source: trunk/sources/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/SingleObjective/Evaluators/SymbolicRegressionConstantOptimizationEvaluator.cs @ 14349

Last change on this file since 14349 was 14349, checked in by gkronber, 4 years ago

#2686: added support for lagged variables to constants optimizer

File size: 24.3 KB
Line 
1#region License Information
2/* HeuristicLab
3 * Copyright (C) 2002-2016 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 AutoDiff;
26using HeuristicLab.Common;
27using HeuristicLab.Core;
28using HeuristicLab.Data;
29using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
30using HeuristicLab.Parameters;
31using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
32
33namespace HeuristicLab.Problems.DataAnalysis.Symbolic.Regression {
34  [Item("Constant Optimization Evaluator", "Calculates Pearson R² of a symbolic regression solution and optimizes the constant used.")]
35  [StorableClass]
36  public class SymbolicRegressionConstantOptimizationEvaluator : SymbolicRegressionSingleObjectiveEvaluator {
37    private const string ConstantOptimizationIterationsParameterName = "ConstantOptimizationIterations";
38    private const string ConstantOptimizationImprovementParameterName = "ConstantOptimizationImprovement";
39    private const string ConstantOptimizationProbabilityParameterName = "ConstantOptimizationProbability";
40    private const string ConstantOptimizationRowsPercentageParameterName = "ConstantOptimizationRowsPercentage";
41    private const string UpdateConstantsInTreeParameterName = "UpdateConstantsInSymbolicExpressionTree";
42    private const string UpdateVariableWeightsParameterName = "Update Variable Weights";
43
44    public IFixedValueParameter<IntValue> ConstantOptimizationIterationsParameter {
45      get { return (IFixedValueParameter<IntValue>)Parameters[ConstantOptimizationIterationsParameterName]; }
46    }
47    public IFixedValueParameter<DoubleValue> ConstantOptimizationImprovementParameter {
48      get { return (IFixedValueParameter<DoubleValue>)Parameters[ConstantOptimizationImprovementParameterName]; }
49    }
50    public IFixedValueParameter<PercentValue> ConstantOptimizationProbabilityParameter {
51      get { return (IFixedValueParameter<PercentValue>)Parameters[ConstantOptimizationProbabilityParameterName]; }
52    }
53    public IFixedValueParameter<PercentValue> ConstantOptimizationRowsPercentageParameter {
54      get { return (IFixedValueParameter<PercentValue>)Parameters[ConstantOptimizationRowsPercentageParameterName]; }
55    }
56    public IFixedValueParameter<BoolValue> UpdateConstantsInTreeParameter {
57      get { return (IFixedValueParameter<BoolValue>)Parameters[UpdateConstantsInTreeParameterName]; }
58    }
59    public IFixedValueParameter<BoolValue> UpdateVariableWeightsParameter {
60      get { return (IFixedValueParameter<BoolValue>)Parameters[UpdateVariableWeightsParameterName]; }
61    }
62
63
64    public IntValue ConstantOptimizationIterations {
65      get { return ConstantOptimizationIterationsParameter.Value; }
66    }
67    public DoubleValue ConstantOptimizationImprovement {
68      get { return ConstantOptimizationImprovementParameter.Value; }
69    }
70    public PercentValue ConstantOptimizationProbability {
71      get { return ConstantOptimizationProbabilityParameter.Value; }
72    }
73    public PercentValue ConstantOptimizationRowsPercentage {
74      get { return ConstantOptimizationRowsPercentageParameter.Value; }
75    }
76    public bool UpdateConstantsInTree {
77      get { return UpdateConstantsInTreeParameter.Value.Value; }
78      set { UpdateConstantsInTreeParameter.Value.Value = value; }
79    }
80
81    public bool UpdateVariableWeights {
82      get { return UpdateVariableWeightsParameter.Value.Value; }
83      set { UpdateVariableWeightsParameter.Value.Value = value; }
84    }
85
86    public override bool Maximization {
87      get { return true; }
88    }
89
90    [StorableConstructor]
91    protected SymbolicRegressionConstantOptimizationEvaluator(bool deserializing) : base(deserializing) { }
