[14872] | 1 | #region License Information
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[14386] | 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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[14888] | 23 | using System.Collections.Generic;
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[14386] | 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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[15249] | 30 | namespace HeuristicLab.Algorithms.DataAnalysis {
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[14386] | 31 | [StorableClass]
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[14887] | 32 | [Item("KernelRidgeRegressionModel", "A kernel ridge regression model")]
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| 33 | public sealed class KernelRidgeRegressionModel : RegressionModel {
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[14892] | 34 | public override IEnumerable<string> VariablesUsedForPrediction {
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[14386] | 35 | get { return allowedInputVariables; }
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| 36 | }
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| 37 |
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| 38 | [Storable]
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[14872] | 39 | private readonly string[] allowedInputVariables;
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[14892] | 40 | public string[] AllowedInputVariables {
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[15249] | 41 | get { return allowedInputVariables.ToArray(); }
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[14386] | 42 | }
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| 43 |
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[14888] | 44 |
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[14386] | 45 | [Storable]
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[14888] | 46 | public double LooCvRMSE { get; private set; }
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| 47 |
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| 48 | [Storable]
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[14872] | 49 | private readonly double[] alpha;
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| 50 |
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[14386] | 51 | [Storable]
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[14872] | 52 | private readonly double[,] trainX; // it is better to store the original training dataset completely because this is more efficient in persistence
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| 53 |
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[14386] | 54 | [Storable]
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[14872] | 55 | private readonly ITransformation<double>[] scaling;
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| 56 |
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[14386] | 57 | [Storable]
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[14872] | 58 | private readonly ICovarianceFunction kernel;
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| 59 |
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[14887] | 60 | [Storable]
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| 61 | private readonly double lambda;
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[14872] | 62 |
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[14386] | 63 | [Storable]
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[14888] | 64 | private readonly double yOffset; // implementation works for zero-mean, unit-variance target variables
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[14386] | 65 |
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[14887] | 66 | [Storable]
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| 67 | private readonly double yScale;
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| 68 |
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[14386] | 69 | [StorableConstructor]
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[14887] | 70 | private KernelRidgeRegressionModel(bool deserializing) : base(deserializing) { }
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| 71 | private KernelRidgeRegressionModel(KernelRidgeRegressionModel original, Cloner cloner)
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[14386] | 72 | : base(original, cloner) {
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| 73 | // shallow copies of arrays because they cannot be modified
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| 74 | allowedInputVariables = original.allowedInputVariables;
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| 75 | alpha = original.alpha;
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[14872] | 76 | trainX = original.trainX;
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| 77 | scaling = original.scaling;
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[14887] | 78 | lambda = original.lambda;
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[14888] | 79 | LooCvRMSE = original.LooCvRMSE;
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[14872] | 80 |
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[14887] | 81 | yOffset = original.yOffset;
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| 82 | yScale = original.yScale;
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[15249] | 83 | kernel = original.kernel;
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[14386] | 84 | }
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[14887] | 85 | public override IDeepCloneable Clone(Cloner cloner) {
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| 86 | return new KernelRidgeRegressionModel(this, cloner);
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| 87 | }
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| 88 |
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[15249] | 89 | public static KernelRidgeRegressionModel Create(IDataset dataset, string targetVariable, IEnumerable<string> allowedInputVariables, IEnumerable<int> rows,
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| 90 | bool scaleInputs, ICovarianceFunction kernel, double lambda = 0.1) {
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[14872] | 91 | var trainingRows = rows.ToArray();
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[15249] | 92 | var model = new KernelRidgeRegressionModel(dataset, targetVariable, allowedInputVariables, trainingRows, scaleInputs, kernel, lambda);
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| 93 |
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[14386] | 94 | try {
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| 95 | int info;
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[15249] | 96 | int n = model.trainX.GetLength(0);
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[14887] | 97 | alglib.densesolverreport denseSolveRep;
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[15249] | 98 | var gram = BuildGramMatrix(model.trainX, lambda, kernel);
