Investigating Knee Values & Fitting

[TomDonoghue]

There is potentially development work around exploring knee fitting.

Open questions to explore:

• Right now we use a seed (guess) value of 0. Is there a better value for this?

  • Originally discussed here: Guess value for knee value fooof#156
  • 0 is currently used as 'least magic'. It doesn't seem that small differences from zero make too much of a difference, though one can drive different result by settings much different seed values. It's unclear if there is a better seed value we could put, or if we could have some kind of data driven seed value (like we do for offset & exponent).

• It seems that sometimes using a knee fit can lead to a worse fit overall than if a knee was not fit. This seems bad (since one would want and expect the model with an extra parameter to converge to the best solution, including setting the knee to zero. Is there something we want to do different related to knee fitting based on this?

  • Originally discussed here: Potentially get worse fits when fitting knee.  fooof#35
  • If the knee value is not equal to zero, then the exponent below the knee frequency decays to zero. This seems to be a an issue, in that fitting a knee can lead to relatively high error in this region.
  • One thing to keep in mind is that the final R^2 we think about is not the objective that is being used to fit the aperiodic component, where the error function is applied to the aperiodic-only spectrum. This is related to thinking about how this could happen - a 'worse fit' with more parameters should be considered in the context that we are evaluating a different metric than the fit procedure for the aperiodic component itself is using.
  • Note that in simulated data, reconstructing knees generally goes fairly well (this is not an ubiquitous problem). However, in this case the simulated data exactly matches model assumptions. In real data, things may be complicated if there are cases in which there is a knee, but not exactly of the same form as the model (for example, not being totally flat below the knee).
    • Sims: https://github.com/TomDonoghue/SimFOOOF/tree/master/notebooks
  • Ideas mentioned in the original issue include:
    • Fit multiple aperiodic modes, and chose the best
    • Use a knee fit, to get a full model, but re-fit a 'fixed' exponent beyond the knee to use as an exponent value
    • Do some more iterations in the model fitting of the aperiodic exponent