1 | #region License Information
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2 | /* HeuristicLab
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3 | * Copyright (C) 2002-2018 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.Collections.Generic;
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24 | using System.Diagnostics;
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25 | using System.Linq;
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26 | using HeuristicLab.Analysis;
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27 | using HeuristicLab.Collections;
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28 | using HeuristicLab.Common;
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29 | using HeuristicLab.Core;
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30 | using HeuristicLab.Data;
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31 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
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32 | using HeuristicLab.Optimization;
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33 | using HeuristicLab.Parameters;
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34 | using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
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35 | using HeuristicLab.Problems.DataAnalysis;
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36 | using HeuristicLab.Problems.DataAnalysis.Symbolic;
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37 | using HeuristicLab.Problems.Instances;
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38 |
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39 | namespace HeuristicLab.Problems.DynamicalSystemsModelling {
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40 | public class Vector {
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41 | public readonly static Vector Zero = new Vector(new double[0]);
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42 |
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43 | public static Vector operator +(Vector a, Vector b) {
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44 | if (a == Zero) return b;
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45 | if (b == Zero) return a;
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46 | Debug.Assert(a.arr.Length == b.arr.Length);
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47 | var res = new double[a.arr.Length];
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48 | for (int i = 0; i < res.Length; i++)
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49 | res[i] = a.arr[i] + b.arr[i];
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50 | return new Vector(res);
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51 | }
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52 | public static Vector operator -(Vector a, Vector b) {
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53 | if (b == Zero) return a;
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54 | if (a == Zero) return -b;
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55 | Debug.Assert(a.arr.Length == b.arr.Length);
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56 | var res = new double[a.arr.Length];
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57 | for (int i = 0; i < res.Length; i++)
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58 | res[i] = a.arr[i] - b.arr[i];
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59 | return new Vector(res);
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60 | }
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61 | public static Vector operator -(Vector v) {
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62 | if (v == Zero) return Zero;
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63 | for (int i = 0; i < v.arr.Length; i++)
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64 | v.arr[i] = -v.arr[i];
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65 | return v;
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66 | }
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67 |
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68 | public static Vector operator *(double s, Vector v) {
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69 | if (v == Zero) return Zero;
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70 | if (s == 0.0) return Zero;
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71 | var res = new double[v.arr.Length];
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72 | for (int i = 0; i < res.Length; i++)
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73 | res[i] = s * v.arr[i];
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74 | return new Vector(res);
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75 | }
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76 | public static Vector operator *(Vector v, double s) {
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77 | return s * v;
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78 | }
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79 | public static Vector operator /(double s, Vector v) {
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80 | if (s == 0.0) return Zero;
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81 | if (v == Zero) throw new ArgumentException("Division by zero vector");
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82 | var res = new double[v.arr.Length];
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83 | for (int i = 0; i < res.Length; i++)
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84 | res[i] = 1.0 / v.arr[i];
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85 | return new Vector(res);
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86 | }
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87 | public static Vector operator /(Vector v, double s) {
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88 | return v * 1.0 / s;
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89 | }
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90 |
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91 |
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92 | private readonly double[] arr; // backing array;
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93 |
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94 | public Vector(double[] v) {
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95 | this.arr = v;
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96 | }
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97 |
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98 | public void CopyTo(double[] target) {
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99 | Debug.Assert(arr.Length <= target.Length);
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100 | Array.Copy(arr, target, arr.Length);
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101 | }
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102 | }
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103 |
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104 | [Item("Dynamical Systems Modelling Problem", "TODO")]
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105 | [Creatable(CreatableAttribute.Categories.GeneticProgrammingProblems, Priority = 900)]
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106 | [StorableClass]
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107 | public sealed class Problem : SingleObjectiveBasicProblem<MultiEncoding>, IRegressionProblem, IProblemInstanceConsumer<IRegressionProblemData>, IProblemInstanceExporter<IRegressionProblemData> {
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108 |
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109 | #region parameter names
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110 | private const string ProblemDataParameterName = "Data";
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111 | private const string TargetVariablesParameterName = "Target variables";
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112 | private const string FunctionSetParameterName = "Function set";
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113 | private const string MaximumLengthParameterName = "Size limit";
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114 | private const string MaximumParameterOptimizationIterationsParameterName = "Max. parameter optimization iterations";
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115 | private const string NumberOfLatentVariablesParameterName = "Number of latent variables";
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116 | private const string NumericIntegrationStepsParameterName = "Steps for numeric integration";
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117 | #endregion
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118 |
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119 | #region Parameter Properties
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120 | IParameter IDataAnalysisProblem.ProblemDataParameter { get { return ProblemDataParameter; } }
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121 |
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122 | public IValueParameter<IRegressionProblemData> ProblemDataParameter {
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123 | get { return (IValueParameter<IRegressionProblemData>)Parameters[ProblemDataParameterName]; }
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124 | }
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125 | public IValueParameter<ReadOnlyCheckedItemCollection<StringValue>> TargetVariablesParameter {
