source: branches/HeuristicLab.Problems.GaussianProcessTuning/HeuristicLab.Algorithms.DataAnalysis.Experimental/TunedGaussianProcessModel.cs @ 10743

#region License Information
/* HeuristicLab
 * Copyright (C) 2002-2012 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.Linq;
using HeuristicLab.Common;
using HeuristicLab.Core;
using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
using HeuristicLab.Problems.DataAnalysis;
using ILNumerics;

namespace HeuristicLab.Algorithms.DataAnalysis {
  /// <summary>
  /// Represents a Gaussian process model.
  /// </summary>
  [StorableClass]
  [Item("TunedGaussianProcessModel", "Gaussian process model implemented using ILNumerics.")]
  public sealed class TunedGaussianProcessModel : NamedItem, IGaussianProcessModel {
    [Storable]
    private double negativeLogLikelihood;
    public double NegativeLogLikelihood {
      get { return negativeLogLikelihood; }
    }

    [Storable]
    private double[] hyperparameterGradients;
    public double[] HyperparameterGradients {
      get {
        var copy = new double[hyperparameterGradients.Length];
        Array.Copy(hyperparameterGradients, copy, copy.Length);
        return copy;
      }
    }

    [Storable]
    private ICovarianceFunction covarianceFunction;
    public ICovarianceFunction CovarianceFunction {
      get { return covarianceFunction; }
    }
    [Storable]
    private IMeanFunction meanFunction;
    public IMeanFunction MeanFunction {
      get { return meanFunction; }
    }
    [Storable]
    private string targetVariable;
    public string TargetVariable {
      get { return targetVariable; }
    }
    [Storable]
    private string[] allowedInputVariables;
    public string[] AllowedInputVariables {
      get { return allowedInputVariables; }
    }

    [Storable]
    private double[] alpha;


    [Storable]
    private double sqrSigmaNoise;
    public double SigmaNoise {
      get { return Math.Sqrt(sqrSigmaNoise); }
    }

    [Storable]
    private double[] meanParameter;
    [Storable]
    private double[] covarianceParameter;

    [Storable]
    private double[] l;

    [Storable]
    private double[,] x;
    [Storable]
    private Scaling inputScaling;


    [StorableConstructor]
    private TunedGaussianProcessModel(bool deserializing) : base(deserializing) { }
    private TunedGaussianProcessModel(TunedGaussianProcessModel original, Cloner cloner)
      : base(original, cloner) {
      this.meanFunction = cloner.Clone(original.meanFunction);
      this.covarianceFunction = cloner.Clone(original.covarianceFunction);
      this.inputScaling = cloner.Clone(original.inputScaling);
      this.negativeLogLikelihood = original.negativeLogLikelihood;
      this.targetVariable = original.targetVariable;
      this.sqrSigmaNoise = original.sqrSigmaNoise;
      if (original.meanParameter != null) {
        this.meanParameter = (double[])original.meanParameter.Clone();
      }
      if (original.covarianceParameter != null) {
        this.covarianceParameter = (double[])original.covarianceParameter.Clone();
      }

      // shallow copies of arrays because they cannot be modified
      this.allowedInputVariables = original.allowedInputVariables;
      this.alpha = original.alpha;
      this.l = original.l;
      this.x = original.x;
    }
    public TunedGaussianProcessModel(Dataset ds, string targetVariable, IEnumerable<string> allowedInputVariables, IEnumerable<int> rows,
      IEnumerable<double> hyp, IMeanFunction meanFunction, ICovarianceFunction covarianceFunction)
      : base() {
      this.name = ItemName;
      this.description = ItemDescription;
      this.meanFunction = (IMeanFunction)meanFunction.Clone();
      this.covarianceFunction = (ICovarianceFunction)covarianceFunction.Clone();
      this.targetVariable = targetVariable;
      this.allowedInputVariables = allowedInputVariables.ToArray();


      int nVariables = this.allowedInputVariables.Length;
      meanParameter = hyp
        .Take(this.meanFunction.GetNumberOfParameters(nVariables))
        .ToArray();

      covarianceParameter = hyp.Skip(this.meanFunction.GetNumberOfParameters(nVariables))
                                             .Take(this.covarianceFunction.GetNumberOfParameters(nVariables))
                                             .ToArray();
      sqrSigmaNoise = Math.Exp(2.0 * hyp.Last());

      CalculateModel(ds, rows);

