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source: trunk/sources/HeuristicLab.Algorithms.DataAnalysis/3.4/GaussianProcess/GaussianProcessModel.cs @ 12792

Last change on this file since 12792 was 12792, checked in by gkronber, 7 years ago

#2435: updated some of the alglib calls (we should only use the external API whenever possible)

File size: 11.7 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 HeuristicLab.Common;
26using HeuristicLab.Core;
27using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
28using HeuristicLab.Problems.DataAnalysis;
29
30namespace HeuristicLab.Algorithms.DataAnalysis {
31  /// <summary>
32  /// Represents a Gaussian process model.
33  /// </summary>
34  [StorableClass]
35  [Item("GaussianProcessModel", "Represents a Gaussian process posterior.")]
36  public sealed class GaussianProcessModel : NamedItem, IGaussianProcessModel {
37    [Storable]
38    private double negativeLogLikelihood;
39    public double NegativeLogLikelihood {
40      get { return negativeLogLikelihood; }
41    }
42
43    [Storable]
44    private double[] hyperparameterGradients;
45    public double[] HyperparameterGradients {
46      get {
47        var copy = new double[hyperparameterGradients.Length];
48        Array.Copy(hyperparameterGradients, copy, copy.Length);
49        return copy;
50      }
51    }
52
53    [Storable]
54    private ICovarianceFunction covarianceFunction;
55    public ICovarianceFunction CovarianceFunction {
56      get { return covarianceFunction; }
57    }
58    [Storable]
59    private IMeanFunction meanFunction;
60    public IMeanFunction MeanFunction {
61      get { return meanFunction; }
62    }
63    [Storable]
64    private string targetVariable;
65    public string TargetVariable {
66      get { return targetVariable; }
67    }
68    [Storable]
69    private string[] allowedInputVariables;
70    public string[] AllowedInputVariables {
71      get { return allowedInputVariables; }
72    }
73
74    [Storable]
75    private double[] alpha;
76    [Storable]
77    private double sqrSigmaNoise;
78    public double SigmaNoise {
79      get { return Math.Sqrt(sqrSigmaNoise); }
80    }
81
82    [Storable]
83    private double[] meanParameter;
84    [Storable]
85    private double[] covarianceParameter;
86
87    [Storable]
88    private double[,] l;
89
90    [Storable]
91    private double[,] x;
92    [Storable]
93    private Scaling inputScaling;
94
95
96    [StorableConstructor]
97    private GaussianProcessModel(bool deserializing) : base(deserializing) { }
98    private GaussianProcessModel(GaussianProcessModel original, Cloner cloner)
99      : base(original, cloner) {
100      this.meanFunction = cloner.Clone(original.meanFunction);
101      this.covarianceFunction = cloner.Clone(original.covarianceFunction);
102      this.inputScaling = cloner.Clone(original.inputScaling);
103      this.negativeLogLikelihood = original.negativeLogLikelihood;
104      this.targetVariable = original.targetVariable;
105      this.sqrSigmaNoise = original.sqrSigmaNoise;
106      if (original.meanParameter != null) {
107        this.meanParameter = (double[])original.meanParameter.Clone();
108      }
109      if (original.covarianceParameter != null) {
110        this.covarianceParameter = (double[])original.covarianceParameter.Clone();
111      }
112
113      // shallow copies of arrays because they cannot be modified
114      this.allowedInputVariables = original.allowedInputVariables;
115      this.alpha = original.alpha;
116      this.l = original.l;
117      this.x = original.x;
118    }
119    public GaussianProcessModel(IDataset ds, string targetVariable, IEnumerable<string> allowedInputVariables, IEnumerable<int> rows,
120      IEnumerable<double> hyp, IMeanFunction meanFunction, ICovarianceFunction covarianceFunction)
121      : base() {
122      this.name = ItemName;
123      this.description = ItemDescription;
124      this.meanFunction = (IMeanFunction)meanFunction.Clone();
