[14630] | 1 | #region License Information
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| 2 | /* HeuristicLab
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[16140] | 3 | * Copyright (C) 2002-2018 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
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[14630] | 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.Core;
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| 26 | using HeuristicLab.Problems.DataAnalysis;
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| 27 | using HeuristicLab.Random;
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| 28 |
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| 29 | namespace HeuristicLab.Problems.Instances.DataAnalysis {
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| 30 | public sealed class GaussianProcessVariableNetwork : VariableNetwork {
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| 31 | private int numberOfFeatures;
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| 32 | private double noiseRatio;
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| 33 |
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| 34 | public override string Name { get { return string.Format("GaussianProcessVariableNetwork-{0:0%} ({1} dim)", noiseRatio, numberOfFeatures); } }
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| 35 |
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| 36 | public GaussianProcessVariableNetwork(int numberOfFeatures, double noiseRatio,
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| 37 | IRandom rand)
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| 38 | : base(250, 250, numberOfFeatures, noiseRatio, rand) {
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| 39 | this.noiseRatio = noiseRatio;
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| 40 | this.numberOfFeatures = numberOfFeatures;
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| 41 | }
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| 42 |
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| 43 | // sample the input variables that are actually used and sample from a Gaussian process
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| 44 | protected override IEnumerable<double> GenerateRandomFunction(IRandom rand, List<List<double>> xs, out string[] selectedVarNames, out double[] relevance) {
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| 45 | int nl = SampleNumberOfVariables(rand, xs.Count);
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| 46 |
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| 47 | var selectedIdx = Enumerable.Range(0, xs.Count).Shuffle(rand)
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| 48 | .Take(nl).ToArray();
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| 49 |
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| 50 | var selectedVars = selectedIdx.Select(i => xs[i]).ToArray();
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| 51 | selectedVarNames = selectedIdx.Select(i => VariableNames[i]).ToArray();
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| 52 | return SampleGaussianProcess(rand, selectedVars, out relevance);
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| 53 | }
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| 54 |
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| 55 | private IEnumerable<double> SampleGaussianProcess(IRandom rand, List<double>[] xs, out double[] relevance) {
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| 56 | int nl = xs.Length;
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| 57 | int nRows = xs.First().Count;
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| 58 |
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| 59 | // sample u iid ~ N(0, 1)
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| 60 | var u = Enumerable.Range(0, nRows).Select(_ => NormalDistributedRandom.NextDouble(rand, 0, 1)).ToArray();
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| 61 |
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| 62 | // sample actual length-scales
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| 63 | var l = Enumerable.Range(0, nl)
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| 64 | .Select(_ => rand.NextDouble() * 2 + 0.5)
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| 65 | .ToArray();
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| 66 |
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| 67 | double[,] K = CalculateCovariance(xs, l);
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| 68 |
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| 69 | // decompose
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| 70 | alglib.trfac.spdmatrixcholesky(ref K, nRows, false);
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| 71 |
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| 72 |
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| 73 | // calc y = Lu
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| 74 | var y = new double[u.Length];
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| 75 | alglib.ablas.rmatrixmv(nRows, nRows, K, 0, 0, 0, u, 0, ref y, 0);
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| 76 |
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| 77 | // calculate relevance by removing dimensions
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| 78 | relevance = CalculateRelevance(y, u, xs, l);
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| 79 |
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| 80 | return y;
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| 81 | }
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| 82 |
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| 83 | // calculate variable relevance based on removal of variables
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| 84 | // 1) to remove a variable we set it's length scale to infinity (no relation of the variable value to the target)
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| 85 | // 2) calculate MSE of the original target values (y) to the updated targes y' (after variable removal)
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| 86 | // 3) relevance is larger if MSE(y,y') is large
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| 87 | // 4) scale impacts so that the most important variable has impact = 1
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| 88 | private double[] CalculateRelevance(double[] y, double[] u, List<double>[] xs, double[] l) {
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| 89 | int nRows = xs.First().Count;
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| 90 | var changedL = new double[l.Length];
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| 91 | var relevance = new double[l.Length];
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| 92 | for(int i = 0; i < l.Length; i++) {
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| 93 | Array.Copy(l, changedL, changedL.Length);
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| 94 | changedL[i] = double.MaxValue;
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| 95 | var changedK = CalculateCovariance(xs, changedL);
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| 96 |
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| 97 | var yChanged = new double[u.Length];
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| 98 | alglib.ablas.rmatrixmv(nRows, nRows, changedK, 0, 0, 0, u, 0, ref yChanged, 0);
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| 99 |
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| 100 | OnlineCalculatorError error;
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| 101 | var mse = OnlineMeanSquaredErrorCalculator.Calculate(y, yChanged, out error);
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| 102 | if(error != OnlineCalculatorError.None) mse = double.MaxValue;
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| 103 | relevance[i] = mse;
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| 104 | }
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| 105 | // scale so that max relevance is 1.0
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| 106 | var maxRel = relevance.Max();
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| 107 | for(int i = 0; i < relevance.Length; i++) relevance[i] /= maxRel;
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| 108 | return relevance;
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| 109 | }
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| 110 |
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| 111 | private double[,] CalculateCovariance(List<double>[] xs, double[] l) {
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| 112 | int nRows = xs.First().Count;
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| 113 | double[,] K = new double[nRows, nRows];
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| 114 | for(int r = 0; r < nRows; r++) {
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| 115 | double[] xi = xs.Select(x => x[r]).ToArray();
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| 116 | for(int c = 0; c <= r; c++) {
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| 117 | double[] xj = xs.Select(x => x[c]).ToArray();
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| 118 | double dSqr = xi.Zip(xj, (xik, xjk) => (xik - xjk))
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| 119 | .Select(dk => dk * dk)
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| 120 | .Zip(l, (dk, lk) => dk / lk)
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| 121 | .Sum();
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| 122 | K[r, c] = Math.Exp(-dSqr);
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| 123 | }
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| 124 | }
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| 125 | // add a small diagonal matrix for numeric stability
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| 126 | for(int i = 0; i < nRows; i++) {
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| 127 | K[i, i] += 1.0E-7;
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| 128 | }
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| 129 |
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| 130 | return K;
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| 131 | }
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| 132 | }
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| 133 | }
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