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| 99 | var l = new double[n, n];
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| 100 | Array.Copy(gram, l, l.Length);
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[14872] | 101 |
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[15249] | 102 | double[] alpha = new double[n];
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[14891] | 103 | double[,] invG;
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[15249] | 104 | var y = dataset.GetDoubleValues(targetVariable, trainingRows).ToArray();
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| 105 | for (int i = 0; i < y.Length; i++) {
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| 106 | y[i] -= model.yOffset;
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| 107 | y[i] *= model.yScale;
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| 108 | }
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[14887] | 109 | // cholesky decomposition
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[14888] | 110 | var res = alglib.trfac.spdmatrixcholesky(ref l, n, false);
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[15249] | 111 | if (res == false) { //try lua decomposition if cholesky faild
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[14891] | 112 | int[] pivots;
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| 113 | var lua = new double[n, n];
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| 114 | Array.Copy(gram, lua, lua.Length);
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| 115 | alglib.rmatrixlu(ref lua, n, n, out pivots);
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| 116 | alglib.rmatrixlusolve(lua, pivots, n, y, out info, out denseSolveRep, out alpha);
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| 117 | if (info != 1) throw new ArgumentException("Could not create model.");
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| 118 | alglib.matinvreport rep;
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| 119 | invG = lua; // rename
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| 120 | alglib.rmatrixluinverse(ref invG, pivots, n, out info, out rep);
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| 121 | } else {
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| 122 | alglib.spdmatrixcholeskysolve(l, n, false, y, out info, out denseSolveRep, out alpha);
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| 123 | if (info != 1) throw new ArgumentException("Could not create model.");
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[14888] | 124 | // for LOO-CV we need to build the inverse of the gram matrix
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| 125 | alglib.matinvreport rep;
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[14891] | 126 | invG = l; // rename
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| 127 | alglib.spdmatrixcholeskyinverse(ref invG, n, false, out info, out rep);
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[14888] | 128 | }
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[15249] | 129 | if (info != 1) throw new ArgumentException("Could not invert Gram matrix.");
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[14891] | 130 |
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| 131 | var ssqLooError = 0.0;
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| 132 | for (int i = 0; i < n; i++) {
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| 133 | var pred_i = Util.ScalarProd(Util.GetRow(gram, i).ToArray(), alpha);
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| 134 | var looPred_i = pred_i - alpha[i] / invG[i, i];
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[15249] | 135 | var error = (y[i] - looPred_i) / model.yScale;
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[14891] | 136 | ssqLooError += error * error;
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| 137 | }
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[15249] | 138 |
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| 139 | Array.Copy(alpha, model.alpha, n);
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| 140 | model.LooCvRMSE = Math.Sqrt(ssqLooError / n);
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[14892] | 141 | } catch (alglib.alglibexception ae) {
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[14386] | 142 | // wrap exception so that calling code doesn't have to know about alglib implementation
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[14887] | 143 | throw new ArgumentException("There was a problem in the calculation of the kernel ridge regression model", ae);
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[14386] | 144 | }
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[15249] | 145 | return model;
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[14386] | 146 | }
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[14872] | 147 |
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[15249] | 148 | private KernelRidgeRegressionModel(IDataset dataset, string targetVariable, IEnumerable<string> allowedInputVariables, int[] rows,
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| 149 | bool scaleInputs, ICovarianceFunction kernel, double lambda = 0.1) : base(targetVariable) {
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| 150 | this.allowedInputVariables = allowedInputVariables.ToArray();
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| 151 | if (kernel.GetNumberOfParameters(this.allowedInputVariables.Length) > 0) throw new ArgumentException("All parameters in the kernel function must be specified.");
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| 152 | name = ItemName;
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| 153 | description = ItemDescription;
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[14887] | 154 |
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[15249] | 155 | this.kernel = (ICovarianceFunction)kernel.Clone();
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| 156 | this.lambda = lambda;
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| 157 | if (scaleInputs) scaling = CreateScaling(dataset, rows, this.allowedInputVariables);
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| 158 | trainX = ExtractData(dataset, rows, this.allowedInputVariables, scaling);
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| 159 | var y = dataset.GetDoubleValues(targetVariable, rows).ToArray();
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| 160 | yOffset = y.Average();
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| 161 | yScale = 1.0 / y.StandardDeviation();
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| 162 | alpha = new double[trainX.GetLength(0)];
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| 163 | }
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| 164 |
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| 165 |
