[Mne_analysis] [Freesurfer] question about how to calculate COV for MNE

Tue Apr 8 11:27:49 EDT 2014

Hi Joe,
   I'm venturing some answers inline..
Hope these help.

Hari

On Mon, April 7, 2014 5:26 pm, Joseph Dien wrote:
> This is helpful, thanks!
>
> Some further thoughts and questions:
>
> 1) Given how whitening is conducted, the reference choice would be
> critical.  I want to make sure that when my software writes out the COV
> information to the -cov.fif file, that it is doing it correctly.  How is
> referencing being handled?  For example, is the COV info always average
> referenced even if the data accompanying it has not been average
> referenced yet?  Or is it always in the current referencing scheme with
> the reference info sent along separately so it can be taken into account
> later?  Or what?
>

Like Alex said MNE enforces the use of average reference for source
estimation. Average reference has some advantages (at least in theory)
compared to an alternate reference (like linked ears) when it is likely
that the forward model estimation will be inaccurate at the reference
electrode of choice. With average reference, the forward calculation at
the reference electrode becomes irrelevant.

> 2) I also see part of what was confusing me.  It sounded as though 4.17
> was for when one is averaging data together whereas 6.3 is for when one is
> subtracting or summing.  So when combining subject averages together into
> a grand average, one would use the 4.17 procedure, which quite rightly
> made no sense to me.  Instead, 4.17 is intended for the situation where
> ideally only noise is present and the goal is to just weight the estimates
> of noise according to their quality (the number of observations used to
> generate them) when combining them, which in the case of two perfect COV
> estimates of noise will not change when combined together (still perfect).
>
> So I understand 4.17 now.  I am still wrestling with how 6.3 is to be
> applied.  My understanding is that when one adds or subtracts two epochs
> with nothing but random noise, the noise level does not change.  If
> anything the noise level (variance over the epoch) increases as I just
> demonstrated to myself with an Excel spreadsheet.  The noise level
> improvement only occurs when one takes the average of the epochs and is
> well known in the EEG field to occur following a square root of the number
> of observations involved.
>

Section 4.17 is about estimating the covariance matrix of the noise in the
*raw* (unaveraged/single-trial) data... When you combine multiple
estimates, you just get a better estimate but it still corresponds to the
cov of the noise in the *raw* data. You are not changing the noise levels
in the procedures described in this sections, just that you are improving
estimates of what the noise is, with the level still corresponding to raw
data

> So what situation is 6.3 intended for?  It seems to indicate that if one
> takes a difference wave (say ERP to incongruent word minus congruent word)
> then one should calculate Leff as described and then obtain the new COV by
> dividing the original COV (C-zero) by Leff.  Given the previous paragraph,
> this procedure doesn’t make sense to me since the noise level (as measured
> by COV) should not be decreasing.  So I’m clearly still missing something.
>
> From a practical perspective, I’m asking because I want to make sure my
> software generates the correct COV for difference waves.
>

The considerations in chapter 6 on the other hand come into play when you
are using a given noise-cov (which always corresponds to raw noise levels)
with your choice of evoked (multitrial averaged) data to compute an
inverse. Since the noise in the evoked data is smaller than the noise in
the raw data (by a factor of #trials), the noise cov matrix is scaled down
before the STC files are generated from it. By default, the scaling here
is the number of trials mentioned in the evoked data file.

Now, to your main question: If you have manipulated your evoked responses
in complex ways that the software cannot keep track of (For instance
subtracting two evoked responses (corresponding to say congruent and
incongrunt words), then it is up to you to specify how to the scale the
noise cov from raw data before calculating the inverse solution (STC file
typically). Otherwise the software will use the default scaling from the
nave field in the header of the evoked fif file that you are supplying to
it. You can specify the scaling by setting the "nave" parameter either in
mne-python or when using the command-line tools the "--nave" for
"mne_make_movie". You don't have to scale the noise-cov files by hand..
They should continue to correspond to raw data. Instead you just specify
the scaling (which is chosen based on what evoked data you supply) when
you come to the stage where you use the noise-cov to generate inverse
estimates.

Just to take an example and talk through the whole process, if you have
two conditions (corresponding to say congruent and incongrunt words), with
50 and 50 trials each and lets say you are interested in localizing the
difference wave (instead of localizing them separately and doing stats
comparing them in source space). When you do the difference, the effective
scaling of the noise you need is:

L_eff = 50*50/(50 + 50) = 25.

So when using mne_make_movie (or the corresponding mne-python function),
you specify explicitly that nave = 25.

