source: branches/HeuristicLab.Problems.GrammaticalOptimization/HeuristicLab.Distributions/GaussianMixtureModel.cs @ 12005

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using HeuristicLab.Common;

namespace HeuristicLab.Algorithms.Bandits.Models {
  public class GaussianMixtureModel : IModel {
    private double[] componentMeans;
    private double[] componentVars;
    private double[] componentProbs;
    private readonly List<double> allRewards = new List<double>();

    private int numComponents;

    public GaussianMixtureModel(int nComponents = 5) {
      this.numComponents = nComponents;

      Reset();
    }


    public double Sample(Random random) {
      var k = Enumerable.Range(0, numComponents).SampleProportional(random, componentProbs);
      return alglib.invnormaldistribution(random.NextDouble()) * Math.Sqrt(componentVars[k]) + componentMeans[k];
    }

    public void Update(double reward) {
      allRewards.Add(reward);
      throw new NotSupportedException("this does not yet work");
      if (allRewards.Count < 1000 && allRewards.Count % 10 == 0) {
        // see http://www.cs.toronto.edu/~mackay/itprnn/ps/302.320.pdf Algorithm 22.2 soft k-means
        Reset();
        for (int i = 0; i < 20; i++) {
          var responsibilities = allRewards.Select(r => CalcResponsibility(r)).ToArray();


          var sumWeightedRewards = new double[numComponents];
          var sumResponsibilities = new double[numComponents];
          foreach (var p in allRewards.Zip(responsibilities, Tuple.Create)) {
            for (int k = 0; k < numComponents; k++) {
              sumWeightedRewards[k] += p.Item2[k] * p.Item1;
              sumResponsibilities[k] += p.Item2[k];
            }
          }
          for (int k = 0; k < numComponents; k++) {
            componentMeans[k] = sumWeightedRewards[k] / sumResponsibilities[k];
          }

          sumWeightedRewards = new double[numComponents];
          foreach (var p in allRewards.Zip(responsibilities, Tuple.Create)) {
            for (int k = 0; k < numComponents; k++) {
              sumWeightedRewards[k] += p.Item2[k] * Math.Pow(p.Item1 - componentMeans[k], 2);
            }
          }
          for (int k = 0; k < numComponents; k++) {
            componentVars[k] = sumWeightedRewards[k] / sumResponsibilities[k];
            componentProbs[k] = sumResponsibilities[k] / sumResponsibilities.Sum();
          }
        }
      }
    }

    private double[] CalcResponsibility(double r) {
      var res = new double[numComponents];
      for (int k = 0; k < numComponents; k++) {
        componentVars[k] = Math.Max(componentVars[k], 0.001);
        res[k] = componentProbs[k] * alglib.normaldistribution((r - componentMeans[k]) / Math.Sqrt(componentVars[k]));
        res[k] = Math.Max(res[k], 0.0001);
      }
      var sum = res.Sum();
      for (int k = 0; k < numComponents; k++) {
        res[k] /= sum;
      }
      return res;
    }

    public void Disable() {
      Array.Clear(componentMeans, 0, numComponents);
      for (int i = 0; i < numComponents; i++)
        componentVars[i] = 0.0;
    }

    public object Clone() {
      return new GaussianMixtureModel(numComponents);
    }

    public void Reset() {
      var rand = new Random();
      this.componentProbs = Enumerable.Range(0, numComponents).Select((_) => rand.NextDouble()).ToArray();
      var sum = componentProbs.Sum();
      for (int i = 0; i < componentProbs.Length; i++) componentProbs[i] /= sum;
      this.componentMeans = Enumerable.Range(0, numComponents).Select((_) => Rand.RandNormal(rand)).ToArray();
      this.componentVars = Enumerable.Range(0, numComponents).Select((_) => 0.01).ToArray();
    }
  }
}