1 | #region License Information
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2 | /* HeuristicLab
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3 | * Copyright (C) 2002-2016 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.Linq;
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25 | using HeuristicLab.Common;
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26 | using HeuristicLab.Core;
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27 | using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
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28 | using HeuristicLab.Problems.DataAnalysis;
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29 |
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30 | namespace HeuristicLab.Algorithms.DataAnalysis {
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31 | /// <summary>
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32 | /// Represents a Gaussian process model.
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33 | /// </summary>
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34 | [StorableClass]
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35 | [Item("GaussianProcessModel", "Represents a Gaussian process posterior.")]
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36 | public sealed class GaussianProcessModel : RegressionModel, IGaussianProcessModel {
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37 | public override IEnumerable<string> VariablesUsedForPrediction {
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38 | get { return allowedInputVariables; }
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39 | }
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40 |
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41 | [Storable]
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42 | private double negativeLogLikelihood;
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43 | public double NegativeLogLikelihood {
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44 | get { return negativeLogLikelihood; }
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45 | }
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46 |
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47 | [Storable]
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48 | private double[] hyperparameterGradients;
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49 | public double[] HyperparameterGradients {
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50 | get {
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51 | var copy = new double[hyperparameterGradients.Length];
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52 | Array.Copy(hyperparameterGradients, copy, copy.Length);
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53 | return copy;
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54 | }
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55 | }
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56 |
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57 | [Storable]
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58 | private ICovarianceFunction covarianceFunction;
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59 | public ICovarianceFunction CovarianceFunction {
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60 | get { return covarianceFunction; }
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61 | }
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62 | [Storable]
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63 | private IMeanFunction meanFunction;
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64 | public IMeanFunction MeanFunction {
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65 | get { return meanFunction; }
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66 | }
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67 |
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68 | [Storable]
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69 | private string[] allowedInputVariables;
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70 | public string[] AllowedInputVariables {
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71 | get { return allowedInputVariables; }
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72 | }
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73 |
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74 | [Storable]
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75 | private double[] alpha;
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76 | [Storable]
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77 | private double sqrSigmaNoise;
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78 | public double SigmaNoise {
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79 | get { return Math.Sqrt(sqrSigmaNoise); }
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80 | }
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81 |
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82 | [Storable]
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83 | private double[] meanParameter;
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84 | [Storable]
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85 | private double[] covarianceParameter;
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86 |
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87 | private double[,] l; // used to be storable in previous versions (is calculated lazily now)
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88 | private double[,] x; // scaled training dataset, used to be storable in previous versions (is calculated lazily now)
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89 |
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90 | // BackwardsCompatibility3.4
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91 | #region Backwards compatible code, remove with 3.5
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92 | [Storable(Name = "l")] // restore if available but don't store anymore
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93 | private double[,] l_storable {
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94 | set { this.l = value; }
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95 | get {
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96 | if (trainingDataset == null) return l; // this model has been created with an old version
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97 | else return null; // if the training dataset is available l should not be serialized
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98 | }
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99 | }
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100 | [Storable(Name = "x")] // restore if available but don't store anymore
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101 | private double[,] x_storable {
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102 | set { this.x = value; }
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103 | get {
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104 | if (trainingDataset == null) return x; // this model has been created with an old version
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105 | else return null; // if the training dataset is available x should not be serialized
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106 | }
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107 | }
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108 | #endregion
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109 |
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110 |
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111 | [Storable]
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112 | private IDataset trainingDataset; // it is better to store the original training dataset completely because this is more efficient in persistence
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113 | [Storable]
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114 | private int[] trainingRows;
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115 |
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116 | [Storable]
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117 | private Scaling inputScaling;
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118 |
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119 |
