Changeset 10489 for trunk/sources/HeuristicLab.Algorithms.DataAnalysis/3.4/GaussianProcess/CovarianceFunctions/CovarianceNeuralNetwork.cs

Timestamp:

02/20/14 17:45:06 (10 years ago)

Author:

gkronber

Message:

#2125 fixed the bug that covariance functions returned the full gradient vector even when parameters are partially fixed.
changed the calculation of NN covariance and gradient to direct calculation (instead of AutoDiff)

File:

• trunk/sources/HeuristicLab.Algorithms.DataAnalysis/3.4/GaussianProcess/CovarianceFunctions/CovarianceNeuralNetwork.cs (modified) (5 diffs)

trunk/sources/HeuristicLab.Algorithms.DataAnalysis/3.4/GaussianProcess/CovarianceFunctions/CovarianceNeuralNetwork.cs

@@ -43 +43 @@
       get { return (IValueParameter<DoubleValue>)Parameters["Length"]; }
     }
+    private bool HasFixedScaleParameter {
+      get { return ScaleParameter.Value != null; }
+    }
+    private bool HasFixedLengthParameter {
+      get { return LengthParameter.Value != null; }
+    }
 
     [StorableConstructor]
@@ -68 +74 @@
     public int GetNumberOfParameters(int numberOfVariables) {
       return
-        (ScaleParameter.Value != null ? 0 : 1) +
-        (LengthParameter.Value != null ? 0 : 1);
+        (HasFixedScaleParameter ? 0 : 1) +
+        (HasFixedLengthParameter ? 0 : 1);
     }
 
@@ -83 +89 @@
       // gather parameter values
       int c = 0;
-      if (LengthParameter.Value != null) {
+      if (HasFixedLengthParameter) {
         length = LengthParameter.Value.Value;
       } else {
@@ -90 +96 @@
       }
 
-      if (ScaleParameter.Value != null) {
+      if (HasFixedScaleParameter) {
         scale = ScaleParameter.Value.Value;
       } else {
@@ -110 +116 @@
       double length, scale;
       GetParameterValues(p, out scale, out length);
-      // create functions
-      AutoDiff.Variable p0 = new AutoDiff.Variable();
-      AutoDiff.Variable p1 = new AutoDiff.Variable();
-      var l = TermBuilder.Exp(2.0 * p0);
-      var s = TermBuilder.Exp(2.0 * p1);
-      AutoDiff.Variable[] x1 = new AutoDiff.Variable[columnIndices.Count()];
-      AutoDiff.Variable[] x2 = new AutoDiff.Variable[columnIndices.Count()];
-      AutoDiff.Term sx = 1;
-      AutoDiff.Term s1 = 1;
-      AutoDiff.Term s2 = 1;
-      for (int k = 0; k < columnIndices.Count(); k++) {
-        x1[k] = new AutoDiff.Variable();
-        x2[k] = new AutoDiff.Variable();
-        sx += x1[k] * x2[k];
-        s1 += x1[k] * x1[k];
-        s2 += x2[k] * x2[k];
-      }
-
-      var parameter = x1.Concat(x2).Concat(new AutoDiff.Variable[] { p0, p1 }).ToArray();
-      var values = new double[x1.Length + x2.Length + 2];
-      var c = (s * asin(sx / (sqrt((l + s1) * (l + s2))))).Compile(parameter);
+      var fixedLength = HasFixedLengthParameter;
+      var fixedScale = HasFixedScaleParameter;
 
       var cov = new ParameterizedCovarianceFunction();
       cov.Covariance = (x, i, j) => {
-        int k = 0;
+        double sx = 1.0;
+        double s1 = 1.0;
+        double s2 = 1.0;
         foreach (var col in columnIndices) {
-          values[k] = x[i, col];
-          k++;
+          sx += x[i, col] * x[j, col];
+          s1 += x[i, col] * x[i, col];
+          s2 += x[j, col] * x[j, col];
         }
-        foreach (var col in columnIndices) {
-          values[k] = x[j, col];
-          k++;
-        }
-        values[k] = Math.Log(Math.Sqrt(length));
-        values[k + 1] = Math.Log(Math.Sqrt(scale));
-        return c.Evaluate(values);
+
+        return (scale * Math.Asin(sx / (Math.Sqrt((length + s1) * (length + s2)))));
       };
       cov.CrossCovariance = (x, xt, i, j) => {
-        int k = 0;
+        double sx = 1.0;
+        double s1 = 1.0;
+        double s2 = 1.0;
         foreach (var col in columnIndices) {
-          values[k] = x[i, col];
-          k++;
+          sx += x[i, col] * xt[j, col];
+          s1 += x[i, col] * x[i, col];
+          s2 += xt[j, col] * xt[j, col];
         }
+
+        return (scale * Math.Asin(sx / (Math.Sqrt((length + s1) * (length + s2)))));
+      };
+      cov.CovarianceGradient = (x, i, j) => GetGradient(x, i, j, length, scale, columnIndices, fixedLength, fixedScale);
+      return cov;
+    }
+
+    // order of returned gradients must match the order in GetParameterValues!
+    private static IEnumerable<double> GetGradient(double[,] x, int i, int j, double length, double scale, IEnumerable<int> columnIndices,
+      bool fixedLength, bool fixedScale) {
+      {
+        double sx = 1.0;
+        double s1 = 1.0;
+        double s2 = 1.0;
         foreach (var col in columnIndices) {
-          values[k] = xt[j, col];
-          k++;
+          sx += x[i, col] * x[j, col];
+          s1 += x[i, col] * x[i, col];
+          s2 += x[j, col] * x[j, col];
         }
-        values[k] = Math.Log(Math.Sqrt(length));
-        values[k + 1] = Math.Log(Math.Sqrt(scale));
-        return c.Evaluate(values);
+        var h = (length + s1) * (length + s2);
+        var f = sx / Math.Sqrt(h);
+        if (!fixedLength) {
+          yield return -scale / Math.Sqrt(1.0 - f * f) * ((length * sx * (2.0 * length + s1 + s2)) / Math.Pow(h, 3.0 / 2.0));
+        }
+        if (!fixedScale) {
+          yield return 2.0 * scale * Math.Asin(f);
+        }
+
       };
-      cov.CovarianceGradient = (x, i, j) => {
-        int k = 0;
-        foreach (var col in columnIndices) {
-          values[k] = x[i, col];
-          k++;
-        }
-        foreach (var col in columnIndices) {
-          values[k] = x[j, col];
-          k++;
-        }
-        values[k] = Math.Log(Math.Sqrt(length));
-        values[k + 1] = Math.Log(Math.Sqrt(scale));
-        return c.Differentiate(values).Item1.Skip(columnIndices.Count() * 2);
-      };
-      return cov;
     }