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126 | get { return (IValueParameter<ReadOnlyCheckedItemCollection<StringValue>>)Parameters[TargetVariablesParameterName]; }
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127 | }
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128 | public IValueParameter<ReadOnlyCheckedItemCollection<StringValue>> FunctionSetParameter {
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129 | get { return (IValueParameter<ReadOnlyCheckedItemCollection<StringValue>>)Parameters[FunctionSetParameterName]; }
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130 | }
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131 | public IFixedValueParameter<IntValue> MaximumLengthParameter {
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132 | get { return (IFixedValueParameter<IntValue>)Parameters[MaximumLengthParameterName]; }
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133 | }
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134 | public IFixedValueParameter<IntValue> MaximumParameterOptimizationIterationsParameter {
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135 | get { return (IFixedValueParameter<IntValue>)Parameters[MaximumParameterOptimizationIterationsParameterName]; }
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136 | }
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137 | public IFixedValueParameter<IntValue> NumberOfLatentVariablesParameter {
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138 | get { return (IFixedValueParameter<IntValue>)Parameters[NumberOfLatentVariablesParameterName]; }
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139 | }
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140 | public IFixedValueParameter<IntValue> NumericIntegrationStepsParameter {
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141 | get { return (IFixedValueParameter<IntValue>)Parameters[NumericIntegrationStepsParameterName]; }
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142 | }
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143 | #endregion
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144 |
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145 | #region Properties
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146 | public IRegressionProblemData ProblemData {
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147 | get { return ProblemDataParameter.Value; }
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148 | set { ProblemDataParameter.Value = value; }
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149 | }
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150 | IDataAnalysisProblemData IDataAnalysisProblem.ProblemData { get { return ProblemData; } }
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151 |
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152 | public ReadOnlyCheckedItemCollection<StringValue> TargetVariables {
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153 | get { return TargetVariablesParameter.Value; }
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154 | }
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155 |
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156 | public ReadOnlyCheckedItemCollection<StringValue> FunctionSet {
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157 | get { return FunctionSetParameter.Value; }
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158 | }
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159 |
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160 | public int MaximumLength {
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161 | get { return MaximumLengthParameter.Value.Value; }
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162 | }
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163 | public int MaximumParameterOptimizationIterations {
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164 | get { return MaximumParameterOptimizationIterationsParameter.Value.Value; }
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165 | }
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166 | public int NumberOfLatentVariables {
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167 | get { return NumberOfLatentVariablesParameter.Value.Value; }
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168 | }
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169 | public int NumericIntegrationSteps {
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170 | get { return NumericIntegrationStepsParameter.Value.Value; }
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171 | }
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172 |
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173 | #endregion
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174 |
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175 | public event EventHandler ProblemDataChanged;
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176 |
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177 | public override bool Maximization {
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178 | get { return false; } // we minimize NMSE
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179 | }
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180 |
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181 | #region item cloning and persistence
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182 | // persistence
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183 | [StorableConstructor]
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184 | private Problem(bool deserializing) : base(deserializing) { }
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185 | [StorableHook(HookType.AfterDeserialization)]
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186 | private void AfterDeserialization() {
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187 | RegisterEventHandlers();
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188 | }
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189 |
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190 | // cloning
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191 | private Problem(Problem original, Cloner cloner)
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192 | : base(original, cloner) {
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193 | RegisterEventHandlers();
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194 | }
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195 | public override IDeepCloneable Clone(Cloner cloner) { return new Problem(this, cloner); }
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196 | #endregion
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197 |
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198 | public Problem()
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199 | : base() {
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200 | var targetVariables = new CheckedItemCollection<StringValue>().AsReadOnly(); // HACK: it would be better to provide a new class derived from IDataAnalysisProblem
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201 | var functions = CreateFunctionSet();
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202 | Parameters.Add(new ValueParameter<IRegressionProblemData>(ProblemDataParameterName, "The data captured from the dynamical system. Use CSV import functionality to import data.", new RegressionProblemData()));
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203 | Parameters.Add(new ValueParameter<ReadOnlyCheckedItemCollection<StringValue>>(TargetVariablesParameterName, "Target variables (overrides setting in ProblemData)", targetVariables));
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204 | Parameters.Add(new ValueParameter<ReadOnlyCheckedItemCollection<StringValue>>(FunctionSetParameterName, "The list of allowed functions", functions));
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205 | Parameters.Add(new FixedValueParameter<IntValue>(MaximumLengthParameterName, "The maximally allowed length of each expression. Set to a small value (5 - 25). Default = 10", new IntValue(10)));
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206 | Parameters.Add(new FixedValueParameter<IntValue>(MaximumParameterOptimizationIterationsParameterName, "The maximum number of iterations for optimization of parameters (using L-BFGS). More iterations makes the algorithm slower, fewer iterations might prevent convergence in the optimization scheme. Default = 100", new IntValue(100)));
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207 | Parameters.Add(new FixedValueParameter<IntValue>(NumberOfLatentVariablesParameterName, "Latent variables (unobserved variables) allow us to produce expressions which are integrated up and can be used in other expressions. They are handled similarly to target variables in forward simulation / integration. The difference to target variables is that there are no data to which the calculated values of latent variables are compared. Set to a small value (0 .. 5) as necessary (default = 0)", new IntValue(0)));
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208 | Parameters.Add(new FixedValueParameter<IntValue>(NumericIntegrationStepsParameterName, "Number of steps in the numeric integration that are taken from one row to the next (set to 1 to 100). More steps makes the algorithm slower, less steps worsens the accuracy of the numeric integration scheme.", new IntValue(10)));
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209 |
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210 | RegisterEventHandlers();
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211 | InitAllParameters();
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212 | }
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213 |
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214 |