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120 | [StorableConstructor]
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121 | private GaussianProcessModel(bool deserializing) : base(deserializing) { }
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122 | private GaussianProcessModel(GaussianProcessModel original, Cloner cloner)
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123 | : base(original, cloner) {
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124 | this.meanFunction = cloner.Clone(original.meanFunction);
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125 | this.covarianceFunction = cloner.Clone(original.covarianceFunction);
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126 | if (original.inputScaling != null)
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127 | this.inputScaling = cloner.Clone(original.inputScaling);
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128 | this.trainingDataset = cloner.Clone(original.trainingDataset);
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129 | this.negativeLogLikelihood = original.negativeLogLikelihood;
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130 | this.sqrSigmaNoise = original.sqrSigmaNoise;
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131 | if (original.meanParameter != null) {
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132 | this.meanParameter = (double[])original.meanParameter.Clone();
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133 | }
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134 | if (original.covarianceParameter != null) {
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135 | this.covarianceParameter = (double[])original.covarianceParameter.Clone();
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136 | }
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137 |
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138 | // shallow copies of arrays because they cannot be modified
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139 | this.trainingRows = original.trainingRows;
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140 | this.allowedInputVariables = original.allowedInputVariables;
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141 | this.alpha = original.alpha;
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142 | this.l = original.l;
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143 | this.x = original.x;
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144 | }
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145 | public GaussianProcessModel(IDataset ds, string targetVariable, IEnumerable<string> allowedInputVariables, IEnumerable<int> rows,
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146 | IEnumerable<double> hyp, IMeanFunction meanFunction, ICovarianceFunction covarianceFunction,
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147 | bool scaleInputs = true)
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148 | : base(targetVariable) {
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149 | this.name = ItemName;
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150 | this.description = ItemDescription;
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151 | this.meanFunction = (IMeanFunction)meanFunction.Clone();
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152 | this.covarianceFunction = (ICovarianceFunction)covarianceFunction.Clone();
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153 | this.allowedInputVariables = allowedInputVariables.ToArray();
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154 |
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155 |
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156 | int nVariables = this.allowedInputVariables.Length;
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157 | meanParameter = hyp
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158 | .Take(this.meanFunction.GetNumberOfParameters(nVariables))
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159 | .ToArray();
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160 |
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161 | covarianceParameter = hyp.Skip(this.meanFunction.GetNumberOfParameters(nVariables))
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162 | .Take(this.covarianceFunction.GetNumberOfParameters(nVariables))
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163 | .ToArray();
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164 | sqrSigmaNoise = Math.Exp(2.0 * hyp.Last());
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165 | try {
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166 | CalculateModel(ds, rows, scaleInputs);
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167 | }
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168 | catch (alglib.alglibexception ae) {
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169 | // wrap exception so that calling code doesn't have to know about alglib implementation
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170 | throw new ArgumentException("There was a problem in the calculation of the Gaussian process model", ae);
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171 | }
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172 | }
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173 |
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174 | private void CalculateModel(IDataset ds, IEnumerable<int> rows, bool scaleInputs = true) {
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175 | this.trainingDataset = (IDataset)ds.Clone();
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176 | this.trainingRows = rows.ToArray();
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177 | this.inputScaling = scaleInputs ? new Scaling(ds, allowedInputVariables, rows) : null;
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178 |
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179 | x = GetData(ds, this.allowedInputVariables, this.trainingRows, this.inputScaling);
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180 |
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181 | IEnumerable<double> y;
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182 | y = ds.GetDoubleValues(TargetVariable, rows);
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183 |
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184 | int n = x.GetLength(0);
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185 |
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186 | var columns = Enumerable.Range(0, x.GetLength(1)).ToArray();
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187 | // calculate cholesky decomposed (lower triangular) covariance matrix
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188 | var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, columns);
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189 | this.l = CalculateL(x, cov, sqrSigmaNoise);
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190 |
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191 | // calculate mean
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192 | var mean = meanFunction.GetParameterizedMeanFunction(meanParameter, columns);
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193 | double[] m = Enumerable.Range(0, x.GetLength(0))
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194 | .Select(r => mean.Mean(x, r))
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195 | .ToArray();
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196 |
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197 | // calculate sum of diagonal elements for likelihood
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198 | double diagSum = Enumerable.Range(0, n).Select(i => Math.Log(l[i, i])).Sum();
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199 |
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200 | // solve for alpha
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201 | double[] ym = y.Zip(m, (a, b) => a - b).ToArray();
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202 |
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203 | int info;
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204 | alglib.densesolverreport denseSolveRep;
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205 |
