[13438] | 1 | #region License Information
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| 2 | /* HeuristicLab
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| 3 | * Copyright (C) 2002-2015 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("StudentTProcessModel", "Represents a Student-t process posterior.")]
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| 36 | public sealed class StudentTProcessModel : NamedItem, IGaussianProcessModel {
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| 37 | [Storable]
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| 38 | private double negativeLogLikelihood;
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| 39 | public double NegativeLogLikelihood {
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| 40 | get { return negativeLogLikelihood; }
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| 41 | }
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| 42 |
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| 43 | [Storable]
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| 44 | private double[] hyperparameterGradients;
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| 45 | public double[] HyperparameterGradients {
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| 46 | get {
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| 47 | var copy = new double[hyperparameterGradients.Length];
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| 48 | Array.Copy(hyperparameterGradients, copy, copy.Length);
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| 49 | return copy;
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| 50 | }
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| 51 | }
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| 52 |
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| 53 | [Storable]
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| 54 | private ICovarianceFunction covarianceFunction;
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| 55 | public ICovarianceFunction CovarianceFunction {
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| 56 | get { return covarianceFunction; }
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| 57 | }
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| 58 | [Storable]
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| 59 | private IMeanFunction meanFunction;
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| 60 | public IMeanFunction MeanFunction {
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| 61 | get { return meanFunction; }
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| 62 | }
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| 63 | [Storable]
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| 64 | private string targetVariable;
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| 65 | public string TargetVariable {
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| 66 | get { return targetVariable; }
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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 beta;
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| 78 |
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| 79 | public double SigmaNoise {
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| 80 | get { return 0; }
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| 81 | }
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| 82 |
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| 83 | [Storable]
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| 84 | private double[] meanParameter;
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| 85 | [Storable]
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| 86 | private double[] covarianceParameter;
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| 87 | [Storable]
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| 88 | private double nu;
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| 89 |
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| 90 | private double[,] l; // used to be storable in previous versions (is calculated lazily now)
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| 91 | private double[,] x; // scaled training dataset, used to be storable in previous versions (is calculated lazily now)
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| 92 |
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| 93 | // BackwardsCompatibility3.4
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| 94 | #region Backwards compatible code, remove with 3.5
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| 95 | [Storable(Name = "l")] // restore if available but don't store anymore
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| 96 | private double[,] l_storable {
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| 97 | set { this.l = value; }
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| 98 | get {
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| 99 | if (trainingDataset == null) return l; // this model has been created with an old version
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| 100 | else return null; // if the training dataset is available l should not be serialized
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| 101 | }
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| 102 | }
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| 103 | [Storable(Name = "x")] // restore if available but don't store anymore
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| 104 | private double[,] x_storable {
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| 105 | set { this.x = value; }
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| 106 | get {
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| 107 | if (trainingDataset == null) return x; // this model has been created with an old version
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| 108 | else return null; // if the training dataset is available x should not be serialized
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| 109 | }
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| 110 | }
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| 111 | #endregion
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| 112 |
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| 113 |
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| 114 | [Storable]
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| 115 | private IDataset trainingDataset; // it is better to store the original training dataset completely because this is more efficient in persistence
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| 116 | [Storable]
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| 117 | private int[] trainingRows;
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| 118 |
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| 119 | [Storable]