      //var cmpModel = new GaussianProcessModel(ds, targetVariable, allowedInputVariables, rows, hyp,
      //                                        (IMeanFunction)meanFunction.Clone(),
      //                                        (ICovarianceFunction)covarianceFunction.Clone());
      //if (!cmpModel.NegativeLogLikelihood.IsAlmost(NegativeLogLikelihood) ||
      //  !cmpModel.HyperparameterGradients.Sum().IsAlmost(HyperparameterGradients.Sum())
      //  )
      //  throw new ArgumentException();
    }

    private void CalculateModel(Dataset ds, IEnumerable<int> rows) {
      inputScaling = new Scaling(ds, allowedInputVariables, rows);
      x = AlglibUtil.PrepareAndScaleInputMatrix(ds, allowedInputVariables, rows, inputScaling);
      var y = ds.GetDoubleValues(targetVariable, rows);
      ILNumerics.Settings.MaxNumberThreads = Environment.ProcessorCount;
      using (ILScope.Enter()) {
        int n = x.GetLength(0);

        // calculate means and covariances
        var mean = meanFunction.GetParameterizedMeanFunction(meanParameter, Enumerable.Range(0, x.GetLength(1)));
        double[] m = Enumerable.Range(0, x.GetLength(0))
          .Select(r => mean.Mean(x, r))
          .ToArray();

        var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, Enumerable.Range(0, x.GetLength(1)));
        ILArray<double> myL = ILMath.zeros<double>(n, n);

        for (int i = 0; i < n; i++) {
          for (int j = i; j < n; j++) {
            double c = cov.Covariance(x, i, j) / sqrSigmaNoise;
            if (i == j) {
              myL.SetValue(c + 1, i, j);
            } else {
              myL.SetValue(c, j, i);
              myL.SetValue(c, i, j);
            }
          }
        }

        // cholesky decomposition
        ILArray<double> chol;
        try {
          chol = ILNumerics.ILMath.chol(myL, false);
        }
        catch (Exception e) {
          throw new ArgumentException("covariance matrix not positive definite", e);
        }
        if (chol == null || chol.IsEmpty || !chol.Size.Equals(myL.Size))
          throw new ArgumentException("covariance matrix not positive definite");
        this.l = new double[n * n];
        chol.ExportValues(ref l);
        // calculate sum of diagonal elements for likelihood

        double diagSum = ILMath.log(ILMath.diag(chol)).Sum();

        // solve for alpha
        ILArray<double> ym = ILMath.array(y.Zip(m, (a, b) => a - b).ToArray());

        MatrixProperties lowerTriProps = MatrixProperties.LowerTriangular;
        MatrixProperties upperTriProps = MatrixProperties.UpperTriangular;
        ILArray<double> alpha;
        try {
          ILArray<double> t1 = ILMath.linsolve(chol.T, ym, ref lowerTriProps);
          alpha = ILMath.linsolve(chol, t1, ref upperTriProps) / sqrSigmaNoise;
        }
        catch (Exception e) {
          throw new ArgumentException("covariance matrix is not positive definite", e);
        }
        if (alpha == null || alpha.IsEmpty) throw new ArgumentException();
        this.alpha = new double[alpha.Length];
        alpha.ExportValues(ref this.alpha);

        negativeLogLikelihood = 0.5 * (double)ILMath.multiply(ym.T, alpha) + diagSum + (n / 2.0) * Math.Log(2.0 * Math.PI * sqrSigmaNoise);

        // derivatives
        int nAllowedVariables = x.GetLength(1);

        ILArray<double> lCopy;
        try {
          ILArray<double> t2 = ILMath.linsolve(chol.T, ILMath.eye<double>(n, n), ref lowerTriProps);
          lCopy = ILMath.linsolve(chol, t2, ref upperTriProps) / sqrSigmaNoise - ILMath.multiply(alpha, alpha.T);
        }
        catch (Exception e) {
          throw new ArgumentException("covariance matrix is not positive definite", e);
        }

        double noiseGradient = sqrSigmaNoise * ILMath.sumall(ILMath.diag(lCopy)).GetValue(0, 0);

        double[] meanGradients = new double[meanFunction.GetNumberOfParameters(nAllowedVariables)];
        for (int k = 0; k < meanGradients.Length; k++) {
          ILArray<double> meanGrad =
            ILMath.array(
              Enumerable.Range(0, alpha.Length)
                .Select(r => mean.Gradient(x, r, k))
                .ToArray());
          meanGradients[k] = -(double)ILMath.multiply(meanGrad.T, alpha);
        }