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215 | public override double Evaluate(Individual individual, IRandom random) {
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216 | var trees = individual.Values.Select(v => v.Value).OfType<ISymbolicExpressionTree>().ToArray(); // extract all trees from individual
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217 |
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218 | var problemData = ProblemData;
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219 | var rows = ProblemData.TrainingIndices.ToArray();
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220 | var targetVars = TargetVariables.CheckedItems.Select(i => i.Value).ToArray();
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221 | var latentVariables = Enumerable.Range(1, NumberOfLatentVariables).Select(i => "λ" + i).ToArray(); // TODO: must coincide with the variables which are actually defined in the grammar and also for which we actually have trees
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222 | var targetValues = new double[rows.Length, targetVars.Length];
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223 |
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224 | // collect values of all target variables
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225 | var colIdx = 0;
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226 | foreach (var targetVar in targetVars) {
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227 | int rowIdx = 0;
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228 | foreach (var value in problemData.Dataset.GetDoubleValues(targetVar, rows)) {
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229 | targetValues[rowIdx, colIdx] = value;
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230 | rowIdx++;
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231 | }
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232 | colIdx++;
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233 | }
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234 |
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235 | var nodeIdx = new Dictionary<ISymbolicExpressionTreeNode, int>();
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236 |
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237 | foreach (var tree in trees) {
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238 | foreach (var node in tree.Root.IterateNodesPrefix().Where(n => IsConstantNode(n))) {
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239 | nodeIdx.Add(node, nodeIdx.Count);
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240 | }
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241 | }
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242 |
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243 | var theta = nodeIdx.Select(_ => random.NextDouble() * 2.0 - 1.0).ToArray(); // init params randomly from Unif(-1,1)
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244 |
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245 | double[] optTheta = new double[0];
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246 | if (theta.Length > 0) {
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247 | alglib.minlbfgsstate state;
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248 | alglib.minlbfgsreport report;
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249 | alglib.minlbfgscreate(Math.Min(theta.Length, 5), theta, out state);
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250 | alglib.minlbfgssetcond(state, 0.0, 0.0, 0.0, MaximumParameterOptimizationIterations);
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251 | alglib.minlbfgsoptimize(state, EvaluateObjectiveAndGradient, null,
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252 | new object[] { trees, targetVars, problemData, nodeIdx, targetValues, rows, NumericIntegrationSteps, latentVariables }); //TODO: create a type
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253 | alglib.minlbfgsresults(state, out optTheta, out report);
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254 |
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255 | /*
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256 | *
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257 | * L-BFGS algorithm results
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258 |
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259 | INPUT PARAMETERS:
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260 | State - algorithm state
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261 |
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262 | OUTPUT PARAMETERS:
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263 | X - array[0..N-1], solution
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264 | Rep - optimization report:
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265 | * Rep.TerminationType completetion code:
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266 | * -7 gradient verification failed.
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267 | See MinLBFGSSetGradientCheck() for more information.
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268 | * -2 rounding errors prevent further improvement.
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269 | X contains best point found.
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270 | * -1 incorrect parameters were specified
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271 | * 1 relative function improvement is no more than
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272 | EpsF.
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273 | * 2 relative step is no more than EpsX.
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274 | * 4 gradient norm is no more than EpsG
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275 | * 5 MaxIts steps was taken
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276 | * 7 stopping conditions are too stringent,
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277 | further improvement is impossible
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278 | * Rep.IterationsCount contains iterations count
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279 | * NFEV countains number of function calculations
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280 | */
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281 | if (report.terminationtype < 0) return double.MaxValue;
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282 | }
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283 |
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284 | // perform evaluation for optimal theta to get quality value
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285 | double[] grad = new double[optTheta.Length];
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286 | double optQuality = double.NaN;
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287 | EvaluateObjectiveAndGradient(optTheta, ref optQuality, grad,
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288 | new object[] { trees, targetVars, problemData, nodeIdx, targetValues, rows, NumericIntegrationSteps, latentVariables });
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289 | if (double.IsNaN(optQuality) || double.IsInfinity(optQuality)) return 10E6; // return a large value (TODO: be consistent by using NMSE)
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290 |
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291 | individual["OptTheta"] = new DoubleArray(optTheta); // write back optimized parameters so that we can use them in the Analysis method
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292 | return optQuality;
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293 | }
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294 |
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295 | private static void EvaluateObjectiveAndGradient(double[] x, ref double f, double[] grad, object obj) {
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296 | var trees = (ISymbolicExpressionTree[])((object[])obj)[0];
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297 | var targetVariables = (string[])((object[])obj)[1];
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298 | var problemData = (IRegressionProblemData)((object[])obj)[2];
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299 | var nodeIdx = (Dictionary<ISymbolicExpressionTreeNode, int>)((object[])obj)[3];
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300 | var targetValues = (double[,])((object[])obj)[4];
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301 | var rows = (int[])((object[])obj)[5];
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302 | var numericIntegrationSteps = (int)((object[])obj)[6];
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303 | var latentVariables = (string[])((object[])obj)[7];
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304 |
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305 | var predicted = Integrate(
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306 | trees, // we assume trees contain expressions for the change of each target variable over time y'(t)
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307 | problemData.Dataset,
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308 | problemData.AllowedInputVariables.ToArray(),
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309 | targetVariables,
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310 | latentVariables,
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311 | rows,
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312 | nodeIdx, // TODO: is it Ok to use rows here ?