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206 | alglib.spdmatrixcholeskysolve(l, n, false, ym, out info, out denseSolveRep, out alpha);
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207 | for (int i = 0; i < alpha.Length; i++)
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208 | alpha[i] = alpha[i] / sqrSigmaNoise;
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209 | negativeLogLikelihood = 0.5 * Util.ScalarProd(ym, alpha) + diagSum + (n / 2.0) * Math.Log(2.0 * Math.PI * sqrSigmaNoise);
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210 |
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211 | // derivatives
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212 | int nAllowedVariables = x.GetLength(1);
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213 |
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214 | alglib.matinvreport matInvRep;
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215 | double[,] lCopy = new double[l.GetLength(0), l.GetLength(1)];
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216 | Array.Copy(l, lCopy, lCopy.Length);
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217 |
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218 | alglib.spdmatrixcholeskyinverse(ref lCopy, n, false, out info, out matInvRep);
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219 | if (info != 1) throw new ArgumentException("Can't invert matrix to calculate gradients.");
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220 | for (int i = 0; i < n; i++) {
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221 | for (int j = 0; j <= i; j++)
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222 | lCopy[i, j] = lCopy[i, j] / sqrSigmaNoise - alpha[i] * alpha[j];
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223 | }
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224 |
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225 | double noiseGradient = sqrSigmaNoise * Enumerable.Range(0, n).Select(i => lCopy[i, i]).Sum();
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226 |
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227 | double[] meanGradients = new double[meanFunction.GetNumberOfParameters(nAllowedVariables)];
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228 | for (int k = 0; k < meanGradients.Length; k++) {
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229 | var meanGrad = new double[alpha.Length];
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230 | for (int g = 0; g < meanGrad.Length; g++)
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231 | meanGrad[g] = mean.Gradient(x, g, k);
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232 | meanGradients[k] = -Util.ScalarProd(meanGrad, alpha);
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233 | }
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234 |
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235 | double[] covGradients = new double[covarianceFunction.GetNumberOfParameters(nAllowedVariables)];
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236 | if (covGradients.Length > 0) {
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237 | for (int i = 0; i < n; i++) {
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238 | for (int j = 0; j < i; j++) {
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239 | var g = cov.CovarianceGradient(x, i, j);
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240 | for (int k = 0; k < covGradients.Length; k++) {
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241 | covGradients[k] += lCopy[i, j] * g[k];
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242 | }
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243 | }
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244 |
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245 | var gDiag = cov.CovarianceGradient(x, i, i);
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246 | for (int k = 0; k < covGradients.Length; k++) {
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247 | // diag
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248 | covGradients[k] += 0.5 * lCopy[i, i] * gDiag[k];
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249 | }
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250 | }
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251 | }
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252 |
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253 | hyperparameterGradients =
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254 | meanGradients
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255 | .Concat(covGradients)
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256 | .Concat(new double[] { noiseGradient }).ToArray();
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257 |
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258 | }
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259 |
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260 | private static double[,] GetData(IDataset ds, IEnumerable<string> allowedInputs, IEnumerable<int> rows, Scaling scaling) {
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261 | if (scaling != null) {
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262 | return AlglibUtil.PrepareAndScaleInputMatrix(ds, allowedInputs, rows, scaling);
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263 | } else {
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264 | return AlglibUtil.PrepareInputMatrix(ds, allowedInputs, rows);
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265 | }
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266 | }
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267 |
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268 | private static double[,] CalculateL(double[,] x, ParameterizedCovarianceFunction cov, double sqrSigmaNoise) {
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269 | int n = x.GetLength(0);
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270 | var l = new double[n, n];
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271 |
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272 | // calculate covariances
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273 | for (int i = 0; i < n; i++) {
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274 | for (int j = i; j < n; j++) {
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275 | l[j, i] = cov.Covariance(x, i, j) / sqrSigmaNoise;
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276 | if (j == i) l[j, i] += 1.0;
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277 | }
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278 | }
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279 |
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280 | // cholesky decomposition
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281 | var res = alglib.trfac.spdmatrixcholesky(ref l, n, false);
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282 | if (!res) throw new ArgumentException("Matrix is not positive semidefinite");
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283 | return l;
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284 | }
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285 |
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286 |
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287 | public override IDeepCloneable Clone(Cloner cloner) {
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288 | return new GaussianProcessModel(this, cloner);
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289 | }
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290 |
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291 | // is called by the solution creator to set all parameter values of the covariance and mean function
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292 | // to the optimized values (necessary to make the values visible in the GUI)
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293 | public void FixParameters() {
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294 | covarianceFunction.SetParameter(covarianceParameter);
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295 | meanFunction.SetParameter(meanParameter);
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296 | covarianceParameter = new double[0];
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297 | meanParameter = new double[0];
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298 | }
