[12946] | 1 | #region License Information
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| 2 | /* HeuristicLab
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[14186] | 3 | * Copyright (C) 2002-2016 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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[12946] | 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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[13287] | 28 | using HeuristicLab.Optimization;
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[12946] | 29 | using HeuristicLab.Parameters;
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| 30 | using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
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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 | [StorableClass]
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[13290] | 39 | public sealed class GaussianProcessCovarianceOptimizationProblem : SymbolicExpressionTreeProblem, IStatefulItem, IRegressionProblem, IProblemInstanceConsumer<IRegressionProblemData>, IProblemInstanceExporter<IRegressionProblemData> {
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[12946] | 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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[13290] | 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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[12946] | 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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[13290] | 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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[12946] | 193 |
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[13290] | 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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[12946] | 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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[13290] | 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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[12946] | 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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[13290] | 256 | UpdateBestSoFar(bestObjValue[0], bestHyperParameters, meanFunction, covarianceFunction);
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| 257 |
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[12946] | 258 | return bestObjValue[0];
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| 259 | }
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| 260 |
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[13290] | 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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[13287] | 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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[13290] | 292 | results["Best Solution"].Value = CreateSolution();
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[13287] | 293 | }
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| 294 | }
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| 295 |
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[13290] | 296 | private IItem CreateSolution() {
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[13287] | 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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[13290] | 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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[13287] | 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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[12946] | 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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[13290] | 329 | }
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| 330 | catch (ArgumentException) {
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[12946] | 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(bool deserializing) : base(deserializing) { }
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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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[13290] | 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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[12946] | 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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