[Eeglablist] Two step source connectivity analysis (as implemented in SIFT)

Andrei Medvedev am236 at georgetown.edu
Wed Feb 19 12:17:47 PST 2014


Hi All,

I believe Iman gave an important point for the discussion. Let me 
reiterate it. Causality (Granger or any other causality algorithm for 
that matter) implies that there is a TIME DELAY between the first signal 
(the source of influence) and the second signal (the recipient of 
influence). While, on the other hand, ICA is essentially tries to 
eliminate INSTANTANEOUS dependence between signals i.e, at each CURRENT 
time point. Therefore, causality and ICA do not contradict (at least, 
conceptually). Any source reconstruction algorithm is also conceptually 
similar to ICA b/c it minimizes this instantaneous dependence between 
signals. The most important issue here is that this way we minimize a 
possible artefactual component present in both signals such as 
'influence' simply due to volume conductance. It makes sense b/c 
(usually) 'real' influence is NOT instantaneous and takes some time to 
occur (but see below for the important exception).

So, if one does ICA and then calculates Granger (or any other type of 
autoregressive (AR) modeling) between components x(t) and y(t), the 
expected (and ideal) result would be that the influence between x(t) and 
y(t) should be close to zero (thanks to ICA) but there may be a non-zero 
influence at time shifts >0 (at t and t-1 etc). All seems to be fine (I 
am putting aside the fact that 'no algorithm is perfect' and small 
delays may still result in some amount of instantaneous correlation b/c 
signals may not be perfect Poisson processes and thus have some 'memory' 
i.e., their autocorrelation functions are not delta-functions).

This approach is similar to the imaginary coherence which is insensitive 
to instantaneous effects of volume conductance (Nolte et al 2004).

But to add more to the discussion, this approach means that when we 
minimize instantaneous effects, we may overlook a real 'zero-delay' 
interaction when two signals are synchronized at phase delay =0. The 
good example of such zero-delay interaction is gamma-band synchrony. 
Here, the zero-phase is achieved through the emergent property of the 
network itself (due to mutual inhibitory and excitatory connections). To 
reveal this zero-delay interaction in the presence of volume conductance 
seems to be a hard problem. But I would still argue in favor of removal 
instantaneous effects simply because they are huge in scalp EEG. Also, 
'physiological'/'real' zero-phase synchrony is likely to be 'not 
perfect' giving rise to small deviations from zero from time to time, 
which would then be 'detected' by Granger/AR/imag coh).

I also agree that going to the source space instead of the channel space 
(through ICA or other source reconstruction algorithms) is not free of 
its own limitations. Perhaps, applying Granger/AR (with 'instantaneous' 
coefficients ignored) or imaginary coh to the channel data could be a 
method of choice as well.

Best,
Andrei Medvedev

-- 
Andrei Medvedev, PhD
Assistant Professor,
Center for Functional and Molecular Imaging
Georgetown University
4000 Reservoir Rd, NW
Washington DC, 20057