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313 | x, numericIntegrationSteps).ToArray();
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314 |
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315 |
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316 | // for normalized MSE = 1/variance(t) * MSE(t, pred)
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317 | // TODO: Perf. (by standardization of target variables before evaluation of all trees)
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318 | var invVar = Enumerable.Range(0, targetVariables.Length)
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319 | .Select(c => rows.Select(row => targetValues[row, c])) // colums vectors
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320 | .Select(vec => vec.Variance())
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321 | .Select(v => 1.0 / v)
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322 | .ToArray();
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323 |
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324 | // objective function is NMSE
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325 | f = 0.0;
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326 | int n = predicted.Length;
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327 | double invN = 1.0 / n;
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328 | var g = Vector.Zero;
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329 | int r = 0;
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330 | foreach (var y_pred in predicted) {
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331 | for (int c = 0; c < y_pred.Length; c++) {
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332 |
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333 | var y_pred_f = y_pred[c].Item1;
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334 | var y = targetValues[r, c];
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335 |
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336 | var res = (y - y_pred_f);
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337 | var ressq = res * res;
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338 | f += ressq * invN * invVar[c];
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339 | g += -2.0 * res * y_pred[c].Item2 * invN * invVar[c];
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340 | }
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341 | r++;
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342 | }
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343 |
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344 | g.CopyTo(grad);
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345 | }
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346 |
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347 | public override void Analyze(Individual[] individuals, double[] qualities, ResultCollection results, IRandom random) {
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348 | base.Analyze(individuals, qualities, results, random);
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349 |
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350 | if (!results.ContainsKey("Prediction (training)")) {
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351 | results.Add(new Result("Prediction (training)", typeof(ReadOnlyItemList<DataTable>)));
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352 | }
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353 | if (!results.ContainsKey("Prediction (test)")) {
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354 | results.Add(new Result("Prediction (test)", typeof(ReadOnlyItemList<DataTable>)));
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355 | }
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356 | if (!results.ContainsKey("Models")) {
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357 | results.Add(new Result("Models", typeof(ReadOnlyItemList<ISymbolicExpressionTree>)));
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358 | }
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359 |
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360 | // TODO extract common functionality from Evaluate and Analyze
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361 | var bestIndividualAndQuality = this.GetBestIndividual(individuals, qualities);
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362 | var optTheta = ((DoubleArray)bestIndividualAndQuality.Item1["OptTheta"]).ToArray(); // see evaluate
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363 | var trees = bestIndividualAndQuality.Item1.Values.Select(v => v.Value).OfType<ISymbolicExpressionTree>().ToArray(); // extract all trees from individual
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364 | var nodeIdx = new Dictionary<ISymbolicExpressionTreeNode, int>();
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365 |
