source: trunk/sources/HeuristicLab.Problems.Instances.DataAnalysis/3.3/Regression/VariableNetworks/VariableNetwork.cs @ 14623

Last change on this file since 14623 was 14623, checked in by gkronber, 3 years ago

#2660: removed obsolete comment

File size: 12.2 KB
Line 
1#region License Information
2/* HeuristicLab
3 * Copyright (C) 2002-2016 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.Globalization;
25using System.Linq;
26using HeuristicLab.Common;
27using HeuristicLab.Core;
28using HeuristicLab.Problems.DataAnalysis;
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      variableRelevances = new Dictionary<string, IEnumerable<KeyValuePair<string, double>>>();
66    }
67
68    private string[] variableNames;
69    protected override string[] VariableNames {
70      get {
71        return variableNames;
72      }
73    }
74
75    // there is no specific target variable in variable network analysis but we still need to specify one
76    protected override string TargetVariable { get { return VariableNames.Last(); } }
77
78    protected override string[] AllowedInputVariables {
79      get {
80        return VariableNames.Take(numberOfFeatures - 1).ToArray();
81      }
82    }
83
84    protected override int TrainingPartitionStart { get { return 0; } }
85    protected override int TrainingPartitionEnd { get { return nTrainingSamples; } }
86    protected override int TestPartitionStart { get { return nTrainingSamples; } }
87    protected override int TestPartitionEnd { get { return nTrainingSamples + nTestSamples; } }
88
89    private Dictionary<string, IEnumerable<KeyValuePair<string, double>>> variableRelevances;
90    public IEnumerable<KeyValuePair<string, double>> GetVariableRelevance(string targetVar) {
91      return variableRelevances[targetVar];
92    }
93
94    protected override List<List<double>> GenerateValues() {
95      // variable names are shuffled in the beginning (and sorted at the end)
96      variableNames = variableNames.Shuffle(random).ToArray();
97
98      // a third of all variables are independent vars
99      List<List<double>> lvl0 = new List<List<double>>();
100      int numLvl0 = (int)Math.Ceiling(numberOfFeatures * 0.33);
101
102      List<string> description = new List<string>(); // store information how the variable is actually produced
103      List<string[]> inputVarNames = new List<string[]>(); // store information to produce graphviz file
104      List<double[]> relevances = new List<double[]>(); // stores variable relevance information (same order as given in inputVarNames)
105
106      var nrand = new NormalDistributedRandom(random, 0, 1);
107      for (int c = 0; c < numLvl0; c++) {
108        inputVarNames.Add(new string[] { });
109        relevances.Add(new double[] { });
110        description.Add(" ~ N(0, 1)");
111        lvl0.Add(Enumerable.Range(0, TestPartitionEnd).Select(_ => nrand.NextDouble()).ToList());
112      }
113
114      // lvl1 contains variables which are functions of vars in lvl0 (+ noise)
115      int numLvl1 = (int)Math.Ceiling(numberOfFeatures * 0.33);
116      List<List<double>> lvl1 = CreateVariables(lvl0, numLvl1, inputVarNames, description, relevances);
117
118      // lvl2 contains variables which are functions of vars in lvl0 and lvl1 (+ noise)
119      int numLvl2 = (int)Math.Ceiling(numberOfFeatures * 0.2);
120      List<List<double>> lvl2 = CreateVariables(lvl0.Concat(lvl1).ToList(), numLvl2, inputVarNames, description, relevances);
121
122      // lvl3 contains variables which are functions of vars in lvl0, lvl1 and lvl2 (+ noise)
123      int numLvl3 = numberOfFeatures - numLvl0 - numLvl1 - numLvl2;
124      List<List<double>> lvl3 = CreateVariables(lvl0.Concat(lvl1).Concat(lvl2).ToList(), numLvl3, inputVarNames, description, relevances);
125
126      this.variableRelevances.Clear();
127      for (int i = 0; i < variableNames.Length; i++) {
128        var targetVarName = variableNames[i];
129        var targetRelevantInputs =
130          inputVarNames[i].Zip(relevances[i], (inputVar, rel) => new KeyValuePair<string, double>(inputVar, rel))
131            .ToArray();
132        variableRelevances.Add(targetVarName, targetRelevantInputs);
133      }
134
135      networkDefinition = string.Join(Environment.NewLine, variableNames.Zip(description, (n, d) => n + d).OrderBy(x => x));
136      // for graphviz
137      networkDefinition += Environment.NewLine + "digraph G {";
138      for (int i = 0; i < variableNames.Length; i++) {
139        var name = variableNames[i];
140        var selectedVarNames = inputVarNames[i];
141        var selectedRelevances = relevances[i];
142        for (int j = 0; j < selectedVarNames.Length; j++) {
143          var selectedVarName = selectedVarNames[j];
144          var selectedRelevance = selectedRelevances[j];
145          networkDefinition += Environment.NewLine + selectedVarName + " -> " + name +
146            string.Format(CultureInfo.InvariantCulture, " [label={0:N3}]", selectedRelevance);
147        }
148      }
149      networkDefinition += Environment.NewLine + "}";
150
151      // return a random permutation of all variables (to mix lvl0, lvl1, ... variables)
152      var allVars = lvl0.Concat(lvl1).Concat(lvl2).Concat(lvl3).ToList();
153      var orderedVars = allVars.Zip(variableNames, Tuple.Create).OrderBy(t => t.Item2).Select(t => t.Item1).ToList();
154      variableNames = variableNames.OrderBy(n => n).ToArray();
155      return orderedVars;
156    }
157
