Changeset 14873

Timestamp:

04/15/17 08:44:15 (7 years ago)

Author:

gkronber

Message:

#2704: added possibility to automatically adjust constants based on the distributions of evaluated expressions to allow limiting distributions for arguments of functions (e.g. log should have positive args only, exp should have rather small args only)

Location:

branches/HeuristicLab.ExpressionGenerator/HeuristicLab.ExpressionGenerator/3.4

Files:

• Expression.cs (modified) (3 diffs)
• ExpressionEvaluator.cs (modified) (1 diff)
• ExpressionGenerator.cs (modified) (5 diffs)
• ExpressionTemplate.cs (modified) (4 diffs)
• HeuristicLab.ExpressionGenerator.csproj (modified) (1 diff)
• PointDistribution.cs (added)
• Properties (modified) (1 prop)

branches/HeuristicLab.ExpressionGenerator/HeuristicLab.ExpressionGenerator/3.4/Expression.cs

@@ -42 +42 @@
     }
 
-    public IRandom Distribution { get; private set; }
-
-    public Func<IEnumerable<double>, double> Transform { get; private set; }
-
-    public double Value { get; private set; }
+    public IRandom Distribution { get; private set; }  // only for random variables
+
+    public Func<IEnumerable<double>, double> Transform { get; private set; } // only for functions
+
+    public double Value { get; private set; } // only for constants
 
     public Expression(string name, double value) {
@@ -85 +85 @@
       switch (Type) {
         case ExpressionType.Constant:
-          sb.Append(Value.ToString("0.000", CultureInfo.CurrentCulture));
+          sb.Append(Value.ToString("0.000", CultureInfo.InvariantCulture));
           break;
         case ExpressionType.RandomVariable:
@@ -108 +108 @@
         case ExpressionType.Constant:
           sb.Append(Value < 0
-              ? string.Format("(- {0})", Math.Abs(Value).ToString("0.000", CultureInfo.CurrentCulture))
-              : Value.ToString("0.000", CultureInfo.CurrentCulture));
+              ? string.Format("(- {0})", Math.Abs(Value).ToString("0.000", CultureInfo.InvariantCulture))
+              : Value.ToString("0.000", CultureInfo.InvariantCulture));
           break;
         case ExpressionType.RandomVariable:

branches/HeuristicLab.ExpressionGenerator/HeuristicLab.ExpressionGenerator/3.4/ExpressionEvaluator.cs

@@ -57 +57 @@
 
     public Dictionary<Expression, List<double>> GenerateData(Expression expression, int rows) {
+      return GenerateData(new [] {expression}, rows);
+    }
+    public Dictionary<Expression, List<double>> GenerateData(IEnumerable<Expression> expressions, int rows) {
       var data = new Dictionary<Expression, List<double>>();
       for (int i = 0; i < rows; ++i) {
         evaluationCache.Clear();
-        Evaluate(expression);
+        foreach(var expr in expressions) Evaluate(expr);
         foreach (var pair in evaluationCache) {
           if (!data.ContainsKey(pair.Key))

branches/HeuristicLab.ExpressionGenerator/HeuristicLab.ExpressionGenerator/3.4/ExpressionGenerator.cs