125      this.covarianceFunction = (ICovarianceFunction)covarianceFunction.Clone();
126      this.targetVariable = targetVariable;
127      this.allowedInputVariables = allowedInputVariables.ToArray();
128
129
130      int nVariables = this.allowedInputVariables.Length;
131      meanParameter = hyp
132        .Take(this.meanFunction.GetNumberOfParameters(nVariables))
133        .ToArray();
134
135      covarianceParameter = hyp.Skip(this.meanFunction.GetNumberOfParameters(nVariables))
136                                             .Take(this.covarianceFunction.GetNumberOfParameters(nVariables))
137                                             .ToArray();
138      sqrSigmaNoise = Math.Exp(2.0 * hyp.Last());
139
140      CalculateModel(ds, rows);
141    }
142
143    private void CalculateModel(IDataset ds, IEnumerable<int> rows) {
144      inputScaling = new Scaling(ds, allowedInputVariables, rows);
145      x = AlglibUtil.PrepareAndScaleInputMatrix(ds, allowedInputVariables, rows, inputScaling);
146      var y = ds.GetDoubleValues(targetVariable, rows);
147
148      int n = x.GetLength(0);
149      l = new double[n, n];
150
151      // calculate means and covariances
152      var mean = meanFunction.GetParameterizedMeanFunction(meanParameter, Enumerable.Range(0, x.GetLength(1)));
153      double[] m = Enumerable.Range(0, x.GetLength(0))
154        .Select(r => mean.Mean(x, r))
155        .ToArray();
156
157      var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, Enumerable.Range(0, x.GetLength(1)));
158      for (int i = 0; i < n; i++) {
159        for (int j = i; j < n; j++) {
160          l[j, i] = cov.Covariance(x, i, j) / sqrSigmaNoise;
161          if (j == i) l[j, i] += 1.0;
162        }
163      }
164
165
166      // cholesky decomposition
167      int info;
168      alglib.densesolverreport denseSolveRep;
169
170      var res = alglib.spdmatrixcholesky(ref l, n, false);
171      if (!res) throw new ArgumentException("Matrix is not positive semidefinite");
172
173      // calculate sum of diagonal elements for likelihood
174      double diagSum = Enumerable.Range(0, n).Select(i => Math.Log(l[i, i])).Sum();
175
176      // solve for alpha
177      double[] ym = y.Zip(m, (a, b) => a - b).ToArray();
178
179      alglib.spdmatrixcholeskysolve(l, n, false, ym, out info, out denseSolveRep, out alpha);
180      for (int i = 0; i < alpha.Length; i++)
181        alpha[i] = alpha[i] / sqrSigmaNoise;
182      negativeLogLikelihood = 0.5 * Util.ScalarProd(ym, alpha) + diagSum + (n / 2.0) * Math.Log(2.0 * Math.PI * sqrSigmaNoise);
183
184      // derivatives
185      int nAllowedVariables = x.GetLength(1);
186
187      alglib.matinvreport matInvRep;
188      double[,] lCopy = new double[l.GetLength(0), l.GetLength(1)];
189      Array.Copy(l, lCopy, lCopy.Length);
190
191      alglib.spdmatrixcholeskyinverse(ref lCopy, n, false, out info, out matInvRep);
192      if (info != 1) throw new ArgumentException("Can't invert matrix to calculate gradients.");
193      for (int i = 0; i < n; i++) {
194        for (int j = 0; j <= i; j++)
195          lCopy[i, j] = lCopy[i, j] / sqrSigmaNoise - alpha[i] * alpha[j];
196      }
197
198      double noiseGradient = sqrSigmaNoise * Enumerable.Range(0, n).Select(i => lCopy[i, i]).Sum();
199
200      double[] meanGradients = new double[meanFunction.GetNumberOfParameters(nAllowedVariables)];
201      for (int k = 0; k < meanGradients.Length; k++) {
202        var meanGrad = Enumerable.Range(0, alpha.Length)
203        .Select(r => mean.Gradient(x, r, k));
204        meanGradients[k] = -Util.ScalarProd(meanGrad, alpha);
205      }
206
207      double[] covGradients = new double[covarianceFunction.GetNumberOfParameters(nAllowedVariables)];
208      if (covGradients.Length > 0) {
209        for (int i = 0; i < n; i++) {
210          for (int j = 0; j < i; j++) {
211            var g = cov.CovarianceGradient(x, i, j).ToArray();