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366 |
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367 | foreach (var tree in trees) {
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368 | foreach (var node in tree.Root.IterateNodesPrefix().Where(n => IsConstantNode(n))) {
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369 | nodeIdx.Add(node, nodeIdx.Count);
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370 | }
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371 | }
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372 | var problemData = ProblemData;
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373 | var targetVars = TargetVariables.CheckedItems.Select(i => i.Value).ToArray();
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374 | var latentVariables = Enumerable.Range(1, NumberOfLatentVariables).Select(i => "λ" + i).ToArray(); // TODO: must coincide with the variables which are actually defined in the grammar and also for which we actually have trees
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375 |
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376 | var trainingList = new ItemList<DataTable>();
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377 | var trainingRows = ProblemData.TrainingIndices.ToArray();
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378 | var trainingPrediction = Integrate(
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379 | trees, // we assume trees contain expressions for the change of each target variable over time y'(t)
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380 | problemData.Dataset,
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381 | problemData.AllowedInputVariables.ToArray(),
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382 | targetVars,
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383 | latentVariables,
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384 | trainingRows,
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385 | nodeIdx,
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386 | optTheta,
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387 | NumericIntegrationSteps).ToArray();
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388 |
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389 | for (int colIdx = 0; colIdx < targetVars.Length; colIdx++) {
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390 | var targetVar = targetVars[colIdx];
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391 | var trainingDataTable = new DataTable(targetVar + " prediction (training)");
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392 | var actualValuesRow = new DataRow(targetVar, "The values of " + targetVar, problemData.Dataset.GetDoubleValues(targetVar, trainingRows));
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393 | var predictedValuesRow = new DataRow(targetVar + " pred.", "Predicted values for " + targetVar, trainingPrediction.Select(arr => arr[colIdx].Item1).ToArray());
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394 | trainingDataTable.Rows.Add(actualValuesRow);
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395 | trainingDataTable.Rows.Add(predictedValuesRow);
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396 | trainingList.Add(trainingDataTable);
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397 | }
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398 |
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399 | // TODO: DRY for training and test
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---|
400 | var testList = new ItemList<DataTable>();
|
---|
401 | var testRows = ProblemData.TestIndices.ToArray();
|
---|
402 | var testPrediction = Integrate(
|
---|
403 | trees, // we assume trees contain expressions for the change of each target variable over time y'(t)
|
---|
404 | problemData.Dataset,
|
---|
405 | problemData.AllowedInputVariables.ToArray(),
|
---|
406 | targetVars,
|
---|
407 | latentVariables,
|
---|
408 | testRows,
|
---|
409 | nodeIdx,
|
---|
410 | optTheta,
|
---|
411 | NumericIntegrationSteps).ToArray();
|
---|
412 |
|
---|
413 | for (int colIdx = 0; colIdx < targetVars.Length; colIdx++) {
|
---|
414 | var targetVar = targetVars[colIdx];
|
---|
415 | var testDataTable = new DataTable(targetVar + " prediction (test)");
|
---|
416 | var actualValuesRow = new DataRow(targetVar, "The values of " + targetVar, problemData.Dataset.GetDoubleValues(targetVar, testRows));
|
---|
417 | var predictedValuesRow = new DataRow(targetVar + " pred.", "Predicted values for " + targetVar, testPrediction.Select(arr => arr[colIdx].Item1).ToArray());
|
---|
418 | testDataTable.Rows.Add(actualValuesRow);
|
---|
419 | testDataTable.Rows.Add(predictedValuesRow);
|
---|
420 | testList.Add(testDataTable);
|
---|
421 | }
|
---|
422 |
|
---|
423 | results["Prediction (training)"].Value = trainingList.AsReadOnly();
|
---|
