[Neuroimaging] covariance estimator in nilearn

[Sam W]

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
>
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