source: stable/HeuristicLab.Algorithms.DataAnalysis/3.4/GaussianProcess/GaussianProcessModel.cs @ 13145

Last change on this file since 13145 was 13145, checked in by gkronber, 5 years ago

#2502 merged r13121 from trunk to stable branch

File size: 14.1 KB
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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      this.inputScaling = cloner.Clone(original.inputScaling);
127      this.trainingDataset = cloner.Clone(original.trainingDataset);
128      this.negativeLogLikelihood = original.negativeLogLikelihood;
129      this.targetVariable = original.targetVariable;
130      this.sqrSigmaNoise = original.sqrSigmaNoise;
131      if (original.meanParameter != null) {
132        this.meanParameter = (double[])original.meanParameter.Clone();
133      }
134      if (original.covarianceParameter != null) {
135        this.covarianceParameter = (double[])original.covarianceParameter.Clone();
136      }
137
138      // shallow copies of arrays because they cannot be modified
139      this.trainingRows = original.trainingRows;
140      this.allowedInputVariables = original.allowedInputVariables;
141      this.alpha = original.alpha;
142      this.l = original.l;
143      this.x = original.x;
144    }
145    public GaussianProcessModel(IDataset ds, string targetVariable, IEnumerable<string> allowedInputVariables, IEnumerable<int> rows,
146      IEnumerable<double> hyp, IMeanFunction meanFunction, ICovarianceFunction covarianceFunction)
147      : base() {
148      this.name = ItemName;
149      this.description = ItemDescription;
150      this.meanFunction = (IMeanFunction)meanFunction.Clone();
151      this.covarianceFunction = (ICovarianceFunction)covarianceFunction.Clone();
152      this.targetVariable = targetVariable;
153      this.allowedInputVariables = allowedInputVariables.ToArray();
154
155
156      int nVariables = this.allowedInputVariables.Length;
157      meanParameter = hyp
158        .Take(this.meanFunction.GetNumberOfParameters(nVariables))
159        .ToArray();
160
161      covarianceParameter = hyp.Skip(this.meanFunction.GetNumberOfParameters(nVariables))
162                                             .Take(this.covarianceFunction.GetNumberOfParameters(nVariables))
163                                             .ToArray();
164      sqrSigmaNoise = Math.Exp(2.0 * hyp.Last());
165      CalculateModel(ds, rows);
166    }
167
168    private void CalculateModel(IDataset ds, IEnumerable<int> rows) {
169      this.trainingDataset = (IDataset)ds.Clone();
170      this.trainingRows = rows.ToArray();
171      this.inputScaling = new Scaling(trainingDataset, allowedInputVariables, rows);
172      this.x = CalculateX(trainingDataset, allowedInputVariables, rows, inputScaling);
173      var y = ds.GetDoubleValues(targetVariable, rows);
174
175      int n = x.GetLength(0);
176
177      // calculate cholesky decomposed (lower triangular) covariance matrix
178      var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, Enumerable.Range(0, x.GetLength(1)));
179      this.l = CalculateL(x, cov, sqrSigmaNoise);
180
181      // calculate mean
182      var mean = meanFunction.GetParameterizedMeanFunction(meanParameter, Enumerable.Range(0, x.GetLength(1)));
183      double[] m = Enumerable.Range(0, x.GetLength(0))
184        .Select(r => mean.Mean(x, r))
185        .ToArray();
186
187
188
189      // calculate sum of diagonal elements for likelihood
190      double diagSum = Enumerable.Range(0, n).Select(i => Math.Log(l[i, i])).Sum();
191
192      // solve for alpha
193      double[] ym = y.Zip(m, (a, b) => a - b).ToArray();
194
195      int info;
196      alglib.densesolverreport denseSolveRep;
197
198      alglib.spdmatrixcholeskysolve(l, n, false, ym, out info, out denseSolveRep, out alpha);
199      for (int i = 0; i < alpha.Length; i++)
200        alpha[i] = alpha[i] / sqrSigmaNoise;
201      negativeLogLikelihood = 0.5 * Util.ScalarProd(ym, alpha) + diagSum + (n / 2.0) * Math.Log(2.0 * Math.PI * sqrSigmaNoise);
202
203      // derivatives
204      int nAllowedVariables = x.GetLength(1);
205
206      alglib.matinvreport matInvRep;
207      double[,] lCopy = new double[l.GetLength(0), l.GetLength(1)];
208      Array.Copy(l, lCopy, lCopy.Length);
209
210      alglib.spdmatrixcholeskyinverse(ref lCopy, n, false, out info, out matInvRep);
211      if (info != 1) throw new ArgumentException("Can't invert matrix to calculate gradients.");
212      for (int i = 0; i < n; i++) {
213        for (int j = 0; j <= i; j++)
214          lCopy[i, j] = lCopy[i, j] / sqrSigmaNoise - alpha[i] * alpha[j];
215      }
216
217      double noiseGradient = sqrSigmaNoise * Enumerable.Range(0, n).Select(i => lCopy[i, i]).Sum();
218
219      double[] meanGradients = new double[meanFunction.GetNumberOfParameters(nAllowedVariables)];
220      for (int k = 0; k < meanGradients.Length; k++) {
221        var meanGrad = Enumerable.Range(0, alpha.Length)
222        .Select(r => mean.Gradient(x, r, k));
223        meanGradients[k] = -Util.ScalarProd(meanGrad, alpha);
224      }
225
226      double[] covGradients = new double[covarianceFunction.GetNumberOfParameters(nAllowedVariables)];
227      if (covGradients.Length > 0) {
228        for (int i = 0; i < n; i++) {
229          for (int j = 0; j < i; j++) {
230            var g = cov.CovarianceGradient(x, i, j).ToArray();
