1 | #region License Information
|
---|
2 | /* HeuristicLab
|
---|
3 | * Copyright (C) 2002-2018 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 |
|
---|
22 | using System;
|
---|
23 | using System.Collections.Generic;
|
---|
24 | using System.Diagnostics;
|
---|
25 | using System.Linq;
|
---|
26 | using HeuristicLab.Analysis;
|
---|
27 | using HeuristicLab.Collections;
|
---|
28 | using HeuristicLab.Common;
|
---|
29 | using HeuristicLab.Core;
|
---|
30 | using HeuristicLab.Data;
|
---|
31 | using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
|
---|
32 | using HeuristicLab.Optimization;
|
---|
33 | using HeuristicLab.Parameters;
|
---|
34 | using HeuristicLab.Persistence.Default.CompositeSerializers.Storable;
|
---|
35 | using HeuristicLab.Problems.DataAnalysis;
|
---|
36 | using HeuristicLab.Problems.DataAnalysis.Symbolic;
|
---|
37 | using HeuristicLab.Problems.Instances;
|
---|
38 | using Variable = HeuristicLab.Problems.DataAnalysis.Symbolic.Variable;
|
---|
39 |
|
---|
40 | namespace HeuristicLab.Problems.DynamicalSystemsModelling {
|
---|
41 |
|
---|
42 |
|
---|
43 |
|
---|
44 |
|
---|
45 | // Eine weitere Möglichkeit ist spline-smoothing der Daten (über Zeit) um damit für jede Zielvariable
|
---|
46 | // einen bereinigten (Rauschen) Wert und die Ableitung dy/dt für alle Beobachtungen zu bekommen
|
---|
47 | // danach kann man die Regression direkt für dy/dt anwenden (mit bereinigten y als inputs)
|
---|
48 | [Item("Dynamical Systems Modelling Problem", "TODO")]
|
---|
49 | [Creatable(CreatableAttribute.Categories.GeneticProgrammingProblems, Priority = 900)]
|
---|
50 | [StorableClass]
|
---|
51 | public sealed class Problem : SingleObjectiveBasicProblem<MultiEncoding>, IRegressionProblem, IProblemInstanceConsumer<IRegressionProblemData>, IProblemInstanceExporter<IRegressionProblemData> {
|
---|
52 | #region parameter names
|
---|
53 | private const string ProblemDataParameterName = "Data";
|
---|
54 | private const string TargetVariablesParameterName = "Target variables";
|
---|
55 | private const string FunctionSetParameterName = "Function set";
|
---|
56 | private const string MaximumLengthParameterName = "Size limit";
|
---|
57 | private const string MaximumParameterOptimizationIterationsParameterName = "Max. parameter optimization iterations";
|
---|
58 | private const string NumberOfLatentVariablesParameterName = "Number of latent variables";
|
---|
59 | private const string NumericIntegrationStepsParameterName = "Steps for numeric integration";
|
---|
60 | private const string TrainingEpisodesParameterName = "Training episodes";
|
---|
61 | private const string OptimizeParametersForEpisodesParameterName = "Optimize parameters for episodes";
|
---|
62 | private const string OdeSolverParameterName = "ODE Solver";
|
---|
63 | #endregion
|
---|
64 |
|
---|
65 | #region Parameter Properties
|
---|
66 | IParameter IDataAnalysisProblem.ProblemDataParameter { get { return ProblemDataParameter; } }
|
---|
67 |
|
---|
68 | public IValueParameter<IRegressionProblemData> ProblemDataParameter {
|
---|
69 | get { return (IValueParameter<IRegressionProblemData>)Parameters[ProblemDataParameterName]; }
|
---|
70 | }
|
---|
71 | public IValueParameter<ReadOnlyCheckedItemList<StringValue>> TargetVariablesParameter {
|
---|
72 | get { return (IValueParameter<ReadOnlyCheckedItemList<StringValue>>)Parameters[TargetVariablesParameterName]; }
|
---|
73 | }
|
---|
74 | public IValueParameter<ReadOnlyCheckedItemList<StringValue>> FunctionSetParameter {
|
---|
75 | get { return (IValueParameter<ReadOnlyCheckedItemList<StringValue>>)Parameters[FunctionSetParameterName]; }
|
---|
76 | }
|
---|
77 | public IFixedValueParameter<IntValue> MaximumLengthParameter {
|
---|
78 | get { return (IFixedValueParameter<IntValue>)Parameters[MaximumLengthParameterName]; }
|
---|
79 | }
|
---|
80 | public IFixedValueParameter<IntValue> MaximumParameterOptimizationIterationsParameter {
|
---|
81 | get { return (IFixedValueParameter<IntValue>)Parameters[MaximumParameterOptimizationIterationsParameterName]; }
|
---|
82 | }
|
---|
83 | public IFixedValueParameter<IntValue> NumberOfLatentVariablesParameter {
|
---|
84 | get { return (IFixedValueParameter<IntValue>)Parameters[NumberOfLatentVariablesParameterName]; }
|
---|
85 | }
|
---|
86 | public IFixedValueParameter<IntValue> NumericIntegrationStepsParameter {
|
---|
87 | get { return (IFixedValueParameter<IntValue>)Parameters[NumericIntegrationStepsParameterName]; }
|
---|
88 | }
|
---|
89 | public IValueParameter<ItemList<IntRange>> TrainingEpisodesParameter {
|
---|
90 | get { return (IValueParameter<ItemList<IntRange>>)Parameters[TrainingEpisodesParameterName]; }
|
---|
91 | }
|
---|
92 | public IFixedValueParameter<BoolValue> OptimizeParametersForEpisodesParameter {
|
---|
93 | get { return (IFixedValueParameter<BoolValue>)Parameters[OptimizeParametersForEpisodesParameterName]; }
|
---|
94 | }
|
---|
95 | public IConstrainedValueParameter<StringValue> OdeSolverParameter {
|
---|
96 | get { return (IConstrainedValueParameter<StringValue>)Parameters[OdeSolverParameterName]; }
|
---|
97 | }
|
---|
98 | #endregion
|
---|
99 |
|
---|
100 | #region Properties
|
---|
101 | public IRegressionProblemData ProblemData {
|
---|
102 | get { return ProblemDataParameter.Value; }
|
---|
103 | set { ProblemDataParameter.Value = value; }
|
---|
104 | }
|
---|
105 | IDataAnalysisProblemData IDataAnalysisProblem.ProblemData { get { return ProblemData; } }
|
---|
106 |
|
---|
107 | public ReadOnlyCheckedItemList<StringValue> TargetVariables {
|
---|
108 | get { return TargetVariablesParameter.Value; }
|
---|
109 | }
|
---|
110 |
|
---|
111 | public ReadOnlyCheckedItemList<StringValue> FunctionSet {
|
---|
112 | get { return FunctionSetParameter.Value; }
|
---|
113 | }
|
---|
114 |
|
---|
115 | public int MaximumLength {
|
---|
116 | get { return MaximumLengthParameter.Value.Value; }
|
---|
117 | }
|
---|
118 | public int MaximumParameterOptimizationIterations {
|
---|
119 | get { return MaximumParameterOptimizationIterationsParameter.Value.Value; }
|
---|
120 | }
|
---|
121 | public int NumberOfLatentVariables {
|
---|
122 | get { return NumberOfLatentVariablesParameter.Value.Value; }
|
---|
123 | }
|
---|
124 | public int NumericIntegrationSteps {
|
---|
125 | get { return NumericIntegrationStepsParameter.Value.Value; }
|
---|
126 | }
|
---|
127 | public IEnumerable<IntRange> TrainingEpisodes {
|
---|
128 | get { return TrainingEpisodesParameter.Value; }
|
---|
129 | }
|
---|
130 | public bool OptimizeParametersForEpisodes {
|
---|
131 | get { return OptimizeParametersForEpisodesParameter.Value.Value; }
|
---|
132 | }
|
---|
133 |
|
---|
134 | public string OdeSolver {
|
---|
135 | get { return OdeSolverParameter.Value.Value; }
|
---|
136 | set {
|
---|
137 | var matchingValue = OdeSolverParameter.ValidValues.FirstOrDefault(v => v.Value == value);
|
---|
138 | if (matchingValue == null) throw new ArgumentOutOfRangeException();
|
---|
139 | else OdeSolverParameter.Value = matchingValue;
|
---|
140 | }
|
---|
141 | }
|
---|
142 |
|
---|
143 | #endregion
|
---|
144 |
|
---|
145 | public event EventHandler ProblemDataChanged;
|
---|
146 |
|
---|
147 | public override bool Maximization {
|
---|
148 | get { return false; } // we minimize NMSE
|
---|
149 | }
|
---|
150 |
|
---|
151 | #region item cloning and persistence
|
---|
152 | // persistence
|
---|
153 | [StorableConstructor]
|
---|
154 | private Problem(bool deserializing) : base(deserializing) { }
|
---|
155 | [StorableHook(HookType.AfterDeserialization)]
|
---|
156 | private void AfterDeserialization() {
|
---|
157 | if (!Parameters.ContainsKey(OptimizeParametersForEpisodesParameterName)) {
|
---|
158 | Parameters.Add(new FixedValueParameter<BoolValue>(OptimizeParametersForEpisodesParameterName, "Flag to select if parameters should be optimized globally or for each episode individually.", new BoolValue(false)));
|
---|
159 | }
|
---|
160 | RegisterEventHandlers();
|
---|
161 | }
|
---|
162 |
|
---|
163 | // cloning
|
---|
164 | private Problem(Problem original, Cloner cloner)
|
---|
165 | : base(original, cloner) {
|
---|
166 | RegisterEventHandlers();
|
---|
167 | }
|
---|
168 | public override IDeepCloneable Clone(Cloner cloner) { return new Problem(this, cloner); }
|
---|
169 | #endregion
|
---|
170 |
|
---|
171 | public Problem()
|
---|
172 | : base() {
