1 | #region License Information
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2 | /* HeuristicLab
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3 | * Copyright (C) Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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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.Linq;
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24 | using HeuristicLab.Common;
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25 | using HeuristicLab.Core;
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26 | using HeuristicLab.Data;
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27 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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28 | using HeuristicLab.Optimization;
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29 | using HeuristicLab.Parameters;
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30 | using HEAL.Attic;
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31 | using HeuristicLab.Problems.DataAnalysis;
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32 | using HeuristicLab.Problems.Instances;
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33 |
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34 |
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35 | namespace HeuristicLab.Algorithms.DataAnalysis {
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36 | [Item("Gaussian Process Covariance Optimization Problem", "")]
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37 | [Creatable(CreatableAttribute.Categories.GeneticProgrammingProblems, Priority = 300)]
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38 | [StorableType("A3EA7CE7-78FA-48FF-9DD5-FBE5AB770A99")]
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39 | public sealed class GaussianProcessCovarianceOptimizationProblem : SymbolicExpressionTreeProblem, IStatefulItem, IRegressionProblem, IProblemInstanceConsumer<IRegressionProblemData>, IProblemInstanceExporter<IRegressionProblemData> {
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40 | #region static variables and ctor
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41 | private static readonly CovarianceMaternIso maternIso1;
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42 | private static readonly CovarianceMaternIso maternIso3;
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43 | private static readonly CovarianceMaternIso maternIso5;
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44 | private static readonly CovariancePiecewisePolynomial piecewisePoly0;
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45 | private static readonly CovariancePiecewisePolynomial piecewisePoly1;
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46 | private static readonly CovariancePiecewisePolynomial piecewisePoly2;
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47 | private static readonly CovariancePiecewisePolynomial piecewisePoly3;
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48 | private static readonly CovariancePolynomial poly2;
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49 | private static readonly CovariancePolynomial poly3;
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50 | private static readonly CovarianceSpectralMixture spectralMixture1;
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51 | private static readonly CovarianceSpectralMixture spectralMixture3;
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52 | private static readonly CovarianceSpectralMixture spectralMixture5;
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53 | private static readonly CovarianceLinear linear;
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54 | private static readonly CovarianceLinearArd linearArd;
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55 | private static readonly CovarianceNeuralNetwork neuralNetwork;
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56 | private static readonly CovariancePeriodic periodic;
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57 | private static readonly CovarianceRationalQuadraticIso ratQuadraticIso;
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58 | private static readonly CovarianceRationalQuadraticArd ratQuadraticArd;
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59 | private static readonly CovarianceSquaredExponentialArd sqrExpArd;
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60 | private static readonly CovarianceSquaredExponentialIso sqrExpIso;
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61 |
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62 | static GaussianProcessCovarianceOptimizationProblem() {
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63 | // cumbersome initialization because of ConstrainedValueParameters
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64 | maternIso1 = new CovarianceMaternIso(); SetConstrainedValueParameter(maternIso1.DParameter, 1);
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65 | maternIso3 = new CovarianceMaternIso(); SetConstrainedValueParameter(maternIso3.DParameter, 3);
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66 | maternIso5 = new CovarianceMaternIso(); SetConstrainedValueParameter(maternIso5.DParameter, 5);
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67 |
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68 | piecewisePoly0 = new CovariancePiecewisePolynomial(); SetConstrainedValueParameter(piecewisePoly0.VParameter, 0);
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69 | piecewisePoly1 = new CovariancePiecewisePolynomial(); SetConstrainedValueParameter(piecewisePoly1.VParameter, 1);
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70 | piecewisePoly2 = new CovariancePiecewisePolynomial(); SetConstrainedValueParameter(piecewisePoly2.VParameter, 2);
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71 | piecewisePoly3 = new CovariancePiecewisePolynomial(); SetConstrainedValueParameter(piecewisePoly3.VParameter, 3);
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72 |
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73 | poly2 = new CovariancePolynomial(); poly2.DegreeParameter.Value.Value = 2;
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74 | poly3 = new CovariancePolynomial(); poly3.DegreeParameter.Value.Value = 3;
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75 |
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76 | spectralMixture1 = new CovarianceSpectralMixture(); spectralMixture1.QParameter.Value.Value = 1;
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77 | spectralMixture3 = new CovarianceSpectralMixture(); spectralMixture3.QParameter.Value.Value = 3;
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78 | spectralMixture5 = new CovarianceSpectralMixture(); spectralMixture5.QParameter.Value.Value = 5;
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79 |
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80 | linear = new CovarianceLinear();
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81 | linearArd = new CovarianceLinearArd();
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82 | neuralNetwork = new CovarianceNeuralNetwork();
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83 | periodic = new CovariancePeriodic();
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84 | ratQuadraticArd = new CovarianceRationalQuadraticArd();
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85 | ratQuadraticIso = new CovarianceRationalQuadraticIso();
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86 | sqrExpArd = new CovarianceSquaredExponentialArd();
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87 | sqrExpIso = new CovarianceSquaredExponentialIso();
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88 | }
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89 |
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90 | private static void SetConstrainedValueParameter(IConstrainedValueParameter<IntValue> param, int val) {
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91 | param.Value = param.ValidValues.Single(v => v.Value == val);
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92 | }
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93 |
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94 | #endregion
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95 |
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96 | #region parameter names
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97 |
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98 | private const string ProblemDataParameterName = "ProblemData";
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99 | private const string ConstantOptIterationsParameterName = "Constant optimization steps";