        double[] covGradients = new double[covarianceFunction.GetNumberOfParameters(nAllowedVariables)];
        if (covGradients.Length > 0) {
          for (int i = 0; i < n; i++) {
            for (int j = 0; j < i; j++) {
              var g = cov.CovarianceGradient(x, i, j).ToArray();
              for (int k = 0; k < covGradients.Length; k++) {
                covGradients[k] += lCopy.GetValue(i, j) * g[k];
              }
            }

            var gDiag = cov.CovarianceGradient(x, i, i).ToArray();
            for (int k = 0; k < covGradients.Length; k++) {
              // diag
              covGradients[k] += 0.5 * lCopy.GetValue(i, i) * gDiag[k];
            }
          }
        }

        hyperparameterGradients =
          meanGradients
            .Concat(covGradients)
            .Concat(new double[] { noiseGradient }).ToArray();
      }
    }


    public override IDeepCloneable Clone(Cloner cloner) {
      return new TunedGaussianProcessModel(this, cloner);
    }

    // is called by the solution creator to set all parameter values of the covariance and mean function
    // to the optimized values (necessary to make the values visible in the GUI)
    public void FixParameters() {
      covarianceFunction.SetParameter(covarianceParameter);
      meanFunction.SetParameter(meanParameter);
      covarianceParameter = new double[0];
      meanParameter = new double[0];
    }

    #region IRegressionModel Members
    public IEnumerable<double> GetEstimatedValues(Dataset dataset, IEnumerable<int> rows) {
      return GetEstimatedValuesHelper(dataset, rows);
    }
    public GaussianProcessRegressionSolution CreateRegressionSolution(IRegressionProblemData problemData) {
      return new GaussianProcessRegressionSolution(this, new RegressionProblemData(problemData));
    }
    IRegressionSolution IRegressionModel.CreateRegressionSolution(IRegressionProblemData problemData) {
      return CreateRegressionSolution(problemData);
    }
    #endregion


    private IEnumerable<double> GetEstimatedValuesHelper(Dataset dataset, IEnumerable<int> rows) {
      var newX = AlglibUtil.PrepareAndScaleInputMatrix(dataset, allowedInputVariables, rows, inputScaling);
      int newN = newX.GetLength(0);
      int n = x.GetLength(0);
      var Ks = new double[newN, n];
      var mean = meanFunction.GetParameterizedMeanFunction(meanParameter, Enumerable.Range(0, newX.GetLength(1)));
      var ms = Enumerable.Range(0, newX.GetLength(0))
      .Select(r => mean.Mean(newX, r))
      .ToArray();
      var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, Enumerable.Range(0, x.GetLength(1)));
      for (int i = 0; i < newN; i++) {
        for (int j = 0; j < n; j++) {
          Ks[i, j] = cov.CrossCovariance(x, newX, j, i);
        }
      }

      return Enumerable.Range(0, newN)
        .Select(i => ms[i] + Util.ScalarProd(Util.GetRow(Ks, i), alpha));
    }

    public IEnumerable<double> GetEstimatedVariance(Dataset dataset, IEnumerable<int> rows) {
      var newX = AlglibUtil.PrepareAndScaleInputMatrix(dataset, allowedInputVariables, rows, inputScaling);
      int newN = newX.GetLength(0);
      int n = x.GetLength(0);
      if (newN == 0) return Enumerable.Empty<double>();

      var kss = new double[newN];
      ILArray<double> sWKs = ILMath.zeros(n, newN);
      var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, Enumerable.Range(0, x.GetLength(1)));

      // for stddev 
      for (int i = 0; i < newN; i++)
        kss[i] = cov.Covariance(newX, i, i);

      for (int i = 0; i < newN; i++) {
        for (int j = 0; j < n; j++) {
          sWKs.SetValue(cov.CrossCovariance(x, newX, j, i) / Math.Sqrt(sqrSigmaNoise), j, i);
        }
      }

      // for stddev 
      var lowerTriangular = MatrixProperties.LowerTriangular;
      ILArray<double> V = ILMath.linsolve(ILMath.array(l, n, n).T, sWKs, ref lowerTriangular);

      // alglib.ablas.rmatrixlefttrsm(n, newN, l, 0, 0, false, false, 0, ref sWKs, 0, 0);

      for (int i = 0; i < newN; i++) {
        double sumV = (double)ILMath.multiply(V[ILMath.full, i].T, V[ILMath.full, i]);
        kss[i] -= sumV;
        if (kss[i] < 0) kss[i] = 0;
      }
      return kss;
    }
  }
}