Note that this confirms that when you subtract two ERPs, the noise
actually doubles in variance (or increases by a factor of sqrt(2) in
standard deviation).. i.e., instead of dividing by 50 which would have
happened if you localized *either* of those conditions, because you
subtracted them, you only divide by 25.

> Respectfully,
>
> Joe
>
>
>
> On Apr 7, 2014, at 10:01 AM, Hari Bharadwaj <hari at nmr.mgh.harvard.edu>
> wrote:
>
>> Hi Joe,
>>     Thought I'll mention a couple of things that might help understand
>> the scaling etc.
>>
>> (1) the noise cov that is computed and stored in the -cov.fif files
>> corresponds to the covariance of the measurement noise in the *raw* data
>> and hence when using it to localize multitrial *averaged* evoked
>> responses, it is scaled by the number of trials in the average (based on
>> the assumption that noise is independent from trial to trial and hence
>> scales that way).. Look for the "nave" input when generating "stc"
>> files.
>>
>> (2) whether you add or subtract two *average* evoked responses, the
>> resulting noise distribution is the same (i.e., still mean zero and
>> variance depending on the numbers of trials in each condition).. More
>> generally when you take an arbitrary linear combination of two or more
>> averaged responses, the mean is still zero for the noise and the
>> variance scales depending of the weights for each condition and numbers
>> of trials that went into the corresponding averages.
>>
>> (3) based on (2), considering the common special case of a difference
>> response of two (separately averaged) conditions, if the number of
>> trials in each of the two conditions that went in were not the same and
>> are instead L1 and L2 respectively, then the effective scaling of the
>> noise (from raw to the difference waveform) variance is what is
>> calculated as Leff.
>>
>> HTH,
>> Hari
>>
>>
>> Hari Bharadwaj
>> PhD Candidate, Biomedical Engineering,
>> Auditory Neuroscience Laboratory
>> Boston University, Boston, MA 02215
>>
>> Martinos Center for Biomedical Imaging,
>> Massachusetts General Hospital
>> Charlestown, MA 02129
>>
>> hari at nmr.mgh.harvard.edu
>> Ph: 734-883-5954
>>
>> On Apr 6, 2014, at 11:40 PM, Joseph Dien <jdien07 at mac.com> wrote:
>>
>>> I should say Python, not C++