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100 | private const string RestartsParameterName = "Restarts";
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101 |
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102 | #endregion
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103 |
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104 | #region Parameter Properties
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105 | IParameter IDataAnalysisProblem.ProblemDataParameter { get { return ProblemDataParameter; } }
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106 |
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107 | public IValueParameter<IRegressionProblemData> ProblemDataParameter {
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108 | get { return (IValueParameter<IRegressionProblemData>)Parameters[ProblemDataParameterName]; }
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109 | }
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110 | public IFixedValueParameter<IntValue> ConstantOptIterationsParameter {
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111 | get { return (IFixedValueParameter<IntValue>)Parameters[ConstantOptIterationsParameterName]; }
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112 | }
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113 | public IFixedValueParameter<IntValue> RestartsParameter {
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114 | get { return (IFixedValueParameter<IntValue>)Parameters[RestartsParameterName]; }
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115 | }
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116 | #endregion
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117 |
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118 | #region Properties
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119 |
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120 | public IRegressionProblemData ProblemData {
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121 | get { return ProblemDataParameter.Value; }
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122 | set { ProblemDataParameter.Value = value; }
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123 | }
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124 | IDataAnalysisProblemData IDataAnalysisProblem.ProblemData { get { return ProblemData; } }
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125 |
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126 | public int ConstantOptIterations {
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127 | get { return ConstantOptIterationsParameter.Value.Value; }
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128 | set { ConstantOptIterationsParameter.Value.Value = value; }
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129 | }
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130 |
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131 | public int Restarts {
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132 | get { return RestartsParameter.Value.Value; }
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133 | set { RestartsParameter.Value.Value = value; }
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134 | }
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135 | #endregion
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136 |
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137 | public override bool Maximization {
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138 | get { return true; } // return log likelihood (instead of negative log likelihood as in GPR
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139 | }
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140 |
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141 | // problem stores a few variables for information exchange from Evaluate() to Analyze()
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142 | private readonly object problemStateLocker = new object();
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143 | [Storable]
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144 | private double bestQ;
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145 | [Storable]
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146 | private double[] bestHyperParameters;
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147 | [Storable]
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148 | private IMeanFunction meanFunc;
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149 | [Storable]
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150 | private ICovarianceFunction covFunc;
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151 |
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152 | public GaussianProcessCovarianceOptimizationProblem()
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153 | : base() {
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154 | Parameters.Add(new ValueParameter<IRegressionProblemData>(ProblemDataParameterName, "The data for the regression problem", new RegressionProblemData()));
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155 | Parameters.Add(new FixedValueParameter<IntValue>(ConstantOptIterationsParameterName, "Number of optimization steps for hyperparameter values", new IntValue(50)));
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156 | Parameters.Add(new FixedValueParameter<IntValue>(RestartsParameterName, "The number of random restarts for constant optimization.", new IntValue(10)));
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157 | Parameters["Restarts"].Hidden = true;
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158 | var g = new SimpleSymbolicExpressionGrammar();
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159 | g.AddSymbols(new string[] { "Sum", "Product" }, 2, 2);
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160 | g.AddTerminalSymbols(new string[]
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161 | {
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162 | "Linear",
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163 | "LinearArd",
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164 | "MaternIso1",
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165 | "MaternIso3",
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166 | "MaternIso5",
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167 | "NeuralNetwork",
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168 | "Periodic",
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169 | "PiecewisePolynomial0",
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170 | "PiecewisePolynomial1",
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171 | "PiecewisePolynomial2",
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172 | "PiecewisePolynomial3",
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173 | "Polynomial2",
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174 | "Polynomial3",
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175 | "RationalQuadraticArd",
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176 | "RationalQuadraticIso",
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177 | "SpectralMixture1",
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178 | "SpectralMixture3",
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179 | "SpectralMixture5",
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180 | "SquaredExponentialArd",
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181 | "SquaredExponentialIso"
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182 | });
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183 | base.Encoding = new SymbolicExpressionTreeEncoding(g, 10, 5);
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184 | }
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185 |
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186 | public void InitializeState() { ClearState(); }
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187 | public void ClearState() {
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188 | meanFunc = null;
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189 | covFunc = null;
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190 | bestQ = double.NegativeInfinity;
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191 | bestHyperParameters = null;
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192 | }
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193 |
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194 | private readonly object syncRoot = new object();
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195 | // Does not produce the same result for the same seed when using parallel engine (see below)!