424 | results["Prediction (test)"].Value = testList.AsReadOnly();
|
---|
425 |
|
---|
426 | var modelList = new ItemList<ISymbolicExpressionTree>();
|
---|
427 | foreach (var tree in trees) {
|
---|
428 | var shownTree = (ISymbolicExpressionTree)tree.Clone();
|
---|
429 | var constantsNodeOrig = tree.IterateNodesPrefix().Where(IsConstantNode);
|
---|
430 | var constantsNodeShown = shownTree.IterateNodesPrefix().Where(IsConstantNode);
|
---|
431 |
|
---|
432 | foreach (var n in constantsNodeOrig.Zip(constantsNodeShown, (original, shown) => new { original, shown })) {
|
---|
433 | double constantsVal = optTheta[nodeIdx[n.original]];
|
---|
434 |
|
---|
435 | ConstantTreeNode replacementNode = new ConstantTreeNode(new Constant()) { Value = constantsVal };
|
---|
436 |
|
---|
437 | var parentNode = n.shown.Parent;
|
---|
438 | int replacementIndex = parentNode.IndexOfSubtree(n.shown);
|
---|
439 | parentNode.RemoveSubtree(replacementIndex);
|
---|
440 | parentNode.InsertSubtree(replacementIndex, replacementNode);
|
---|
441 | }
|
---|
442 | // TODO: simplify trees
|
---|
443 |
|
---|
444 | modelList.Add(shownTree);
|
---|
445 | }
|
---|
446 | results["Models"].Value = modelList.AsReadOnly();
|
---|
447 | }
|
---|
448 |
|
---|
449 |
|
---|
450 | #region interpretation
|
---|
451 | private static IEnumerable<Tuple<double, Vector>[]> Integrate(
|
---|
452 | ISymbolicExpressionTree[] trees, IDataset dataset, string[] inputVariables, string[] targetVariables, string[] latentVariables, IEnumerable<int> rows,
|
---|
453 | Dictionary<ISymbolicExpressionTreeNode, int> nodeIdx, double[] parameterValues, int numericIntegrationSteps = 100) {
|
---|
454 |
|
---|
455 | int NUM_STEPS = numericIntegrationSteps ;
|
---|
456 | double h = 1.0 / NUM_STEPS;
|
---|
457 |
|
---|
458 | // return first value as stored in the dataset
|
---|
459 | yield return targetVariables
|
---|
460 | .Select(targetVar => Tuple.Create(dataset.GetDoubleValue(targetVar, rows.First()), Vector.Zero))
|
---|
461 | .ToArray();
|
---|
462 |
|
---|
463 | // integrate forward starting with known values for the target in t0
|
---|
464 |
|
---|
465 | var variableValues = new Dictionary<string, Tuple<double, Vector>>();
|
---|
466 | var t0 = rows.First();
|
---|
467 | foreach (var varName in inputVariables) {
|
---|
468 | variableValues.Add(varName, Tuple.Create(dataset.GetDoubleValue(varName, t0), Vector.Zero));
|
---|
469 | }
|
---|
470 | foreach (var varName in targetVariables) {
|
---|
471 | variableValues.Add(varName, Tuple.Create(dataset.GetDoubleValue(varName, t0), Vector.Zero));
|
---|
472 | }
|
---|
473 | // add value entries for latent variables which are also integrated
|
---|
474 | foreach(var latentVar in latentVariables) {
|
---|
475 | variableValues.Add(latentVar, Tuple.Create(0.0, Vector.Zero)); // we don't have observations for latent variables -> assume zero as starting value
|
---|
476 | }
|
---|
477 | var calculatedVariables = targetVariables.Concat(latentVariables); // TODO: must conincide with the order of trees in the encoding
|
---|
478 |
|
---|
479 | foreach (var t in rows.Skip(1)) {
|
---|
480 | for (int step = 0; step < NUM_STEPS; step++) {
|
---|
481 | var deltaValues = new Dictionary<string, Tuple<double, Vector>>();
|
---|
482 | foreach (var tup in trees.Zip(calculatedVariables, Tuple.Create)) {
|
---|
483 | var tree = tup.Item1;
|
---|
484 | var targetVarName = tup.Item2;
|
---|
485 | // skip programRoot and startSymbol
|
---|
486 | var res = InterpretRec(tree.Root.GetSubtree(0).GetSubtree(0), variableValues, nodeIdx, parameterValues);
|
---|
487 | deltaValues.Add(targetVarName, res);
|
---|
488 | }
|
---|
489 |
|
---|
490 | // update variableValues for next step
|
---|
491 | foreach (var kvp in deltaValues) {
|
---|
492 | var oldVal = variableValues[kvp.Key];
|
---|
493 | variableValues[kvp.Key] = Tuple.Create(
|
---|
494 | oldVal.Item1 + h * kvp.Value.Item1,
|
---|
495 | oldVal.Item2 + h * kvp.Value.Item2
|
---|
496 | );
|
---|
497 | }
|
---|
498 | }
|
---|
499 |
|
---|
500 | // only return the target variables for calculation of errors
|
---|
501 | yield return targetVariables
|
---|
502 | .Select(targetVar => variableValues[targetVar])
|
---|
503 | .ToArray();
|
---|
504 |
|
---|
505 | // update for next time step
|
---|
506 | foreach (var varName in inputVariables) {
|
---|
507 | variableValues[varName] = Tuple.Create(dataset.GetDoubleValue(varName, t), Vector.Zero);
|
---|
508 | }
|
---|
509 | }
|
---|
510 | }
|
---|
511 |
|
---|
512 | private static Tuple<double, Vector> InterpretRec(
|
---|
513 | ISymbolicExpressionTreeNode node,
|
---|
514 | Dictionary<string, Tuple<double, Vector>> variableValues,
|
---|
515 | Dictionary<ISymbolicExpressionTreeNode, int> nodeIdx,
|
---|
516 | double[] parameterValues
|
---|
517 | ) {
|
---|
518 |
|
---|
519 | switch (node.Symbol.Name) {
|
---|
520 | case "+": {
|
---|
