[Mne_analysis] MNE method is invariant to the scale of noise

[Evgenii Kalenkovich]

 Alexandre  thank you for your reply. It did help. I now understand why
dSPM and sLORETA results differ even though MNE results do not. I am still
confused as to why MNE results do not change.

If I were to, say, go from millivolts to microvolts, then both the noise
and the data would be scaled by 1e3 and noise covariance matrix - by 1e6
and the SNR would stay the same. Same results of MNE with the same input
but scaled covariance mean that here - where the data is scaled by 1e3 as
well - I would get the source estimates scaled by 1e3 which is strange. I
would expect (from the formulas on The minimum-norm current estimates
<https://martinos.org/mne/stable/manual/source_localization/inverse.html>)
that scaling of all the data should not change anything because the kernel
would have changed reciprocally - by 1e-3. What am I missing?

In my application I know the subject's structural information and electrode
locations beforehand but I do not know how the data that I get in real time
was preprocessed. At first, I used an identity covariance matrix to make
the inverse solution. Then I scaled it by the mean variance of all EEG
signals to tell mne-python the scale of the data but nothing changed, which
is what led me to this question. Just explaining that I do not multiply
random parts of the pipeline by random numbers :-)

Evgenii


> ---------- Forwarded message ----------
> From: Alexandre Gramfort <alexandre.gramfort at inria.fr>
> To: Discussion and support forum for the users of MNE Software <
> mne_analysis at nmr.mgh.harvard.edu>
> Cc:
> Bcc:
> Date: Wed, 14 Feb 2018 21:15:10 +0100
> Subject: Re: [Mne_analysis] MNE method is invariant to the scale of noise
> if you change noise scaling you should change the SNR as it means you have
> a lot worse SNR. the regularization parameter lambda is a function of the
> snr
> as you can see in the script.
>
> dSPM and sLORETA are like t-stat or f-stat. So if you multiply the cov by
> 1e6
> then you will have dSPM and sLORETA solutions which are just divided by 1e3
> (the scale of the standard deviation).
>
> HTH
> Alex
>
>
>
>
> On Wed, Feb 14, 2018 at 8:33 PM, Evgenii Kalenkovich <
> e.kalenkovich at gmail.com> wrote:
>
>> Hi all,
>>
>> I noticed that if I scale the noise covariance matrix, it does not change
>> the source estimates in any way. In this example
>> <https://martinos.org/mne/stable/auto_tutorials/plot_mne_dspm_source_localization.html#sphx-glr-auto-tutorials-plot-mne-dspm-source-localization-py> from
>> the example gallery if I change  the method to "MNE" before the first stc
>> calculation and then do this:
>>
>> inverse_operator = make_inverse_operator(info, fwd, noise_cov,
>>                                          loose=0.2, depth=0.8)
>> stc = apply_inverse(evoked, inverse_operator, lambda2,
>>                     method=method, pick_ori=None)
>>
>> from copy import deepcopy
>> noise_cov_scaled = deepcopy(noise_cov)
>> noise_cov_scaled['data'] *= 1000000
>> inverse_operator_scaled = make_inverse_operator(info, fwd, noise_cov_scaled,
>>                                          loose=0.2, depth=0.8)
>> stc_scaled = apply_inverse(evoked, inverse_operator_scaled, lambda2,
>>                            method=method, pick_ori=None)
>>
>>
>> Then stc_scaled contains exactly the same data as stc. With "dSMP" and
>> "sLORETA" the result do differ. Why doesn't "MNE" care about the scale of
>> the covariance matrix?
>>
>> Evgenii
>>
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