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196 | public override double Evaluate(ISymbolicExpressionTree tree, IRandom random) {
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197 | var meanFunction = new MeanConst();
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198 | var problemData = ProblemData;
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199 | var ds = problemData.Dataset;
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200 | var targetVariable = problemData.TargetVariable;
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201 | var allowedInputVariables = problemData.AllowedInputVariables.ToArray();
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202 | var nVars = allowedInputVariables.Length;
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203 | var trainingRows = problemData.TrainingIndices.ToArray();
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204 |
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205 | // use the same covariance function for each restart
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206 | var covarianceFunction = TreeToCovarianceFunction(tree);
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207 |
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208 | // allocate hyperparameters
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209 | var hyperParameters = new double[meanFunction.GetNumberOfParameters(nVars) + covarianceFunction.GetNumberOfParameters(nVars) + 1]; // mean + cov + noise
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210 | double[] bestHyperParameters = new double[hyperParameters.Length];
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211 | var bestObjValue = new double[1] { double.MinValue };
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212 |
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213 | // data that is necessary for the objective function
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214 | var data = Tuple.Create(ds, targetVariable, allowedInputVariables, trainingRows, (IMeanFunction)meanFunction, covarianceFunction, bestObjValue);
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215 |
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216 | for (int t = 0; t < Restarts; t++) {
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217 | var prevBest = bestObjValue[0];
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218 | var prevBestHyperParameters = new double[hyperParameters.Length];
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219 | Array.Copy(bestHyperParameters, prevBestHyperParameters, bestHyperParameters.Length);
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220 |
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221 | // initialize hyperparameters
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222 | hyperParameters[0] = ds.GetDoubleValues(targetVariable).Average(); // mean const
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223 |
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224 | // Evaluate might be called concurrently therefore access to random has to be synchronized.
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225 | // However, results of multiple runs with the same seed will be different when using the parallel engine.
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226 | lock (syncRoot) {
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227 | for (int i = 0; i < covarianceFunction.GetNumberOfParameters(nVars); i++) {
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228 | hyperParameters[1 + i] = random.NextDouble() * 2.0 - 1.0;
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229 | }
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230 | }
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231 | hyperParameters[hyperParameters.Length - 1] = 1.0; // s² = exp(2), TODO: other inits better?
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232 |
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233 | // use alglib.bfgs for hyper-parameter optimization ...