@@ -23 +23 @@
 using System.Collections.Generic;
 using System.Linq;
+using System.Runtime.InteropServices;
+using HeuristicLab.Common;
 using HeuristicLab.Core;
 using HeuristicLab.Random;
@@ -30 +32 @@
     public static IEnumerable<Expression> GenerateRandomDistributedVariables(int numberOfVariables, string variablePrefix, IRandom randomDistribution) {
       return Enumerable.Range(1, numberOfVariables).Select(x => Expression.RandomVariable(string.Format("{0}{1}", variablePrefix, x), randomDistribution));
+    }
+
+    public static Expression NonlinearExpression(IRandom uniformRandom, Expression[] variables, bool useLog, bool useExp) {
+      var scalingTemplate = ScaledExpression(uniformRandom, variables, varianceRandom: new UniformDistributedRandom(uniformRandom, 1, 10));
+      var scaledVars = Instantiate(scalingTemplate, uniformRandom, 100, "scaledVar");
+
+      var sumTemplate = new RandomArityTemplate(Sum, new UniformDistributedRandom(uniformRandom, 1, 3)) { Label = "+" };
+      sumTemplate.AddArguments(scaledVars);
+      var prodTemplate = new RandomArityTemplate(Product, new UniformDistributedRandom(uniformRandom, 1, 3)) { Label = "*" };
+      prodTemplate.AddArguments(variables);
+
+      var logTemplate = LogOfScaledExpression(uniformRandom, Instantiate(sumTemplate, uniformRandom, 100, "sumOfScaledVars"),
+        minValue: new UniformDistributedRandom(uniformRandom, 0.1, 2),
+        valueRange: new UniformDistributedRandom(uniformRandom, 1, 10));
+
+      var expTemplate = ExpOfScaledExpression(uniformRandom, Instantiate(prodTemplate, uniformRandom, 100, "prodOfVars"),
+        valueRange: new UniformDistributedRandom(uniformRandom, 1, 4)); // TODO should also specify an offset
+
+      var scaledExprTemplate = new ScalingTemplate(new UniformDistributedRandom(uniformRandom, 1, 10)) { Label = "*" };
+      if (useLog) scaledExprTemplate.AddArguments(Instantiate(logTemplate, uniformRandom, 100, "log"));
+      if (useExp) scaledExprTemplate.AddArguments(Instantiate(expTemplate, uniformRandom, 100, "exp"));
+
+      var mainTemplate = new RandomArityTemplate(Sum, new UniformDistributedRandom(uniformRandom, 3, 5));
+      mainTemplate.AddArguments(scaledVars);
+      if (useLog || useExp) {
+        mainTemplate.AddArguments(Instantiate(scaledExprTemplate, uniformRandom, 100, "scaledExpr"));
+      }
+      mainTemplate.Label = "+";
+
+      return mainTemplate.Instantiate("main", uniformRandom, false);
     }
 
@@ -70 +102 @@
     }
 
+    // variance random must have support only positive numbers
+    private static ExpressionTemplate ScaledExpression(IRandom uniformRandom, IEnumerable<Expression> arguments, IRandom varianceRandom) {
+      var scalingTemplate = new ScalingTemplate(scaledVariance: varianceRandom);
+      scalingTemplate.AddArguments(arguments);
+      scalingTemplate.Label = "*";
+      return scalingTemplate;
+    }
+
+    /// template scales and translates the argument expression first to guarantee positive values
+    private static ExpressionTemplate LogOfScaledExpression(IRandom uniformRandom, IEnumerable<Expression> arguments,
+      IRandom minValue = null, IRandom valueRange = null) {
+      var limitToRangeTemplate = new RangeTemplate(minValue, valueRange);
+      limitToRangeTemplate.AddArguments(arguments);
+
+      var logTemplate = new FixedArityTemplate(Log, 1) { Label = "log" };
+      logTemplate.AddArguments(Enumerable.Range(1, 100).Select(i => limitToRangeTemplate.Instantiate(string.Format("log{0}", i), uniformRandom, false)));
+      return logTemplate;
+    }
+
+    /// template scales the argument expression first to guarantee reasonable values
+    private static ExpressionTemplate ExpOfScaledExpression(IRandom uniformRandom, IEnumerable<Expression> arguments,
+      IRandom valueRange = null) {
+      var limitToRangeTemplate = new RangeTemplate(null, valueRange);
+      limitToRangeTemplate.AddArguments(arguments);
+
+      var expTemplate = new FixedArityTemplate(Exp, 1) { Label = "exp" };
+      expTemplate.AddArguments(Enumerable.Range(1, 100).Select(i => limitToRangeTemplate.Instantiate(string.Format("exp{0}", i), uniformRandom, false)));
+      return expTemplate;
+    }
+
+    public static IEnumerable<Expression> Instantiate(ExpressionTemplate template, IRandom random, int count, string name) {
+      return Enumerable.Range(1, count).Select(i => template.Instantiate(name + i, random, false));
+    }
+
     #region static functions
-    private static double Sum(IEnumerable<double> args) {
+    public static double Sum(IEnumerable<double> args) {
       return args.Sum();
     }
 