92    protected SymbolicRegressionConstantOptimizationEvaluator(SymbolicRegressionConstantOptimizationEvaluator original, Cloner cloner)
93      : base(original, cloner) {
94    }
95    public SymbolicRegressionConstantOptimizationEvaluator()
96      : base() {
97      Parameters.Add(new FixedValueParameter<IntValue>(ConstantOptimizationIterationsParameterName, "Determines how many iterations should be calculated while optimizing the constant of a symbolic expression tree (0 indicates other or default stopping criterion).", new IntValue(10), true));
98      Parameters.Add(new FixedValueParameter<DoubleValue>(ConstantOptimizationImprovementParameterName, "Determines the relative improvement which must be achieved in the constant optimization to continue with it (0 indicates other or default stopping criterion).", new DoubleValue(0), true) { Hidden = true });
99      Parameters.Add(new FixedValueParameter<PercentValue>(ConstantOptimizationProbabilityParameterName, "Determines the probability that the constants are optimized", new PercentValue(1), true));
100      Parameters.Add(new FixedValueParameter<PercentValue>(ConstantOptimizationRowsPercentageParameterName, "Determines the percentage of the rows which should be used for constant optimization", new PercentValue(1), true));
101      Parameters.Add(new FixedValueParameter<BoolValue>(UpdateConstantsInTreeParameterName, "Determines if the constants in the tree should be overwritten by the optimized constants.", new BoolValue(true)) { Hidden = true });
102      Parameters.Add(new FixedValueParameter<BoolValue>(UpdateVariableWeightsParameterName, "Determines if the variable weights in the tree should be  optimized.", new BoolValue(true)) { Hidden = true });
103    }
104
105    public override IDeepCloneable Clone(Cloner cloner) {
106      return new SymbolicRegressionConstantOptimizationEvaluator(this, cloner);
107    }
108
109    [StorableHook(HookType.AfterDeserialization)]
110    private void AfterDeserialization() {
111      if (!Parameters.ContainsKey(UpdateConstantsInTreeParameterName))
112        Parameters.Add(new FixedValueParameter<BoolValue>(UpdateConstantsInTreeParameterName, "Determines if the constants in the tree should be overwritten by the optimized constants.", new BoolValue(true)));
113      if (!Parameters.ContainsKey(UpdateVariableWeightsParameterName))
114        Parameters.Add(new FixedValueParameter<BoolValue>(UpdateVariableWeightsParameterName, "Determines if the variable weights in the tree should be  optimized.", new BoolValue(true)));
115    }
116
117    public override IOperation InstrumentedApply() {
118      var solution = SymbolicExpressionTreeParameter.ActualValue;
119      double quality;
120      if (RandomParameter.ActualValue.NextDouble() < ConstantOptimizationProbability.Value) {
121        IEnumerable<int> constantOptimizationRows = GenerateRowsToEvaluate(ConstantOptimizationRowsPercentage.Value);
122        quality = OptimizeConstants(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, solution, ProblemDataParameter.ActualValue,
123           constantOptimizationRows, ApplyLinearScalingParameter.ActualValue.Value, ConstantOptimizationIterations.Value, updateVariableWeights: UpdateVariableWeights, lowerEstimationLimit: EstimationLimitsParameter.ActualValue.Lower, upperEstimationLimit: EstimationLimitsParameter.ActualValue.Upper, updateConstantsInTree: UpdateConstantsInTree);
124
125        if (ConstantOptimizationRowsPercentage.Value != RelativeNumberOfEvaluatedSamplesParameter.ActualValue.Value) {
126          var evaluationRows = GenerateRowsToEvaluate();
127          quality = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, solution, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, ProblemDataParameter.ActualValue, evaluationRows, ApplyLinearScalingParameter.ActualValue.Value);
128        }
129      } else {
130        var evaluationRows = GenerateRowsToEvaluate();
131        quality = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, solution, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, ProblemDataParameter.ActualValue, evaluationRows, ApplyLinearScalingParameter.ActualValue.Value);