|
---|
173 | var targetVariables = new CheckedItemList<StringValue>().AsReadOnly(); // HACK: it would be better to provide a new class derived from IDataAnalysisProblem
|
---|
174 | var functions = CreateFunctionSet();
|
---|
175 | Parameters.Add(new ValueParameter<IRegressionProblemData>(ProblemDataParameterName, "The data captured from the dynamical system. Use CSV import functionality to import data.", new RegressionProblemData()));
|
---|
176 | Parameters.Add(new ValueParameter<ReadOnlyCheckedItemList<StringValue>>(TargetVariablesParameterName, "Target variables (overrides setting in ProblemData)", targetVariables));
|
---|
177 | Parameters.Add(new ValueParameter<ReadOnlyCheckedItemList<StringValue>>(FunctionSetParameterName, "The list of allowed functions", functions));
|
---|
178 | Parameters.Add(new FixedValueParameter<IntValue>(MaximumLengthParameterName, "The maximally allowed length of each expression. Set to a small value (5 - 25). Default = 10", new IntValue(10)));
|
---|
179 | Parameters.Add(new FixedValueParameter<IntValue>(MaximumParameterOptimizationIterationsParameterName, "The maximum number of iterations for optimization of parameters (using L-BFGS). More iterations makes the algorithm slower, fewer iterations might prevent convergence in the optimization scheme. Default = 100", new IntValue(100)));
|
---|
180 | Parameters.Add(new FixedValueParameter<IntValue>(NumberOfLatentVariablesParameterName, "Latent variables (unobserved variables) allow us to produce expressions which are integrated up and can be used in other expressions. They are handled similarly to target variables in forward simulation / integration. The difference to target variables is that there are no data to which the calculated values of latent variables are compared. Set to a small value (0 .. 5) as necessary (default = 0)", new IntValue(0)));
|
---|
181 | Parameters.Add(new FixedValueParameter<IntValue>(NumericIntegrationStepsParameterName, "Number of steps in the numeric integration that are taken from one row to the next (set to 1 to 100). More steps makes the algorithm slower, less steps worsens the accuracy of the numeric integration scheme.", new IntValue(10)));
|
---|
182 | Parameters.Add(new ValueParameter<ItemList<IntRange>>(TrainingEpisodesParameterName, "A list of ranges that should be used for training, each range represents an independent episode. This overrides the TrainingSet parameter in ProblemData.", new ItemList<IntRange>()));
|
---|
183 | Parameters.Add(new FixedValueParameter<BoolValue>(OptimizeParametersForEpisodesParameterName, "Flag to select if parameters should be optimized globally or for each episode individually.", new BoolValue(false)));
|
---|
184 |
|
---|
185 | var solversStr = new string[] { "HeuristicLab", "CVODES" };
|
---|
186 | var solvers = new ItemSet<StringValue>(
|
---|
187 | solversStr.Select(s => new StringValue(s).AsReadOnly())
|
---|
188 | );
|
---|
189 | Parameters.Add(new ConstrainedValueParameter<StringValue>(OdeSolverParameterName, "The solver to use for solving the initial value ODE problems", solvers, solvers.First()));
|
---|
190 |
|
---|
191 | RegisterEventHandlers();
|
---|
192 | InitAllParameters();
|
---|
193 |
|
---|
194 | // TODO: do not clear selection of target variables when the input variables are changed (keep selected target variables)
|
---|
195 | // TODO: UI hangs when selecting / deselecting input variables because the encoding is updated on each item
|
---|
196 | // TODO: use training range as default training episode
|
---|
197 | // TODO: write back optimized parameters to solution?
|
---|
198 |
|
---|
199 | }
|
---|
200 |
|
---|
201 | public override double Evaluate(Individual individual, IRandom random) {
|
---|
202 | var trees = individual.Values.Select(v => v.Value).OfType<ISymbolicExpressionTree>().ToArray(); // extract all trees from individual
|
---|
203 | // write back optimized parameters to tree nodes instead of the separate OptTheta variable
|
---|
204 | // retreive optimized parameters from nodes?
|
---|
205 |
|
---|
206 | if (OptimizeParametersForEpisodes) {
|
---|
207 | int eIdx = 0;
|
---|
208 | double totalNMSE = 0.0;
|
---|
209 | int totalSize = 0;
|
---|
210 | foreach (var episode in TrainingEpisodes) {
|
---|
211 | double[] optTheta;
|
---|
212 | double nmse;
|
---|
213 | OptimizeForEpisodes(trees, random, new[] { episode }, out optTheta, out nmse);
|
---|
214 | individual["OptTheta_" + eIdx] = new DoubleArray(optTheta); // write back optimized parameters so that we can use them in the Analysis method
|
---|
215 | eIdx++;
|
---|
216 | totalNMSE += nmse * episode.Size;
|
---|
217 | totalSize += episode.Size;
|
---|
218 | }
|
---|
219 | return totalNMSE / totalSize;
|
---|
220 | } else {
|
---|
221 | double[] optTheta;
|
---|
222 | double nmse;
|
---|
223 | OptimizeForEpisodes(trees, random, TrainingEpisodes, out optTheta, out nmse);
|
---|
224 | individual["OptTheta"] = new DoubleArray(optTheta); // write back optimized parameters so that we can use them in the Analysis method
|
---|
225 | return nmse;
|
---|
226 | }
|
---|
227 | }
|
---|
228 |
|
---|
229 | private void OptimizeForEpisodes(
|
---|
230 | ISymbolicExpressionTree[] trees,
|
---|
231 | IRandom random,
|
---|
232 | IEnumerable<IntRange> episodes,
|
---|
233 | out double[] optTheta,
|
---|
234 | out double nmse) {
|
---|
235 | var rows = episodes.SelectMany(e => Enumerable.Range(e.Start, e.End - e.Start)).ToArray();
|
---|
236 | var problemData = ProblemData;
|
---|
237 | var targetVars = TargetVariables.CheckedItems.OrderBy(i => i.Index).Select(i => i.Value.Value).ToArray();
|
---|
238 | var latentVariables = Enumerable.Range(1, NumberOfLatentVariables).Select(i => "λ" + i).ToArray(); // TODO: must coincide with the variables which are actually defined in the grammar and also for which we actually have trees
|
---|
239 | var targetValues = new double[rows.Length, targetVars.Length];
|
---|
240 |
|
---|
241 | // collect values of all target variables
|
---|
242 | var colIdx = 0;
|
---|
243 | foreach (var targetVar in targetVars) {
|
---|
244 | int rowIdx = 0;
|
---|
245 | foreach (var value in problemData.Dataset.GetDoubleValues(targetVar, rows)) {
|
---|
246 | targetValues[rowIdx, colIdx] = value;
|
---|
247 | rowIdx++;
|
---|
248 | }
|
---|
249 | colIdx++;
|
---|
250 | }
|
---|
251 |
|
---|
252 | // NOTE: the order of values in parameter matches prefix order of constant nodes in trees
|
---|
253 | var paramNodes = new List<ISymbolicExpressionTreeNode>();
|
---|
254 | foreach (var t in trees) {
|
---|
255 | foreach (var n in t.IterateNodesPrefix()) {
|
---|
256 | if (IsConstantNode(n))
|
---|
257 | paramNodes.Add(n);
|
---|
258 | }
|
---|
259 | }
|
---|
260 | // init params randomly from Unif(-1e-5, 1e-5)
|
---|
261 | var theta = paramNodes.Select(_ => random.NextDouble() * 2.0e-2 - 1.0e-2).ToArray();
|
---|
262 |
|
---|
263 | optTheta = new double[0];
|
---|
264 | if (theta.Length > 0) {
|
---|
265 | alglib.minlbfgsstate state;
|
---|
266 | alglib.minlbfgsreport report;
|
---|
267 | alglib.minlbfgscreate(Math.Min(theta.Length, 5), theta, out state);
|
---|
268 | alglib.minlbfgssetcond(state, 0.0, 0.0, 0.0, MaximumParameterOptimizationIterations);
|
---|
269 | //alglib.minlbfgssetgradientcheck(state, 1e-6);
|
---|
270 | alglib.minlbfgsoptimize(state, EvaluateObjectiveAndGradient, null,
|
---|
271 | new object[] { trees, targetVars, problemData, targetValues, episodes.ToArray(), NumericIntegrationSteps, latentVariables, OdeSolver }); //TODO: create a type
|
---|
272 |
|
---|
273 | alglib.minlbfgsresults(state, out optTheta, out report);
|
---|
274 |
|
---|
275 | /*
|
---|
276 | *
|
---|
277 | * L-BFGS algorithm results
|
---|
278 |
|
---|
279 | INPUT PARAMETERS:
|
---|
280 | State - algorithm state
|
---|
281 |
|
---|
282 | OUTPUT PARAMETERS:
|
---|
283 | X - array[0..N-1], solution
|
---|
284 | Rep - optimization report:
|
---|
285 | * Rep.TerminationType completetion code:
|
---|
286 | * -7 gradient verification failed.
|
---|
287 | See MinLBFGSSetGradientCheck() for more information.
|
---|
288 | * -2 rounding errors prevent further improvement.
|
---|
289 | X contains best point found.
|
---|
290 | * -1 incorrect parameters were specified
|
---|
291 | * 1 relative function improvement is no more than
|
---|
292 | EpsF.
|
---|
293 | * 2 relative step is no more than EpsX.