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| 120 | private Scaling inputScaling;
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| 121 |
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| 122 |
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| 123 | [StorableConstructor]
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| 124 | private StudentTProcessModel(bool deserializing) : base(deserializing) { }
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| 125 | private StudentTProcessModel(StudentTProcessModel original, Cloner cloner)
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| 126 | : base(original, cloner) {
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| 127 | this.meanFunction = cloner.Clone(original.meanFunction);
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| 128 | this.covarianceFunction = cloner.Clone(original.covarianceFunction);
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| 129 | if (original.inputScaling != null)
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| 130 | this.inputScaling = cloner.Clone(original.inputScaling);
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| 131 | this.trainingDataset = cloner.Clone(original.trainingDataset);
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| 132 | this.negativeLogLikelihood = original.negativeLogLikelihood;
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| 133 | this.targetVariable = original.targetVariable;
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| 134 | if (original.meanParameter != null) {
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| 135 | this.meanParameter = (double[])original.meanParameter.Clone();
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| 136 | }
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| 137 | if (original.covarianceParameter != null) {
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| 138 | this.covarianceParameter = (double[])original.covarianceParameter.Clone();
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| 139 | }
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| 140 | nu = original.nu;
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| 141 |
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| 142 | // shallow copies of arrays because they cannot be modified
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| 143 | this.trainingRows = original.trainingRows;
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| 144 | this.allowedInputVariables = original.allowedInputVariables;
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| 145 | this.alpha = original.alpha;
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| 146 | this.beta = original.beta;
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| 147 | this.l = original.l;
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| 148 | this.x = original.x;
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| 149 | }
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| 150 | public StudentTProcessModel(IDataset ds, string targetVariable, IEnumerable<string> allowedInputVariables, IEnumerable<int> rows,
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| 151 | IEnumerable<double> hyp, IMeanFunction meanFunction, ICovarianceFunction covarianceFunction,
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| 152 | bool scaleInputs = true)
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| 153 | : base() {
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| 154 | this.name = ItemName;
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| 155 | this.description = ItemDescription;
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| 156 | this.meanFunction = (IMeanFunction)meanFunction.Clone();
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| 157 | this.covarianceFunction = (ICovarianceFunction)covarianceFunction.Clone();
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| 158 | this.targetVariable = targetVariable;
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| 159 | this.allowedInputVariables = allowedInputVariables.ToArray();
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| 160 |
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| 161 |
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| 162 | int nVariables = this.allowedInputVariables.Length;
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| 163 | meanParameter = hyp
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| 164 | .Take(this.meanFunction.GetNumberOfParameters(nVariables))
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| 165 | .ToArray();
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| 166 |
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| 167 | covarianceParameter = hyp.Skip(meanParameter.Length)
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| 168 | .Take(this.covarianceFunction.GetNumberOfParameters(nVariables))
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| 169 | .ToArray();
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| 170 | nu = Math.Exp(hyp.Skip(meanParameter.Length + covarianceParameter.Length).First()) + 2; //TODO check gradient
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| 171 | try {
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| 172 | CalculateModel(ds, rows, scaleInputs);
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[13721] | 173 | }
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| 174 | catch (alglib.alglibexception ae) {
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[13438] | 175 | // wrap exception so that calling code doesn't have to know about alglib implementation
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| 176 | throw new ArgumentException("There was a problem in the calculation of the Gaussian process model", ae);
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| 177 | }
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| 178 | }
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| 179 |
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| 180 | private void CalculateModel(IDataset ds, IEnumerable<int> rows, bool scaleInputs = true) {
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| 181 | this.trainingDataset = (IDataset)ds.Clone();
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| 182 | this.trainingRows = rows.ToArray();
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| 183 | this.inputScaling = scaleInputs ? new Scaling(ds, allowedInputVariables, rows) : null;
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| 184 |
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| 185 | x = GetData(ds, this.allowedInputVariables, this.trainingRows, this.inputScaling);
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| 186 |
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| 187 | IEnumerable<double> y;
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| 188 | y = ds.GetDoubleValues(targetVariable, rows);
