223 | // calculate variable relevance based on removal of variables
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| 224 | // 1) to remove a variable we set it's length scale to infinity (no relation of the variable value to the target)
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| 225 | // 2) calculate MSE of the original target values (y) to the updated targes y' (after variable removal)
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| 226 | // 3) relevance is larger if MSE(y,y') is large
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| 227 | // 4) scale impacts so that the most important variable has impact = 1
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| 228 | private double[] CalculateRelevance(double[] y, double[] u, List<double>[] xs, double[] l) {
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| 229 | int nRows = xs.First().Count;
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| 230 | var changedL = new double[l.Length];
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| 231 | var relevance = new double[l.Length];
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| 232 | for (int i = 0; i < l.Length; i++) {
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| 233 | Array.Copy(l, changedL, changedL.Length);
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| 234 | changedL[i] = double.MaxValue;
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| 235 | var changedK = CalculateCovariance(xs, changedL);
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| 236 |
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| 237 | var yChanged = new double[u.Length];
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| 238 | alglib.ablas.rmatrixmv(nRows, nRows, changedK, 0, 0, 0, u, 0, ref yChanged, 0);
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| 239 |
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| 240 | OnlineCalculatorError error;
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| 241 | var mse = OnlineMeanSquaredErrorCalculator.Calculate(y, yChanged, out error);
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| 242 | if (error != OnlineCalculatorError.None) mse = double.MaxValue;
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| 243 | relevance[i] = mse;
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| 244 | }
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| 245 | // scale so that max relevance is 1.0
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| 246 | var maxRel = relevance.Max();
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| 247 | for (int i = 0; i < relevance.Length; i++) relevance[i] /= maxRel;
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| 248 | return relevance;
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| 249 | }
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| 250 |
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| 251 | private double[,] CalculateCovariance(List<double>[] xs, double[] l) {
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| 252 | int nRows = xs.First().Count;
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| 253 | double[,] K = new double[nRows, nRows];
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| 254 | for (int r = 0; r < nRows; r++) {
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| 255 | double[] xi = xs.Select(x => x[r]).ToArray();
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| 256 | for (int c = 0; c <= r; c++) {
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| 257 | double[] xj = xs.Select(x => x[c]).ToArray();
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| 258 | double dSqr = xi.Zip(xj, (xik, xjk) => (xik - xjk))
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| 259 | .Select(dk => dk * dk)
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| 260 | .Zip(l, (dk, lk) => dk / lk)
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| 261 | .Sum();
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| 262 | K[r, c] = Math.Exp(-dSqr);
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| 263 | }
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| 264 | }
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| 265 | // add a small diagonal matrix for numeric stability
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| 266 | for (int i = 0; i < nRows; i++) {
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| 267 | K[i, i] += 1.0E-7;
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| 268 | }
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| 269 |
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| 270 | return K;
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| 271 | }
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[13939] | 272 | }
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| 273 | }
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