|
---|
294 | * 4 gradient norm is no more than EpsG
|
---|
295 | * 5 MaxIts steps was taken
|
---|
296 | * 7 stopping conditions are too stringent,
|
---|
297 | further improvement is impossible
|
---|
298 | * Rep.IterationsCount contains iterations count
|
---|
299 | * NFEV countains number of function calculations
|
---|
300 | */
|
---|
301 | if (report.terminationtype < 0) { nmse = 10E6; return; }
|
---|
302 | }
|
---|
303 |
|
---|
304 | // perform evaluation for optimal theta to get quality value
|
---|
305 | double[] grad = new double[optTheta.Length];
|
---|
306 | nmse = double.NaN;
|
---|
307 | EvaluateObjectiveAndGradient(optTheta, ref nmse, grad,
|
---|
308 | new object[] { trees, targetVars, problemData, targetValues, episodes.ToArray(), NumericIntegrationSteps, latentVariables, OdeSolver });
|
---|
309 | if (double.IsNaN(nmse) || double.IsInfinity(nmse)) { nmse = 10E6; return; } // return a large value (TODO: be consistent by using NMSE)
|
---|
310 | }
|
---|
311 |
|
---|
312 | private static void EvaluateObjectiveAndGradient(double[] x, ref double f, double[] grad, object obj) {
|
---|
313 | var trees = (ISymbolicExpressionTree[])((object[])obj)[0];
|
---|
314 | var targetVariables = (string[])((object[])obj)[1];
|
---|
315 | var problemData = (IRegressionProblemData)((object[])obj)[2];
|
---|
316 | var targetValues = (double[,])((object[])obj)[3];
|
---|
317 | var episodes = (IntRange[])((object[])obj)[4];
|
---|
318 | var numericIntegrationSteps = (int)((object[])obj)[5];
|
---|
319 | var latentVariables = (string[])((object[])obj)[6];
|
---|
320 | var odeSolver = (string)((object[])obj)[7];
|
---|
321 |
|
---|
322 |
|
---|
323 | Tuple<double, Vector>[][] predicted = null; // one array of predictions for each episode
|
---|
324 | // TODO: stop integration early for diverging solutions
|
---|
325 | predicted = Integrate(
|
---|
326 | trees, // we assume trees contain expressions for the change of each target variable over time y'(t)
|
---|
327 | problemData.Dataset,
|
---|
328 | problemData.AllowedInputVariables.ToArray(),
|
---|
329 | targetVariables,
|
---|
330 | latentVariables,
|
---|
331 | episodes,
|
---|
332 | x,
|
---|
333 | odeSolver,
|
---|
334 | numericIntegrationSteps).ToArray();
|
---|
335 |
|
---|
336 | if (predicted.Length != targetValues.GetLength(0)) {
|
---|
337 | f = double.MaxValue;
|
---|
338 | Array.Clear(grad, 0, grad.Length);
|
---|
339 | return;
|
---|
340 | }
|
---|
341 |
|
---|
342 | // for normalized MSE = 1/variance(t) * MSE(t, pred)
|
---|
343 | // TODO: Perf. (by standardization of target variables before evaluation of all trees)
|
---|
344 | var invVar = Enumerable.Range(0, targetVariables.Length)
|
---|
345 | .Select(c => Enumerable.Range(0, targetValues.GetLength(0)).Select(row => targetValues[row, c])) // column vectors
|
---|
346 | .Select(vec => vec.Variance())
|
---|
347 | .Select(v => 1.0 / v)
|
---|
348 | .ToArray();
|
---|
349 |
|
---|
350 | // objective function is NMSE
|
---|
351 | f = 0.0;
|
---|
352 | int n = predicted.Length;
|
---|
353 | double invN = 1.0 / n;
|
---|
354 | var g = Vector.Zero;
|
---|
355 | int r = 0;
|
---|
356 | foreach (var y_pred in predicted) {
|
---|
357 | for (int c = 0; c < y_pred.Length; c++) {
|
---|
358 |
|
---|
359 | var y_pred_f = y_pred[c].Item1;
|
---|
360 | var y = targetValues[r, c];
|
---|
361 |
|
---|
362 | var res = (y - y_pred_f);
|
---|
363 | var ressq = res * res;
|
---|
364 | f += ressq * invN * invVar[c];
|
---|
365 | g += -2.0 * res * y_pred[c].Item2 * invN * invVar[c];
|
---|
366 | }
|
---|
367 | r++;
|
---|
368 | }
|
---|
369 |
|
---|
370 | g.CopyTo(grad);
|
---|
371 | }
|
---|
372 |
|
---|
373 | public override void Analyze(Individual[] individuals, double[] qualities, ResultCollection results, IRandom random) {
|
---|
374 | base.Analyze(individuals, qualities, results, random);
|
---|
375 |
|
---|
376 | if (!results.ContainsKey("Prediction (training)")) {
|
---|
377 | results.Add(new Result("Prediction (training)", typeof(ReadOnlyItemList<DataTable>)));
|
---|
378 | }
|
---|
379 | if (!results.ContainsKey("Prediction (test)")) {
|
---|
380 | results.Add(new Result("Prediction (test)", typeof(ReadOnlyItemList<DataTable>)));
|
---|
381 | }
|
---|
382 | if (!results.ContainsKey("Models")) {
|
---|
383 | results.Add(new Result("Models", typeof(VariableCollection)));
|
---|
384 | }
|
---|
385 |
|
---|
386 | var bestIndividualAndQuality = this.GetBestIndividual(individuals, qualities);
|
---|
387 | var trees = bestIndividualAndQuality.Item1.Values.Select(v => v.Value).OfType<ISymbolicExpressionTree>().ToArray(); // extract all trees from individual
|
---|
388 |
|
---|
389 | var problemData = ProblemData;
|
---|
390 | var targetVars = TargetVariables.CheckedItems.OrderBy(i => i.Index).Select(i => i.Value.Value).ToArray();
|
---|
391 | var latentVariables = Enumerable.Range(1, NumberOfLatentVariables).Select(i => "λ" + i).ToArray(); // TODO: must coincide with the variables which are actually defined in the grammar and also for which we actually have trees
|
---|
392 |
|
---|
393 | var trainingList = new ItemList<DataTable>();
|
---|
394 |
|
---|
395 | if (OptimizeParametersForEpisodes) {
|
---|
396 | var eIdx = 0;
|
---|
397 | var trainingPredictions = new List<Tuple<double, Vector>[][]>();
|
---|
398 | foreach (var episode in TrainingEpisodes) {
|
---|
399 | var episodes = new[] { episode };
|
---|
400 | var optTheta = ((DoubleArray)bestIndividualAndQuality.Item1["OptTheta_" + eIdx]).ToArray(); // see evaluate
|
---|
401 | var trainingPrediction = Integrate(
|
---|
402 | trees, // we assume trees contain expressions for the change of each target variable over time y'(t)
|
---|
403 | problemData.Dataset,
|
---|
404 | problemData.AllowedInputVariables.ToArray(),
|
---|
405 | targetVars,
|
---|
406 | latentVariables,
|
---|
407 | episodes,
|
---|
408 | optTheta,
|
---|
409 | OdeSolver,
|
---|
410 | NumericIntegrationSteps).ToArray();
|
---|
411 | trainingPredictions.Add(trainingPrediction);
|
---|
412 | eIdx++;
|
---|
413 | }
|
---|
414 |
|
---|
415 | // only for actual target values
|
---|
416 | var trainingRows = TrainingEpisodes.SelectMany(e => Enumerable.Range(e.Start, e.End - e.Start));
|
---|
417 | for (int colIdx = 0; colIdx < targetVars.Length; colIdx++) {
|
---|
418 | var targetVar = targetVars[colIdx];
|
---|
419 | var trainingDataTable = new DataTable(targetVar + " prediction (training)");
|
---|
420 | var actualValuesRow = new DataRow(targetVar, "The values of " + targetVar, problemData.Dataset.GetDoubleValues(targetVar, trainingRows));
|
---|
421 | var predictedValuesRow = new DataRow(targetVar + " pred.", "Predicted values for " + targetVar, trainingPredictions.SelectMany(arr => arr.Select(row => row[colIdx].Item1)).ToArray());
|
---|
422 | trainingDataTable.Rows.Add(actualValuesRow);
|
---|
423 | trainingDataTable.Rows.Add(predictedValuesRow);
|
---|
424 | trainingList.Add(trainingDataTable);
|
---|
425 | }
|
---|
426 | results["Prediction (training)"].Value = trainingList.AsReadOnly();
|
---|
427 |
|
---|
428 |
|
---|
429 | var models = new VariableCollection();
|
---|
430 |
|
---|
431 | foreach (var tup in targetVars.Zip(trees, Tuple.Create)) {
|
---|
432 | var targetVarName = tup.Item1;
|
---|
433 | var tree = tup.Item2;
|
---|
434 |
|
---|
435 | var origTreeVar = new HeuristicLab.Core.Variable(targetVarName + "(original)");
|
---|
436 | origTreeVar.Value = (ISymbolicExpressionTree)tree.Clone();
|
---|
437 | models.Add(origTreeVar);
|
---|
438 | }
|
---|
439 | results["Models"].Value = models;
|
---|
440 | } else {
|
---|
441 | var optTheta = ((DoubleArray)bestIndividualAndQuality.Item1["OptTheta"]).ToArray(); // see evaluate
|
---|
442 | var trainingPrediction = Integrate(
|
---|
443 | trees, // we assume trees contain expressions for the change of each target variable over time dy/dt
|
---|
444 | problemData.Dataset,
|
---|
