Changeset 17991 for branches/3128_Prediction_Intervals/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/SymbolicRegressionModel.cs

Timestamp:

06/16/21 21:35:37 (3 years ago)

Author:

gkronber

Message:

#3128: first dump of exploratory work-in-progress code to make sure the working copy is not lost.

File:

• branches/3128_Prediction_Intervals/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/SymbolicRegressionModel.cs (modified) (4 diffs)

branches/3128_Prediction_Intervals/HeuristicLab.Problems.DataAnalysis.Symbolic.Regression/3.4/SymbolicRegressionModel.cs

@@ -26 +26 @@
 using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
 using HEAL.Attic;
+using HeuristicLab.Data;
+using System.Linq;
 
 namespace HeuristicLab.Problems.DataAnalysis.Symbolic.Regression {
@@ -45 +47 @@
     }
 
+    [Storable]
+    private readonly double[,] parameterCovariance;
+    [Storable]
+    private readonly double sigma;
+
     [StorableConstructor]
     protected SymbolicRegressionModel(StorableConstructorFlag _) : base(_) {
@@ -53 +60 @@
       : base(original, cloner) {
       this.targetVariable = original.targetVariable;
+      this.parameterCovariance = original.parameterCovariance; // immutable
+      this.sigma = original.sigma;
     }
 
     public SymbolicRegressionModel(string targetVariable, ISymbolicExpressionTree tree,
       ISymbolicDataAnalysisExpressionTreeInterpreter interpreter,
-      double lowerEstimationLimit = double.MinValue, double upperEstimationLimit = double.MaxValue)
+      double lowerEstimationLimit = double.MinValue, double upperEstimationLimit = double.MaxValue, double[,] parameterCovariance = null, double sigma = 0.0)
       : base(tree, interpreter, lowerEstimationLimit, upperEstimationLimit) {
       this.targetVariable = targetVariable;
+      if (parameterCovariance != null)
+        this.parameterCovariance = (double[,])parameterCovariance.Clone();
+      this.sigma = sigma;
     }
 
@@ -69 +81 @@
       return Interpreter.GetSymbolicExpressionTreeValues(SymbolicExpressionTree, dataset, rows)
         .LimitToRange(LowerEstimationLimit, UpperEstimationLimit);
+    }
+
+    public IEnumerable<double> GetEstimatedVariances(IDataset dataset, IEnumerable<int> rows) {
+      // must work with a copy because we change tree nodes
+      var treeCopy = (ISymbolicExpressionTree)SymbolicExpressionTree.Clone();
+      // uses sampling to produce prediction intervals
+      alglib.hqrndseed(31415, 926535, out var state);
+      var cov = parameterCovariance;
+      if (cov == null || cov.Length == 0) return rows.Select(_ => 0.0);
+      var n = 30;
+      var M = rows.Select(_ => new double[n]).ToArray();
+      var paramNodes = new List<ISymbolicExpressionTreeNode>();
+      var coeffList = new List<double>();
+      // HACK: skip linear scaling parameters because the analyzer doesn't use them (and they are likely correlated with the remaining parameters)
+      // only works with linear scaling
+      if (!(treeCopy.Root.GetSubtree(0).GetSubtree(0).Symbol is Addition) ||
+          !(treeCopy.Root.GetSubtree(0).GetSubtree(0).GetSubtree(0).Symbol is Multiplication)) 
+        throw new NotImplementedException("prediction intervals are implemented only for linear scaling");
+
+      foreach (var node in treeCopy.Root.GetSubtree(0).GetSubtree(0).IterateNodesPostfix()) {
+        if (node is ConstantTreeNode constNode) {
+          paramNodes.Add(constNode);
+          coeffList.Add(constNode.Value);
+        } else if (node is VariableTreeNode varNode) {
+          paramNodes.Add(varNode);
+          coeffList.Add(varNode.Weight);
+        }
+      }
+      var coeff = coeffList.ToArray();
+      var numParams = coeff.Length;
+      if (cov.GetLength(0) != numParams) throw new InvalidProgramException();
+
+      // TODO: probably we do not need to sample but can instead use a first-order or second-order approximation of f
+      // see http://sia.webpopix.org/nonlinearRegression.html
+      // also see https://rmazing.wordpress.com/2013/08/26/predictnls-part-2-taylor-approximation-confidence-intervals-for-nls-models/
+      // https://www.rdocumentation.org/packages/propagate/versions/1.0-4/topics/predictNLS
+      double[] p = new double[numParams];
+      for (int i = 0; i < 30; i++) {
+        // sample and update parameter vector delta is 
+        alglib.hqrndnormalv(state, numParams, out var delta);
+        alglib.rmatrixmv(numParams, numParams, cov, 0, 0, 0, delta, 0, ref p, 0);
+        for (int j = 0; j < numParams; j++) {
+          if (paramNodes[j] is ConstantTreeNode constNode) constNode.Value = coeff[j] + p[j];
+          else if (paramNodes[j] is VariableTreeNode varNode) varNode.Weight = coeff[j] + p[j];
+        }
+        var r = 0;
+        var estimatedValues = Interpreter.GetSymbolicExpressionTreeValues(treeCopy, dataset, rows).LimitToRange(LowerEstimationLimit, UpperEstimationLimit);
+
+        foreach (var pred in estimatedValues) {
+          M[r++][i] = pred;
+        }
+      }
+
+      // reset parameters
+      for (int j = 0; j < numParams; j++) {
+        if (paramNodes[j] is ConstantTreeNode constNode) constNode.Value = coeff[j];
+        else if (paramNodes[j] is VariableTreeNode varNode) varNode.Weight = coeff[j];
+      }
+      var sigma2 = sigma * sigma;
+      return M.Select(M_i => M_i.Variance() + sigma2).ToArray();
     }