[Eeglablist] Causality between Independent Sources from ICA ! A contradiction !!!

Thu May 8 09:54:11 PDT 2014

Dear Iman,

I like that analogy.

My usual anthropomorphism is that an ICA has an eye that captures only 1
time frame and does not know extension in time.

Makoto

2014-04-30 16:58 GMT-07:00 Iman M.Rezazadeh <irezazadeh at ucdavis.edu>:

> Hi all ,
>
> I just want to add more to the following comments from me and other folks.
> I have been thinking about independent sources and causality btw them !!!
> and coming up with the following example. Hope it is helpful :
>
>
>
> Suppose that John and Mary and other people are in a party and John asked
> Mary “How are you?” and Mary replied “I am fine, yourself?”. A listener
> from a distance could hardly hear the communication because of a lot of
> noises from people in the environment. If ICA is applied to the sounds
> properly then it is possible to separate John’s, Mary’s and other people’s
> voices. Now, there are three independent (separate) sources but Mary’s
> dialog is correlated with John’s dialog or more precisely John’s dialog is
> a causal factor of Mary’s dialog.  Thus, being independent does not imply
> being uncorrelated or non-causal.
>
>
>
> Best
>
> Iman
>
>
>
> ============================================
>
> *Iman M.Rezazadeh, Ph.D. , M.Sc., B.Sc.*
>
> UCLA David Geffen School of Medicine
>
> Semel Institute for Neuroscience and Human Behavior
>
> 760 Westwood Plaza, Ste 47-448
>
> Los Angeles, CA  90095
>
> Join me on LinkedIn at :
> http://www.linkedin.com/pub/iman-m-rezazadeh/10/859/840/
>
>
>
>
>
> *From:* eeglablist-bounces at sccn.ucsd.edu [mailto:
> eeglablist-bounces at sccn.ucsd.edu] *On Behalf Of *Iman M.Rezazadeh
> *Sent:* Wednesday, February 19, 2014 2:34 PM
> *To:* 'Andrei Medvedev'; eeglablist at sccn.ucsd.edu
> *Subject:* Re: [Eeglablist] Two step source connectivity analysis (as
> implemented in SIFT)
>
>
>
> Thanks Andrei for elaborating this in more details. Also in  my former
> post,
>
> I forgot to mentioned the imaginary coherence method as suggested on Nolte
> et al. work and I agree with you on this as well.
>
> -Iman
>
>
>
> *From:* eeglablist-bounces at sccn.ucsd.edu [
> mailto:eeglablist-bounces at sccn.ucsd.edu <eeglablist-bounces at sccn.ucsd.edu>]
> *On Behalf Of *Andrei Medvedev
> *Sent:* Wednesday, February 19, 2014 12:18 PM
> *To:* eeglablist at sccn.ucsd.edu
> *Subject:* Re: [Eeglablist] Two step source connectivity analysis (as
> implemented in SIFT)
>
>
>
> 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>:
>
> 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, Xt, Yt, and Wt, and that we first
> attempt to forecast Xt+1 using past terms of Yt and Wt. We then try to
> forecast Xt+1 using past terms of Xt, Yt, and Wt. 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 Xt+1that is not in past X
> t or Wt. … Thus, Yt would "Granger cause" Xt+1 if (a) Yt occurs before X
> t+1 ; and (b) it contains information useful in forecasting Xt+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] *On Behalf Of *Makoto Miyakoshi
> *Sent:* Tuesday, February 18, 2014 3:54 PM
> *To:* mullen.tim at gmail.com
> *Cc:* 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>:
>
> 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>:
>
>
>
> 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 [eeglablist-bounces at sccn.ucsd.edu]
> On Behalf Of IMALI THANUJA HETTIARACHCHI [ith at deakin.edu.au]
> Sent: 07 February 2014 01:27
> To: mullen.tim at gmail.com
> Cc: 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
>
> Email: ith at deakin.edu.au<mailto:ith at deakin.edu.au>
> Web :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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-- 
Makoto Miyakoshi
Swartz Center for Computational Neuroscience
Institute for Neural Computation, University of California San Diego
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