[Neuroimaging] covariance estimator in nilearn

[bthirion]

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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