source: trunk/sources/HeuristicLab.Problems.Instances.DataAnalysis/3.3/Regression/VariableNetworks/VariableNetwork.cs @ 13963

Last change on this file since 13963 was 13963, checked in by gkronber, 6 years ago

#2618: added graphviz output for the variable network instances

File size: 9.7 KB
Line 
1#region License Information
2/* HeuristicLab
3 * Copyright (C) 2002-2015 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
22using System;
23using System.Collections.Generic;
24using System.Linq;
25using System.Text;
26using System.Windows.Forms;
27using HeuristicLab.Common;
28using HeuristicLab.Core;
29using HeuristicLab.Random;
30
31namespace HeuristicLab.Problems.Instances.DataAnalysis {
32  public class VariableNetwork : ArtificialRegressionDataDescriptor {
33    private int nTrainingSamples;
34    private int nTestSamples;
35
36    private int numberOfFeatures;
37    private double noiseRatio;
38    private IRandom random;
39
40    public override string Name { get { return string.Format("VariableNetwork-{0:0%} ({1} dim)", noiseRatio, numberOfFeatures); } }
41    private string networkDefinition;
42    public string NetworkDefinition { get { return networkDefinition; } }
43    public override string Description {
44      get {
45        return "The data are generated specifically to test methods for variable network analysis.";
46      }
47    }
48
49    public VariableNetwork(int numberOfFeatures, double noiseRatio,
50      IRandom rand)
51      : this(250, 250, numberOfFeatures, noiseRatio, rand) { }
52
53    public VariableNetwork(int nTrainingSamples, int nTestSamples,
54      int numberOfFeatures, double noiseRatio, IRandom rand) {
55      this.nTrainingSamples = nTrainingSamples;
56      this.nTestSamples = nTestSamples;
57      this.noiseRatio = noiseRatio;
58      this.random = rand;
59      this.numberOfFeatures = numberOfFeatures;
60      // default variable names
61      variableNames = Enumerable.Range(1, numberOfFeatures)
62        .Select(i => string.Format("X{0:000}", i))
63        .ToArray();
64    }
65
66    private string[] variableNames;
67    protected override string[] VariableNames {
68      get {
69        return variableNames;
70      }
71    }
72
73    // there is no specific target variable in variable network analysis but we still need to specify one
74    protected override string TargetVariable { get { return VariableNames.Last(); } }
75
76    protected override string[] AllowedInputVariables {
77      get {
78        return VariableNames.Take(numberOfFeatures - 1).ToArray();
79      }
80    }
81
82    protected override int TrainingPartitionStart { get { return 0; } }
83    protected override int TrainingPartitionEnd { get { return nTrainingSamples; } }
84    protected override int TestPartitionStart { get { return nTrainingSamples; } }
85    protected override int TestPartitionEnd { get { return nTrainingSamples + nTestSamples; } }
86
87
88    protected override List<List<double>> GenerateValues() {
89      // var shuffledIdx = Enumerable.Range(0, numberOfFeatures).Shuffle(random).ToList();
90
91      // variable names are shuffled in the beginning (and sorted at the end)
92      variableNames = variableNames.Shuffle(random).ToArray();
93
94      // a third of all variables are independen vars
95      List<List<double>> lvl0 = new List<List<double>>();
96      int numLvl0 = (int)Math.Ceiling(numberOfFeatures * 0.33);
97
98      List<string> description = new List<string>(); // store information how the variable is actually produced
99      List<string[]> inputVarNames = new List<string[]>(); // store information to produce graphviz file
100
101      var nrand = new NormalDistributedRandom(random, 0, 1);
102      for (int c = 0; c < numLvl0; c++) {
103        var datai = Enumerable.Range(0, TestPartitionEnd).Select(_ => nrand.NextDouble()).ToList();
104        inputVarNames.Add(new string[] { });
105        description.Add("~ N(0, 1)");
106        lvl0.Add(datai);
107      }
108
109      // lvl1 contains variables which are functions of vars in lvl0 (+ noise)
110      List<List<double>> lvl1 = new List<List<double>>();
111      int numLvl1 = (int)Math.Ceiling(numberOfFeatures * 0.33);
112      for (int c = 0; c < numLvl1; c++) {
113        string[] selectedVarNames;
114        var x = GenerateRandomFunction(random, lvl0, out selectedVarNames);
115        var sigma = x.StandardDeviation();
116        var noisePrng = new NormalDistributedRandom(random, 0, sigma * Math.Sqrt(noiseRatio / (1.0 - noiseRatio)));
117        lvl1.Add(x.Select(t => t + noisePrng.NextDouble()).ToList());
118
119        inputVarNames.Add(selectedVarNames);
120        var desc = string.Format("f({0})", string.Join(",", selectedVarNames));
121        description.Add(string.Format(" ~ N({0}, {1:N3})", desc, noisePrng.Sigma));
122      }
123
124      // lvl2 contains variables which are functions of vars in lvl0 and lvl1 (+ noise)