-    private static double Product(IEnumerable<double> args) {
+    public static double Product(IEnumerable<double> args) {
       return args.Aggregate((x, y) => x * y);
     }
 
-    private static double Division(IEnumerable<double> args) {
+    public static double Division(IEnumerable<double> args) {
       if (args.Count() == 1)
         return 1 / args.First();
@@ -86 +152 @@
     }
 
-    private static double Subtraction(IEnumerable<double> args) {
+    public static double Subtraction(IEnumerable<double> args) {
       if (args.Count() == 1)
         return -args.First();
@@ -93 +159 @@
     }
 
-    private static double Exp(IEnumerable<double> args) {
+    public static double Exp(IEnumerable<double> args) {
       return Math.Exp(args.Single());
     }
 
-    private static double Log(IEnumerable<double> args) {
+    public static double Log(IEnumerable<double> args) {
       return Math.Log(args.Single());
     }
 
-    private static double Square(IEnumerable<double> args) {
+    public static double Square(IEnumerable<double> args) {
       var v = args.Single();
       return v * v;

branches/HeuristicLab.ExpressionGenerator/HeuristicLab.ExpressionGenerator/3.4/ExpressionTemplate.cs

@@ -23 +23 @@
 using System.Collections.Generic;
 using System.Linq;
+using HeuristicLab.Common;
 using HeuristicLab.Core;
 using HeuristicLab.Random;
@@ -28 +29 @@
 namespace HeuristicLab.ExpressionGenerator {
   public abstract class ExpressionTemplate {
-    private List<Tuple<Expression, double>> arguments;
-    private readonly Func<IEnumerable<double>, double> transform;
+    protected List<Tuple<Expression, double>> arguments;
+    protected readonly Func<IEnumerable<double>, double> transform;
     public string Label { get; set; }
 
     protected Expression Instantiate(string name, IRandom random, int n, bool sampleWithRepetition = false) {
+      var func = Expression.Function(name, transform, SampleArguments(random, n, sampleWithRepetition));
+      func.Label = Label;
+      return func;
+    }
+
+    protected IEnumerable<Expression> SampleArguments(IRandom random, int n, bool sampleWithRepetition = false) {
       var weights = arguments.Select(x => x.Item2);
       var args = sampleWithRepetition
        ? arguments.SampleProportional(random, n, weights).Select(x => x.Item1)
        : arguments.SampleProportionalWithoutRepetition(random, n, weights).Select(x => x.Item1);
-      var func = Expression.Function(name, transform, args);
-      func.Label = Label;
-      return func;
+      return args;
     }
 