445 | problemData.AllowedInputVariables.ToArray(),
|
---|
446 | targetVars,
|
---|
447 | latentVariables,
|
---|
448 | TrainingEpisodes,
|
---|
449 | optTheta,
|
---|
450 | OdeSolver,
|
---|
451 | NumericIntegrationSteps).ToArray();
|
---|
452 | // only for actual target values
|
---|
453 | var trainingRows = TrainingEpisodes.SelectMany(e => Enumerable.Range(e.Start, e.End - e.Start));
|
---|
454 | for (int colIdx = 0; colIdx < targetVars.Length; colIdx++) {
|
---|
455 | var targetVar = targetVars[colIdx];
|
---|
456 | var trainingDataTable = new DataTable(targetVar + " prediction (training)");
|
---|
457 | var actualValuesRow = new DataRow(targetVar, "The values of " + targetVar, problemData.Dataset.GetDoubleValues(targetVar, trainingRows));
|
---|
458 | var predictedValuesRow = new DataRow(targetVar + " pred.", "Predicted values for " + targetVar, trainingPrediction.Select(arr => arr[colIdx].Item1).ToArray());
|
---|
459 | trainingDataTable.Rows.Add(actualValuesRow);
|
---|
460 | trainingDataTable.Rows.Add(predictedValuesRow);
|
---|
461 | trainingList.Add(trainingDataTable);
|
---|
462 | }
|
---|
463 | // TODO: DRY for training and test
|
---|
464 | var testList = new ItemList<DataTable>();
|
---|
465 | var testRows = ProblemData.TestIndices.ToArray();
|
---|
466 | var testPrediction = Integrate(
|
---|
467 | trees, // we assume trees contain expressions for the change of each target variable over time y'(t)
|
---|
468 | problemData.Dataset,
|
---|
469 | problemData.AllowedInputVariables.ToArray(),
|
---|
470 | targetVars,
|
---|
471 | latentVariables,
|
---|
472 | new IntRange[] { ProblemData.TestPartition },
|
---|
473 | optTheta,
|
---|
474 | OdeSolver,
|
---|
475 | NumericIntegrationSteps).ToArray();
|
---|
476 |
|
---|
477 | for (int colIdx = 0; colIdx < targetVars.Length; colIdx++) {
|
---|
478 | var targetVar = targetVars[colIdx];
|
---|
479 | var testDataTable = new DataTable(targetVar + " prediction (test)");
|
---|
480 | var actualValuesRow = new DataRow(targetVar, "The values of " + targetVar, problemData.Dataset.GetDoubleValues(targetVar, testRows));
|
---|
481 | var predictedValuesRow = new DataRow(targetVar + " pred.", "Predicted values for " + targetVar, testPrediction.Select(arr => arr[colIdx].Item1).ToArray());
|
---|
482 | testDataTable.Rows.Add(actualValuesRow);
|
---|
483 | testDataTable.Rows.Add(predictedValuesRow);
|
---|
484 | testList.Add(testDataTable);
|
---|
485 | }
|
---|
486 |
|
---|
487 | results["Prediction (training)"].Value = trainingList.AsReadOnly();
|
---|
488 | results["Prediction (test)"].Value = testList.AsReadOnly();
|
---|
489 | #region simplification of models
|
---|
490 | // TODO the dependency of HeuristicLab.Problems.DataAnalysis.Symbolic is not ideal
|
---|
491 | var models = new VariableCollection(); // to store target var names and original version of tree
|
---|
492 |
|
---|
493 | int nextParIdx = 0;
|
---|
494 | foreach (var tup in targetVars.Zip(trees, Tuple.Create)) {
|
---|
495 | var targetVarName = tup.Item1;
|
---|
496 | var tree = tup.Item2;
|
---|
497 |
|
---|
498 | // when we reference HeuristicLab.Problems.DataAnalysis.Symbolic we can translate symbols
|
---|
499 | var shownTree = new SymbolicExpressionTree(TranslateTreeNode(tree.Root, optTheta, ref nextParIdx));
|
---|
500 |
|
---|
501 | // var shownTree = (SymbolicExpressionTree)tree.Clone();
|
---|
502 | // var constantsNodeOrig = tree.IterateNodesPrefix().Where(IsConstantNode);
|
---|
503 | // var constantsNodeShown = shownTree.IterateNodesPrefix().Where(IsConstantNode);
|
---|
504 | //
|
---|
505 | // foreach (var n in constantsNodeOrig.Zip(constantsNodeShown, (original, shown) => new { original, shown })) {
|
---|
506 | // double constantsVal = optTheta[nodeIdx[n.original]];
|
---|
507 | //
|
---|
508 | // ConstantTreeNode replacementNode = new ConstantTreeNode(new Constant()) { Value = constantsVal };
|
---|
509 | //
|
---|
510 | // var parentNode = n.shown.Parent;
|
---|
511 | // int replacementIndex = parentNode.IndexOfSubtree(n.shown);
|
---|
512 | // parentNode.RemoveSubtree(replacementIndex);
|
---|
513 | // parentNode.InsertSubtree(replacementIndex, replacementNode);
|
---|
514 | // }
|
---|
515 |
|
---|
516 | var origTreeVar = new HeuristicLab.Core.Variable(targetVarName + "(original)");
|
---|
517 | origTreeVar.Value = (ISymbolicExpressionTree)tree.Clone();
|
---|
518 | models.Add(origTreeVar);
|
---|
519 | var simplifiedTreeVar = new HeuristicLab.Core.Variable(targetVarName + "(simplified)");
|
---|
520 | simplifiedTreeVar.Value = TreeSimplifier.Simplify(shownTree);
|
---|
521 | models.Add(simplifiedTreeVar);
|
---|
522 |
|
---|
523 | }
|
---|
524 | results["Models"].Value = models;
|
---|
525 | #endregion
|
---|
526 | }
|
---|
527 | }
|
---|
528 |
|
---|
529 |
|
---|
530 | #region interpretation
|
---|
531 |
|
---|
532 | // the following uses auto-diff to calculate the gradient w.r.t. the parameters forward in time.
|
---|
533 | // this is basically the method described in Gronwall T. Note on the derivatives with respect to a parameter of the solutions of a system of differential equations. Ann. Math. 1919;20:292–296.
|
---|
534 |
|
---|
535 | // a comparison of three potential calculation methods for the gradient is given in:
|
---|
536 | // Sengupta, B., Friston, K. J., & Penny, W. D. (2014). Efficient gradient computation for dynamical models. Neuroimage, 98(100), 521–527. http://doi.org/10.1016/j.neuroimage.2014.04.040
|
---|
537 | // "Our comparison establishes that the adjoint method is computationally more efficient for numerical estimation of parametric gradients
|
---|
538 | // for state-space models — both linear and non-linear, as in the case of a dynamical causal model (DCM)"
|
---|
539 |
|
---|
540 | // for a solver with the necessary features see: https://computation.llnl.gov/projects/sundials/cvodes
|
---|
541 |
|
---|
542 | private static IEnumerable<Tuple<double, Vector>[]> Integrate(
|
---|
543 | ISymbolicExpressionTree[] trees, IDataset dataset, string[] inputVariables, string[] targetVariables, string[] latentVariables, IEnumerable<IntRange> episodes,
|
---|
544 | double[] parameterValues,
|
---|
545 | string odeSolver, int numericIntegrationSteps = 100) {
|
---|
546 |
|
---|
547 | // TODO: numericIntegrationSteps is only relevant for the HeuristicLab solver
|
---|
548 |
|
---|
549 | foreach (var episode in episodes) {
|
---|
550 | var rows = Enumerable.Range(episode.Start, episode.End - episode.Start);
|
---|
551 | // return first value as stored in the dataset
|
---|
552 | yield return targetVariables
|
---|
553 | .Select(targetVar => Tuple.Create(dataset.GetDoubleValue(targetVar, rows.First()), Vector.Zero))
|
---|
554 | .ToArray();
|
---|
555 |
|
---|
556 | // integrate forward starting with known values for the target in t0
|
---|
557 |
|
---|
558 | var variableValues = new Dictionary<string, Tuple<double, Vector>>();
|
---|
559 | var t0 = rows.First();
|
---|
560 | foreach (var varName in inputVariables) {
|
---|
561 | variableValues.Add(varName, Tuple.Create(dataset.GetDoubleValue(varName, t0), Vector.Zero));
|
---|
562 | }
|
---|
563 | foreach (var varName in targetVariables) {
|
---|
564 | variableValues.Add(varName, Tuple.Create(dataset.GetDoubleValue(varName, t0), Vector.Zero));
|
---|
565 | }
|
---|
566 | // add value entries for latent variables which are also integrated
|
---|
567 | foreach (var latentVar in latentVariables) {
|
---|
568 | variableValues.Add(latentVar, Tuple.Create(0.0, Vector.Zero)); // we don't have observations for latent variables -> assume zero as starting value TODO
|
---|
569 | }
|
---|
570 | var calculatedVariables = targetVariables.Concat(latentVariables).ToArray(); // TODO: must conincide with the order of trees in the encoding
|
---|
571 |
|
---|
572 | var prevT = rows.First(); // TODO: here we should use a variable for t if it is available. Right now we assume equidistant measurements.