231            for (int k = 0; k < covGradients.Length; k++) {
232              covGradients[k] += lCopy[i, j] * g[k];
233            }
234          }
235
236          var gDiag = cov.CovarianceGradient(x, i, i).ToArray();
237          for (int k = 0; k < covGradients.Length; k++) {
238            // diag
239            covGradients[k] += 0.5 * lCopy[i, i] * gDiag[k];
240          }
241        }
242      }
243
244      hyperparameterGradients =
245        meanGradients
246        .Concat(covGradients)
247        .Concat(new double[] { noiseGradient }).ToArray();
248
249    }
250
251    private static double[,] CalculateX(IDataset ds, IEnumerable<string> allowedInputVariables, IEnumerable<int> rows, Scaling inputScaling) {
252      return AlglibUtil.PrepareAndScaleInputMatrix(ds, allowedInputVariables, rows, inputScaling);
253    }
254
255    private static double[,] CalculateL(double[,] x, ParameterizedCovarianceFunction cov, double sqrSigmaNoise) {
256      int n = x.GetLength(0);
257      var l = new double[n, n];
258
259      // calculate covariances
260      for (int i = 0; i < n; i++) {
261        for (int j = i; j < n; j++) {
262          l[j, i] = cov.Covariance(x, i, j) / sqrSigmaNoise;
263          if (j == i) l[j, i] += 1.0;
264        }
265      }
266
267      // cholesky decomposition
268      var res = alglib.trfac.spdmatrixcholesky(ref l, n, false);
269      if (!res) throw new ArgumentException("Matrix is not positive semidefinite");
270      return l;
271    }
272
273
274    public override IDeepCloneable Clone(Cloner cloner) {
275      return new GaussianProcessModel(this, cloner);
276    }
277
278    // is called by the solution creator to set all parameter values of the covariance and mean function
279    // to the optimized values (necessary to make the values visible in the GUI)
280    public void FixParameters() {
281      covarianceFunction.SetParameter(covarianceParameter);
282      meanFunction.SetParameter(meanParameter);
283      covarianceParameter = new double[0];
284      meanParameter = new double[0];
285    }
286
287    #region IRegressionModel Members
288    public IEnumerable<double> GetEstimatedValues(IDataset dataset, IEnumerable<int> rows) {
289      return GetEstimatedValuesHelper(dataset, rows);
290    }
291    public GaussianProcessRegressionSolution CreateRegressionSolution(IRegressionProblemData problemData) {
292      return new GaussianProcessRegressionSolution(this, new RegressionProblemData(problemData));
293    }
294    IRegressionSolution IRegressionModel.CreateRegressionSolution(IRegressionProblemData problemData) {
295      return CreateRegressionSolution(problemData);
296    }
297    #endregion
298
299
300    private IEnumerable<double> GetEstimatedValuesHelper(IDataset dataset, IEnumerable<int> rows) {
301      if (x == null) {
302        this.x = CalculateX(trainingDataset, allowedInputVariables, trainingRows, inputScaling);
303      }
304      int n = x.GetLength(0);
305
306      var newX = AlglibUtil.PrepareAndScaleInputMatrix(dataset, allowedInputVariables, rows, inputScaling);
307      int newN = newX.GetLength(0);
308
309      var Ks = new double[newN, n];
310      var mean = meanFunction.GetParameterizedMeanFunction(meanParameter, Enumerable.Range(0, newX.GetLength(1)));
311      var ms = Enumerable.Range(0, newX.GetLength(0))
312      .Select(r => mean.Mean(newX, r))
313      .ToArray();
314      var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, Enumerable.Range(0, newX.GetLength(1)));
315      for (int i = 0; i < newN; i++) {
316        for (int j = 0; j < n; j++) {
317          Ks[i, j] = cov.CrossCovariance(x, newX, j, i);
318        }
319      }
320
321      return Enumerable.Range(0, newN)
322        .Select(i => ms[i] + Util.ScalarProd(Util.GetRow(Ks, i), alpha));
323    }
324
325    public IEnumerable<double> GetEstimatedVariance(IDataset dataset, IEnumerable<int> rows) {
326      if (x == null) {
327        this.x = CalculateX(trainingDataset, allowedInputVariables, trainingRows, inputScaling);
328      }
329      int n = x.GetLength(0);
330
331      var newX = AlglibUtil.PrepareAndScaleInputMatrix(dataset, allowedInputVariables, rows, inputScaling);
332      int newN = newX.GetLength(0);
333
334      var kss = new double[newN];
335      double[,] sWKs = new double[n, newN];
336      var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, Enumerable.Range(0, x.GetLength(1)));
337
338      if (l == null) {
339        l = CalculateL(x, cov, sqrSigmaNoise);
340      }
341
342      // for stddev
343      for (int i = 0; i < newN; i++)
344        kss[i] = cov.Covariance(newX, i, i);
345
346      for (int i = 0; i < newN; i++) {
347        for (int j = 0; j < n; j++) {
348          sWKs[j, i] = cov.CrossCovariance(x, newX, j, i) / Math.Sqrt(sqrSigmaNoise);
349        }
350      }
351
352      // for stddev
353      alglib.ablas.rmatrixlefttrsm(n, newN, l, 0, 0, false, false, 0, ref sWKs, 0, 0);
354
355      for (int i = 0; i < newN; i++) {
356        var sumV = Util.ScalarProd(Util.GetCol(sWKs, i), Util.GetCol(sWKs, i));
357        kss[i] += sqrSigmaNoise; // kss is V(f), add noise variance of predictive distibution to get V(y)
358        kss[i] -= sumV;
359        if (kss[i] < 0) kss[i] = 0;
360      }
361      return kss;
362    }
363  }
364}
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