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source: trunk/sources/HeuristicLab.Algorithms.DataAnalysis/3.4/GaussianProcess/GaussianProcessModel.cs @ 13160

Last change on this file since 13160 was 13160, checked in by gkronber, 8 years ago

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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    private double[,] l; // used to be storable in previous versions (is calculated lazily now)
88    private double[,] x; // scaled training dataset, used to be storable in previous versions (is calculated lazily now)
89
90    // BackwardsCompatibility3.4
91    #region Backwards compatible code, remove with 3.5
92    [Storable(Name = "l")] // restore if available but don't store anymore
93    private double[,] l_storable {
94      set { this.l = value; }
95      get {
96        if (trainingDataset == null) return l; // this model has been created with an old version
97        else return null; // if the training dataset is available l should not be serialized
98      }
99    }
100    [Storable(Name = "x")] // restore if available but don't store anymore
101    private double[,] x_storable {
102      set { this.x = value; }
103      get {
104        if (trainingDataset == null) return x; // this model has been created with an old version
105        else return null; // if the training dataset is available x should not be serialized
106      }
107    }
108    #endregion
109
110
111    [Storable]
112    private IDataset trainingDataset; // it is better to store the original training dataset completely because this is more efficient in persistence
113    [Storable]
114    private int[] trainingRows;
115
116    [Storable]
117    private Scaling inputScaling;
118
119
120    [StorableConstructor]
121    private GaussianProcessModel(bool deserializing) : base(deserializing) { }
122    private GaussianProcessModel(GaussianProcessModel original, Cloner cloner)
123      : base(original, cloner) {
124      this.meanFunction = cloner.Clone(original.meanFunction);
125      this.covarianceFunction = cloner.Clone(original.covarianceFunction);
126      if (original.inputScaling != null)
127        this.inputScaling = cloner.Clone(original.inputScaling);
128      this.trainingDataset = cloner.Clone(original.trainingDataset);
129      this.negativeLogLikelihood = original.negativeLogLikelihood;
130      this.targetVariable = original.targetVariable;
131      this.sqrSigmaNoise = original.sqrSigmaNoise;
132      if (original.meanParameter != null) {
133        this.meanParameter = (double[])original.meanParameter.Clone();
134      }
135      if (original.covarianceParameter != null) {
136        this.covarianceParameter = (double[])original.covarianceParameter.Clone();
137      }
138
139      // shallow copies of arrays because they cannot be modified
140      this.trainingRows = original.trainingRows;
141      this.allowedInputVariables = original.allowedInputVariables;
142      this.alpha = original.alpha;
143      this.l = original.l;
144      this.x = original.x;
145    }
146    public GaussianProcessModel(IDataset ds, string targetVariable, IEnumerable<string> allowedInputVariables, IEnumerable<int> rows,
147      IEnumerable<double> hyp, IMeanFunction meanFunction, ICovarianceFunction covarianceFunction,
148      bool scaleInputs = true)
149      : base() {
150      this.name = ItemName;
151      this.description = ItemDescription;
152      this.meanFunction = (IMeanFunction)meanFunction.Clone();
153      this.covarianceFunction = (ICovarianceFunction)covarianceFunction.Clone();
154      this.targetVariable = targetVariable;
155      this.allowedInputVariables = allowedInputVariables.ToArray();
156
157
158      int nVariables = this.allowedInputVariables.Length;
159      meanParameter = hyp
160        .Take(this.meanFunction.GetNumberOfParameters(nVariables))
161        .ToArray();
162
163      covarianceParameter = hyp.Skip(this.meanFunction.GetNumberOfParameters(nVariables))
164                                             .Take(this.covarianceFunction.GetNumberOfParameters(nVariables))
165                                             .ToArray();
166      sqrSigmaNoise = Math.Exp(2.0 * hyp.Last());
167      try {
168        CalculateModel(ds, rows, scaleInputs);
169      } catch (alglib.alglibexception ae) {
170        // wrap exception so that calling code doesn't have to know about alglib implementation
171        throw new ArgumentException("There was a problem in the calculation of the Gaussian process model", ae);
172      }