|
---|
573 | foreach (var t in rows.Skip(1)) {
|
---|
574 | if (odeSolver == "HeuristicLab")
|
---|
575 | IntegrateHL(trees, calculatedVariables, variableValues, parameterValues, numericIntegrationSteps);
|
---|
576 | else if (odeSolver == "CVODES")
|
---|
577 | IntegrateCVODES(trees, calculatedVariables, variableValues, parameterValues, t - prevT);
|
---|
578 | else throw new InvalidOperationException("Unknown ODE solver " + odeSolver);
|
---|
579 | prevT = t;
|
---|
580 |
|
---|
581 | // This check doesn't work with the HeuristicLab integrator if there are input variables
|
---|
582 | //if (variableValues.Count == targetVariables.Length) {
|
---|
583 | // only return the target variables for calculation of errors
|
---|
584 | var res = targetVariables
|
---|
585 | .Select(targetVar => variableValues[targetVar])
|
---|
586 | .ToArray();
|
---|
587 | if (res.Any(ri => double.IsNaN(ri.Item1) || double.IsInfinity(ri.Item1))) yield break;
|
---|
588 | yield return res;
|
---|
589 | //} else {
|
---|
590 | // yield break; // stop early on problems
|
---|
591 | //}
|
---|
592 |
|
---|
593 |
|
---|
594 | // update for next time step
|
---|
595 | foreach (var varName in inputVariables) {
|
---|
596 | variableValues[varName] = Tuple.Create(dataset.GetDoubleValue(varName, t), Vector.Zero);
|
---|
597 | }
|
---|
598 | }
|
---|
599 | }
|
---|
600 | }
|
---|
601 |
|
---|
602 |
|
---|
603 | /// <summary>
|
---|
604 | /// Here we use CVODES to solve the ODE. Forward sensitivities are used to calculate the gradient for parameter optimization
|
---|
605 | /// </summary>
|
---|
606 | /// <param name="trees">Each equation in the ODE represented as a tree</param>
|
---|
607 | /// <param name="calculatedVariables">The names of the calculated variables</param>
|
---|
608 | /// <param name="variableValues">The start values of the calculated variables as well as their sensitivites over parameters</param>
|
---|
609 | /// <param name="parameterValues">The current parameter values</param>
|
---|
610 | /// <param name="t">The time t up to which we need to integrate.</param>
|
---|
611 | private static void IntegrateCVODES(
|
---|
612 | ISymbolicExpressionTree[] trees, // f(y,p) in tree representation
|
---|
613 | string[] calculatedVariables, // names of elements of y
|
---|
614 | Dictionary<string, Tuple<double, Vector>> variableValues, // y (intput and output) input: y(t0), output: y(t0+t)
|
---|
615 | double[] parameterValues, // p
|
---|
616 | double t // duration t for which we want to integrate
|
---|
617 | ) {
|
---|
618 |
|
---|
619 | // the RHS of the ODE
|
---|
620 | // dy/dt = f(y_t,x_t,p)
|
---|
621 | CVODES.CVRhsFunc f = CreateOdeRhs(trees, calculatedVariables, parameterValues);
|
---|
622 | // the Jacobian ∂f/∂y
|
---|
623 | CVODES.CVDlsJacFunc jac = CreateJac(trees, calculatedVariables, parameterValues);
|
---|
624 |
|
---|
625 | // the RHS for the forward sensitivities (∂f/∂y)s_i(t) + ∂f/∂p_i
|
---|
626 | CVODES.CVSensRhsFn sensF = CreateSensitivityRhs(trees, calculatedVariables, parameterValues);
|
---|
627 |
|
---|
628 | // setup solver
|
---|
629 | int numberOfEquations = trees.Length;
|
---|
630 | IntPtr y = IntPtr.Zero;
|
---|
631 | IntPtr cvode_mem = IntPtr.Zero;
|
---|
632 | IntPtr A = IntPtr.Zero;
|
---|
633 | IntPtr yS0 = IntPtr.Zero;
|
---|
634 | IntPtr linearSolver = IntPtr.Zero;
|
---|
635 | var ns = parameterValues.Length; // number of parameters
|
---|
636 |
|
---|
637 | try {
|
---|
638 | y = CVODES.N_VNew_Serial(numberOfEquations);
|
---|
639 | // init y to current values of variables
|
---|
640 | // y must be initialized before calling CVodeInit
|
---|
641 | for (int i = 0; i < calculatedVariables.Length; i++) {
|
---|
642 | CVODES.NV_Set_Ith_S(y, i, variableValues[calculatedVariables[i]].Item1);
|
---|
643 | }
|
---|
644 |
|
---|
645 | cvode_mem = CVODES.CVodeCreate(CVODES.MultistepMethod.CV_ADAMS, CVODES.NonlinearSolverIteration.CV_FUNCTIONAL);
|
---|
646 |
|
---|
647 | var flag = CVODES.CVodeInit(cvode_mem, f, 0.0, y);
|
---|
648 | Debug.Assert(CVODES.CV_SUCCESS == flag);
|
---|
649 |
|
---|
650 | double relTol = 1.0e-2;
|
---|
651 | double absTol = 1.0;
|
---|
652 | flag = CVODES.CVodeSStolerances(cvode_mem, relTol, absTol); // TODO: probably need to adjust absTol per variable
|
---|
653 | Debug.Assert(CVODES.CV_SUCCESS == flag);
|
---|
654 |
|
---|
655 | A = CVODES.SUNDenseMatrix(numberOfEquations, numberOfEquations);
|
---|
656 | Debug.Assert(A != IntPtr.Zero);
|
---|
657 |
|
---|
658 | linearSolver = CVODES.SUNDenseLinearSolver(y, A);
|
---|
659 | Debug.Assert(linearSolver != IntPtr.Zero);
|
---|
660 |
|
---|
661 | flag = CVODES.CVDlsSetLinearSolver(cvode_mem, linearSolver, A);
|
---|
662 | Debug.Assert(CVODES.CV_SUCCESS == flag);
|
---|
663 |
|
---|
664 | flag = CVODES.CVDlsSetJacFn(cvode_mem, jac);
|
---|
665 | Debug.Assert(CVODES.CV_SUCCESS == flag);
|
---|
666 |
|
---|
667 | yS0 = CVODES.N_VCloneVectorArray_Serial(ns, y); // clone the output vector for each parameter
|
---|
668 | unsafe {
|
---|
669 | // set to initial sensitivities supplied by caller
|
---|
670 | for (int pIdx = 0; pIdx < ns; pIdx++) {
|
---|
671 | var yS0_i = *((IntPtr*)yS0.ToPointer() + pIdx);
|
---|
672 | for (var varIdx = 0; varIdx < calculatedVariables.Length; varIdx++) {
|
---|
673 | CVODES.NV_Set_Ith_S(yS0_i, varIdx, variableValues[calculatedVariables[varIdx]].Item2[pIdx]);
|
---|
674 | }
|
---|
675 | }
|
---|
676 | }
|
---|
677 |
|
---|
678 | flag = CVODES.CVodeSensInit(cvode_mem, ns, CVODES.CV_SIMULTANEOUS, sensF, yS0);
|
---|
679 | Debug.Assert(CVODES.CV_SUCCESS == flag);
|
---|
680 |
|
---|
681 | flag = CVODES.CVodeSensEEtolerances(cvode_mem);
|
---|
682 | Debug.Assert(CVODES.CV_SUCCESS == flag);
|
---|
683 |
|
---|
684 | // make one forward integration step
|
---|
685 | double tout = 0.0; // first output time
|
---|
686 | flag = CVODES.CVode(cvode_mem, t, y, ref tout, CVODES.CV_NORMAL);
|
---|
687 | if (flag == CVODES.CV_SUCCESS) {
|
---|
688 | Debug.Assert(t == tout);
|
---|
689 |
|
---|
690 | // get sensitivities
|
---|
691 | flag = CVODES.CVodeGetSens(cvode_mem, ref tout, yS0);
|
---|
692 | Debug.Assert(CVODES.CV_SUCCESS == flag);
|
---|
693 |
|
---|
694 | // update variableValues based on integration results
|
---|
695 | for (int varIdx = 0; varIdx < calculatedVariables.Length; varIdx++) {
|
---|
696 | var yi = CVODES.NV_Get_Ith_S(y, varIdx);
|
---|
697 | var gArr = new double[parameterValues.Length];
|
---|
698 | for (var pIdx = 0; pIdx < parameterValues.Length; pIdx++) {
|
---|
699 | unsafe {
|
---|
700 | var yS0_pi = *((IntPtr*)yS0.ToPointer() + pIdx);
|
---|
701 | gArr[pIdx] = CVODES.NV_Get_Ith_S(yS0_pi, varIdx);
|
---|
702 | }
|
---|
703 | }
|
---|
704 | variableValues[calculatedVariables[varIdx]] = Tuple.Create(yi, new Vector(gArr));
|
---|
705 | }
|
---|
706 | } else {
|
---|
707 | variableValues.Clear(); // indicate problems by not returning new values
|
---|
708 | }
|
---|
709 |
|
---|
710 | // cleanup all allocated objects
|
---|
711 | } finally {
|
---|
712 | if (y != IntPtr.Zero) CVODES.N_VDestroy_Serial(y);
|
---|
713 | if (cvode_mem != IntPtr.Zero) CVODES.CVodeFree(ref cvode_mem);
|
---|
714 | if (linearSolver != IntPtr.Zero) CVODES.SUNLinSolFree(linearSolver);
|
---|
715 | if (A != IntPtr.Zero) CVODES.SUNMatDestroy(A);
|
---|
716 | if (yS0 != IntPtr.Zero) CVODES.N_VDestroyVectorArray_Serial(yS0, ns);
|
---|
717 | }
|
---|
718 | }
|
---|
719 |
|
---|
720 |
|
---|
721 | private static CVODES.CVRhsFunc CreateOdeRhs(
|
---|
722 | ISymbolicExpressionTree[] trees,
|
---|
723 | string[] calculatedVariables,
|
---|
724 | double[] parameterValues) {
|
---|
725 | // we don't need to calculate a gradient here -> no nodes are selected for
|
---|
726 | // --> no nodes are selected to be included in the gradient calculation
|
---|
727 | var nodeIdx = new Dictionary<ISymbolicExpressionTreeNode, int>();
|
---|
728 | return (double t,
|
---|
729 | IntPtr y, // N_Vector, current value of y (input)
|
---|
730 | IntPtr ydot, // N_Vector (calculated value of y' (output)
|
---|
731 | IntPtr user_data // optional user data, (unused here)
|
---|
732 | ) => {
|
---|
733 | // TODO: perf
|
---|
734 | var nodeValues = new Dictionary<ISymbolicExpressionTreeNode, Tuple<double, Vector>>();
|
---|
735 |
|
---|
736 | int pIdx = 0;
|
---|
737 | foreach (var tree in trees) {
|
---|
738 | foreach (var n in tree.IterateNodesPrefix()) {
|
---|
739 | if (IsConstantNode(n)) {
|
---|
740 | nodeValues.Add(n, Tuple.Create(parameterValues[pIdx], Vector.Zero)); // here we do not need a gradient
|
---|
741 | pIdx++;
|
---|
742 | } else if (n.SubtreeCount == 0) {
|
---|
743 | // for variables and latent variables get the value from variableValues
|
---|
744 | var varName = n.Symbol.Name;
|
---|
745 | var varIdx = Array.IndexOf(calculatedVariables, varName); // TODO: perf!