132      }
133      QualityParameter.ActualValue = new DoubleValue(quality);
134
135      return base.InstrumentedApply();
136    }
137
138    public override double Evaluate(IExecutionContext context, ISymbolicExpressionTree tree, IRegressionProblemData problemData, IEnumerable<int> rows) {
139      SymbolicDataAnalysisTreeInterpreterParameter.ExecutionContext = context;
140      EstimationLimitsParameter.ExecutionContext = context;
141      ApplyLinearScalingParameter.ExecutionContext = context;
142
143      // Pearson R² evaluator is used on purpose instead of the const-opt evaluator,
144      // because Evaluate() is used to get the quality of evolved models on
145      // different partitions of the dataset (e.g., best validation model)
146      double r2 = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(SymbolicDataAnalysisTreeInterpreterParameter.ActualValue, tree, EstimationLimitsParameter.ActualValue.Lower, EstimationLimitsParameter.ActualValue.Upper, problemData, rows, ApplyLinearScalingParameter.ActualValue.Value);
147
148      SymbolicDataAnalysisTreeInterpreterParameter.ExecutionContext = null;
149      EstimationLimitsParameter.ExecutionContext = null;
150      ApplyLinearScalingParameter.ExecutionContext = null;
151
152      return r2;
153    }
154
155    #region derivations of functions
156    // create function factory for arctangent
157    private readonly Func<Term, UnaryFunc> arctan = UnaryFunc.Factory(
158      eval: Math.Atan,
159      diff: x => 1 / (1 + x * x));
160    private static readonly Func<Term, UnaryFunc> sin = UnaryFunc.Factory(
161      eval: Math.Sin,
162      diff: Math.Cos);
163    private static readonly Func<Term, UnaryFunc> cos = UnaryFunc.Factory(
164       eval: Math.Cos,
165       diff: x => -Math.Sin(x));
166    private static readonly Func<Term, UnaryFunc> tan = UnaryFunc.Factory(
167      eval: Math.Tan,
168      diff: x => 1 + Math.Tan(x) * Math.Tan(x));
169    private static readonly Func<Term, UnaryFunc> erf = UnaryFunc.Factory(
170      eval: alglib.errorfunction,
171      diff: x => 2.0 * Math.Exp(-(x * x)) / Math.Sqrt(Math.PI));
172    private static readonly Func<Term, UnaryFunc> norm = UnaryFunc.Factory(
173      eval: alglib.normaldistribution,
174      diff: x => -(Math.Exp(-(x * x)) * Math.Sqrt(Math.Exp(x * x)) * x) / Math.Sqrt(2 * Math.PI));
175    #endregion
176
177
178    public static double OptimizeConstants(ISymbolicDataAnalysisExpressionTreeInterpreter interpreter, ISymbolicExpressionTree tree, IRegressionProblemData problemData, IEnumerable<int> rows, bool applyLinearScaling, int maxIterations, bool updateVariableWeights = true, double lowerEstimationLimit = double.MinValue, double upperEstimationLimit = double.MaxValue, bool updateConstantsInTree = true) {
179
180      List<AutoDiff.Variable> variables = new List<AutoDiff.Variable>();
181      List<AutoDiff.Variable> parameters = new List<AutoDiff.Variable>();
182      List<string> variableNames = new List<string>();
183      List<int> lags = new List<int>();
184
185      AutoDiff.Term func;
186      if (!TryTransformToAutoDiff(tree.Root.GetSubtree(0), variables, parameters, variableNames, lags, updateVariableWeights, out func))
187        throw new NotSupportedException("Could not optimize constants of symbolic expression tree due to not supported symbols used in the tree.");
188      if (variableNames.Count == 0) return 0.0;
189
190      AutoDiff.IParametricCompiledTerm compiledFunc = func.Compile(variables.ToArray(), parameters.ToArray());
191
192      List<SymbolicExpressionTreeTerminalNode> terminalNodes = null;
193      if (updateVariableWeights)
194        terminalNodes = tree.Root.IterateNodesPrefix().OfType<SymbolicExpressionTreeTerminalNode>().ToList();
195      else
196        terminalNodes = new List<SymbolicExpressionTreeTerminalNode>(tree.Root.IterateNodesPrefix().OfType<ConstantTreeNode>());
197
198      //extract inital constants
199      double[] c = new double[variables.Count];
200      {
201        c[0] = 0.0;
202        c[1] = 1.0;
203        int i = 2;
204        foreach (var node in terminalNodes) {