212            for (int k = 0; k < covGradients.Length; k++) {
213              covGradients[k] += lCopy[i, j] * g[k];
214            }
215          }
216
217          var gDiag = cov.CovarianceGradient(x, i, i).ToArray();
218          for (int k = 0; k < covGradients.Length; k++) {
219            // diag
220            covGradients[k] += 0.5 * lCopy[i, i] * gDiag[k];
221          }
222        }
223      }
224
225      hyperparameterGradients =
226        meanGradients
227        .Concat(covGradients)
228        .Concat(new double[] { noiseGradient }).ToArray();
229
230    }
231
232
233    public override IDeepCloneable Clone(Cloner cloner) {
234      return new GaussianProcessModel(this, cloner);
235    }
236
237    // is called by the solution creator to set all parameter values of the covariance and mean function
238    // to the optimized values (necessary to make the values visible in the GUI)
239    public void FixParameters() {
240      covarianceFunction.SetParameter(covarianceParameter);
241      meanFunction.SetParameter(meanParameter);
242      covarianceParameter = new double[0];
243      meanParameter = new double[0];
244    }
245
246    #region IRegressionModel Members
247    public IEnumerable<double> GetEstimatedValues(IDataset dataset, IEnumerable<int> rows) {
248      return GetEstimatedValuesHelper(dataset, rows);
249    }
250    public GaussianProcessRegressionSolution CreateRegressionSolution(IRegressionProblemData problemData) {
251      return new GaussianProcessRegressionSolution(this, new RegressionProblemData(problemData));
252    }
253    IRegressionSolution IRegressionModel.CreateRegressionSolution(IRegressionProblemData problemData) {
254      return CreateRegressionSolution(problemData);
255    }
256    #endregion
257
258
259    private IEnumerable<double> GetEstimatedValuesHelper(IDataset dataset, IEnumerable<int> rows) {
260      var newX = AlglibUtil.PrepareAndScaleInputMatrix(dataset, allowedInputVariables, rows, inputScaling);
261      int newN = newX.GetLength(0);
262      int n = x.GetLength(0);
263      var Ks = new double[newN, n];
264      var mean = meanFunction.GetParameterizedMeanFunction(meanParameter, Enumerable.Range(0, newX.GetLength(1)));
265      var ms = Enumerable.Range(0, newX.GetLength(0))
266      .Select(r => mean.Mean(newX, r))
267      .ToArray();
268      var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, Enumerable.Range(0, newX.GetLength(1)));
269      for (int i = 0; i < newN; i++) {
270        for (int j = 0; j < n; j++) {
271          Ks[i, j] = cov.CrossCovariance(x, newX, j, i);
272        }
273      }
274
275      return Enumerable.Range(0, newN)
276        .Select(i => ms[i] + Util.ScalarProd(Util.GetRow(Ks, i), alpha));
277    }
278
279    public IEnumerable<double> GetEstimatedVariance(IDataset dataset, IEnumerable<int> rows) {
280      var newX = AlglibUtil.PrepareAndScaleInputMatrix(dataset, allowedInputVariables, rows, inputScaling);
281      int newN = newX.GetLength(0);
282      int n = x.GetLength(0);
283
284      var kss = new double[newN];
285      double[,] sWKs = new double[n, newN];
286      var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, Enumerable.Range(0, x.GetLength(1)));
287
288      // for stddev
289      for (int i = 0; i < newN; i++)
290        kss[i] = cov.Covariance(newX, i, i);
291
292      for (int i = 0; i < newN; i++) {
293        for (int j = 0; j < n; j++) {
294          sWKs[j, i] = cov.CrossCovariance(x, newX, j, i) / Math.Sqrt(sqrSigmaNoise);
295        }
296      }
297
298      // for stddev
299      alglib.rmatrixlefttrsm(n, newN, l, 0, 0, false, false, 0, ref sWKs, 0, 0);
300
301      for (int i = 0; i < newN; i++) {
302        var sumV = Util.ScalarProd(Util.GetCol(sWKs, i), Util.GetCol(sWKs, i));
303        kss[i] -= sumV;
304        if (kss[i] < 0) kss[i] = 0;
305      }
306      return kss;
307    }
308  }
309}
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