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234 | double epsg = 0;
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235 | double epsf = 0.00001;
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236 | double epsx = 0;
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237 | double stpmax = 1;
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238 | int maxits = ConstantOptIterations;
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239 | alglib.mincgstate state;
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240 | alglib.mincgreport rep;
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241 |
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242 | alglib.mincgcreate(hyperParameters, out state);
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243 | alglib.mincgsetcond(state, epsg, epsf, epsx, maxits);
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244 | alglib.mincgsetstpmax(state, stpmax);
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245 | alglib.mincgoptimize(state, ObjectiveFunction, null, data);
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246 |
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247 | alglib.mincgresults(state, out bestHyperParameters, out rep);
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248 |
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249 | if (rep.terminationtype < 0) {
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250 | // error -> restore previous best quality
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251 | bestObjValue[0] = prevBest;
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252 | Array.Copy(prevBestHyperParameters, bestHyperParameters, prevBestHyperParameters.Length);
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253 | }
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254 | }
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255 |
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256 | UpdateBestSoFar(bestObjValue[0], bestHyperParameters, meanFunction, covarianceFunction);
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257 |
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258 | return bestObjValue[0];
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259 | }
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260 |
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261 | // updates the overall best quality and overall best model for Analyze()
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262 | private void UpdateBestSoFar(double bestQ, double[] bestHyperParameters, IMeanFunction meanFunc, ICovarianceFunction covFunc) {
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263 | lock (problemStateLocker) {
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264 | if (bestQ > this.bestQ) {
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265 | this.bestQ = bestQ;
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266 | this.bestHyperParameters = new double[bestHyperParameters.Length];
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267 | Array.Copy(bestHyperParameters, this.bestHyperParameters, this.bestHyperParameters.Length);
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268 | this.meanFunc = meanFunc;
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269 | this.covFunc = covFunc;
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270 | }
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271 | }
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272 | }
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273 |
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274 | public override void Analyze(ISymbolicExpressionTree[] trees, double[] qualities, ResultCollection results, IRandom random) {
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275 | if (!results.ContainsKey("Best Solution Quality")) {
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276 | results.Add(new Result("Best Solution Quality", typeof(DoubleValue)));
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277 | }
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278 | if (!results.ContainsKey("Best Tree")) {
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279 | results.Add(new Result("Best Tree", typeof(ISymbolicExpressionTree)));
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280 | }
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281 | if (!results.ContainsKey("Best Solution")) {
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282 | results.Add(new Result("Best Solution", typeof(GaussianProcessRegressionSolution)));
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283 | }
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284 |
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285 | var bestQuality = qualities.Max();
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286 |
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287 | if (results["Best Solution Quality"].Value == null || bestQuality > ((DoubleValue)results["Best Solution Quality"].Value).Value) {
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288 | var bestIdx = Array.IndexOf(qualities, bestQuality);
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289 | var bestClone = (ISymbolicExpressionTree)trees[bestIdx].Clone();
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290 | results["Best Tree"].Value = bestClone;
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291 | results["Best Solution Quality"].Value = new DoubleValue(bestQuality);
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292 | results["Best Solution"].Value = CreateSolution();
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293 | }
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294 | }
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295 |
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296 | private IItem CreateSolution() {
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297 | var problemData = ProblemData;
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298 | var ds = problemData.Dataset;
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299 | var targetVariable = problemData.TargetVariable;
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300 | var allowedInputVariables = problemData.AllowedInputVariables.ToArray();
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301 | var trainingRows = problemData.TrainingIndices.ToArray();
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302 |
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303 | lock (problemStateLocker) {
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304 | var model = new GaussianProcessModel(ds, targetVariable, allowedInputVariables, trainingRows, bestHyperParameters, (IMeanFunction)meanFunc.Clone(), (ICovarianceFunction)covFunc.Clone());
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305 | model.FixParameters();
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306 | return model.CreateRegressionSolution((IRegressionProblemData)ProblemData.Clone());
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307 | }
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308 | }
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309 |
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310 | private void ObjectiveFunction(double[] x, ref double func, double[] grad, object obj) {
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311 | // we want to optimize the model likelihood by changing the hyperparameters and also return the gradient for each hyperparameter
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312 | var data = (Tuple<IDataset, string, string[], int[], IMeanFunction, ICovarianceFunction, double[]>)obj;
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313 | var ds = data.Item1;
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314 | var targetVariable = data.Item2;
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315 | var allowedInputVariables = data.Item3;
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316 | var trainingRows = data.Item4;
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317 | var meanFunction = data.Item5;
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318 | var covarianceFunction = data.Item6;
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319 | var bestObjValue = data.Item7;
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320 | var hyperParameters = x; // the decision variable vector
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321 |
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322 | try {
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323 | var model = new GaussianProcessModel(ds, targetVariable, allowedInputVariables, trainingRows, hyperParameters, meanFunction, covarianceFunction);
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324 |
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325 | func = model.NegativeLogLikelihood; // mincgoptimize, so we return negative likelihood
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326 | bestObjValue[0] = Math.Max(bestObjValue[0], -func); // problem itself is a maximization problem
