1  #region License Information


2  /* HeuristicLab


3  * Copyright (C) 20022015 Heuristic and Evolutionary Algorithms Laboratory (HEAL)


4  *


5  * This file is part of HeuristicLab.


6  *


7  * HeuristicLab is free software: you can redistribute it and/or modify


8  * it under the terms of the GNU General Public License as published by


9  * the Free Software Foundation, either version 3 of the License, or


10  * (at your option) any later version.


11  *


12  * HeuristicLab is distributed in the hope that it will be useful,


13  * but WITHOUT ANY WARRANTY; without even the implied warranty of


14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the


15  * GNU General Public License for more details.


16  *


17  * You should have received a copy of the GNU General Public License


18  * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.


19  */


20  #endregion


21 


22  using System;


23  using System.Collections.Generic;


24  using System.Linq;


25  using System.Text;


26  using HeuristicLab.Common;


27  using HeuristicLab.Core;


28  using HeuristicLab.Random;


29 


30  namespace HeuristicLab.Problems.Instances.DataAnalysis {


31  public class VariableNetwork : ArtificialRegressionDataDescriptor {


32  private int nTrainingSamples;


33  private int nTestSamples;


34 


35  private int numberOfFeatures;


36  private double noiseRatio;


37  private IRandom random;


38 


39  public override string Name { get { return string.Format("VariableNetwork{0:0%} ({1} dim)", noiseRatio, numberOfFeatures); } }


40  private string networkDefinition;


41  public string NetworkDefinition { get { return networkDefinition; } }


42  public override string Description {


43  get {


44  return "The data are generated specifically to test methods for variable network analysis.";


45  }


46  }


47 


48  public VariableNetwork(int numberOfFeatures, double noiseRatio,


49  IRandom rand)


50  : this(250, 250, numberOfFeatures, noiseRatio, rand) { }


51 


52  public VariableNetwork(int nTrainingSamples, int nTestSamples,


53  int numberOfFeatures, double noiseRatio, IRandom rand) {


54  this.nTrainingSamples = nTrainingSamples;


55  this.nTestSamples = nTestSamples;


56  this.noiseRatio = noiseRatio;


57  this.random = rand;


58  this.numberOfFeatures = numberOfFeatures;


59  // default variable names


60  variableNames = Enumerable.Range(1, numberOfFeatures)


61  .Select(i => string.Format("X{0:000}", i))


62  .ToArray();


63  }


64 


65  private string[] variableNames;


66  protected override string[] VariableNames {


67  get {


68  return variableNames;


69  }


70  }


71 


72  // there is no specific target variable in variable network analysis but we still need to specify one


73  protected override string TargetVariable { get { return VariableNames.Last(); } }


74 


75  protected override string[] AllowedInputVariables {


76  get {


77  return VariableNames.Take(numberOfFeatures  1).ToArray();


78  }


79  }


80 


81  protected override int TrainingPartitionStart { get { return 0; } }


82  protected override int TrainingPartitionEnd { get { return nTrainingSamples; } }


83  protected override int TestPartitionStart { get { return nTrainingSamples; } }


84  protected override int TestPartitionEnd { get { return nTrainingSamples + nTestSamples; } }


85 


86 


87  protected override List<List<double>> GenerateValues() {


88  // var shuffledIdx = Enumerable.Range(0, numberOfFeatures).Shuffle(random).ToList();


89 


90  // variable names are shuffled in the beginning (and sorted at the end)


91  variableNames = variableNames.Shuffle(random).ToArray();


92 


93  // a third of all variables are independen vars


94  List<List<double>> lvl0 = new List<List<double>>();


95  int numLvl0 = (int)Math.Ceiling(numberOfFeatures * 0.33);


96 


97  List<string> description = new List<string>(); // store information how the variable is actually produced


98 


99  var nrand = new NormalDistributedRandom(random, 0, 1);


100  for (int c = 0; c < numLvl0; c++) {


101  var datai = Enumerable.Range(0, TestPartitionEnd).Select(_ => nrand.NextDouble()).ToList();


102  description.Add("~ N(0, 1)");


103  lvl0.Add(datai);


104  }


105 


106  // lvl1 contains variables which are functions of vars in lvl0 (+ noise)


107  List<List<double>> lvl1 = new List<List<double>>();


108  int numLvl1 = (int)Math.Ceiling(numberOfFeatures * 0.33);


109  for (int c = 0; c < numLvl1; c++) {


110  string desc;


111  var x = GenerateRandomFunction(random, lvl0, out desc);


112  var sigma = x.StandardDeviation();


113  var noisePrng = new NormalDistributedRandom(random, 0, sigma * Math.Sqrt(noiseRatio / (1.0  noiseRatio)));


114  lvl1.Add(x.Select(t => t + noisePrng.NextDouble()).ToList());


115  description.Add(string.Format(" ~ N({0}, {1:N3})", desc, noisePrng.Sigma));


