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

jfochoaster . jfochoaster at gmail.com
Sat May 17 07:46:02 PDT 2014


Dear Makoto, what about PCA? We can expect that the PCA destroy the linear
relation between the variables implying that the MVAR model become
impossible to find?

I do this question because many ICA approaches uses PCA as a previous step

Best"

JOhn Ochoa


On Thu, May 8, 2014 at 11:54 AM, Makoto Miyakoshi <mmiyakoshi at ucsd.edu>wrote:

> 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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>>
>>
>>
>>
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>
>
>
> --
> Makoto Miyakoshi
> Swartz Center for Computational Neuroscience
> Institute for Neural Computation, University of California San Diego
>
> _______________________________________________
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-- 
John Ochoa
Docente de Bioingeniería
Universidad de Antioquia
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