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327 | var gradients = model.HyperparameterGradients;
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328 | Array.Copy(gradients, grad, gradients.Length);
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329 | }
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330 | catch (ArgumentException) {
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331 | // building the GaussianProcessModel might fail, in this case we return the worst possible objective value
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332 | func = 1.0E+300;
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333 | Array.Clear(grad, 0, grad.Length);
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334 | }
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335 | }
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336 |
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337 | private ICovarianceFunction TreeToCovarianceFunction(ISymbolicExpressionTree tree) {
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338 | return TreeToCovarianceFunction(tree.Root.GetSubtree(0).GetSubtree(0)); // skip programroot and startsymbol
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339 | }
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340 |
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341 | private ICovarianceFunction TreeToCovarianceFunction(ISymbolicExpressionTreeNode node) {
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342 | switch (node.Symbol.Name) {
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343 | case "Sum": {
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344 | var sum = new CovarianceSum();
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345 | sum.Terms.Add(TreeToCovarianceFunction(node.GetSubtree(0)));
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346 | sum.Terms.Add(TreeToCovarianceFunction(node.GetSubtree(1)));
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347 | return sum;
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348 | }
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349 | case "Product": {
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350 | var prod = new CovarianceProduct();
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351 | prod.Factors.Add(TreeToCovarianceFunction(node.GetSubtree(0)));
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352 | prod.Factors.Add(TreeToCovarianceFunction(node.GetSubtree(1)));
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353 | return prod;
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354 | }
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355 | // covFunction is cloned by the model so we can reuse instances of terminal covariance functions
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356 | case "Linear": return linear;
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357 | case "LinearArd": return linearArd;
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358 | case "MaternIso1": return maternIso1;
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359 | case "MaternIso3": return maternIso3;
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360 | case "MaternIso5": return maternIso5;
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361 | case "NeuralNetwork": return neuralNetwork;
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362 | case "Periodic": return periodic;
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363 | case "PiecewisePolynomial0": return piecewisePoly0;
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364 | case "PiecewisePolynomial1": return piecewisePoly1;
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365 | case "PiecewisePolynomial2": return piecewisePoly2;
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366 | case "PiecewisePolynomial3": return piecewisePoly3;
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367 | case "Polynomial2": return poly2;
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368 | case "Polynomial3": return poly3;
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369 | case "RationalQuadraticArd": return ratQuadraticArd;
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370 | case "RationalQuadraticIso": return ratQuadraticIso;
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371 | case "SpectralMixture1": return spectralMixture1;
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372 | case "SpectralMixture3": return spectralMixture3;
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373 | case "SpectralMixture5": return spectralMixture5;
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374 | case "SquaredExponentialArd": return sqrExpArd;
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375 | case "SquaredExponentialIso": return sqrExpIso;
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376 | default: throw new InvalidProgramException(string.Format("Found invalid symbol {0}", node.Symbol.Name));
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377 | }
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378 | }
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379 |
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380 |
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381 | // persistence
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382 | [StorableConstructor]
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383 | private GaussianProcessCovarianceOptimizationProblem(StorableConstructorFlag _) : base(_) { }
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384 | [StorableHook(HookType.AfterDeserialization)]
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385 | private void AfterDeserialization() {
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386 | }
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387 |
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388 | // cloning
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389 | private GaussianProcessCovarianceOptimizationProblem(GaussianProcessCovarianceOptimizationProblem original, Cloner cloner)
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390 | : base(original, cloner) {
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391 | bestQ = original.bestQ;
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392 | meanFunc = cloner.Clone(original.meanFunc);
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393 | covFunc = cloner.Clone(original.covFunc);
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394 | if (bestHyperParameters != null) {
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395 | bestHyperParameters = new double[original.bestHyperParameters.Length];
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396 | Array.Copy(original.bestHyperParameters, bestHyperParameters, bestHyperParameters.Length);
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397 | }
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398 | }
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399 | public override IDeepCloneable Clone(Cloner cloner) {
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400 | return new GaussianProcessCovarianceOptimizationProblem(this, cloner);
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401 | }
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402 |
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403 | public void Load(IRegressionProblemData data) {
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404 | this.ProblemData = data;
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405 | OnProblemDataChanged();
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406 | }
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407 |
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408 | public IRegressionProblemData Export() {
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409 | return ProblemData;
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410 | }
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411 |
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412 | #region events
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413 | public event EventHandler ProblemDataChanged;
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414 |
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415 |
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416 | private void OnProblemDataChanged() {
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417 | var handler = ProblemDataChanged;
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418 | if (handler != null)
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419 | handler(this, EventArgs.Empty);
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420 | }
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421 | #endregion
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422 |
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423 | }
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424 | }
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