205          ConstantTreeNode constantTreeNode = node as ConstantTreeNode;
206          VariableTreeNode variableTreeNode = node as VariableTreeNode;
207          if (constantTreeNode != null)
208            c[i++] = constantTreeNode.Value;
209          else if (updateVariableWeights && variableTreeNode != null)
210            c[i++] = variableTreeNode.Weight;
211        }
212      }
213      double[] originalConstants = (double[])c.Clone();
214      double originalQuality = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(interpreter, tree, lowerEstimationLimit, upperEstimationLimit, problemData, rows, applyLinearScaling);
215
216      alglib.lsfitstate state;
217      alglib.lsfitreport rep;
218      int info;
219
220      IDataset ds = problemData.Dataset;
221      double[,] x = new double[rows.Count(), variableNames.Count];
222      int row = 0;
223      foreach (var r in rows) {
224        for (int col = 0; col < variableNames.Count; col++) {
225          int lag = lags[col];
226          x[row, col] = ds.GetDoubleValue(variableNames[col], r + lag);
227        }
228        row++;
229      }
230      double[] y = ds.GetDoubleValues(problemData.TargetVariable, rows).ToArray();
231      int n = x.GetLength(0);
232      int m = x.GetLength(1);
233      int k = c.Length;
234
235      alglib.ndimensional_pfunc function_cx_1_func = CreatePFunc(compiledFunc);
236      alglib.ndimensional_pgrad function_cx_1_grad = CreatePGrad(compiledFunc);
237
238      try {
239        alglib.lsfitcreatefg(x, y, c, n, m, k, false, out state);
240        alglib.lsfitsetcond(state, 0.0, 0.0, maxIterations);
241        //alglib.lsfitsetgradientcheck(state, 0.001);
242        alglib.lsfitfit(state, function_cx_1_func, function_cx_1_grad, null, null);
243        alglib.lsfitresults(state, out info, out c, out rep);
244      } catch (ArithmeticException) {
245        return originalQuality;
246      } catch (alglib.alglibexception) {
247        return originalQuality;
248      }
249
250      //info == -7  => constant optimization failed due to wrong gradient
251      if (info != -7) UpdateConstants(tree, c.Skip(2).ToArray(), updateVariableWeights);
252      var quality = SymbolicRegressionSingleObjectivePearsonRSquaredEvaluator.Calculate(interpreter, tree, lowerEstimationLimit, upperEstimationLimit, problemData, rows, applyLinearScaling);
253
254      if (!updateConstantsInTree) UpdateConstants(tree, originalConstants.Skip(2).ToArray(), updateVariableWeights);
255      if (originalQuality - quality > 0.001 || double.IsNaN(quality)) {
256        UpdateConstants(tree, originalConstants.Skip(2).ToArray(), updateVariableWeights);
257        return originalQuality;
258      }
259      return quality;
260    }
261
262    private static void UpdateConstants(ISymbolicExpressionTree tree, double[] constants, bool updateVariableWeights) {
263      int i = 0;
264      foreach (var node in tree.Root.IterateNodesPrefix().OfType<SymbolicExpressionTreeTerminalNode>()) {
265        ConstantTreeNode constantTreeNode = node as ConstantTreeNode;
266        VariableTreeNode variableTreeNode = node as VariableTreeNode;
267        if (constantTreeNode != null)
268          constantTreeNode.Value = constants[i++];
269        else if (updateVariableWeights && variableTreeNode != null)
270          variableTreeNode.Weight = constants[i++];
271      }
272    }
273
274    private static alglib.ndimensional_pfunc CreatePFunc(AutoDiff.IParametricCompiledTerm compiledFunc) {
275      return (double[] c, double[] x, ref double func, object o) => {
276        func = compiledFunc.Evaluate(c, x);
277      };
278    }
279
280    private static alglib.ndimensional_pgrad CreatePGrad(AutoDiff.IParametricCompiledTerm compiledFunc) {
281      return (double[] c, double[] x, ref double func, double[] grad, object o) => {
282        var tupel = compiledFunc.Differentiate(c, x);
283        func = tupel.Item2;
284        Array.Copy(tupel.Item1, grad, grad.Length);
285      };
286    }
287
288    private static bool TryTransformToAutoDiff(ISymbolicExpressionTreeNode node, List<AutoDiff.Variable> variables, List<AutoDiff.Variable> parameters, List<string> variableNames, List<int> lags, bool updateVariableWeights, out AutoDiff.Term term) {