173    }
174
175    private void CalculateModel(IDataset ds, IEnumerable<int> rows, bool scaleInputs = true) {
176      this.trainingDataset = (IDataset)ds.Clone();
177      this.trainingRows = rows.ToArray();
178      this.inputScaling = scaleInputs ? new Scaling(ds, allowedInputVariables, rows) : null;
179
180      x = GetData(ds, this.allowedInputVariables, this.trainingRows, this.inputScaling);
181
182      IEnumerable<double> y;
183      y = ds.GetDoubleValues(targetVariable, rows);
184
185      int n = x.GetLength(0);
186
187      // calculate cholesky decomposed (lower triangular) covariance matrix
188      var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, Enumerable.Range(0, x.GetLength(1)));
189      this.l = CalculateL(x, cov, sqrSigmaNoise);
190
191      // calculate mean
192      var mean = meanFunction.GetParameterizedMeanFunction(meanParameter, Enumerable.Range(0, x.GetLength(1)));
193      double[] m = Enumerable.Range(0, x.GetLength(0))
194        .Select(r => mean.Mean(x, r))
195        .ToArray();
196
197      // calculate sum of diagonal elements for likelihood
198      double diagSum = Enumerable.Range(0, n).Select(i => Math.Log(l[i, i])).Sum();
199
200      // solve for alpha
201      double[] ym = y.Zip(m, (a, b) => a - b).ToArray();
202
203      int info;
204      alglib.densesolverreport denseSolveRep;
205
206      alglib.spdmatrixcholeskysolve(l, n, false, ym, out info, out denseSolveRep, out alpha);
207      for (int i = 0; i < alpha.Length; i++)
208        alpha[i] = alpha[i] / sqrSigmaNoise;
209      negativeLogLikelihood = 0.5 * Util.ScalarProd(ym, alpha) + diagSum + (n / 2.0) * Math.Log(2.0 * Math.PI * sqrSigmaNoise);
210
211      // derivatives
212      int nAllowedVariables = x.GetLength(1);
213
214      alglib.matinvreport matInvRep;
215      double[,] lCopy = new double[l.GetLength(0), l.GetLength(1)];
216      Array.Copy(l, lCopy, lCopy.Length);
217
218      alglib.spdmatrixcholeskyinverse(ref lCopy, n, false, out info, out matInvRep);
219      if (info != 1) throw new ArgumentException("Can't invert matrix to calculate gradients.");
220      for (int i = 0; i < n; i++) {
221        for (int j = 0; j <= i; j++)
222          lCopy[i, j] = lCopy[i, j] / sqrSigmaNoise - alpha[i] * alpha[j];
223      }
224
225      double noiseGradient = sqrSigmaNoise * Enumerable.Range(0, n).Select(i => lCopy[i, i]).Sum();
226
227      double[] meanGradients = new double[meanFunction.GetNumberOfParameters(nAllowedVariables)];
228      for (int k = 0; k < meanGradients.Length; k++) {
229        var meanGrad = Enumerable.Range(0, alpha.Length)
230        .Select(r => mean.Gradient(x, r, k));
231        meanGradients[k] = -Util.ScalarProd(meanGrad, alpha);
232      }
233
234      double[] covGradients = new double[covarianceFunction.GetNumberOfParameters(nAllowedVariables)];
235      if (covGradients.Length > 0) {
236        for (int i = 0; i < n; i++) {
237          for (int j = 0; j < i; j++) {
238            var g = cov.CovarianceGradient(x, i, j).ToArray();
239            for (int k = 0; k < covGradients.Length; k++) {
240              covGradients[k] += lCopy[i, j] * g[k];
241            }
242          }
243
244          var gDiag = cov.CovarianceGradient(x, i, i).ToArray();
245          for (int k = 0; k < covGradients.Length; k++) {
246            // diag
247            covGradients[k] += 0.5 * lCopy[i, i] * gDiag[k];
248          }
249        }
250      }
251
252      hyperparameterGradients =
253        meanGradients
254        .Concat(covGradients)
255        .Concat(new double[] { noiseGradient }).ToArray();
256
257    }
258
259    private static double[,] GetData(IDataset ds, IEnumerable<string> allowedInputs, IEnumerable<int> rows, Scaling scaling) {
260      if (scaling != null) {
261        return AlglibUtil.PrepareAndScaleInputMatrix(ds, allowedInputs, rows, scaling);
262      } else {
263        return AlglibUtil.PrepareInputMatrix(ds, allowedInputs, rows);
264      }
265    }
266
267    private static double[,] CalculateL(double[,] x, ParameterizedCovarianceFunction cov, double sqrSigmaNoise) {
268      int n = x.GetLength(0);
269      var l = new double[n, n];
270
271      // calculate covariances
272      for (int i = 0; i < n; i++) {
273        for (int j = i; j < n; j++) {
274          l[j, i] = cov.Covariance(x, i, j) / sqrSigmaNoise;
275          if (j == i) l[j, i] += 1.0;
276        }
277      }
278
279      // cholesky decomposition
280      var res = alglib.trfac.spdmatrixcholesky(ref l, n, false);