>>>
>>> On Apr 6, 2014, at 11:31 PM, Joseph Dien <jdien07 at mac.com> wrote:
>>>
>>>> Fair enough!  Just trying to understand what Section 6.3 is trying to
>>>> communicate.  So let me try another possible interpretation:
>>>>
>>>> Compute the COV for the two conditions.  When subtracting the two
>>>> conditions, the accompanying COV matrix (same for both conditions
>>>> since they were pooled when computing it) is divided by Leff.
>>>> Likewise the accompanying degrees of freedom (used if it is
>>>> subsequently averaged together with another COV matrix per Section
>>>> 4.17) is set equal to Leff.
>>>>
>>>> Not saying this is a procedure that makes sense to me either, just
>>>> asking what the intent is of the MNE developers.  Based on your
>>>> response, this is currently my best guess, although it doesn’t make
>>>> sense to me either since dividing the COV matrix by a single scalar
>>>> (however computed) shouldn’t affect computations about relative noise
>>>> levels in the channels.  Basically, I’m not sure what is being done
>>>> with COV so it’s hard for me to judge what is a reasonable
>>>> interpretation of Section 6.3.
>>>>
>>>> I appreciate the link to the code, but since I’m a Matlab programmer
>>>> not a C++ programmer, it’s very hard for me to parse the code.  If
>>>> someone could just tell me what is to be done according to 6.3 when
>>>> computing a difference wave rather than just what not to do, this
>>>> would be greatly appreciated.  I’m trying to add support for FIFF file
>>>> format to my Matlab EEG software analysis suite
>>>> (http://sourceforge.net/projects/erppcatoolkit/) and want to make sure
>>>> I’m doing it in a manner that would be acceptable to the MNE
>>>> developers, for the benefit of the users of my package.
>>>>
>>>> Thanks for taking the time to read my question!
>>>>
>>>> Joe
>>>>
>>>>
>>>>
>>>> On Apr 5, 2014, at 5:51 AM, Alexandre Gramfort
>>>> <alexandre.gramfort at telecom-paristech.fr> wrote:
>>>>
>>>>> hi joe,
>>>>>
>>>>>>>   I have a question about how to calculate the COV for the MNE
>>>>>>> software.
>>>>>>> As I understand it from Section 4.17 of the 2.7.3 MNE manual, if
>>>>>>> one is
>>>>>>> averaging together COV matrices, one weights them by the number of
>>>>>>> observations going into each one.  I also see from Section 4.17.2
>>>>>>> that these
>>>>>>> are technically not covariance matrices so much as sum-of-squares
>>>>>>> matrices
>>>>>>> where the epochs going into each variable has been baseline
>>>>>>> corrected.
>>>>>>>
>>>>>>>   Assuming my understanding so far is correct, my question is about
>>>>>>> how to
>>>>>>> proceed when making linear combinations of COV matrices, as in a
>>>>>>> difference
>>>>>>> wave, as discussed in Section 6.3.  Would the following be the
>>>>>>> correct
>>>>>>> procedure?
>>>>>>>
>>>>>>>   Compute the COV separately for the two conditions (say standard
>>>>>>> and rare
>>>>>>> oddballs).  Subtract the two COV matrices to obtain C0.
>>>>>
>>>>> Subtracting two COV matrices is a bad idea. You can make the new cov
>>>>> non positive.
>>>>>
>>>>> basically the noise cov is just to estimate the noise so any sample
>>>>> you use
>>>>> to get a better estimate the better. There is no condition or
>>>>> contrast
>>>>> at this stage.
>>>>>
>>>>> for source reconstruction you should use the same noise cov for the
>>>>> two
>>>>> conditions to have the same inverse operator.
>>>>>
>>>>> you can look at this file to know more about the internals:
>>>>>
>>>>> https://github.com/mne-tools/mne-python/blob/master/mne/cov.py
>>>>>
>>>>> HTH
>>>>> Alex
>>>>>
>>>>>
>>>>>>> Then calculate C by
>>>>>>> dividing by Leff, which in turn is calculated as Leff=
>>>>>>> (L1*L2)/(L1+L2) where
>>>>>>> L1 is the number of observations in the first COV matrix and L2 is
>>>>>>> for the
>>>>>>> second.
>>>>>>>
>>>>>>>   But if done in this way, the two COV matrices would not be
>>>>>>> weighted by
>>>>>>> their relative sample sizes.  So would I also weight them by L1 and
>>>>>>> L2
>>>>>>> during the subtraction, as done for averaging per 4.17?  But then
>>>>>>> what is
>>>>>>> the purpose of the Leff calculation? Or is the idea that one would
>>>>>>> calculate
>>>>>>> a single COV based on both conditions and then one would modify COV
>>>>>>> by Leff
>>>>>>> to reflect that the signal-to-noise ratio has been reduced by
>>>>>>> combining two
>>>>>>> averages with differing sample sizes?  But in the case where both
>>>>>>> samples
>>>>>>> equal, say, 10, Leff would end up equalling 100/20=5.  Dividing C
>>>>>>> by 5 seems
>>>>>>> like too much.  Anyway, very confused.  Any guidance would be
>>>>>>> appreciated.
>>>>>>>
>>>>>>> Respectfully,
>>>>>>>
>>>>>>> Joe
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> --------------------------------------------------------------------------------
>>>>>>>
>>>>>>> Joseph Dien,
>>>>>>> Senior Research Scientist
>>>>>>> Maryland Neuroimaging Center
>>>>>>> University of Maryland
>>>>>>>
>>>>>>> E-mail: jdien07 at mac.com
>>>>>>> Phone: 202-297-8117
>>>>>>> http://joedien.com
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
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>>>>
>>>> --------------------------------------------------------------------------------
>>>>
>>>> Joseph Dien,
>>>> Senior Research Scientist
>>>> Maryland Neuroimaging Center
>>>> University of Maryland
>>>>
>>>> E-mail: jdien07 at mac.com
>>>> Phone: 202-297-8117
>>>> http://joedien.com
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>
>>>
>>> --------------------------------------------------------------------------------
>>>
>>> Joseph Dien,
>>> Senior Research Scientist
>>> Maryland Neuroimaging Center
>>> University of Maryland
>>>
>>> E-mail: jdien07 at mac.com
>>> Phone: 202-297-8117
>>> http://joedien.com
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>
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>>> Mne_analysis at nmr.mgh.harvard.edu
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>
>
> --------------------------------------------------------------------------------
>
> Joseph Dien,
> Senior Research Scientist
> Maryland Neuroimaging Center
> University of Maryland
>
> E-mail: jdien07 at mac.com
> Phone: 202-297-8117
> http://joedien.com
>
>
>
>
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-- 
Hari Bharadwaj
PhD Candidate, Biomedical Engineering,
Boston University
677 Beacon St.,
Boston, MA 02215

Martinos Center for Biomedical Imaging,
Massachusetts General Hospital
149 Thirteenth Street,
Charlestown, MA 02129

hari at nmr.mgh.harvard.edu
Ph: 734-883-5954