521 | var l = InterpretRec(node.GetSubtree(0), variableValues, nodeIdx, parameterValues); // TODO capture all parameters into a state type for interpretation
|
---|
522 | var r = InterpretRec(node.GetSubtree(1), variableValues, nodeIdx, parameterValues);
|
---|
523 |
|
---|
524 | return Tuple.Create(l.Item1 + r.Item1, l.Item2 + r.Item2);
|
---|
525 | }
|
---|
526 | case "*": {
|
---|
527 | var l = InterpretRec(node.GetSubtree(0), variableValues, nodeIdx, parameterValues);
|
---|
528 | var r = InterpretRec(node.GetSubtree(1), variableValues, nodeIdx, parameterValues);
|
---|
529 |
|
---|
530 | return Tuple.Create(l.Item1 * r.Item1, l.Item2 * r.Item1 + l.Item1 * r.Item2);
|
---|
531 | }
|
---|
532 |
|
---|
533 | case "-": {
|
---|
534 | var l = InterpretRec(node.GetSubtree(0), variableValues, nodeIdx, parameterValues);
|
---|
535 | var r = InterpretRec(node.GetSubtree(1), variableValues, nodeIdx, parameterValues);
|
---|
536 |
|
---|
537 | return Tuple.Create(l.Item1 - r.Item1, l.Item2 - r.Item2);
|
---|
538 | }
|
---|
539 | case "%": {
|
---|
540 | var l = InterpretRec(node.GetSubtree(0), variableValues, nodeIdx, parameterValues);
|
---|
541 | var r = InterpretRec(node.GetSubtree(1), variableValues, nodeIdx, parameterValues);
|
---|
542 |
|
---|
543 | // protected division
|
---|
544 | if (r.Item1.IsAlmost(0.0)) {
|
---|
545 | return Tuple.Create(0.0, Vector.Zero);
|
---|
546 | } else {
|
---|
547 | return Tuple.Create(
|
---|
548 | l.Item1 / r.Item1,
|
---|
549 | l.Item1 * -1.0 / (r.Item1 * r.Item1) * r.Item2 + 1.0 / r.Item1 * l.Item2 // (f/g)' = f * (1/g)' + 1/g * f' = f * -1/g² * g' + 1/g * f'
|
---|
550 | );
|
---|
551 | }
|
---|
552 | }
|
---|
553 | default: {
|
---|
554 | // distinguish other cases
|
---|
555 | if (IsConstantNode(node)) {
|
---|
556 | var vArr = new double[parameterValues.Length]; // backing array for vector
|
---|
557 | vArr[nodeIdx[node]] = 1.0;
|
---|
558 | var g = new Vector(vArr);
|
---|
559 | return Tuple.Create(parameterValues[nodeIdx[node]], g);
|
---|
560 | } else {
|
---|
561 | // assume a variable name
|
---|
562 | var varName = node.Symbol.Name;
|
---|
563 | return variableValues[varName];
|
---|
564 | }
|
---|
565 | }
|
---|
566 | }
|
---|
567 | }
|
---|
568 | #endregion
|
---|
569 |
|
---|
570 | #region events
|
---|
571 | /*
|
---|
572 | * Dependencies between parameters:
|
---|
573 | *
|
---|
574 | * ProblemData
|
---|
575 | * |
|
---|
576 | * V
|
---|
577 | * TargetVariables FunctionSet MaximumLength NumberOfLatentVariables
|
---|
578 | * | | | |
|
---|
579 | * V V | |
|
---|
580 | * Grammar <---------------+-------------------
|
---|
581 | * |
|
---|
582 | * V
|
---|
583 | * Encoding
|
---|
584 | */
|
---|
585 | private void RegisterEventHandlers() {
|
---|
586 | ProblemDataParameter.ValueChanged += ProblemDataParameter_ValueChanged;
|
---|
587 | if (ProblemDataParameter.Value != null) ProblemDataParameter.Value.Changed += ProblemData_Changed;
|
---|
588 |
|
---|
589 | TargetVariablesParameter.ValueChanged += TargetVariablesParameter_ValueChanged;
|
---|
590 | if (TargetVariablesParameter.Value != null) TargetVariablesParameter.Value.CheckedItemsChanged += CheckedTargetVariablesChanged;
|
---|
591 |
|
---|
592 | FunctionSetParameter.ValueChanged += FunctionSetParameter_ValueChanged;
|
---|
593 | if (FunctionSetParameter.Value != null) FunctionSetParameter.Value.CheckedItemsChanged += CheckedFunctionsChanged;
|
---|
594 |
|
---|
595 | MaximumLengthParameter.Value.ValueChanged += MaximumLengthChanged;
|
---|
596 |
|
---|
597 | NumberOfLatentVariablesParameter.Value.ValueChanged += NumLatentVariablesChanged;
|
---|
598 | }
|
---|
599 |
|
---|
600 | private void NumLatentVariablesChanged(object sender, EventArgs e) {
|
---|
601 | UpdateGrammarAndEncoding();
|
---|
602 | }
|
---|
603 |
|
---|
604 | private void MaximumLengthChanged(object sender, EventArgs e) {
|
---|
605 | UpdateGrammarAndEncoding();
|
---|
606 | }
|
---|
607 |
|
---|
608 | private void FunctionSetParameter_ValueChanged(object sender, EventArgs e) {
|
---|
609 | FunctionSetParameter.Value.CheckedItemsChanged += CheckedFunctionsChanged;
|
---|
610 | }
|
---|
611 |
|
---|
612 | private void CheckedFunctionsChanged(object sender, CollectionItemsChangedEventArgs<StringValue> e) {
|
---|
613 | UpdateGrammarAndEncoding();
|
---|
614 | }
|
---|
615 |
|
---|
616 | private void TargetVariablesParameter_ValueChanged(object sender, EventArgs e) {
|
---|
617 | TargetVariablesParameter.Value.CheckedItemsChanged += CheckedTargetVariablesChanged;
|
---|
618 | }
|
---|
619 |
|
---|
620 | private void CheckedTargetVariablesChanged(object sender, CollectionItemsChangedEventArgs<StringValue> e) {
|
---|
621 | UpdateGrammarAndEncoding();
|
---|
622 | }
|
---|
623 |
|
---|
624 | private void ProblemDataParameter_ValueChanged(object sender, EventArgs e) {
|
---|
625 | ProblemDataParameter.Value.Changed += ProblemData_Changed;
|
---|
626 | OnProblemDataChanged();
|
---|
627 | OnReset();
|
---|
628 | }
|
---|
629 |
|
---|