281      if (!res) throw new ArgumentException("Matrix is not positive semidefinite");
282      return l;
283    }
284
285
286    public override IDeepCloneable Clone(Cloner cloner) {
287      return new GaussianProcessModel(this, cloner);
288    }
289
290    // is called by the solution creator to set all parameter values of the covariance and mean function
291    // to the optimized values (necessary to make the values visible in the GUI)
292    public void FixParameters() {
293      covarianceFunction.SetParameter(covarianceParameter);
294      meanFunction.SetParameter(meanParameter);
295      covarianceParameter = new double[0];
296      meanParameter = new double[0];
297    }
298
299    #region IRegressionModel Members
300    public IEnumerable<double> GetEstimatedValues(IDataset dataset, IEnumerable<int> rows) {
301      return GetEstimatedValuesHelper(dataset, rows);
302    }
303    public GaussianProcessRegressionSolution CreateRegressionSolution(IRegressionProblemData problemData) {
304      return new GaussianProcessRegressionSolution(this, new RegressionProblemData(problemData));
305    }
306    IRegressionSolution IRegressionModel.CreateRegressionSolution(IRegressionProblemData problemData) {
307      return CreateRegressionSolution(problemData);
308    }
309    #endregion
310
311
312    private IEnumerable<double> GetEstimatedValuesHelper(IDataset dataset, IEnumerable<int> rows) {
313      try {
314        if (x == null) {
315          x = GetData(trainingDataset, allowedInputVariables, trainingRows, inputScaling);
316        }
317        int n = x.GetLength(0);
318
319        double[,] newX = GetData(dataset, allowedInputVariables, rows, inputScaling);
320        int newN = newX.GetLength(0);
321
322        var Ks = new double[newN, n];
323        var mean = meanFunction.GetParameterizedMeanFunction(meanParameter, Enumerable.Range(0, newX.GetLength(1)));
324        var ms = Enumerable.Range(0, newX.GetLength(0))
325        .Select(r => mean.Mean(newX, r))
326        .ToArray();
327        var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, Enumerable.Range(0, newX.GetLength(1)));
328        for (int i = 0; i < newN; i++) {
329          for (int j = 0; j < n; j++) {
330            Ks[i, j] = cov.CrossCovariance(x, newX, j, i);
331          }
332        }
333
334        return Enumerable.Range(0, newN)
335          .Select(i => ms[i] + Util.ScalarProd(Util.GetRow(Ks, i), alpha));
336      } catch (alglib.alglibexception ae) {
337        // wrap exception so that calling code doesn't have to know about alglib implementation
338        throw new ArgumentException("There was a problem in the calculation of the Gaussian process model", ae);
339      }
340    }
341
342    public IEnumerable<double> GetEstimatedVariance(IDataset dataset, IEnumerable<int> rows) {
343      try {
344        if (x == null) {
345          x = GetData(trainingDataset, allowedInputVariables, trainingRows, inputScaling);
346        }
347        int n = x.GetLength(0);
348
349        var newX = GetData(dataset, allowedInputVariables, rows, inputScaling);
350        int newN = newX.GetLength(0);
351
352        var kss = new double[newN];
353        double[,] sWKs = new double[n, newN];
354        var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, Enumerable.Range(0, x.GetLength(1)));
355
356        if (l == null) {
357          l = CalculateL(x, cov, sqrSigmaNoise);
358        }
359
360        // for stddev
361        for (int i = 0; i < newN; i++)
362          kss[i] = cov.Covariance(newX, i, i);
363
364        for (int i = 0; i < newN; i++) {
365          for (int j = 0; j < n; j++) {
366            sWKs[j, i] = cov.CrossCovariance(x, newX, j, i) / Math.Sqrt(sqrSigmaNoise);
367          }
368        }
369
370        // for stddev
371        alglib.ablas.rmatrixlefttrsm(n, newN, l, 0, 0, false, false, 0, ref sWKs, 0, 0);
372
373        for (int i = 0; i < newN; i++) {
374          var sumV = Util.ScalarProd(Util.GetCol(sWKs, i), Util.GetCol(sWKs, i));
375          kss[i] += sqrSigmaNoise; // kss is V(f), add noise variance of predictive distibution to get V(y)
376          kss[i] -= sumV;
377          if (kss[i] < 0) kss[i] = 0;
378        }
379        return kss;
380      } catch (alglib.alglibexception ae) {
381        // wrap exception so that calling code doesn't have to know about alglib implementation
382        throw new ArgumentException("There was a problem in the calculation of the Gaussian process model", ae);
383      }
384    }
385  }
386}
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