@@ -58 +63 @@
     }
 
-    public void AddArguments(IEnumerable<Expression> expressions, IEnumerable<double> weights) { 
+    public void AddArguments(IEnumerable<Expression> expressions, IEnumerable<double> weights) {
       arguments = arguments ?? new List<Tuple<Expression, double>>();
       arguments.AddRange(expressions.Zip(weights, Tuple.Create));
@@ -87 +92 @@
     }
   }
+
+  public class ScalingTemplate : ExpressionTemplate {
+    private readonly IRandom scaledVariance;
+    // w * expr
+    public ScalingTemplate(IRandom scaledVariance = null) : base(ExpressionGenerator.Product) {
+      this.scaledVariance = scaledVariance;
+    }
+
+    public override Expression Instantiate(string name, IRandom random, bool sampleWithRepetition = false) {
+      var expr = SampleArguments(random, 1, sampleWithRepetition).First();
+
+      // use the evaluator to determine variance of the sampled expression and initialize the constant accordingly to reach the target variance
+      var @const = 1.0;
+      if (scaledVariance != null) {
+        var evaluator = new ExpressionEvaluator();
+        var data = evaluator.GenerateData(expr, 10000);
+        var variance = data[expr].VariancePop();
+        @const = scaledVariance.NextDouble() / variance;
+      }
+
+      var func = Expression.Function(name, transform, new Expression[] { Expression.Constant(name, @const), expr });
+      func.Label = "*";
+      return func;
+    }
+  }
+
+  public class OffsetTemplate : ExpressionTemplate {
+    private readonly IRandom offset;
+    // expr + offset
+    public OffsetTemplate(IRandom offset = null) : base(ExpressionGenerator.Sum) {
+      this.offset = offset;
+    }
+
+    public override Expression Instantiate(string name, IRandom random, bool sampleWithRepetition = false) {
+      var expr = SampleArguments(random, 1, sampleWithRepetition).First();
+
+      // use the evaluator to determine variance of the sampled expression and initialize the constant accordingly to reach the target offset
+      var @const = 0.0;
+      if (offset != null) {
+        var evaluator = new ExpressionEvaluator();
+        var data = evaluator.GenerateData(expr, 10000);
+        var average = data[expr].Average();
+        @const = offset.NextDouble() - average;
+      }
+
+      var func = Expression.Function(name, transform, new Expression[] { Expression.Constant(name, @const), expr });
+      func.Label = "+";
+      return func;
+    }
+  }
+
+  public class RangeTemplate : ExpressionTemplate {
+    private readonly IRandom minValue;
+    private readonly IRandom valueRange;
+    // expr + offset
+    public RangeTemplate(IRandom minValue = null, IRandom valueRange = null) : base(null) {
+      this.minValue = minValue;
+      this.valueRange = valueRange;
+    }
+
+    public override Expression Instantiate(string name, IRandom random, bool sampleWithRepetition = false) {
+      var expr = SampleArguments(random, 1, sampleWithRepetition).First();
+
+      // use the evaluator to determine variance of the sampled expression and initialize the constant accordingly to reach the target offset
+      var mult = 1.0;
+      var add = 0.0;
+
+      if (minValue != null || valueRange != null) {
+        var evaluator = new ExpressionEvaluator();
+        var data = evaluator.GenerateData(expr, 10000);
+        if (valueRange != null) {
+          var targetRange = valueRange.NextDouble();
+          var min = data[expr].Min();
+          var max = data[expr].Max();
+          var range = max - min;
+          mult = targetRange / range;
+          add = -min + min / mult;
+        }
+        if (minValue != null) {
+          var targetMin = minValue.NextDouble();
+          var min = data[expr].Min();
+          add += (targetMin - min) / mult;
+        }
+
+        expr = Expression.Function(name + "-toZero", ExpressionGenerator.Sum, new Expression[] { Expression.Constant("name-add0", add), expr });
+        expr.Label = "+";
+        expr = Expression.Function(name + "-mult", ExpressionGenerator.Product, new Expression[] { Expression.Constant("name-mult", mult), expr });
+        expr.Label = "*";
+      }
+
+      return expr;
+    }
+  }
 }

branches/HeuristicLab.ExpressionGenerator/HeuristicLab.ExpressionGenerator/3.4/HeuristicLab.ExpressionGenerator.csproj

@@ -77 +77 @@
     <Compile Include="ExpressionTemplate.cs" />
     <Compile Include="Interfaces\IExpression.cs" />
+    <Compile Include="PointDistribution.cs" />
     <Compile Include="Plugin.cs" />
   </ItemGroup>