Fitting procedure and peak parameter estimation

[vferat]

Hello,

First, thank you for all the work that has gone into this project, it is very helpful and easy to use !

While trying to better understand the fitting procedure, I noticed that the final aperiodic fit (L178) is performed after the peak parameters have been estimated (L171)

fooof/specparam/algorithms/spectral_fit.py

Line 156 in 05b9871

def _fit(self):

Did I understand the workflow correctly?

If so, could this lead to slight differences between the estimated peak parameters and the final model, since the aperiodic component may change after the peak fitting step? In particular, I am wondering about peak heights, which are defined relative to the aperiodic fit.

My intuition is that any effect would likely be very small, but I wanted to check whether this interpretation is correct.

Thank for your feedback,
Victor

[TomDonoghue]

Hey @vferat - yeh, you are right that at the end, the model does an updated / refit of the aperiodic component, after the peaks have been estimated. As such, there could be some slight deviations between the peaks as fit in the model, and would would be refit as peaks if one re-computed the new aperiodic-removed component with the updated / final aperiodic fit (since the peaks are not fit based of what becomes the final aperiodic fit). In the final output, the 'converted' peak heights are the distance from the model peak height, to the final aperiodic component, so at that point the full model, peak parameters (& fit quality, etc), are all with respect to the final components & parameters.

If the model iterated further (took the updated aperiodic, went back to the peaks and edited), the peak fit parameters could end up being a bit different - in our development and testing going further on this never made much of a different (any improvement didn't seem worth the computational cost, with changes typically being very minor), so this is why the default algorithm stops where it does.

[vferat]

Hey @TomDonoghue thanks a lot for the details !

The part I was missing was:

In the final output, the 'converted' peak heights are the distance from the model peak height, to the final aperiodic component, so at that point the full model, peak parameters (& fit quality, etc), are all with respect to the final components & parameters.

It means that the outputs are re-computed in gen_periodic after the .fit method which explains the difference in peak height between:

fm.gaussian_params_ 
array([[ 6.24470895,  0.35415922,  1.5       ],
       [10.06718697,  1.30800565,  1.5321775 ],
       [17.4944412 ,  0.41706193,  3.68958762]])

and

fm.get_results().peak_params
array([[ 6.24470895,  0.41196112,  3.        ],
       [10.06718697,  1.37517122,  3.064355  ],
       [17.4944412 ,  0.41693922,  7.37917524]])

am I right ? (I might be using the old FOOF API sorry..)

thanks again for your help, I let you close the issue if you have nothing more to add :)

Have a nice day,
Victor

[TomDonoghue]

The main difference between those two print outs above is looking at 'fit' vs 'converted' parameters. There's some info on this here: https://specparam-tools.github.io/auto_tutorials/plot_04-PeriodicFitting.html#fit-vs-converted-parameters

Short version of that is we recompute (after the fitting process, and so using the final aperiodic component), 'converted' peak parameters whereby the height of the peak is the actual distance from peak height to aperiodic component. This might not be the same as the Gaussian height in the case of overlapping peaks (where the total height is a combination of different peaks). To not always have to deal with potential overlaps, we recompute and typically use the converted params.

Circling back to your original point, as well as the overlap a source of difference between the two could also be the change in the aperiodic component (though typically this won't be much of a change)