source: branches/2994-AutoDiffForIntervals/HeuristicLab.Problems.Instances.DataAnalysis/3.3/Regression/VariableNetworks/VariableNetwork.cs

#region License Information
/* HeuristicLab
 * Copyright (C) Heuristic and Evolutionary Algorithms Laboratory (HEAL)
 *
 * This file is part of HeuristicLab.
 *
 * HeuristicLab is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * HeuristicLab is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
 */
#endregion

using System;
using System.Collections.Generic;
using System.Globalization;
using System.Linq;
using HeuristicLab.Common;
using HeuristicLab.Core;
using HeuristicLab.Problems.DataAnalysis;
using HeuristicLab.Random;

namespace HeuristicLab.Problems.Instances.DataAnalysis {
  public abstract class VariableNetwork : ArtificialRegressionDataDescriptor {
    private int nTrainingSamples;
    private int nTestSamples;

    private int numberOfFeatures;
    private double noiseRatio;
    private IRandom random;

    private string networkDefinition;
    public string NetworkDefinition { get { return networkDefinition; } }
    public override string Description {
      get {
        return "The data are generated specifically to test methods for variable network analysis.";
      }
    }

    protected VariableNetwork(int nTrainingSamples, int nTestSamples,
      int numberOfFeatures, double noiseRatio, IRandom rand) {
      this.nTrainingSamples = nTrainingSamples;
      this.nTestSamples = nTestSamples;
      this.noiseRatio = noiseRatio;
      this.random = rand;
      this.numberOfFeatures = numberOfFeatures;
      // default variable names
      variableNames = Enumerable.Range(1, numberOfFeatures)
        .Select(i => string.Format("X{0:000}", i))
        .ToArray();

      variableRelevances = new Dictionary<string, IEnumerable<KeyValuePair<string, double>>>();
    }

    private string[] variableNames;
    protected override string[] VariableNames {
      get {
        return variableNames;
      }
    }

    // there is no specific target variable in variable network analysis but we still need to specify one
    protected override string TargetVariable { get { return VariableNames.Last(); } }

    protected override string[] AllowedInputVariables {
      get {
        return VariableNames.Take(numberOfFeatures - 1).ToArray();
      }
    }

    protected override int TrainingPartitionStart { get { return 0; } }
    protected override int TrainingPartitionEnd { get { return nTrainingSamples; } }
    protected override int TestPartitionStart { get { return nTrainingSamples; } }
    protected override int TestPartitionEnd { get { return nTrainingSamples + nTestSamples; } }

    private Dictionary<string, IEnumerable<KeyValuePair<string, double>>> variableRelevances;
    public IEnumerable<KeyValuePair<string, double>> GetVariableRelevance(string targetVar) {
      return variableRelevances[targetVar];
    }

    protected override List<List<double>> GenerateValues() {
      // variable names are shuffled in the beginning (and sorted at the end)
      variableNames = variableNames.Shuffle(random).ToArray();

      // a third of all variables are independent vars
      List<List<double>> lvl0 = new List<List<double>>();
      int numLvl0 = (int)Math.Ceiling(numberOfFeatures * 0.33);

      List<string> description = new List<string>(); // store information how the variable is actually produced
      List<string[]> inputVarNames = new List<string[]>(); // store information to produce graphviz file
      List<double[]> relevances = new List<double[]>(); // stores variable relevance information (same order as given in inputVarNames)

      var nrand = new NormalDistributedRandom(random, 0, 1);
      for(int c = 0; c < numLvl0; c++) {
        inputVarNames.Add(new string[] { });
        relevances.Add(new double[] { });
        description.Add(" ~ N(0, 1 + noiseLvl)");
        // use same generation procedure for all variables
        var x = Enumerable.Range(0, TestPartitionEnd).Select(_ => nrand.NextDouble()).ToList();
        var sigma = x.StandardDeviationPop();
        var mean = x.Average();
        for(int i = 0; i < x.Count; i++) x[i] = (x[i] - mean) / sigma;
        var noisePrng = new NormalDistributedRandom(random, 0, Math.Sqrt(noiseRatio / (1.0 - noiseRatio)));
        lvl0.Add(x.Select(t => t + noisePrng.NextDouble()).ToList());
      }

      // lvl1 contains variables which are functions of vars in lvl0 (+ noise)
      int numLvl1 = (int)Math.Ceiling(numberOfFeatures * 0.33);
      List<List<double>> lvl1 = CreateVariables(lvl0, numLvl1, inputVarNames, description, relevances);