|
---|
746 | if (varIdx < 0) throw new InvalidProgramException();
|
---|
747 | var y_i = CVODES.NV_Get_Ith_S(y, (long)varIdx);
|
---|
748 | nodeValues.Add(n, Tuple.Create(y_i, Vector.Zero)); // no gradient needed
|
---|
749 | }
|
---|
750 | }
|
---|
751 | }
|
---|
752 | for (int i = 0; i < trees.Length; i++) {
|
---|
753 | var tree = trees[i];
|
---|
754 | var res_i = InterpretRec(tree.Root.GetSubtree(0).GetSubtree(0), nodeValues);
|
---|
755 | CVODES.NV_Set_Ith_S(ydot, i, res_i.Item1);
|
---|
756 | }
|
---|
757 | return 0;
|
---|
758 | };
|
---|
759 | }
|
---|
760 |
|
---|
761 | private static CVODES.CVDlsJacFunc CreateJac(
|
---|
762 | ISymbolicExpressionTree[] trees,
|
---|
763 | string[] calculatedVariables,
|
---|
764 | double[] parameterValues) {
|
---|
765 |
|
---|
766 | return (
|
---|
767 | double t, // current time (input)
|
---|
768 | IntPtr y, // N_Vector, current value of y (input)
|
---|
769 | IntPtr fy, // N_Vector, current value of f (input)
|
---|
770 | IntPtr Jac, // SUNMatrix ∂f/∂y (output, rows i contains are ∂f_i/∂y vector)
|
---|
771 | IntPtr user_data, // optional (unused here)
|
---|
772 | IntPtr tmp1, // N_Vector, optional (unused here)
|
---|
773 | IntPtr tmp2, // N_Vector, optional (unused here)
|
---|
774 | IntPtr tmp3 // N_Vector, optional (unused here)
|
---|
775 | ) => {
|
---|
776 | // here we need to calculate partial derivatives for the calculated variables y
|
---|
777 | var nodeValues = new Dictionary<ISymbolicExpressionTreeNode, Tuple<double, Vector>>();
|
---|
778 | int pIdx = 0;
|
---|
779 | foreach (var tree in trees) {
|
---|
780 | foreach (var n in tree.IterateNodesPrefix()) {
|
---|
781 | if (IsConstantNode(n)) {
|
---|
782 | nodeValues.Add(n, Tuple.Create(parameterValues[pIdx], Vector.Zero)); // here we need a gradient over y which is zero for parameters
|
---|
783 | pIdx++;
|
---|
784 | } else if (n.SubtreeCount == 0) {
|
---|
785 | // for variables and latent variables we use values supplied in y and init gradient vectors accordingly
|
---|
786 | var varName = n.Symbol.Name;
|
---|
787 | var varIdx = Array.IndexOf(calculatedVariables, varName); // TODO: perf!
|
---|
788 | if (varIdx < 0) throw new InvalidProgramException();
|
---|
789 |
|
---|
790 | var y_i = CVODES.NV_Get_Ith_S(y, (long)varIdx);
|
---|
791 | var gArr = new double[CVODES.NV_LENGTH_S(y)]; // backing array
|
---|
792 | gArr[varIdx] = 1.0;
|
---|
793 | var g = new Vector(gArr);
|
---|
794 | nodeValues.Add(n, Tuple.Create(y_i, g));
|
---|
795 | }
|
---|
796 | }
|
---|
797 | }
|
---|
798 |
|
---|
799 | for (int i = 0; i < trees.Length; i++) {
|
---|
800 | var tree = trees[i];
|
---|
801 | var res = InterpretRec(tree.Root.GetSubtree(0).GetSubtree(0), nodeValues);
|
---|
802 | var g = res.Item2;
|
---|
803 | for (int j = 0; j < calculatedVariables.Length; j++) {
|
---|
804 | CVODES.SUNDenseMatrix_Set(Jac, i, j, g[j]);
|
---|
805 | }
|
---|
806 | }
|
---|
807 | return 0; // on success
|
---|
808 | };
|
---|
809 | }
|
---|
810 |
|
---|
811 |
|
---|
812 | // to calculate sensitivities RHS for all equations at once
|
---|
813 | // must compute (∂f/∂y)s_i(t) + ∂f/∂p_i and store in ySdot.
|
---|
814 | // Index i refers to parameters, dimensionality of matrix and vectors is number of equations
|
---|
815 | private static CVODES.CVSensRhsFn CreateSensitivityRhs(ISymbolicExpressionTree[] trees, string[] calculatedVariables, double[] parameterValues) {
|
---|
816 | return (
|
---|
817 | int Ns, // number of parameters
|
---|
818 | double t, // current time
|
---|
819 | IntPtr y, // N_Vector y(t) (input)
|
---|
820 | IntPtr ydot, // N_Vector dy/dt(t) (input)
|
---|
821 | IntPtr yS, // N_Vector*, one vector for each parameter (input)
|
---|
822 | IntPtr ySdot, // N_Vector*, one vector for each parameter (output)
|
---|
823 | IntPtr user_data, // optional (unused here)
|
---|
824 | IntPtr tmp1, // N_Vector, optional (unused here)
|
---|
825 | IntPtr tmp2 // N_Vector, optional (unused here)
|
---|
826 | ) => {
|
---|
827 | // here we need to calculate partial derivatives for the calculated variables y as well as for the parameters
|
---|
828 | var nodeValues = new Dictionary<ISymbolicExpressionTreeNode, Tuple<double, Vector>>();
|
---|
829 | var d = calculatedVariables.Length + parameterValues.Length; // dimensionality of gradient
|
---|
830 | // first collect variable values
|
---|
831 | foreach (var tree in trees) {
|
---|
832 | foreach (var n in tree.IterateNodesPrefix()) {
|
---|
833 | if (IsVariableNode(n)) {
|
---|
834 | // for variables and latent variables we use values supplied in y and init gradient vectors accordingly
|
---|
835 | var varName = n.Symbol.Name;
|
---|
836 | var varIdx = Array.IndexOf(calculatedVariables, varName); // TODO: perf!
|
---|
837 | if (varIdx < 0) throw new InvalidProgramException();
|
---|
838 |
|
---|
839 | var y_i = CVODES.NV_Get_Ith_S(y, (long)varIdx);
|
---|
840 | var gArr = new double[d]; // backing array
|
---|
841 | gArr[varIdx] = 1.0;
|
---|
842 | var g = new Vector(gArr);
|
---|
843 | nodeValues.Add(n, Tuple.Create(y_i, g));
|
---|
844 | }
|
---|
845 | }
|
---|
846 | }
|
---|
847 | // then collect constants
|
---|
848 | int pIdx = 0;
|
---|
849 | foreach (var tree in trees) {
|
---|
850 | foreach (var n in tree.IterateNodesPrefix()) {
|
---|
851 | if (IsConstantNode(n)) {
|
---|
852 | var gArr = new double[d];
|
---|
853 | gArr[calculatedVariables.Length + pIdx] = 1.0;
|
---|
854 | var g = new Vector(gArr);
|
---|
855 | nodeValues.Add(n, Tuple.Create(parameterValues[pIdx], g));
|
---|
856 | pIdx++;
|
---|
857 | }
|
---|
858 | }
|
---|
859 | }
|
---|
860 | // gradient vector is [∂f/∂y_1, ∂f/∂y_2, ... ∂f/∂yN, ∂f/∂p_1 ... ∂f/∂p_K]
|
---|
861 |
|
---|
862 |
|
---|
863 | for (pIdx = 0; pIdx < Ns; pIdx++) {
|
---|
864 | unsafe {
|
---|
865 | var sDot_pi = *((IntPtr*)ySdot.ToPointer() + pIdx);
|
---|
866 | CVODES.N_VConst_Serial(0.0, sDot_pi);
|
---|
867 | }
|
---|
868 | }
|
---|
869 |
|
---|
870 | for (int i = 0; i < trees.Length; i++) {
|
---|
871 | var tree = trees[i];
|
---|
872 | var res = InterpretRec(tree.Root.GetSubtree(0).GetSubtree(0), nodeValues);
|
---|
873 | var g = res.Item2;
|
---|
874 |
|
---|
875 |
|
---|
876 | // update ySdot = (∂f/∂y)s_i(t) + ∂f/∂p_i
|
---|
877 |
|
---|
878 | for (pIdx = 0; pIdx < Ns; pIdx++) {
|
---|
879 | unsafe {
|
---|
880 | var sDot_pi = *((IntPtr*)ySdot.ToPointer() + pIdx);
|
---|
881 | var s_pi = *((IntPtr*)yS.ToPointer() + pIdx);
|
---|
882 |
|
---|
883 | var v = CVODES.NV_Get_Ith_S(sDot_pi, i);
|
---|
884 | // (∂f/∂y)s_i(t)
|
---|
885 | var p = 0.0;
|
---|
886 | for (int yIdx = 0; yIdx < calculatedVariables.Length; yIdx++) {
|
---|
887 | p += g[yIdx] * CVODES.NV_Get_Ith_S(s_pi, yIdx);
|
---|
888 | }
|
---|
889 | // + ∂f/∂p_i
|
---|
890 | CVODES.NV_Set_Ith_S(sDot_pi, i, v + p + g[calculatedVariables.Length + pIdx]);
|
---|
891 | }
|
---|
892 | }
|
---|
893 |
|
---|
894 | }
|
---|
895 | return 0; // on success
|
---|
896 | };
|
---|
897 | }
|
---|
898 |
|
---|
899 | private static void IntegrateHL(
|
---|
900 | ISymbolicExpressionTree[] trees,
|
---|
901 | string[] calculatedVariables, // names of integrated variables
|
---|
902 | Dictionary<string, Tuple<double, Vector>> variableValues, //y (intput and output) input: y(t0), output: y(t0+1)
|
---|
903 | double[] parameterValues,
|
---|
904 | int numericIntegrationSteps) {
|
---|
905 |
|
---|
906 | var nodeValues = new Dictionary<ISymbolicExpressionTreeNode, Tuple<double, Vector>>();
|
---|
907 |
|
---|
908 | // the nodeValues for parameters are constant over time
|