158    private List<List<double>> CreateVariables(List<List<double>> allowedInputs, int numVars, List<string[]> inputVarNames, List<string> description, List<double[]> relevances) {
159      var res = new List<List<double>>();
160      for (int c = 0; c < numVars; c++) {
161        string[] selectedVarNames;
162        double[] relevance;
163        var x = GenerateRandomFunction(random, allowedInputs, out selectedVarNames, out relevance);
164        var sigma = x.StandardDeviation();
165        var noisePrng = new NormalDistributedRandom(random, 0, sigma * Math.Sqrt(noiseRatio / (1.0 - noiseRatio)));
166        res.Add(x.Select(t => t + noisePrng.NextDouble()).ToList());
167        Array.Sort(selectedVarNames, relevance);
168        inputVarNames.Add(selectedVarNames);
169        relevances.Add(relevance);
170        var desc = string.Format("f({0})", string.Join(",", selectedVarNames));
171        // for the relevance information order variables by decreasing relevance
172        var relevanceStr = string.Join(", ",
173          selectedVarNames.Zip(relevance, Tuple.Create)
174          .OrderByDescending(t => t.Item2)
175          .Select(t => string.Format(CultureInfo.InvariantCulture, "{0}: {1:N3}", t.Item1, t.Item2)));
176        description.Add(string.Format(" ~ N({0}, {1:N3}) [Relevances: {2}]", desc, noisePrng.Sigma, relevanceStr));
177      }
178      return res;
179    }
180
181    // sample the input variables that are actually used and sample from a Gaussian process
182    private IEnumerable<double> GenerateRandomFunction(IRandom rand, List<List<double>> xs, out string[] selectedVarNames, out double[] relevance) {
183      double r = -Math.Log(1.0 - rand.NextDouble()) * 2.0; // r is exponentially distributed with lambda = 2
184      int nl = (int)Math.Floor(1.5 + r); // number of selected vars is likely to be between three and four
185      if (nl > xs.Count) nl = xs.Count; // limit max
186
187      var selectedIdx = Enumerable.Range(0, xs.Count).Shuffle(random)
188        .Take(nl).ToArray();
189
190      var selectedVars = selectedIdx.Select(i => xs[i]).ToArray();
191      selectedVarNames = selectedIdx.Select(i => VariableNames[i]).ToArray();
192      return SampleGaussianProcess(random, selectedVars, out relevance);
193    }
194
195    private IEnumerable<double> SampleGaussianProcess(IRandom random, List<double>[] xs, out double[] relevance) {
196      int nl = xs.Length;
197      int nRows = xs.First().Count;
198
199      // sample u iid ~ N(0, 1)
200      var u = Enumerable.Range(0, nRows).Select(_ => NormalDistributedRandom.NextDouble(random, 0, 1)).ToArray();
201
202      // sample actual length-scales
203      var l = Enumerable.Range(0, nl)
204        .Select(_ => random.NextDouble() * 2 + 0.5)
205        .ToArray();
206
207      double[,] K = CalculateCovariance(xs, l);
208
209      // decompose
210      alglib.trfac.spdmatrixcholesky(ref K, nRows, false);
211
212
213      // calc y = Lu
214      var y = new double[u.Length];
215      alglib.ablas.rmatrixmv(nRows, nRows, K, 0, 0, 0, u, 0, ref y, 0);
216
217      // calculate relevance by removing dimensions
218      relevance = CalculateRelevance(y, u, xs, l);
219
220      return y;
221    }
222
223    // calculate variable relevance based on removal of variables
224    //  1) to remove a variable we set it's length scale to infinity (no relation of the variable value to the target)
225    //  2) calculate MSE of the original target values (y) to the updated targes y' (after variable removal)
226    //  3) relevance is larger if MSE(y,y') is large
227    //  4) scale impacts so that the most important variable has impact = 1
228    private double[] CalculateRelevance(double[] y, double[] u, List<double>[] xs, double[] l) {
229      int nRows = xs.First().Count;
230      var changedL = new double[l.Length];
231      var relevance = new double[l.Length];
232      for (int i = 0; i < l.Length; i++) {
233        Array.Copy(l, changedL, changedL.Length);
234        changedL[i] = double.MaxValue;
235        var changedK = CalculateCovariance(xs, changedL);
236
237        var yChanged = new double[u.Length];
238        alglib.ablas.rmatrixmv(nRows, nRows, changedK, 0, 0, 0, u, 0, ref yChanged, 0);
239
240        OnlineCalculatorError error;
241        var mse = OnlineMeanSquaredErrorCalculator.Calculate(y, yChanged, out error);
242        if (error != OnlineCalculatorError.None) mse = double.MaxValue;
243        relevance[i] = mse;
244      }
245      // scale so that max relevance is 1.0
246      var maxRel = relevance.Max();
247      for (int i = 0; i < relevance.Length; i++) relevance[i] /= maxRel;
248      return relevance;
249    }
250
251    private double[,] CalculateCovariance(List<double>[] xs, double[] l) {
252      int nRows = xs.First().Count;
253      double[,] K = new double[nRows, nRows];
254      for (int r = 0; r < nRows; r++) {
255        double[] xi = xs.Select(x => x[r]).ToArray();
256        for (int c = 0; c <= r; c++) {
257          double[] xj = xs.Select(x => x[c]).ToArray();
258          double dSqr = xi.Zip(xj, (xik, xjk) => (xik - xjk))
259            .Select(dk => dk * dk)
260            .Zip(l, (dk, lk) => dk / lk)
261            .Sum();
262          K[r, c] = Math.Exp(-dSqr);
263        }
264      }
265      // add a small diagonal matrix for numeric stability
266      for (int i = 0; i < nRows; i++) {
267        K[i, i] += 1.0E-7;
268      }
269
270      return K;
271    }
272  }
273}
Note: See TracBrowser for help on using the repository browser.