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299 |
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300 | #region IRegressionModel Members
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301 | public override IEnumerable<double> GetEstimatedValues(IDataset dataset, IEnumerable<int> rows) {
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302 | return GetEstimatedValuesHelper(dataset, rows);
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303 | }
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304 | public override IRegressionSolution CreateRegressionSolution(IRegressionProblemData problemData) {
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305 | return new GaussianProcessRegressionSolution(this, new RegressionProblemData(problemData));
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306 | }
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307 | #endregion
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308 |
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309 |
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310 | private IEnumerable<double> GetEstimatedValuesHelper(IDataset dataset, IEnumerable<int> rows) {
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311 | try {
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312 | if (x == null) {
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313 | x = GetData(trainingDataset, allowedInputVariables, trainingRows, inputScaling);
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314 | }
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315 | int n = x.GetLength(0);
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316 |
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317 | double[,] newX = GetData(dataset, allowedInputVariables, rows, inputScaling);
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318 | int newN = newX.GetLength(0);
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319 |
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320 | var Ks = new double[newN][];
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321 | var columns = Enumerable.Range(0, newX.GetLength(1)).ToArray();
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322 | var mean = meanFunction.GetParameterizedMeanFunction(meanParameter, columns);
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323 | var ms = Enumerable.Range(0, newX.GetLength(0))
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324 | .Select(r => mean.Mean(newX, r))
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325 | .ToArray();
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326 | var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, columns);
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327 | for (int i = 0; i < newN; i++) {
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328 | Ks[i] = new double[n];
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329 | for (int j = 0; j < n; j++) {
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330 | Ks[i][j] = cov.CrossCovariance(x, newX, j, i);
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331 | }
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332 | }
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333 |
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334 | return Enumerable.Range(0, newN)
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335 | .Select(i => ms[i] + Util.ScalarProd(Ks[i], alpha));
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336 | }
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337 | catch (alglib.alglibexception ae) {
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338 | // wrap exception so that calling code doesn't have to know about alglib implementation
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339 | throw new ArgumentException("There was a problem in the calculation of the Gaussian process model", ae);
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340 | }
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341 | }
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342 |
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343 | public IEnumerable<double> GetEstimatedVariances(IDataset dataset, IEnumerable<int> rows) {
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344 | try {
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345 | if (x == null) {
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346 | x = GetData(trainingDataset, allowedInputVariables, trainingRows, inputScaling);
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347 | }
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348 | int n = x.GetLength(0);
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349 |
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350 | var newX = GetData(dataset, allowedInputVariables, rows, inputScaling);
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351 | int newN = newX.GetLength(0);
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352 |
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353 | var kss = new double[newN];
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354 | double[,] sWKs = new double[n, newN];
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355 | var columns = Enumerable.Range(0, newX.GetLength(1)).ToArray();
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356 | var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, columns);
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357 |
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358 | if (l == null) {
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359 | l = CalculateL(x, cov, sqrSigmaNoise);
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360 | }
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361 |
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362 | // for stddev
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363 | for (int i = 0; i < newN; i++)
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364 | kss[i] = cov.Covariance(newX, i, i);
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365 |
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366 | for (int i = 0; i < newN; i++) {
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367 | for (int j = 0; j < n; j++) {
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368 | sWKs[j, i] = cov.CrossCovariance(x, newX, j, i) / Math.Sqrt(sqrSigmaNoise);
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369 | }
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370 | }
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371 |
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372 | // for stddev
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373 | alglib.ablas.rmatrixlefttrsm(n, newN, l, 0, 0, false, false, 0, ref sWKs, 0, 0);
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374 |
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375 | for (int i = 0; i < newN; i++) {
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376 | var col = Util.GetCol(sWKs, i).ToArray();
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377 | var sumV = Util.ScalarProd(col, col);
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378 | kss[i] += sqrSigmaNoise; // kss is V(f), add noise variance of predictive distibution to get V(y)
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379 | kss[i] -= sumV;
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380 | if (kss[i] < 0) kss[i] = 0;
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381 | }
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382 | return kss;
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383 | }
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384 | catch (alglib.alglibexception ae) {
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385 | // wrap exception so that calling code doesn't have to know about alglib implementation
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386 | throw new ArgumentException("There was a problem in the calculation of the Gaussian process model", ae);
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387 | }
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388 | }
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389 |
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390 | }
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391 | }
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