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| 189 |
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| 190 | int n = x.GetLength(0);
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[13721] | 191 | var columns = Enumerable.Range(0, x.GetLength(1)).ToArray();
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[13438] | 192 |
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| 193 | // calculate cholesky decomposed (lower triangular) covariance matrix
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[13721] | 194 | var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, columns);
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[13438] | 195 | this.l = CalculateL(x, cov);
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| 196 |
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| 197 | // calculate mean
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[13721] | 198 | var mean = meanFunction.GetParameterizedMeanFunction(meanParameter, columns);
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[13438] | 199 | double[] m = Enumerable.Range(0, x.GetLength(0))
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| 200 | .Select(r => mean.Mean(x, r))
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| 201 | .ToArray();
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| 202 |
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| 203 | // calculate sum of diagonal elements for likelihood
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| 204 | double diagSum = Enumerable.Range(0, n).Select(i => Math.Log(l[i, i])).Sum();
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| 205 |
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| 206 | // solve for alpha
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| 207 | double[] ym = y.Zip(m, (a, b) => a - b).ToArray();
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| 208 |
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| 209 | int info;
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| 210 | alglib.densesolverreport denseSolveRep;
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| 211 |
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| 212 | alglib.spdmatrixcholeskysolve(l, n, false, ym, out info, out denseSolveRep, out alpha);
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| 213 |
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| 214 | beta = Util.ScalarProd(ym, alpha);
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| 215 | double sign0, sign1;
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| 216 | double lngamma0 = alglib.lngamma(0.5 * (nu + n), out sign0);
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| 217 | lngamma0 *= sign0;
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| 218 | double lngamma1 = alglib.lngamma(0.5 * nu, out sign1);
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| 219 | lngamma1 *= sign1;
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| 220 | negativeLogLikelihood =
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| 221 | 0.5 * n * Math.Log((nu - 2) * Math.PI) +
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| 222 | diagSum +
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| 223 | -lngamma0 + lngamma1 +
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| 224 | //-Math.Log(alglib.gammafunction((n + nu) / 2) / alglib.gammafunction(nu / 2)) +
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| 225 | 0.5 * (nu + n) * Math.Log(1 + beta / (nu - 2));
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| 226 |
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| 227 | // derivatives
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| 228 | int nAllowedVariables = x.GetLength(1);
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| 229 |
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| 230 | alglib.matinvreport matInvRep;
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| 231 | double[,] lCopy = new double[l.GetLength(0), l.GetLength(1)];
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| 232 | Array.Copy(l, lCopy, lCopy.Length);
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| 233 |
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| 234 | alglib.spdmatrixcholeskyinverse(ref lCopy, n, false, out info, out matInvRep);
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| 235 | double c = (nu + n) / (nu + beta - 2);
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| 236 | if (info != 1) throw new ArgumentException("Can't invert matrix to calculate gradients.");
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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 | lCopy[i, j] = lCopy[i, j] - c * alpha[i] * alpha[j];
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| 240 | }
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| 241 |
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| 242 | double[] meanGradients = new double[meanFunction.GetNumberOfParameters(nAllowedVariables)];
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| 243 | for (int k = 0; k < meanGradients.Length; k++) {
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[13721] | 244 | var meanGrad = new double[alpha.Length];
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| 245 | for (int g = 0; g < meanGrad.Length; g++)
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| 246 | meanGrad[g] = mean.Gradient(x, g, k);
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| 247 | meanGradients[k] = -Util.ScalarProd(meanGrad, alpha);//TODO not working yet, try to fix with gradient check
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[13438] | 248 | }
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| 249 |
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| 250 | double[] covGradients = new double[covarianceFunction.GetNumberOfParameters(nAllowedVariables)];
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| 251 | if (covGradients.Length > 0) {
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| 252 | for (int i = 0; i < n; i++) {
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| 253 | for (int j = 0; j < i; j++) {
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| 254 | var g = cov.CovarianceGradient(x, i, j).ToArray();
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| 255 | for (int k = 0; k < covGradients.Length; k++) {
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| 256 | covGradients[k] += lCopy[i, j] * g[k];
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| 257 | }
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| 258 | }
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| 259 |
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| 260 | var gDiag = cov.CovarianceGradient(x, i, i).ToArray();
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| 261 | for (int k = 0; k < covGradients.Length; k++) {
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| 262 | // diag