116  }


117 


118  // lvl2 contains variables which are functions of vars in lvl0 and lvl1 (+ noise)


119  List<List<double>> lvl2 = new List<List<double>>();


120  int numLvl2 = (int)Math.Ceiling(numberOfFeatures * 0.2);


121  for (int c = 0; c < numLvl2; c++) {


122  string desc;


123  var x = GenerateRandomFunction(random, lvl0.Concat(lvl1).ToList(), out desc);


124  var sigma = x.StandardDeviation();


125  var noisePrng = new NormalDistributedRandom(random, 0, sigma * Math.Sqrt(noiseRatio / (1.0  noiseRatio)));


126  lvl2.Add(x.Select(t => t + noisePrng.NextDouble()).ToList());


127  description.Add(string.Format(" ~ N({0}, {1:N3})", desc, noisePrng.Sigma));


128  }


129 


130  // lvl3 contains variables which are functions of vars in lvl0, lvl1 and lvl2 (+ noise)


131  List<List<double>> lvl3 = new List<List<double>>();


132  int numLvl3 = numberOfFeatures  numLvl0  numLvl1  numLvl2;


133  for (int c = 0; c < numLvl3; c++) {


134  string desc;


135  var x = GenerateRandomFunction(random, lvl0.Concat(lvl1).Concat(lvl2).ToList(), out desc);


136  var sigma = x.StandardDeviation();


137  var noisePrng = new NormalDistributedRandom(random, 0, sigma * Math.Sqrt(noiseRatio / (1.0  noiseRatio)));


138  lvl3.Add(x.Select(t => t + noisePrng.NextDouble()).ToList());


139  description.Add(string.Format(" ~ N({0}, {1:N3})", desc, noisePrng.Sigma));


140  }


141 


142  // return a random permutation of all variables


143  var allVars = lvl0.Concat(lvl1).Concat(lvl2).Concat(lvl3).ToList();


144  networkDefinition = string.Join(Environment.NewLine, variableNames.Zip(description, (n, d) => n + d));


145  var orderedVars = allVars.Zip(variableNames, Tuple.Create).OrderBy(t => t.Item2).Select(t => t.Item1).ToList();


146  variableNames = variableNames.OrderBy(n => n).ToArray();


147  return orderedVars;


148  }


149 


150  // sample the input variables that are actually used and sample from a Gaussian process


151  private IEnumerable<double> GenerateRandomFunction(IRandom rand, List<List<double>> xs, out string desc) {


152  int nRows = xs.First().Count;


153 


154  double r = Math.Log(1.0  rand.NextDouble()) * 2.0; // r is exponentially distributed with lambda = 2


155  int nl = (int)Math.Floor(1.5 + r); // number of selected vars is likely to be between three and four


156  if (nl > xs.Count) nl = xs.Count; // limit max


157 


158  var selectedIdx = Enumerable.Range(0, xs.Count).Shuffle(random)


159  .Take(nl).ToArray();


160 


161  var selectedVars = selectedIdx.Select(i => xs[i]).ToArray();


162  desc = string.Format("f({0})", string.Join(",", selectedIdx.Select(i => VariableNames[i])));


163  return SampleGaussianProcess(random, selectedVars);


164  }


165 


166  private IEnumerable<double> SampleGaussianProcess(IRandom random, List<double>[] xs) {


167  int nl = xs.Length;


168  int nRows = xs.First().Count;


169  double[,] K = new double[nRows, nRows];


170 


171  // sample lengthscales


172  var l = Enumerable.Range(0, nl)


173  .Select(_ => random.NextDouble()*2+0.5)


174  .ToArray();


175  // calculate covariance matrix


176  for (int r = 0; r < nRows; r++) {


177  double[] xi = xs.Select(x => x[r]).ToArray();


178  for (int c = 0; c <= r; c++) {


179  double[] xj = xs.Select(x => x[c]).ToArray();


180  double dSqr = xi.Zip(xj, (xik, xjk) => (xik  xjk))


181  .Select(dk => dk * dk)


182  .Zip(l, (dk, lk) => dk / lk)


183  .Sum();


184  K[r, c] = Math.Exp(dSqr);


185  }


186  }


187 


188  // add a small diagonal matrix for numeric stability


189  for (int i = 0; i < nRows; i++) {


190  K[i, i] += 1.0E7;


191  }


192 


193  // decompose


194  alglib.trfac.spdmatrixcholesky(ref K, nRows, false);


195 


196  // sample u iid ~ N(0, 1)


197  var u = Enumerable.Range(0, nRows).Select(_ => NormalDistributedRandom.NextDouble(random, 0, 1)).ToArray();


198 


199  // calc y = Lu


200  var y = new double[u.Length];


201  alglib.ablas.rmatrixmv(nRows, nRows, K, 0, 0, 0, u, 0, ref y, 0);


202 


203  return y;


204  }


205  }


206  }

