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

Mon May 19 19:28:04 PDT 2014

Dear John,

> We can expect that the PCA destroy the linear relation between the
variables

No, I think the higher-order correlation is still there.
PCA achieves uncorrelation, while ICA achieves independence. The difference
between the two is higher-order correlation, if I understand it correctly.

Makoto

2014-05-17 7:46 GMT-07:00 jfochoaster . <jfochoaster at gmail.com>:

> 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+1 that is not in past Xt or Wt. … Thus, Yt would
>>> "Granger cause" Xt+1 if (a) Yt occurs before Xt+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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>
>
>
> --
> John Ochoa
> Docente de Bioingeniería
> Universidad de Antioquia
>

-- 
Makoto Miyakoshi
Swartz Center for Computational Neuroscience
Institute for Neural Computation, University of California San Diego
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