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| 263 | covGradients[k] += 0.5 * lCopy[i, i] * gDiag[k];
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| 264 | }
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| 265 | }
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| 266 | }
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| 267 |
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| 268 | double nuGradient = 0.5 * n
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| 269 | - 0.5 * (nu - 2) * alglib.psi((n + nu) / 2) + 0.5 * (nu - 2) * alglib.psi(nu / 2)
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| 270 | + 0.5 * (nu - 2) * Math.Log(1 + beta / (nu - 2)) - beta * (n + nu) / (2 * (beta + (nu - 2)));
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| 271 |
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| 272 | //nuGradient = (nu-2) * nuGradient;
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| 273 | hyperparameterGradients =
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| 274 | meanGradients
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| 275 | .Concat(covGradients)
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| 276 | .Concat(new double[] { nuGradient }).ToArray();
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| 277 |
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| 278 | }
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| 279 |
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| 280 | private static double[,] GetData(IDataset ds, IEnumerable<string> allowedInputs, IEnumerable<int> rows, Scaling scaling) {
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| 281 | if (scaling != null) {
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| 282 | return AlglibUtil.PrepareAndScaleInputMatrix(ds, allowedInputs, rows, scaling);
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| 283 | } else {
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| 284 | return AlglibUtil.PrepareInputMatrix(ds, allowedInputs, rows);
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| 285 | }
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| 286 | }
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| 287 |
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| 288 | private static double[,] CalculateL(double[,] x, ParameterizedCovarianceFunction cov) {
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| 289 | int n = x.GetLength(0);
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| 290 | var l = new double[n, n];
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| 291 |
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| 292 | // calculate covariances
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| 293 | for (int i = 0; i < n; i++) {
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| 294 | for (int j = i; j < n; j++) {
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| 295 | l[j, i] = cov.Covariance(x, i, j);
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| 296 | }
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| 297 | }
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| 298 |
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| 299 | // cholesky decomposition
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| 300 | var res = alglib.trfac.spdmatrixcholesky(ref l, n, false);
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| 301 | if (!res) throw new ArgumentException("Matrix is not positive semidefinite");
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| 302 | return l;
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| 303 | }
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| 304 |
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| 305 |
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| 306 | public override IDeepCloneable Clone(Cloner cloner) {
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| 307 | return new StudentTProcessModel(this, cloner);
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| 308 | }
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| 309 |
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| 310 | // is called by the solution creator to set all parameter values of the covariance and mean function
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| 311 | // to the optimized values (necessary to make the values visible in the GUI)
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| 312 | public void FixParameters() {
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| 313 | covarianceFunction.SetParameter(covarianceParameter);
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| 314 | meanFunction.SetParameter(meanParameter);
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| 315 | covarianceParameter = new double[0];
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| 316 | meanParameter = new double[0];
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| 317 | }
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| 318 |
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| 319 | #region IRegressionModel Members
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| 320 | public IEnumerable<double> GetEstimatedValues(IDataset dataset, IEnumerable<int> rows) {
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| 321 | return GetEstimatedValuesHelper(dataset, rows);
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| 322 | }
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| 323 | public GaussianProcessRegressionSolution CreateRegressionSolution(IRegressionProblemData problemData) {
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| 324 | return new GaussianProcessRegressionSolution(this, new RegressionProblemData(problemData));
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| 325 | }
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| 326 | IRegressionSolution IRegressionModel.CreateRegressionSolution(IRegressionProblemData problemData) {
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| 327 | return CreateRegressionSolution(problemData);
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| 328 | }
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| 329 | #endregion
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| 330 |
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| 331 |
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| 332 | private IEnumerable<double> GetEstimatedValuesHelper(IDataset dataset, IEnumerable<int> rows) {
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| 333 | try {
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| 334 | if (x == null) {
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| 335 | x = GetData(trainingDataset, allowedInputVariables, trainingRows, inputScaling);
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| 336 | }
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| 337 | int n = x.GetLength(0);