630 | private void ProblemData_Changed(object sender, EventArgs e) {
|
---|
631 | OnProblemDataChanged();
|
---|
632 | OnReset();
|
---|
633 | }
|
---|
634 |
|
---|
635 | private void OnProblemDataChanged() {
|
---|
636 | UpdateTargetVariables(); // implicitly updates other dependent parameters
|
---|
637 | UpdateGrammarAndEncoding();
|
---|
638 | var handler = ProblemDataChanged;
|
---|
639 | if (handler != null) handler(this, EventArgs.Empty);
|
---|
640 | }
|
---|
641 |
|
---|
642 | #endregion
|
---|
643 |
|
---|
644 | #region helper
|
---|
645 |
|
---|
646 | private void InitAllParameters() {
|
---|
647 | UpdateTargetVariables(); // implicitly updates the grammar and the encoding
|
---|
648 | }
|
---|
649 |
|
---|
650 | private ReadOnlyCheckedItemCollection<StringValue> CreateFunctionSet() {
|
---|
651 | var l = new CheckedItemCollection<StringValue>();
|
---|
652 | l.Add(new StringValue("+").AsReadOnly());
|
---|
653 | l.Add(new StringValue("*").AsReadOnly());
|
---|
654 | l.Add(new StringValue("%").AsReadOnly());
|
---|
655 | l.Add(new StringValue("-").AsReadOnly());
|
---|
656 | return l.AsReadOnly();
|
---|
657 | }
|
---|
658 |
|
---|
659 | private static bool IsConstantNode(ISymbolicExpressionTreeNode n) {
|
---|
660 | return n.Symbol.Name.StartsWith("θ");
|
---|
661 | }
|
---|
662 | private static bool IsLatentVariableNode(ISymbolicExpressionTreeNode n) {
|
---|
663 | return n.Symbol.Name.StartsWith("λ");
|
---|
664 | }
|
---|
665 |
|
---|
666 |
|
---|
667 | private void UpdateTargetVariables() {
|
---|
668 | var currentlySelectedVariables = TargetVariables.CheckedItems.Select(i => i.Value).ToArray();
|
---|
669 |
|
---|
670 | var newVariablesList = new CheckedItemCollection<StringValue>(ProblemData.Dataset.VariableNames.Select(str => new StringValue(str).AsReadOnly()).ToArray()).AsReadOnly();
|
---|
671 | var matchingItems = newVariablesList.Where(item => currentlySelectedVariables.Contains(item.Value)).ToArray();
|
---|
672 | foreach (var matchingItem in matchingItems) {
|
---|
673 | newVariablesList.SetItemCheckedState(matchingItem, true);
|
---|
674 | }
|
---|
675 | TargetVariablesParameter.Value = newVariablesList;
|
---|
676 | }
|
---|
677 |
|
---|
678 | private void UpdateGrammarAndEncoding() {
|
---|
679 | var encoding = new MultiEncoding();
|
---|
680 | var g = CreateGrammar();
|
---|
681 | foreach (var targetVar in TargetVariables.CheckedItems) {
|
---|
682 | encoding = encoding.Add(new SymbolicExpressionTreeEncoding(targetVar + "_tree", g, MaximumLength, MaximumLength)); // only limit by length
|
---|
683 | }
|
---|
684 | for (int i = 1; i <= NumberOfLatentVariables; i++) {
|
---|
685 | encoding = encoding.Add(new SymbolicExpressionTreeEncoding("λ" + i + "_tree", g, MaximumLength, MaximumLength));
|
---|
686 | }
|
---|
687 | Encoding = encoding;
|
---|
688 | }
|
---|
689 |
|
---|
690 | private ISymbolicExpressionGrammar CreateGrammar() {
|
---|
691 | // whenever ProblemData is changed we create a new grammar with the necessary symbols
|
---|
692 | var g = new SimpleSymbolicExpressionGrammar();
|
---|
693 | g.AddSymbols(FunctionSet.CheckedItems.Select(i => i.Value).ToArray(), 2, 2);
|
---|
694 |
|
---|
695 | // TODO
|
---|
696 | //g.AddSymbols(new[] {
|
---|
697 | // "exp",
|
---|
698 | // "log", // log( <expr> ) // TODO: init a theta to ensure the value is always positive
|
---|
699 | // "exp_minus" // exp((-1) * <expr>
|
---|
700 | //}, 1, 1);
|
---|
701 |
|
---|
702 | foreach (var variableName in ProblemData.AllowedInputVariables.Union(TargetVariables.CheckedItems.Select(i => i.Value)))
|
---|
703 | g.AddTerminalSymbol(variableName);
|
---|
704 |
|
---|
705 | // generate symbols for numeric parameters for which the value is optimized using AutoDiff
|
---|
706 | // we generate multiple symbols to balance the probability for selecting a numeric parameter in the generation of random trees
|
---|
707 | var numericConstantsFactor = 2.0;
|
---|
708 | for (int i = 0; i < numericConstantsFactor * (ProblemData.AllowedInputVariables.Count() + TargetVariables.CheckedItems.Count()); i++) {
|
---|
709 | g.AddTerminalSymbol("θ" + i); // numeric parameter for which the value is optimized using AutoDiff
|
---|
710 | }
|
---|
711 |
|
---|
712 | // generate symbols for latent variables
|
---|
713 | for (int i = 1; i <= NumberOfLatentVariables; i++) {
|
---|
714 | g.AddTerminalSymbol("λ" + i); // numeric parameter for which the value is optimized using AutoDiff
|
---|
715 | }
|
---|
716 |
|
---|
717 | return g;
|
---|
718 | }
|
---|
719 |
|
---|
720 | #endregion
|
---|
721 |
|
---|
722 | #region Import & Export
|
---|
723 | public void Load(IRegressionProblemData data) {
|
---|
724 | Name = data.Name;
|
---|
725 | Description = data.Description;
|
---|
726 | ProblemData = data;
|
---|
727 | }
|
---|
728 |
|
---|
729 | public IRegressionProblemData Export() {
|
---|
730 | return ProblemData;
|
---|
731 | }
|
---|
732 | #endregion
|
---|
733 |
|
---|
734 | }
|
---|
735 | }
|
---|