source: branches/2796_SymbReg/HeuristicLab.Algorithms.DataAnalysis/3.4/Heuristics.cs @ 17607

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using HeuristicLab.Problems.DataAnalysis;

namespace HeuristicLab.Algorithms.DataAnalysis.MCTSSymbReg {
  // experimenting with heuristics
  // 
  // question: how can relevant interacting terms be reliably detected? 
  //           - is this even feasible?
  //           - even if variables are colinear?
  //           - even for non-linear transformations
  // 
  // Also see Multi-variate adaptive regression splines (MARS)
  // Maybe we could use MARS-style basis functions to identify the relevant interaction terms. (tune split points and find optimal interaction term with max spearmans rank) 
  //
  // assuming we interactions of have scaled/shifted variables (x + xo) * (y + yo) with constant xo and yo
  // this leads to: x y + x yo + y xo + yo xo. 
  // We only need to identify the x y as we assume that all other terms are accounted for
  public static class Heuristics {
    public static double CorrelationForInteraction(double[] a, double[] b, double[] c, double[] target) {
      var am = a.Average();
      var bm = b.Average();
      var cm = c.Average();
      var p1 = Enumerable.Range(0, a.Length).Where(i => a[i] < am);
      var p2 = Enumerable.Range(0, a.Length).Where(i => a[i] > am);
      var p3 = Enumerable.Range(0, a.Length).Where(i => b[i] < bm);
      var p4 = Enumerable.Range(0, a.Length).Where(i => b[i] > bm);
      var p5 = Enumerable.Range(0, a.Length).Where(i => c[i] < cm);
      var p6 = Enumerable.Range(0, a.Length).Where(i => c[i] > cm);

      return 1.0 / (p1.Count() + p2.Count() + p3.Count() + p4.Count() + p5.Count() + p6.Count()) * 
        (
        p1.Count() * CorrelationForInteraction(b, c, target, p1) +
        p2.Count() * CorrelationForInteraction(b, c, target, p2) +
        p3.Count() * CorrelationForInteraction(a, c, target, p3) +
        p4.Count() * CorrelationForInteraction(a, c, target, p3) +
        p5.Count() * CorrelationForInteraction(a, b, target, p5) +
        p6.Count() * CorrelationForInteraction(a, b, target, p6)
      );
    }
    public static double CorrelationForInteraction(double[] a, double[] b, double[] z) {
      return CorrelationForInteraction(a, b, z, Enumerable.Range(0, a.Length));
    }
    public static double CorrelationForInteraction(double[] a, double[] b, double[] z, IEnumerable<int> idx) {
      // 
      var am = a.Average();
      var bm = b.Average();
      var p1 = idx.Where(i => a[i] < am);
      var p2 = idx.Where(i => a[i] > am);
      var p3 = idx.Where(i => b[i] < bm);
      var p4 = idx.Where(i => b[i] > bm);

      return 1.0 / (p1.Count() + p2.Count() + p3.Count() + p4.Count()) *
             (p1.Count() * CorrelForPartition(b, z, p1) +
             p2.Count() * CorrelForPartition(b, z, p2) +
             p3.Count() * CorrelForPartition(a, z, p3) +
             p4.Count() * CorrelForPartition(a, z, p4));
    }

    public static double CorrelForPartition(double[] a, double[] z, IEnumerable<int> idx) {
      var zp = new List<double>();
      var ap = new List<double>();
      foreach (var i in idx) {
        zp.Add(z[i]);
        ap.Add(a[i]);
      }
      OnlineCalculatorError error;
      var r = SpearmansRankCorrelationCoefficientCalculator.CalculateSpearmansRank(zp, ap, out error);
      if (error != OnlineCalculatorError.None) r = 0;
      return r * r;
    }
  }
}