source: branches/HeuristicLab.Problems.GrammaticalOptimization/HeuristicLab.Problems.GrammaticalOptimization.SymbReg/SymbolicRegressionProblem.cs @ 12014

using System;
using System.CodeDom.Compiler;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Security;
using System.Security.AccessControl;
using System.Security.Authentication.ExtendedProtection.Configuration;
using System.Text;
using AutoDiff;
using HeuristicLab.Algorithms.Bandits;
using HeuristicLab.Common;
using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding;
using HeuristicLab.Problems.DataAnalysis;
using HeuristicLab.Problems.Instances;
using HeuristicLab.Problems.Instances.DataAnalysis;

namespace HeuristicLab.Problems.GrammaticalOptimization.SymbReg {
  // provides bridge to HL regression problem instances
  public class SymbolicRegressionProblem : ISymbolicExpressionTreeProblem {

    // C represents Koza-style ERC (the symbol is the index of the ERC), the values are initialized below
    private const string grammarString = @"
        G(E):
        E -> V | C | V+E | V-E | V*E | V%E | (E) | C+E | C-E | C*E | C%E 
        C -> 0..9
        V -> <variables>
        ";

    // when using constant opt optimal constants are generated in the evaluation step so we don't need them in the grammar
    private const string grammarConstOptString = @"
        G(E):
        E -> V | V+E | V*E | V%E | (E) 
        V -> <variables>
        ";

    // S .. Sum (+), N .. Neg. sum (-), P .. Product (*), D .. Division (%)
    private const string treeGrammarString = @"
        G(E):
        E -> V | C | S | N | P | D 
        S -> EE | EEE
        N -> EE | EEE
        P -> EE | EEE
        D -> EE
        C -> 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
        V -> <variables>
        ";
    private const string treeGrammarConstOptString = @"
        G(E):
        E -> V | S | P | D 
        S -> EE | EEE
        P -> EE | EEE
        D -> EE
        V -> <variables>
        ";

    // when we use constants optimization we can completely ignore all constants by a simple strategy:
    // introduce a constant factor for each complete term
    // introduce a constant offset for each complete expression (including expressions in brackets)
    // e.g. 1*(2*a + b - 3 + 4) is the same as c0*a + c1*b + c2

    private readonly IGrammar grammar;

    private readonly int N;
    private readonly double[,] x;
    private readonly double[] y;
    private readonly int d;
    private readonly double[] erc;
    private readonly bool useConstantOpt;


    public SymbolicRegressionProblem(Random random, string partOfName, bool useConstantOpt = true) {
      var instanceProviders = new RegressionInstanceProvider[] 
      {new RegressionRealWorldInstanceProvider(),
        new HeuristicLab.Problems.Instances.DataAnalysis.VariousInstanceProvider(),
        new KeijzerInstanceProvider(), 
        new VladislavlevaInstanceProvider(), 
        new NguyenInstanceProvider(), 
        new KornsInstanceProvider(), 
    };
      var instanceProvider = instanceProviders.FirstOrDefault(prov => prov.GetDataDescriptors().Any(dd => dd.Name.Contains(partOfName)));
      if (instanceProvider == null) throw new ArgumentException("instance not found");

      this.useConstantOpt = useConstantOpt;

      var dds = instanceProvider.GetDataDescriptors();
      var problemData = instanceProvider.LoadData(dds.Single(ds => ds.Name.Contains(partOfName)));

      this.N = problemData.TrainingIndices.Count();
      this.d = problemData.AllowedInputVariables.Count();
      if (d > 26) throw new NotSupportedException(); // we only allow single-character terminal symbols so far
      this.x = new double[N, d];
      this.y = problemData.Dataset.GetDoubleValues(problemData.TargetVariable, problemData.TrainingIndices).ToArray();

      int i = 0;
      foreach (var r in problemData.TrainingIndices) {
        int j = 0;
        foreach (var inputVariable in problemData.AllowedInputVariables) {
          x[i, j++] = problemData.Dataset.GetDoubleValue(inputVariable, r);
        }
        i++;
      }
      // initialize ERC values
      erc = Enumerable.Range(0, 10).Select(_ => Rand.RandNormal(random) * 10).ToArray();

      char firstVar = 'a';
      char lastVar = Convert.ToChar(Convert.ToByte('a') + d - 1);
      if (!useConstantOpt) {
        this.grammar = new Grammar(grammarString.Replace("<variables>", firstVar + " .. " + lastVar));
        this.TreeBasedGPGrammar = new Grammar(treeGrammarString.Replace("<variables>", firstVar + " .. " + lastVar));
      } else {
        this.grammar = new Grammar(grammarConstOptString.Replace("<variables>", firstVar + " .. " + lastVar));
        this.TreeBasedGPGrammar = new Grammar(treeGrammarConstOptString.Replace("<variables>", firstVar + " .. " + lastVar));
      }
    }


    public double BestKnownQuality(int maxLen) {
      // for now only an upper bound is returned, ideally we have an R² of 1.0
      return 1.0;
    }

    public IGrammar Grammar {
      get { return grammar; }
    }

    public double Evaluate(string sentence) {
      if (useConstantOpt)
        return OptimizeConstantsAndEvaluate(sentence);
      else {
        var extender = new ExpressionExtender();