289      if (node.Symbol is Constant) {
290        var var = new AutoDiff.Variable();
291        variables.Add(var);
292        term = var;
293        return true;
294      }
295      if (node.Symbol is Variable) {
296        var varNode = node as VariableTreeNode;
297        var par = new AutoDiff.Variable();
298        parameters.Add(par);
299        variableNames.Add(varNode.VariableName);
300        lags.Add(0);
301
302        if (updateVariableWeights) {
303          var w = new AutoDiff.Variable();
304          variables.Add(w);
305          term = AutoDiff.TermBuilder.Product(w, par);
306        } else {
307          term = par;
308        }
309        return true;
310      }
311      if (node.Symbol is LaggedVariable) {
312        var varNode = node as LaggedVariableTreeNode;
313        var par = new AutoDiff.Variable();
314        parameters.Add(par);
315        variableNames.Add(varNode.VariableName);
316        lags.Add(varNode.Lag);
317
318        if (updateVariableWeights) {
319          var w = new AutoDiff.Variable();
320          variables.Add(w);
321          term = AutoDiff.TermBuilder.Product(w, par);
322        } else {
323          term = par;
324        }
325        return true;
326      }
327      if (node.Symbol is Addition) {
328        List<AutoDiff.Term> terms = new List<Term>();
329        foreach (var subTree in node.Subtrees) {
330          AutoDiff.Term t;
331          if (!TryTransformToAutoDiff(subTree, variables, parameters, variableNames, lags, updateVariableWeights, out t)) {
332            term = null;
333            return false;
334          }
335          terms.Add(t);
336        }
337        term = AutoDiff.TermBuilder.Sum(terms);
338        return true;
339      }
340      if (node.Symbol is Subtraction) {
341        List<AutoDiff.Term> terms = new List<Term>();
342        for (int i = 0; i < node.SubtreeCount; i++) {
343          AutoDiff.Term t;
344          if (!TryTransformToAutoDiff(node.GetSubtree(i), variables, parameters, variableNames, lags, updateVariableWeights, out t)) {
345            term = null;
346            return false;
347          }
348          if (i > 0) t = -t;
349          terms.Add(t);
350        }
351        if (terms.Count == 1) term = -terms[0];
352        else term = AutoDiff.TermBuilder.Sum(terms);
353        return true;
354      }
355      if (node.Symbol is Multiplication) {
356        List<AutoDiff.Term> terms = new List<Term>();
357        foreach (var subTree in node.Subtrees) {
358          AutoDiff.Term t;
359          if (!TryTransformToAutoDiff(subTree, variables, parameters, variableNames, lags, updateVariableWeights, out t)) {
360            term = null;
361            return false;
362          }
363          terms.Add(t);
364        }
365        if (terms.Count == 1) term = terms[0];
366        else term = terms.Aggregate((a, b) => new AutoDiff.Product(a, b));
367        return true;
368
369      }
370      if (node.Symbol is Division) {
371        List<AutoDiff.Term> terms = new List<Term>();
372        foreach (var subTree in node.Subtrees) {
373          AutoDiff.Term t;
374          if (!TryTransformToAutoDiff(subTree, variables, parameters, variableNames, lags, updateVariableWeights, out t)) {
375            term = null;
376            return false;
377          }
378          terms.Add(t);
379        }
380        if (terms.Count == 1) term = 1.0 / terms[0];
381        else term = terms.Aggregate((a, b) => new AutoDiff.Product(a, 1.0 / b));
382        return true;
383      }
384      if (node.Symbol is Logarithm) {
385        AutoDiff.Term t;
386        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, lags, updateVariableWeights, out t)) {
387          term = null;
388          return false;
389        } else {
390          term = AutoDiff.TermBuilder.Log(t);
391          return true;
392        }
393      }
394      if (node.Symbol is Exponential) {
395        AutoDiff.Term t;
396        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, lags, updateVariableWeights, out t)) {