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| 338 |
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| 339 | double[,] newX = GetData(dataset, allowedInputVariables, rows, inputScaling);
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| 340 | int newN = newX.GetLength(0);
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[13721] | 341 | var columns = Enumerable.Range(0, newX.GetLength(1)).ToArray();
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[13438] | 342 |
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[13721] | 343 | var Ks = new double[newN][];
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| 344 | var mean = meanFunction.GetParameterizedMeanFunction(meanParameter, columns);
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[13438] | 345 | var ms = Enumerable.Range(0, newX.GetLength(0))
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| 346 | .Select(r => mean.Mean(newX, r))
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| 347 | .ToArray();
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[13721] | 348 | var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, columns);
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[13438] | 349 | for (int i = 0; i < newN; i++) {
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[13721] | 350 | Ks[i] = new double[n];
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[13438] | 351 | for (int j = 0; j < n; j++) {
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[13721] | 352 | Ks[i][j] = cov.CrossCovariance(x, newX, j, i);
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[13438] | 353 | }
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| 354 | }
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| 355 |
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| 356 | return Enumerable.Range(0, newN)
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[13721] | 357 | .Select(i => ms[i] + Util.ScalarProd(Ks[i], alpha));
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| 358 | }
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| 359 | catch (alglib.alglibexception ae) {
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[13438] | 360 | // wrap exception so that calling code doesn't have to know about alglib implementation
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| 361 | throw new ArgumentException("There was a problem in the calculation of the Gaussian process model", ae);
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| 362 | }
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| 363 | }
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| 364 |
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| 365 | public IEnumerable<double> GetEstimatedVariance(IDataset dataset, IEnumerable<int> rows) {
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| 366 | try {
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| 367 | if (x == null) {
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| 368 | x = GetData(trainingDataset, allowedInputVariables, trainingRows, inputScaling);
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| 369 | }
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| 370 | int n = x.GetLength(0);
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| 371 |
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| 372 | var newX = GetData(dataset, allowedInputVariables, rows, inputScaling);
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| 373 | int newN = newX.GetLength(0);
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| 374 |
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| 375 | var kss = new double[newN];
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| 376 | double[,] sWKs = new double[n, newN];
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[13721] | 377 | var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, Enumerable.Range(0, x.GetLength(1)).ToArray());
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| 378 |
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[13438] | 379 | if (l == null) {
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| 380 | l = CalculateL(x, cov);
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| 381 | }
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[13721] | 382 |
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[13438] | 383 | // for stddev
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| 384 | for (int i = 0; i < newN; i++)
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| 385 | kss[i] = cov.Covariance(newX, i, i);
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[13721] | 386 |
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[13438] | 387 | for (int i = 0; i < newN; i++) {
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| 388 | for (int j = 0; j < n; j++) {
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[13721] | 389 | sWKs[j, i] = cov.CrossCovariance(x, newX, j, i);
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[13438] | 390 | }
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| 391 | }
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[13721] | 392 |
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[13438] | 393 | // for stddev
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| 394 | alglib.ablas.rmatrixlefttrsm(n, newN, l, 0, 0, false, false, 0, ref sWKs, 0, 0);
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[13721] | 395 |
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[13438] | 396 | for (int i = 0; i < newN; i++) {
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[13721] | 397 | var col = Util.GetCol(sWKs, i).ToArray();
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| 398 | var sumV = Util.ScalarProd(col, col);
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[13438] | 399 | kss[i] -= sumV;
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[13721] | 400 | kss[i] *= (nu + beta - 2) / (nu + n - 2);
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[13438] | 401 | if (kss[i] < 0) kss[i] = 0;
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| 402 | }
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| 403 | return kss;
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[13721] | 404 | }
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| 405 | catch (alglib.alglibexception ae) {
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[13438] | 406 | // wrap exception so that calling code doesn't have to know about alglib implementation
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| 407 | throw new ArgumentException("There was a problem in the calculation of the Gaussian process model", ae);
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| 408 | }
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| 409 | }
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| 410 | }
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| 411 | }
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