125      List<List<double>> lvl2 = new List<List<double>>();
126      int numLvl2 = (int)Math.Ceiling(numberOfFeatures * 0.2);
127      for (int c = 0; c < numLvl2; c++) {
128        string[] selectedVarNames;
129        var x = GenerateRandomFunction(random, lvl0.Concat(lvl1).ToList(), out selectedVarNames);
130        var sigma = x.StandardDeviation();
131        var noisePrng = new NormalDistributedRandom(random, 0, sigma * Math.Sqrt(noiseRatio / (1.0 - noiseRatio)));
132        lvl2.Add(x.Select(t => t + noisePrng.NextDouble()).ToList());
133
134        inputVarNames.Add(selectedVarNames);
135        var desc = string.Format("f({0})", string.Join(",", selectedVarNames));
136        description.Add(string.Format(" ~ N({0}, {1:N3})", desc, noisePrng.Sigma));
137      }
138
139      // lvl3 contains variables which are functions of vars in lvl0, lvl1 and lvl2 (+ noise)
140      List<List<double>> lvl3 = new List<List<double>>();
141      int numLvl3 = numberOfFeatures - numLvl0 - numLvl1 - numLvl2;
142      for (int c = 0; c < numLvl3; c++) {
143        string[] selectedVarNames;
144        var x = GenerateRandomFunction(random, lvl0.Concat(lvl1).Concat(lvl2).ToList(), out selectedVarNames);
145        var sigma = x.StandardDeviation();
146        var noisePrng = new NormalDistributedRandom(random, 0, sigma * Math.Sqrt(noiseRatio / (1.0 - noiseRatio)));
147        lvl3.Add(x.Select(t => t + noisePrng.NextDouble()).ToList());
148
149        inputVarNames.Add(selectedVarNames);
150        var desc = string.Format("f({0})", string.Join(",", selectedVarNames));
151        description.Add(string.Format(" ~ N({0}, {1:N3})", desc, noisePrng.Sigma));
152      }
153
154      networkDefinition = string.Join(Environment.NewLine, variableNames.Zip(description, (n, d) => n + d));
155      // for graphviz
156      networkDefinition += Environment.NewLine + "digraph G {";
157      foreach (var t in variableNames.Zip(inputVarNames, Tuple.Create).OrderBy(t => t.Item1)) {
158        var name = t.Item1;
159        var selectedVarNames = t.Item2;
160        foreach (var selectedVarName in selectedVarNames) {
161          networkDefinition += Environment.NewLine + selectedVarName + " -> " + name;
162        }
163      }
164      networkDefinition += Environment.NewLine + "}";
165
166      // return a random permutation of all variables
167      var allVars = lvl0.Concat(lvl1).Concat(lvl2).Concat(lvl3).ToList();
168      var orderedVars = allVars.Zip(variableNames, Tuple.Create).OrderBy(t => t.Item2).Select(t => t.Item1).ToList();
169      variableNames = variableNames.OrderBy(n => n).ToArray();
170      return orderedVars;
171    }
172
173    // sample the input variables that are actually used and sample from a Gaussian process
174    private IEnumerable<double> GenerateRandomFunction(IRandom rand, List<List<double>> xs, out string[] selectedVarNames) {
175      double r = -Math.Log(1.0 - rand.NextDouble()) * 2.0; // r is exponentially distributed with lambda = 2
176      int nl = (int)Math.Floor(1.5 + r); // number of selected vars is likely to be between three and four
177      if (nl > xs.Count) nl = xs.Count; // limit max
178
179      var selectedIdx = Enumerable.Range(0, xs.Count).Shuffle(random)
180        .Take(nl).ToArray();
181
182      var selectedVars = selectedIdx.Select(i => xs[i]).ToArray();
183      selectedVarNames = selectedIdx.Select(i => VariableNames[i]).ToArray();
184      return SampleGaussianProcess(random, selectedVars);
185    }
186
187    private IEnumerable<double> SampleGaussianProcess(IRandom random, List<double>[] xs) {
188      int nl = xs.Length;
189      int nRows = xs.First().Count;
190      double[,] K = new double[nRows, nRows];
191
192      // sample length-scales
193      var l = Enumerable.Range(0, nl)
194        .Select(_ => random.NextDouble() * 2 + 0.5)
195        .ToArray();
196      // calculate covariance matrix
197      for (int r = 0; r < nRows; r++) {
198        double[] xi = xs.Select(x => x[r]).ToArray();
199        for (int c = 0; c <= r; c++) {
200          double[] xj = xs.Select(x => x[c]).ToArray();
201          double dSqr = xi.Zip(xj, (xik, xjk) => (xik - xjk))
202            .Select(dk => dk * dk)
203            .Zip(l, (dk, lk) => dk / lk)
204            .Sum();
205          K[r, c] = Math.Exp(-dSqr);
206        }
207      }
208
209      // add a small diagonal matrix for numeric stability
210      for (int i = 0; i < nRows; i++) {
211        K[i, i] += 1.0E-7;
212      }
213
214      // decompose
215      alglib.trfac.spdmatrixcholesky(ref K, nRows, false);
216
217      // sample u iid ~ N(0, 1)
218      var u = Enumerable.Range(0, nRows).Select(_ => NormalDistributedRandom.NextDouble(random, 0, 1)).ToArray();
219
220      // calc y = Lu
221      var y = new double[u.Length];
222      alglib.ablas.rmatrixmv(nRows, nRows, K, 0, 0, 0, u, 0, ref y, 0);
223
224      return y;
225    }
226  }
227}
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