---|
909 | // TODO: this needs to be done only once for each iteration in gradient descent (whenever parameter values change)
|
---|
910 | // NOTE: the order must be the same as above (prefix order for nodes)
|
---|
911 | int pIdx = 0;
|
---|
912 | foreach (var tree in trees) {
|
---|
913 | foreach (var node in tree.Root.IterateNodesPrefix()) {
|
---|
914 | if (IsConstantNode(node)) {
|
---|
915 | var gArr = new double[parameterValues.Length]; // backing array
|
---|
916 | gArr[pIdx] = 1.0;
|
---|
917 | var g = new Vector(gArr);
|
---|
918 | nodeValues.Add(node, new Tuple<double, Vector>(parameterValues[pIdx], g));
|
---|
919 | pIdx++;
|
---|
920 | } else if (node.SubtreeCount == 0) {
|
---|
921 | // for (latent) variables get the values from variableValues
|
---|
922 | var varName = node.Symbol.Name;
|
---|
923 | nodeValues.Add(node, variableValues[varName]);
|
---|
924 | }
|
---|
925 | }
|
---|
926 | }
|
---|
927 |
|
---|
928 |
|
---|
929 | double h = 1.0 / numericIntegrationSteps;
|
---|
930 | for (int step = 0; step < numericIntegrationSteps; step++) {
|
---|
931 | var deltaValues = new Dictionary<string, Tuple<double, Vector>>();
|
---|
932 | for (int i = 0; i < trees.Length; i++) {
|
---|
933 | var tree = trees[i];
|
---|
934 | var targetVarName = calculatedVariables[i];
|
---|
935 |
|
---|
936 | // Root.GetSubtree(0).GetSubtree(0) skips programRoot and startSymbol
|
---|
937 | var res = InterpretRec(tree.Root.GetSubtree(0).GetSubtree(0), nodeValues);
|
---|
938 | deltaValues.Add(targetVarName, res);
|
---|
939 | }
|
---|
940 |
|
---|
941 | // update variableValues for next step, trapezoid integration
|
---|
942 | foreach (var kvp in deltaValues) {
|
---|
943 | var oldVal = variableValues[kvp.Key];
|
---|
944 | var newVal = Tuple.Create(
|
---|
945 | oldVal.Item1 + h * kvp.Value.Item1,
|
---|
946 | oldVal.Item2 + h * kvp.Value.Item2
|
---|
947 | );
|
---|
948 | variableValues[kvp.Key] = newVal;
|
---|
949 | }
|
---|
950 | // update nodeValues from variableValues
|
---|
951 | // TODO: perf using dictionary with list of nodes for each variable
|
---|
952 | foreach (var tree in trees) {
|
---|
953 | foreach (var node in tree.Root.IterateNodesPrefix().Where(n => IsVariableNode(n))) {
|
---|
954 | var varName = node.Symbol.Name;
|
---|
955 | nodeValues[node] = variableValues[varName];
|
---|
956 | }
|
---|
957 | }
|
---|
958 | }
|
---|
959 | }
|
---|
960 |
|
---|
961 | private static Tuple<double, Vector> InterpretRec(
|
---|
962 | ISymbolicExpressionTreeNode node,
|
---|
963 | Dictionary<ISymbolicExpressionTreeNode, Tuple<double, Vector>> nodeValues // contains value and gradient vector for a node (variables and constants only)
|
---|
964 | ) {
|
---|
965 |
|
---|
966 | switch (node.Symbol.Name) {
|
---|
967 | case "+": {
|
---|
968 | var l = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
969 | var r = InterpretRec(node.GetSubtree(1), nodeValues);
|
---|
970 |
|
---|
971 | return Tuple.Create(l.Item1 + r.Item1, l.Item2 + r.Item2);
|
---|
972 | }
|
---|
973 | case "*": {
|
---|
974 | var l = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
975 | var r = InterpretRec(node.GetSubtree(1), nodeValues);
|
---|
976 |
|
---|
977 | return Tuple.Create(l.Item1 * r.Item1, l.Item2 * r.Item1 + l.Item1 * r.Item2);
|
---|
978 | }
|
---|
979 |
|
---|
980 | case "-": {
|
---|
981 | var l = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
982 | var r = InterpretRec(node.GetSubtree(1), nodeValues);
|
---|
983 |
|
---|
984 | return Tuple.Create(l.Item1 - r.Item1, l.Item2 - r.Item2);
|
---|
985 | }
|
---|
986 | case "%": {
|
---|
987 | var l = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
988 | var r = InterpretRec(node.GetSubtree(1), nodeValues);
|
---|
989 |
|
---|
990 | // protected division
|
---|
991 | if (r.Item1.IsAlmost(0.0)) {
|
---|
992 | return Tuple.Create(0.0, Vector.Zero);
|
---|
993 | } else {
|
---|
994 | return Tuple.Create(
|
---|
995 | l.Item1 / r.Item1,
|
---|
996 | l.Item1 * -1.0 / (r.Item1 * r.Item1) * r.Item2 + 1.0 / r.Item1 * l.Item2 // (f/g)' = f * (1/g)' + 1/g * f' = f * -1/g² * g' + 1/g * f'
|
---|
997 | );
|
---|
998 | }
|
---|
999 | }
|
---|
1000 | case "sin": {
|
---|
1001 | var x = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
1002 | return Tuple.Create(
|
---|
1003 | Math.Sin(x.Item1),
|
---|
1004 | Vector.Cos(x.Item2) * x.Item2
|
---|
1005 | );
|
---|
1006 | }
|
---|
1007 | case "cos": {
|
---|
1008 | var x = InterpretRec(node.GetSubtree(0), nodeValues);
|
---|
1009 | return Tuple.Create(
|
---|
1010 | Math.Cos(x.Item1),
|
---|
1011 | -Vector.Sin(x.Item2) * x.Item2
|
---|
1012 | );
|
---|
1013 | }
|
---|
1014 | default: {
|
---|
1015 | return nodeValues[node]; // value and gradient for constants and variables must be set by the caller
|
---|
1016 | }
|
---|
1017 | }
|
---|
1018 | }
|
---|
1019 | #endregion
|
---|
1020 |
|
---|
1021 | #region events
|
---|
1022 | /*
|
---|
1023 | * Dependencies between parameters:
|
---|
1024 | *
|
---|
1025 | * ProblemData
|
---|
1026 | * |
|
---|
1027 | * V
|
---|
1028 | * TargetVariables FunctionSet MaximumLength NumberOfLatentVariables
|
---|
1029 | * | | | |
|
---|
1030 | * V V | |
|
---|
1031 | * Grammar <---------------+-------------------
|
---|
1032 | * |
|
---|
1033 | * V
|
---|
1034 | * Encoding
|
---|
1035 | */
|
---|
1036 | private void RegisterEventHandlers() {
|
---|
1037 | ProblemDataParameter.ValueChanged += ProblemDataParameter_ValueChanged;
|
---|
1038 | if (ProblemDataParameter.Value != null) ProblemDataParameter.Value.Changed += ProblemData_Changed;
|
---|
1039 |
|
---|
1040 | TargetVariablesParameter.ValueChanged += TargetVariablesParameter_ValueChanged;
|
---|
1041 | if (TargetVariablesParameter.Value != null) TargetVariablesParameter.Value.CheckedItemsChanged += CheckedTargetVariablesChanged;
|
---|
1042 |
|
---|
1043 | FunctionSetParameter.ValueChanged += FunctionSetParameter_ValueChanged;
|
---|
1044 | if (FunctionSetParameter.Value != null) FunctionSetParameter.Value.CheckedItemsChanged += CheckedFunctionsChanged;
|
---|
1045 |
|
---|
1046 | MaximumLengthParameter.Value.ValueChanged += MaximumLengthChanged;
|
---|
1047 |
|
---|
1048 | NumberOfLatentVariablesParameter.Value.ValueChanged += NumLatentVariablesChanged;
|
---|
1049 | }
|
---|
1050 |
|
---|
1051 | private void NumLatentVariablesChanged(object sender, EventArgs e) {
|
---|
1052 | UpdateGrammarAndEncoding();
|
---|
1053 | }
|
---|
1054 |
|
---|
1055 | private void MaximumLengthChanged(object sender, EventArgs e) {
|
---|
1056 | UpdateGrammarAndEncoding();
|
---|
1057 | }
|
---|
1058 |
|
---|
1059 | private void FunctionSetParameter_ValueChanged(object sender, EventArgs e) {
|
---|
1060 | FunctionSetParameter.Value.CheckedItemsChanged += CheckedFunctionsChanged;
|
---|
1061 | }
|
---|
1062 |
|
---|
1063 | private void CheckedFunctionsChanged(object sender, CollectionItemsChangedEventArgs<IndexedItem<StringValue>> e) {
|
---|
1064 | UpdateGrammarAndEncoding();
|
---|
1065 | }
|
---|
1066 |
|
---|
1067 | private void TargetVariablesParameter_ValueChanged(object sender, EventArgs e) {
|
---|
1068 | TargetVariablesParameter.Value.CheckedItemsChanged += CheckedTargetVariablesChanged;
|
---|
1069 | }
|
---|
1070 |
|
---|
1071 | private void CheckedTargetVariablesChanged(object sender, CollectionItemsChangedEventArgs<IndexedItem<StringValue>> e) {
|
---|
1072 | UpdateGrammarAndEncoding();
|
---|
1073 | }
|
---|
1074 |
|
---|
1075 | private void ProblemDataParameter_ValueChanged(object sender, EventArgs e) {
|
---|