On 2/19/2014 1:18 PM, Makoto Miyakoshi wrote:
> Dear Iman and all,
>
> So are you saying independent sources can Granger cause each other?
>
> I agree with Joe and you. I'm not a specialist, but I would imagine 
> (correct me if I'm wrong) that ICs are /usually/ independent /except/ 
> when they are perturbed event-relatedly. In such moments independence 
> are transiently lost and ICs start to Granger cause each other... I 
> tend to think in this way because stationarity depends on time scale. 
> So in the sense it's correct to say ICs are /not always/ independent, 
> because its independency changes from timepoint to timepoint. You can 
> see this visualization with one of AMICA tools. However I haven't seen 
> a log likelihood drop around the event, which contradicts my 
> explanation above, so I could be wrong somewhere. Multiple model AMICA 
> does extract peri-event-onset periods as a different model though.
>
> Note also that there is an issue of IC subspace within which ICs are 
> always intra-dependent.
>
> Makoto
>
>
> 2014-02-19 0:53 GMT-08:00 Iman M.Rezazadeh <irezazadeh at ucdavis.edu 
> <mailto:irezazadeh at ucdavis.edu>>:
>
>     I would like step in and add more comments which may be helpful
>     (hopefully):
>
>     The assumption of ICA is : The observed data is the sum of a set
>     of inputs which have been mixed together in an unknown fashion and
>     the aim of ICA is to discover both the inputs and how they were
>     mixed. So, after ICA we have some sources which are temporally
>     independent. In other words, they are independent at time t
>      McKeown, et al. (1998)
>
>     However and based on Clive Granger talk at 2003 Nobel Laureate in
>     Economics "The basic "Granger Causality" definition is quite
>     simple. Suppose that we have three terms, X_t , Y_t , and W_t ,
>     and that we first attempt to forecast X_t+1 using past terms of
>     Y_t and W_t . We then try to forecast X_t+1 using past terms of
>     X_t , Y_t , and W_t . If the second forecast is found to be more
>     successful, according to standard cost functions, then the past of
>     Y appears to contain information helping in forecasting X_t+1 that
>     is not in past X_t or W_t. ... Thus, Y_t would "Granger cause"
>     X_t+1 if (a) Y_t occurs before X_t+1 ; and (b) it contains
>     information useful in forecasting X_t+1 that is not found in a
>     group of other appropriate variables."  So, in Granger causality
>     we try to relate time t+1 to t.
>
>     So, ICA and Granger causality are not contradicting each other and
>     finding causality btw sources would not have anything to do with
>     source space or channel space data. In my point of view, using ICA
>     and source signal for Granger causality is good because you do not
>     have to worry about the volume conductance problem. However, one
>     can apply Granger causality in the channel space as well since the
>     dipole localization has its own limitations. One clue code be
>     transforming the channel space data to  current source density
>     (CSD) format and then applying any causality/connectivity analysis
>     you would like to study.
>
>     Best
>
>     Iman
>
>     *-------------------------------------------------------------*
>
>     *Iman M.Rezazadeh, Ph.D*
>
>     Research Fellow
>
>     Semel Intitute, UCLA , Los Angeles
>
>     & Center for Mind and Brain, UC DAVIS, Davis
>
>     *From:*eeglablist-bounces at sccn.ucsd.edu
>     <mailto:eeglablist-bounces at sccn.ucsd.edu>
>     [mailto:eeglablist-bounces at sccn.ucsd.edu
>     <mailto:eeglablist-bounces at sccn.ucsd.edu>] *On Behalf Of *Makoto
>     Miyakoshi
>     *Sent:* Tuesday, February 18, 2014 3:54 PM
>     *To:* mullen.tim at gmail.com <mailto:mullen.tim at gmail.com>
>     *Cc:* eeglablist at sccn.ucsd.edu <mailto:eeglablist at sccn.ucsd.edu>
>     *Subject:* Re: [Eeglablist] Two step source connectivity analysis
>     (as implemented in SIFT)
>
>     Dear Tim,
>
>     Why don't you comment on the following question: If independent
>     components are truly independent, how do causality analyses work?
>
>     Dear Joe,
>
>     Your inputs are too difficult for me to understand. In short, are
>     you saying causality analysis works on independent components
>     because they are not completely independent?
>
>     Makoto
>
>     2014-02-18 15:46 GMT-08:00 Makoto Miyakoshi <mmiyakoshi at ucsd.edu
>     <mailto:mmiyakoshi at ucsd.edu>>:
>
>         Dear Bethel,
>
>         > say A=sunrise and B=ice-cream-sale, then the ICA in EEGLAB
>         should find that A is maximally  temporaly independent from B.
>
>         ICA would find a correlation between sunrise and ice-cream-sale.
