[Neuroimaging] covariance estimator in nilearn

[Gael Varoquaux]

For lay-person references on shrinkage:

* Stein shrinkage
  https://pdfs.semanticscholar.org/26c0/98a24a8e8039219dca341a74d7ddb2419cb6.pdf

* Covariance shrinkage
  https://jpm.pm-research.com/content/30/4/110

These are different settings than covariance for fMRI, however the
message is the same: shrunk estimates are better estimates to use for a
analysis or to make a decision.

Gaël

On Fri, May 29, 2020 at 06:01:18AM +0200, Sam W wrote:
> Hi Bertrand,
> Thank you for your reply.
> >LW is meant to improve covariance estimation (in the least-squares
> >sense, see the paper of Ledoit and Wolf), so for many tasks you want to
> >achieve, it is a rather good idea to use it.
> I understand that shrinkage is a good idea for calculating things like partial
> correlations with many ROIs. My question was rather what advantage does
> shrinkage bring when you compute the (pearson) correlation between only 2 time
> series. Is shrinkage still relevant in that case?
> Best regards,
> Sam


> On Thu, May 28, 2020 at 7:23 PM bthirion <bertrand.thirion at inria.fr> wrote:

>     Hi,

>     Please post this type of question on Neurostars.

>     LW is meant to improve covariance estimation (in the least-squares sense,
>     see the paper of Ledoit and Wolf), so for many tasks you want to achieve,
>     it is a rather good idea to use it.
>     Indeed this weakens the correlations values (downward bias), but IMHO these
>     values alone do not make sense: what matters are correlations differences
>     across subjects, conditions etc.
>     HTH,
>     Bertrand


>     On 28/05/2020 18:42, Sam W wrote:

>         Hello!
>         I see that ConnectivityMeasure() uses the LedoitWolf shrinkage by
>         default. I've been reading about shrinkage but it seems it's mostly
>         explained in the context of ridge regression, when there is more than
>         one coefficient in the model.
>         If I'm simply interested in the correlation between two time series,
>         why would shrinkage still be important? Wouldn't the correlation
>         coefficient between the two time series (np.corrcoef(TS1,TS2)) provide
>         the best estimation of the relationship between them?
>         Also is it true that correlations with shrinkage estimator like
>         LedoitWolf will always be weaker than using the Maximum Likelihood
>         Estimator?
>         Thank you!
>         Best regards,
>         Sam


>         _______________________________________________
>         Neuroimaging mailing list
>         Neuroimaging at python.org
>         https://mail.python.org/mailman/listinfo/neuroimaging


>     _______________________________________________
>     Neuroimaging mailing list
>     Neuroimaging at python.org
>     https://mail.python.org/mailman/listinfo/neuroimaging


> _______________________________________________
> Neuroimaging mailing list
> Neuroimaging at python.org
> https://mail.python.org/mailman/listinfo/neuroimaging


-- 
    Gael Varoquaux
    Research Director, INRIA		  Visiting professor, McGill 
    http://gael-varoquaux.info            http://twitter.com/GaelVaroquaux