        Debug.Assert(SimpleEvaluate(sentence) == SimpleEvaluate(extender.CanonicalRepresentation(sentence)));
        return SimpleEvaluate(sentence);
      }
    }

    public double SimpleEvaluate(string sentence) {
      var interpreter = new ExpressionInterpreter();
      var rowData = new double[d];
      return HeuristicLab.Common.Extensions.RSq(y, Enumerable.Range(0, N).Select(i => {
        for (int j = 0; j < d; j++) rowData[j] = x[i, j];
        return interpreter.Interpret(sentence, rowData, erc);
      }));
    }


    public string CanonicalRepresentation(string phrase) {
      var extender = new ExpressionExtender();
      return extender.CanonicalRepresentation(phrase);
    }

    public IEnumerable<Feature> GetFeatures(string phrase) {
      phrase = CanonicalRepresentation(phrase);
      return new Feature[] { new Feature(phrase, 1.0) };
    }



    public double OptimizeConstantsAndEvaluate(string sentence) {
      AutoDiff.Term func;
      int n = x.GetLength(0);
      int m = x.GetLength(1);

      var compiler = new ExpressionCompiler();
      Variable[] variables = Enumerable.Range(0, m).Select(_ => new Variable()).ToArray();
      Variable[] constants;
      compiler.Compile(sentence, out func, variables, out constants);

      // constants are manipulated 

      if (!constants.Any()) return SimpleEvaluate(sentence);

      AutoDiff.IParametricCompiledTerm compiledFunc = func.Compile(constants, variables); // variate constants leave variables fixed to data

      double[] c = constants.Select(_ => 1.0).ToArray(); // start with ones

      alglib.lsfitstate state;
      alglib.lsfitreport rep;
      int info;


      int k = c.Length;

      alglib.ndimensional_pfunc function_cx_1_func = CreatePFunc(compiledFunc);
      alglib.ndimensional_pgrad function_cx_1_grad = CreatePGrad(compiledFunc);

      const int maxIterations = 10;
      try {
        alglib.lsfitcreatefg(x, y, c, n, m, k, false, out state);
        alglib.lsfitsetcond(state, 0.0, 0.0, maxIterations);
        //alglib.lsfitsetgradientcheck(state, 0.001);
        alglib.lsfitfit(state, function_cx_1_func, function_cx_1_grad, null, null);
        alglib.lsfitresults(state, out info, out c, out rep);
      } catch (ArithmeticException) {
        return 0.0;
      } catch (alglib.alglibexception) {
        return 0.0;
      }

      //info == -7  => constant optimization failed due to wrong gradient
      if (info == -7) throw new ArgumentException();
      {
        var rowData = new double[d];
        return HeuristicLab.Common.Extensions.RSq(y, Enumerable.Range(0, N).Select(i => {
          for (int j = 0; j < d; j++) rowData[j] = x[i, j];
          return compiledFunc.Evaluate(c, rowData);
        }));
      }
    }


    private static alglib.ndimensional_pfunc CreatePFunc(AutoDiff.IParametricCompiledTerm compiledFunc) {
      return (double[] c, double[] x, ref double func, object o) => {
        func = compiledFunc.Evaluate(c, x);
      };
    }

    private static alglib.ndimensional_pgrad CreatePGrad(AutoDiff.IParametricCompiledTerm compiledFunc) {
      return (double[] c, double[] x, ref double func, double[] grad, object o) => {
        var tupel = compiledFunc.Differentiate(c, x);
        func = tupel.Item2;
        Array.Copy(tupel.Item1, grad, grad.Length);
      };
    }

    public IGrammar TreeBasedGPGrammar { get; private set; }
    public string ConvertTreeToSentence(ISymbolicExpressionTree tree) {
      var sb = new StringBuilder();

      TreeToSentence(tree.Root.GetSubtree(0).GetSubtree(0), sb);

      return sb.ToString();
    }


    private void TreeToSentence(ISymbolicExpressionTreeNode treeNode, StringBuilder sb) {
      if (treeNode.SubtreeCount == 0) {
        // terminal
        sb.Append(treeNode.Symbol.Name);
      } else {
        string op = string.Empty;
        switch (treeNode.Symbol.Name) {
          case "S": op = "+"; break;
          case "N": op = "-"; break;
          case "P": op = "*"; break;
          case "D": op = "%"; break;
          default: {
              Debug.Assert(treeNode.SubtreeCount == 1);
              break;
            }
        }
        // nonterminal
        if (treeNode.SubtreeCount > 1) sb.Append("(");
        TreeToSentence(treeNode.Subtrees.First(), sb);
        foreach (var subTree in treeNode.Subtrees.Skip(1)) {
          sb.Append(op);
          TreeToSentence(subTree, sb);
        }
        if (treeNode.SubtreeCount > 1) sb.Append(")");
      }
    }
  }
}