>
>         Makoto
>
>         2014-02-10 4:57 GMT-08:00 Bethel Osuagwu
>         <b.osuagwu.1 at research.gla.ac.uk
>         <mailto:b.osuagwu.1 at research.gla.ac.uk>>:
>
>             Hi
>             I am not an expert but I just want to give my own opinion!
>
>             I do not think that temporal independence of two variables
>             (A and B) violets causality between them as implemented in
>             SIFT. In fact if  say A=sunrise and B=ice-cream-sale, then
>             the ICA in EEGLAB should find that A is maximally
>              temporaly independent from B. However we know there is
>             causal flow from A to B.
>
>             This is what I think, but I wait to be corrected so that I
>             can learn!
>
>             Thanks
>             Bethel
>             ________________________________________
>             From: eeglablist-bounces at sccn.ucsd.edu
>             <mailto:eeglablist-bounces at sccn.ucsd.edu>
>             [eeglablist-bounces at sccn.ucsd.edu
>             <mailto:eeglablist-bounces at sccn.ucsd.edu>] On Behalf Of
>             IMALI THANUJA HETTIARACHCHI [ith at deakin.edu.au
>             <mailto:ith at deakin.edu.au>]
>             Sent: 07 February 2014 01:27
>             To: mullen.tim at gmail.com <mailto:mullen.tim at gmail.com>
>             Cc: eeglablist at sccn.ucsd.edu <mailto:eeglablist at sccn.ucsd.edu>
>             Subject: [Eeglablist] Two step source connectivity
>             analysis (as implemented     in SIFT)
>
>
>             Hi Tim and the list,
>
>             I am just in need of a clarification regarding the ICA
>             source reconstruction and the subsequent MVAR --based
>             effective connectivity analysis using the components,
>             which is the basis of the SIFT toolbox. I was trying to
>             use this approach in my work but was questioned on the
>             validity using ICA and subsequent MVAR analysis by my
>             colleagues.
>
>             "When using independent component analysis (ICA), we
>             assume the mutual independence
>             of underlying sources, however when we try to estimate
>             connectivity between EEG sources,
>             we implicitly assume that the sources may be  influenced
>             by each other. This contradicts the
>             fundamental assumption of mutual independence between
>             sources in ICA [Cheung et al., 2010, Chiang et al., 2012,
>             Haufe et al., 2009 ]. "
>
>             So due to this reason different approaches such as
>             MVARICA, CICAAR(convolution ICA+MVAR),  SCSA and state
>             space-based methods have been proposed as ICA+MVAR based
>             source connectivity analysis techniques.
>
>
>             ·         So, how would you support the valid use of SIFT
>             ( ICA+MVAR as a two-step procedure) for the source
>             connectivity analysis?
>
>
>             ·         If I argue that I do not assume independent
>             sources but rely on the fact that ICA will decompose the
>             EEG signals and output 'maximally independent' sources and
>             then, I subsequently model for the dependency, will you
>             agree with me? How valid would my argument be?
>
>             It would be really great to see different thoughts and
>             opinions.
>
>             Kind regards
>
>             Imali
>
>
>             Dr. Imali Thanuja Hettiarachchi
>             Researcher
>             Centre for Intelligent Systems research
>             Deakin University, Geelong 3217, Australia.
>
>             Mobile : +61430321972 <tel:%2B61430321972>
>
>             Email: ith at deakin.edu.au
>             <mailto:ith at deakin.edu.au><mailto:ith at deakin.edu.au
>             <mailto:ith at deakin.edu.au>>
>             Web :www.deakin.edu.au/cisr
>             <http://www.deakin.edu.au/cisr><http://www.deakin.edu.au/cisr>
>
>             [cid:image001.jpg at 01CF23FF.F8259940]
>
>
>
>
>
>
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>
>
>         -- 
>
>         Makoto Miyakoshi
>         Swartz Center for Computational Neuroscience
>         Institute for Neural Computation, University of California San
>         Diego
>
>
>
>     -- 
>
>     Makoto Miyakoshi
>     Swartz Center for Computational Neuroscience
>     Institute for Neural Computation, University of California San Diego
>
>
>
>
> -- 
> Makoto Miyakoshi
> Swartz Center for Computational Neuroscience
> Institute for Neural Computation, University of California San Diego
>
>
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