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[14887] | 166 | #region IRegressionModel Members
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| 167 | public override IEnumerable<double> GetEstimatedValues(IDataset dataset, IEnumerable<int> rows) {
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[15249] | 168 | var newX = ExtractData(dataset, rows, allowedInputVariables, scaling);
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[14887] | 169 | var dim = newX.GetLength(1);
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| 170 | var cov = kernel.GetParameterizedCovarianceFunction(new double[0], Enumerable.Range(0, dim).ToArray());
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| 171 |
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| 172 | var pred = new double[newX.GetLength(0)];
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| 173 | for (int i = 0; i < pred.Length; i++) {
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| 174 | double sum = 0.0;
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| 175 | for (int j = 0; j < alpha.Length; j++) {
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| 176 | sum += alpha[j] * cov.CrossCovariance(trainX, newX, j, i);
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| 177 | }
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| 178 | pred[i] = sum / yScale + yOffset;
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| 179 | }
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| 180 | return pred;
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| 181 | }
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| 182 | public override IRegressionSolution CreateRegressionSolution(IRegressionProblemData problemData) {
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| 183 | return new RegressionSolution(this, new RegressionProblemData(problemData));
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| 184 | }
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| 185 | #endregion
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| 186 |
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| 187 | #region helpers
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[15249] | 188 | private static double[,] BuildGramMatrix(double[,] data, double lambda, ICovarianceFunction kernel) {
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[14887] | 189 | var n = data.GetLength(0);
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| 190 | var dim = data.GetLength(1);
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| 191 | var cov = kernel.GetParameterizedCovarianceFunction(new double[0], Enumerable.Range(0, dim).ToArray());
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| 192 | var gram = new double[n, n];
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| 193 | // G = (K + λ I)
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| 194 | for (var i = 0; i < n; i++) {
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| 195 | for (var j = i; j < n; j++) {
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[14888] | 196 | gram[i, j] = gram[j, i] = cov.Covariance(data, i, j); // symmetric matrix
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[14887] | 197 | }
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| 198 | gram[i, i] += lambda;
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| 199 | }
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| 200 | return gram;
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| 201 | }
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| 202 |
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[15249] | 203 | private static ITransformation<double>[] CreateScaling(IDataset dataset, int[] rows, IReadOnlyCollection<string> allowedInputVariables) {
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| 204 | var trans = new ITransformation<double>[allowedInputVariables.Count];
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[14872] | 205 | int i = 0;
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| 206 | foreach (var variable in allowedInputVariables) {
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| 207 | var lin = new LinearTransformation(allowedInputVariables);
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| 208 | var max = dataset.GetDoubleValues(variable, rows).Max();
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| 209 | var min = dataset.GetDoubleValues(variable, rows).Min();
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| 210 | lin.Multiplier = 1.0 / (max - min);
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| 211 | lin.Addend = -min / (max - min);
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| 212 | trans[i] = lin;
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| 213 | i++;
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| 214 | }
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| 215 | return trans;
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[14386] | 216 | }
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| 217 |
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[15249] | 218 | private static double[,] ExtractData(IDataset dataset, IEnumerable<int> rows, IReadOnlyCollection<string> allowedInputVariables, ITransformation<double>[] scaling = null) {
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[14872] | 219 | double[][] variables;
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| 220 | if (scaling != null) {
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| 221 | variables =
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| 222 | allowedInputVariables.Select((var, i) => scaling[i].Apply(dataset.GetDoubleValues(var, rows)).ToArray())
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| 223 | .ToArray();
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| 224 | } else {
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| 225 | variables =
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| 226 | allowedInputVariables.Select(var => dataset.GetDoubleValues(var, rows).ToArray()).ToArray();
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| 227 | }
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| 228 | int n = variables.First().Length;
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| 229 | var res = new double[n, variables.Length];
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| 230 | for (int r = 0; r < n; r++)
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| 231 | for (int c = 0; c < variables.Length; c++) {
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| 232 | res[r, c] = variables[c][r];
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| 233 | }
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| 234 | return res;
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| 235 | }
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[14386] | 236 | #endregion
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| 237 | }
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| 238 | }
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