397          term = null;
398          return false;
399        } else {
400          term = AutoDiff.TermBuilder.Exp(t);
401          return true;
402        }
403      }
404      if (node.Symbol is Square) {
405        AutoDiff.Term t;
406        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, lags, updateVariableWeights, out t)) {
407          term = null;
408          return false;
409        } else {
410          term = AutoDiff.TermBuilder.Power(t, 2.0);
411          return true;
412        }
413      }
414      if (node.Symbol is SquareRoot) {
415        AutoDiff.Term t;
416        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, lags, updateVariableWeights, out t)) {
417          term = null;
418          return false;
419        } else {
420          term = AutoDiff.TermBuilder.Power(t, 0.5);
421          return true;
422        }
423      }
424      if (node.Symbol is Sine) {
425        AutoDiff.Term t;
426        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, lags, updateVariableWeights, out t)) {
427          term = null;
428          return false;
429        } else {
430          term = sin(t);
431          return true;
432        }
433      }
434      if (node.Symbol is Cosine) {
435        AutoDiff.Term t;
436        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, lags, updateVariableWeights, out t)) {
437          term = null;
438          return false;
439        } else {
440          term = cos(t);
441          return true;
442        }
443      }
444      if (node.Symbol is Tangent) {
445        AutoDiff.Term t;
446        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, lags, updateVariableWeights, out t)) {
447          term = null;
448          return false;
449        } else {
450          term = tan(t);
451          return true;
452        }
453      }
454      if (node.Symbol is Erf) {
455        AutoDiff.Term t;
456        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, lags, updateVariableWeights, out t)) {
457          term = null;
458          return false;
459        } else {
460          term = erf(t);
461          return true;
462        }
463      }
464      if (node.Symbol is Norm) {
465        AutoDiff.Term t;
466        if (!TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, lags, updateVariableWeights, out t)) {
467          term = null;
468          return false;
469        } else {
470          term = norm(t);
471          return true;
472        }
473      }
474      if (node.Symbol is StartSymbol) {
475        var alpha = new AutoDiff.Variable();
476        var beta = new AutoDiff.Variable();
477        variables.Add(beta);
478        variables.Add(alpha);
479        AutoDiff.Term branchTerm;
480        if (TryTransformToAutoDiff(node.GetSubtree(0), variables, parameters, variableNames, lags, updateVariableWeights, out branchTerm)) {
481          term = branchTerm * alpha + beta;
482          return true;
483        } else {
484          term = null;
485          return false;
486        }
487      }
488      term = null;
489      return false;
490    }
491
492    public static bool CanOptimizeConstants(ISymbolicExpressionTree tree) {
493      var containsUnknownSymbol = (
494        from n in tree.Root.GetSubtree(0).IterateNodesPrefix()
495        where
496         !(n.Symbol is Variable) &&
497         !(n.Symbol is LaggedVariable) &&
498         !(n.Symbol is Constant) &&
499         !(n.Symbol is Addition) &&
500         !(n.Symbol is Subtraction) &&
501         !(n.Symbol is Multiplication) &&
502         !(n.Symbol is Division) &&
503         !(n.Symbol is Logarithm) &&
504         !(n.Symbol is Exponential) &&
505         !(n.Symbol is SquareRoot) &&
506         !(n.Symbol is Square) &&
507         !(n.Symbol is Sine) &&
508         !(n.Symbol is Cosine) &&
509         !(n.Symbol is Tangent) &&
510         !(n.Symbol is Erf) &&
511         !(n.Symbol is Norm) &&
512         !(n.Symbol is StartSymbol)
513        select n).
514      Any();
515      return !containsUnknownSymbol;
516    }
517  }
518}
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