Opened 5 months ago

Last modified 5 weeks ago

#2722 accepted feature request

Evaluator for symbolic regression models for learning a variance model

Reported by: gkronber Owned by: gkronber
Priority: medium Milestone: HeuristicLab 3.3.x Backlog
Component: Problems.DataAnalysis.Symbolic.Regression Version: 3.3.14
Keywords: Cc:

Description


Change History (7)

comment:1 Changed 5 months ago by gkronber

  • Status changed from new to accepted

comment:2 Changed 5 months ago by gkronber

r14528: added an evaluator for symbolic regression models which calculates the likelihood that variable values are sampled from a zero mean Gaussian distribution where the variance is given by the model. This can be used to learn input-dependent variances.

comment:3 Changed 3 months ago by gkronber

  • Owner changed from gkronber to mkommend
  • Status changed from accepted to reviewing

comment:4 Changed 6 weeks ago by gkronber

Linear scaling needs to be turned off.

comment:5 Changed 6 weeks ago by gkronber

The objective is to maximize the following log likelihood that the observed residuals stem from a zero-mean normal distribution with std. dev. s = f(x).

      var l2pi = Math.Log(2.0 * Math.PI);
      var ll = -0.5 *
               boundedEstimatedValues.Zip(targetValues, (s, t) =>
                 +l2pi
                 + Math.Log(s * s)
                 + (t * t) / (s * s)
                 ).Sum();

      return ll;

This is problematic as the sign of s has no effect on the result (same for the sign of t). It would probably be better to model the variance s2 directly. However, in this case negative values for s2 are not possible and must be prevented. On option would be to produce a model for log(s2) instead.

comment:6 Changed 6 weeks ago by gkronber

  • Owner changed from mkommend to gkronber
  • Status changed from reviewing to assigned

comment:7 Changed 5 weeks ago by gkronber

  • Milestone changed from HeuristicLab 3.3.15 to HeuristicLab 3.3.x Backlog
  • Status changed from assigned to accepted
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