[ENH]: investigate more reasonable default for reg param in ProjCommon

[dengemann]

@apmellot has made the discovery that the strange necessity to scale by trace of cov can be avoided when reducing the amount of shrinkage via reg in ProjCommon. This makes intuitively sense and I think we should simply not shrink by default, especially, as we commonly used regularized covariance estimates to begin with and dimensionality reduction has a shrinking effect.

FYI @DavidSabbagh @agramfort

[agramfort]

The typical way of doing is to have the shrink parameter proportional to the trace of the matrix

[dengemann]

... we could also remove the paramter all together. Why re-implement shrinkage if the user has all the options to estimate robust covariances using OAS, Ledoit-Wolf, etc. ?

[agramfort]

yes agreed

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Message ID: ***@***.***>

[DavidSabbagh]

Give me some time to think about it

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On Nov 7, 2022, 23:11, at 23:11, Alexandre Gramfort ***@***.***> wrote: yes agreed > Message ID: ***@***.***> > -- Reply to this email directly or view it on GitHub: #35 (comment) You are receiving this because you were mentioned. Message ID: ***@***.***>

[DavidSabbagh]

The projection step in Riemann include 1/ a PCA (ProjCommon) 2/ a normalization by the trace 1/ PCA is designed to overcome rank-deficient covs by making them full rank at a reduced dimension. If the covs are already full rank (eg. covs from Larib project) this step is unnecessary as a full rank PCA keeps the same number of dimensions, hence is just doing a rotation which has no impact on Riemann thanks to affine invariance. If the covs are not full rank this step is necessary for Riemann to work. 2/ normalization by the trace: covs are scaled before vectorization by being divided by the mean trace *across subjects*, *separately in each frequency bands*. Initially made to handle numeric instabilities with the PCA for rank-reduced covs. This normalization could in principle make a difference in performance since the scaling factor is different per freq band and we concatenate the resulting band-specific vectors to make our final vector (input of the ridge model). If this scaling factor is similar per frequency band (at the limit if they are all equal) the perf of Riemann stays the same thanks to affine-invariance. I think this is what happens with Lariboisiere full-rank covs on which normalization makes almost no difference in performance. But we can't be sure it is always the case in general. Le lun. 7 nov. 2022 à 22:35, Denis A. Engemann ***@***.***> a écrit :

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... we could also remove the paramter all together. Why re-implement shrinkage if the user has all the options to estimate robust covariances using OAS, Ledoit-Wolf, etc. ? — Reply to this email directly, view it on GitHub <#35 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AIC2QGXX5MB24S4FLHS3VDDWHFYYVANCNFSM6AAAAAARZLNYJE> . You are receiving this because you were mentioned.Message ID: ***@***.***>

[dengemann]

Now for the Cam-CAN data, Apolline finds that you can avoid the 2nd step by not additionally regulating the covariance in PCA space.
Also note that the trace scaling is part of MNE's CSP / SPoC procedures and is turned off by default (not recommended according to documentation).
I think we should by default try to offer a clean method that does not do too much of correction by default.

[dengemann]

@DavidSabbagh and did you think about it? Meanwhile, @apmellot keeps having good results across all benchmarks using the new settings.

[DavidSabbagh]

I agree. Let's turn off that normalization by default, while keeping it as an available option.

[dengemann]

this should be addressed now by #51 – let's keep it open to see if we're happy