1076 | ProblemDataParameter.Value.Changed += ProblemData_Changed;
|
---|
1077 | OnProblemDataChanged();
|
---|
1078 | OnReset();
|
---|
1079 | }
|
---|
1080 |
|
---|
1081 | private void ProblemData_Changed(object sender, EventArgs e) {
|
---|
1082 | OnProblemDataChanged();
|
---|
1083 | OnReset();
|
---|
1084 | }
|
---|
1085 |
|
---|
1086 | private void OnProblemDataChanged() {
|
---|
1087 | UpdateTargetVariables(); // implicitly updates other dependent parameters
|
---|
1088 | var handler = ProblemDataChanged;
|
---|
1089 | if (handler != null) handler(this, EventArgs.Empty);
|
---|
1090 | }
|
---|
1091 |
|
---|
1092 | #endregion
|
---|
1093 |
|
---|
1094 | #region helper
|
---|
1095 |
|
---|
1096 | private void InitAllParameters() {
|
---|
1097 | UpdateTargetVariables(); // implicitly updates the grammar and the encoding
|
---|
1098 | }
|
---|
1099 |
|
---|
1100 | private ReadOnlyCheckedItemList<StringValue> CreateFunctionSet() {
|
---|
1101 | var l = new CheckedItemList<StringValue>();
|
---|
1102 | l.Add(new StringValue("+").AsReadOnly());
|
---|
1103 | l.Add(new StringValue("*").AsReadOnly());
|
---|
1104 | l.Add(new StringValue("%").AsReadOnly());
|
---|
1105 | l.Add(new StringValue("-").AsReadOnly());
|
---|
1106 | l.Add(new StringValue("sin").AsReadOnly());
|
---|
1107 | l.Add(new StringValue("cos").AsReadOnly());
|
---|
1108 | return l.AsReadOnly();
|
---|
1109 | }
|
---|
1110 |
|
---|
1111 | private static bool IsConstantNode(ISymbolicExpressionTreeNode n) {
|
---|
1112 | return n.Symbol.Name.StartsWith("θ");
|
---|
1113 | }
|
---|
1114 | private static bool IsLatentVariableNode(ISymbolicExpressionTreeNode n) {
|
---|
1115 | return n.Symbol.Name.StartsWith("λ");
|
---|
1116 | }
|
---|
1117 | private static bool IsVariableNode(ISymbolicExpressionTreeNode n) {
|
---|
1118 | return (n.SubtreeCount == 0) && !IsConstantNode(n) && !IsLatentVariableNode(n);
|
---|
1119 | }
|
---|
1120 |
|
---|
1121 |
|
---|
1122 | private void UpdateTargetVariables() {
|
---|
1123 | var currentlySelectedVariables = TargetVariables.CheckedItems
|
---|
1124 | .OrderBy(i => i.Index)
|
---|
1125 | .Select(i => i.Value.Value)
|
---|
1126 | .ToArray();
|
---|
1127 |
|
---|
1128 | var newVariablesList = new CheckedItemList<StringValue>(ProblemData.Dataset.VariableNames.Select(str => new StringValue(str).AsReadOnly()).ToArray()).AsReadOnly();
|
---|
1129 | var matchingItems = newVariablesList.Where(item => currentlySelectedVariables.Contains(item.Value)).ToArray();
|
---|
1130 | foreach (var matchingItem in matchingItems) {
|
---|
1131 | newVariablesList.SetItemCheckedState(matchingItem, true);
|
---|
1132 | }
|
---|
1133 | TargetVariablesParameter.Value = newVariablesList;
|
---|
1134 | }
|
---|
1135 |
|
---|
1136 | private void UpdateGrammarAndEncoding() {
|
---|
1137 | var encoding = new MultiEncoding();
|
---|
1138 | var g = CreateGrammar();
|
---|
1139 | foreach (var targetVar in TargetVariables.CheckedItems) {
|
---|
1140 | encoding = encoding.Add(new SymbolicExpressionTreeEncoding(targetVar + "_tree", g, MaximumLength, MaximumLength)); // only limit by length
|
---|
1141 | }
|
---|
1142 | for (int i = 1; i <= NumberOfLatentVariables; i++) {
|
---|
1143 | encoding = encoding.Add(new SymbolicExpressionTreeEncoding("λ" + i + "_tree", g, MaximumLength, MaximumLength));
|
---|
1144 | }
|
---|
1145 | Encoding = encoding;
|
---|
1146 | }
|
---|
1147 |
|
---|
1148 | private ISymbolicExpressionGrammar CreateGrammar() {
|
---|
1149 | // whenever ProblemData is changed we create a new grammar with the necessary symbols
|
---|
1150 | var g = new SimpleSymbolicExpressionGrammar();
|
---|
1151 | g.AddSymbols(FunctionSet.CheckedItems.OrderBy(i => i.Index).Select(i => i.Value.Value).ToArray(), 2, 2);
|
---|
1152 |
|
---|
1153 | // TODO
|
---|
1154 | //g.AddSymbols(new[] {
|
---|
1155 | // "exp",
|
---|
1156 | // "log", // log( <expr> ) // TODO: init a theta to ensure the value is always positive
|
---|
1157 | // "exp_minus" // exp((-1) * <expr>
|
---|
1158 | //}, 1, 1);
|
---|
1159 |
|
---|
1160 | foreach (var variableName in ProblemData.AllowedInputVariables.Union(TargetVariables.CheckedItems.Select(i => i.Value.Value)))
|
---|
1161 | g.AddTerminalSymbol(variableName);
|
---|
1162 |
|
---|
1163 | // generate symbols for numeric parameters for which the value is optimized using AutoDiff
|
---|
1164 | // we generate multiple symbols to balance the probability for selecting a numeric parameter in the generation of random trees
|
---|
1165 | var numericConstantsFactor = 2.0;
|
---|
1166 | for (int i = 0; i < numericConstantsFactor * (ProblemData.AllowedInputVariables.Count() + TargetVariables.CheckedItems.Count()); i++) {
|
---|
1167 | g.AddTerminalSymbol("θ" + i); // numeric parameter for which the value is optimized using AutoDiff
|
---|
1168 | }
|
---|
1169 |
|
---|
1170 | // generate symbols for latent variables
|
---|
1171 | for (int i = 1; i <= NumberOfLatentVariables; i++) {
|
---|
1172 | g.AddTerminalSymbol("λ" + i); // numeric parameter for which the value is optimized using AutoDiff
|
---|
1173 | }
|
---|
1174 |
|
---|
1175 | return g;
|
---|
1176 | }
|
---|
1177 |
|
---|
1178 |
|
---|
1179 | private ISymbolicExpressionTreeNode TranslateTreeNode(ISymbolicExpressionTreeNode n, double[] parameterValues, ref int nextParIdx) {
|
---|
1180 | ISymbolicExpressionTreeNode translatedNode = null;
|
---|
1181 | if (n.Symbol is StartSymbol) {
|
---|
1182 | translatedNode = new StartSymbol().CreateTreeNode();
|
---|
1183 | } else if (n.Symbol is ProgramRootSymbol) {
|
---|
1184 | translatedNode = new ProgramRootSymbol().CreateTreeNode();
|
---|
1185 | } else if (n.Symbol.Name == "+") {
|
---|
1186 | translatedNode = new Addition().CreateTreeNode();
|
---|
1187 | } else if (n.Symbol.Name == "-") {
|
---|
1188 | translatedNode = new Subtraction().CreateTreeNode();
|
---|
1189 | } else if (n.Symbol.Name == "*") {
|
---|
1190 | translatedNode = new Multiplication().CreateTreeNode();
|
---|
1191 | } else if (n.Symbol.Name == "%") {
|
---|
1192 | translatedNode = new Division().CreateTreeNode();
|
---|
1193 | } else if (n.Symbol.Name == "sin") {
|
---|
1194 | translatedNode = new Sine().CreateTreeNode();
|
---|
1195 | } else if (n.Symbol.Name == "cos") {
|
---|
1196 | translatedNode = new Cosine().CreateTreeNode();
|
---|
1197 | } else if (IsConstantNode(n)) {
|
---|
1198 | var constNode = (ConstantTreeNode)new Constant().CreateTreeNode();
|
---|
1199 | constNode.Value = parameterValues[nextParIdx];
|
---|
1200 | nextParIdx++;
|
---|
1201 | translatedNode = constNode;
|
---|
1202 | } else {
|
---|
1203 | // assume a variable name
|
---|
1204 | var varName = n.Symbol.Name;
|
---|
1205 | var varNode = (VariableTreeNode)new Variable().CreateTreeNode();
|
---|
1206 | varNode.Weight = 1.0;
|
---|
1207 | varNode.VariableName = varName;
|
---|
1208 | translatedNode = varNode;
|
---|
1209 | }
|
---|
1210 | foreach (var child in n.Subtrees) {
|
---|
1211 | translatedNode.AddSubtree(TranslateTreeNode(child, parameterValues, ref nextParIdx));
|
---|
1212 | }
|
---|
1213 | return translatedNode;
|
---|
1214 | }
|
---|
1215 | #endregion
|
---|
1216 |
|
---|
1217 | #region Import & Export
|
---|
1218 | public void Load(IRegressionProblemData data) {
|
---|
1219 | Name = data.Name;
|
---|
1220 | Description = data.Description;
|
---|
1221 | ProblemData = data;
|
---|
1222 | }
|
---|
1223 |
|
---|
1224 | public IRegressionProblemData Export() {
|
---|
1225 | return ProblemData;
|
---|
1226 | }
|
---|
1227 | #endregion
|
---|
1228 |
|
---|
1229 | }
|
---|
1230 | }
|
---|