      // lvl2 contains variables which are functions of vars in lvl0 and lvl1 (+ noise)
      int numLvl2 = (int)Math.Ceiling(numberOfFeatures * 0.2);
      List<List<double>> lvl2 = CreateVariables(lvl0.Concat(lvl1).ToList(), numLvl2, inputVarNames, description, relevances);

      // lvl3 contains variables which are functions of vars in lvl0, lvl1 and lvl2 (+ noise)
      int numLvl3 = numberOfFeatures - numLvl0 - numLvl1 - numLvl2;
      List<List<double>> lvl3 = CreateVariables(lvl0.Concat(lvl1).Concat(lvl2).ToList(), numLvl3, inputVarNames, description, relevances);

      this.variableRelevances.Clear();
      for(int i = 0; i < variableNames.Length; i++) {
        var targetVarName = variableNames[i];
        var targetRelevantInputs =
          inputVarNames[i].Zip(relevances[i], (inputVar, rel) => new KeyValuePair<string, double>(inputVar, rel))
            .ToArray();
        variableRelevances.Add(targetVarName, targetRelevantInputs);
      }

      networkDefinition = string.Join(Environment.NewLine, variableNames.Zip(description, (n, d) => n + d).OrderBy(x => x));
      // for graphviz
      networkDefinition += Environment.NewLine + "digraph G {";
      for(int i = 0; i < variableNames.Length; i++) {
        var name = variableNames[i];
        var selectedVarNames = inputVarNames[i];
        var selectedRelevances = relevances[i];
        for(int j = 0; j < selectedVarNames.Length; j++) {
          var selectedVarName = selectedVarNames[j];
          var selectedRelevance = selectedRelevances[j];
          networkDefinition += Environment.NewLine + selectedVarName + " -> " + name +
            string.Format(CultureInfo.InvariantCulture, " [label={0:N3}]", selectedRelevance);
        }
      }
      networkDefinition += Environment.NewLine + "}";

      // return a random permutation of all variables (to mix lvl0, lvl1, ... variables)
      var allVars = lvl0.Concat(lvl1).Concat(lvl2).Concat(lvl3).ToList();
      var orderedVars = allVars.Zip(variableNames, Tuple.Create).OrderBy(t => t.Item2).Select(t => t.Item1).ToList();
      variableNames = variableNames.OrderBy(n => n).ToArray();
      return orderedVars;
    }

    private List<List<double>> CreateVariables(List<List<double>> allowedInputs, int numVars, List<string[]> inputVarNames, List<string> description, List<double[]> relevances) {
      var newVariables = new List<List<double>>();
      for(int c = 0; c < numVars; c++) {
        string[] selectedVarNames;
        double[] relevance;
        var x = GenerateRandomFunction(random, allowedInputs, out selectedVarNames, out relevance).ToArray();
        // standardize x
        var sigma = x.StandardDeviation();
        var mean = x.Average();
        for(int i = 0; i < x.Length; i++) x[i] = (x[i] - mean) / sigma;

        var noisePrng = new NormalDistributedRandom(random, 0, Math.Sqrt(noiseRatio / (1.0 - noiseRatio)));
        newVariables.Add(x.Select(t => t + noisePrng.NextDouble()).ToList());
        Array.Sort(selectedVarNames, relevance);
        inputVarNames.Add(selectedVarNames);
        relevances.Add(relevance);
        var desc = string.Format("f({0})", string.Join(",", selectedVarNames));
        // for the relevance information order variables by decreasing relevance
        var relevanceStr = string.Join(", ",
          selectedVarNames.Zip(relevance, Tuple.Create)
          .OrderByDescending(t => t.Item2)
          .Select(t => string.Format(CultureInfo.InvariantCulture, "{0}: {1:N3}", t.Item1, t.Item2)));
        description.Add(string.Format(" ~ N({0}, {1:N3}) [Relevances: {2}]", desc, noisePrng.Sigma, relevanceStr));
      }
      return newVariables;
    }

    public int SampleNumberOfVariables(IRandom rand, int maxNumberOfVariables) {
      double r = -Math.Log(1.0 - rand.NextDouble()) * 2.0; // r is exponentially distributed with lambda = 2
      int nl = (int)Math.Floor(1.5 + r); // number of selected vars is likely to be between three and four
      return Math.Min(maxNumberOfVariables, nl);
    }

    // sample a random function and calculate the variable relevances
    protected abstract IEnumerable<double> GenerateRandomFunction(IRandom rand, List<List<double>> xs, out string[] selectedVarNames, out double[] relevance);
  }
}