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    Hi All,<br>
    <br>
    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).<br>
    <br>
    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 &gt;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).<br>
    <br>
    This approach is similar to the imaginary coherence which is
    insensitive to instantaneous effects of volume conductance (Nolte et
    al 2004). <br>
    <br>
    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).<br>
    <br>
    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.<br>
    <br>
    Best,<br>
    Andrei Medvedev<font size="+1"><br>
    </font>
    <pre class="moz-signature" cols="72">-- 
Andrei Medvedev, PhD
Assistant Professor,
Center for Functional and Molecular Imaging
Georgetown University
4000 Reservoir Rd, NW
Washington DC, 20057
</pre>
    <br>
    On 2/19/2014 1:18 PM, Makoto Miyakoshi wrote:
    <blockquote
cite="mid:CAEqC+SX_eOu_zkc=FRnJdEr-nqnmAtBeQZ1jw6v61gqdt3CeBw@mail.gmail.com"
      type="cite">
      <div dir="ltr">Dear Iman and all,
        <div><br>
        </div>
        <div>So are you saying independent sources can Granger cause
          each other?</div>
        <div><br>
        </div>
        <div>I agree with Joe and you. I'm not a specialist, but I would
          imagine (correct me if I'm wrong) that ICs are <i>usually</i>
          independent <i>except</i> 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 <i>not always</i>
          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.</div>
        <div><br>
        </div>
        <div>Note also that there is an issue of IC subspace within
          which ICs are always intra-dependent.</div>
        <div><br>
        </div>
        <div>Makoto&nbsp;</div>
      </div>
      <div class="gmail_extra"><br>
        <br>
        <div class="gmail_quote">2014-02-19 0:53 GMT-08:00 Iman
          M.Rezazadeh <span dir="ltr">&lt;<a moz-do-not-send="true"
              href="mailto:irezazadeh@ucdavis.edu" target="_blank">irezazadeh@ucdavis.edu</a>&gt;</span>:<br>
          <blockquote class="gmail_quote" style="margin: 0pt 0pt 0pt
            0.8ex; border-left: 1px solid rgb(204, 204, 204);
            padding-left: 1ex;">
            <div link="blue" vlink="purple" lang="EN-US">
              <div>
                <p class="MsoNormal"><span style="font-size: 11pt;
                    font-family:
                    &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                    rgb(31, 73, 125);">I would like step in and add more
                    comments which may be helpful (hopefully):</span></p>
                <p class="MsoNormal"><span style="font-size: 11pt;
                    font-family:
                    &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                    rgb(31, 73, 125);">&nbsp;</span></p>
                <p class="MsoNormal"><a moz-do-not-send="true"
                    name="144495a6d99af755__MailEndCompose"><span
                      style="font-size: 11pt; font-family:
                      &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                      rgb(31, 73, 125);">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 &nbsp;McKeown, et
                      al. (1998)</span></a></p>
                <p class="MsoNormal"><span style="font-size: 11pt;
                    font-family:
                    &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                    rgb(31, 73, 125);">&nbsp;</span></p>
                <p class="MsoNormal"><span style="font-size: 11pt;
                    font-family:
                    &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                    rgb(31, 73, 125);">However and based on Clive
                    Granger talk at 2003 Nobel Laureate in Economics
                    &#8220;The basic "Granger Causality" definition is quite
                    simple. Suppose that we have three terms, X<sub>t</sub>,
                    Y<sub>t</sub>, and W<sub>t</sub>, and that we first
                    attempt to forecast X<sub>t+1</sub> using past terms
                    of Y<sub>t</sub> and W<sub>t</sub>. We then try to
                    forecast X<sub>t+1</sub> using past terms of X<sub>t</sub>,
                    Y<sub>t</sub>, and W<sub>t</sub>. 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<sub>t+1</sub> that is not in past X<sub>t</sub>
                    or W<sub>t. </sub>&#8230; Thus, Y<sub>t</sub> would
                    "Granger cause" X<sub>t+1</sub> if (a) Y<sub>t</sub>
                    occurs before X<sub>t+1</sub> ; and (b) it contains
                    information useful in forecasting X<sub>t+1</sub>
                    that is not found in a group of other appropriate
                    variables.&#8221; &nbsp;So, in Granger causality we try to
                    relate time t+1 to t.</span></p>
                <p class="MsoNormal"><span style="font-size: 11pt;
                    font-family:
                    &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                    rgb(31, 73, 125);">&nbsp;</span></p>
                <p class="MsoNormal"><span style="font-size: 11pt;
                    font-family:
                    &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                    rgb(31, 73, 125);">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 &nbsp;current source density (CSD)
                    format and then applying any causality/connectivity
                    analysis you would like to study.</span></p>
                <p class="MsoNormal"><span style="font-size: 11pt;
                    font-family:
                    &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                    rgb(31, 73, 125);">&nbsp;</span></p>
                <p class="MsoNormal"><span style="font-size: 11pt;
                    font-family:
                    &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                    rgb(31, 73, 125);">Best</span></p>
                <p class="MsoNormal"><span style="font-size: 11pt;
                    font-family:
                    &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                    rgb(31, 73, 125);">Iman </span></p>
                <p class="MsoNormal"><span style="font-size: 11pt;
                    font-family:
                    &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                    rgb(31, 73, 125);">&nbsp;</span></p>
                <p class="MsoNormal"><b><span style="font-size: 11pt;
                      font-family:
                      &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                      rgb(31, 73, 125);">-------------------------------------------------------------</span></b></p>
                <p class="MsoNormal">
                  <b><span style="font-size: 11pt; font-family:
                      &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                      rgb(31, 73, 125);">Iman M.Rezazadeh, Ph.D</span></b></p>
                <p class="MsoNormal"><span style="font-size: 11pt;
                    font-family:
                    &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                    rgb(31, 73, 125);">Research Fellow</span></p>
                <p class="MsoNormal"><span style="font-size: 11pt;
                    font-family:
                    &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                    rgb(31, 73, 125);">Semel Intitute, UCLA , Los
                    Angeles</span></p>
                <p class="MsoNormal"><span style="font-size: 11pt;
                    font-family:
                    &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                    rgb(31, 73, 125);">&amp; Center for Mind and Brain,
                    UC DAVIS, Davis</span></p>
                <p class="MsoNormal"><span style="font-size: 11pt;
                    font-family:
                    &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                    rgb(31, 73, 125);">&nbsp;</span></p>
                <p class="MsoNormal"><span style="font-size: 11pt;
                    font-family:
                    &quot;Calibri&quot;,&quot;sans-serif&quot;; color:
                    rgb(31, 73, 125);">&nbsp;</span></p>
                <p class="MsoNormal"><b><span style="font-size: 11pt;
                      font-family:
                      &quot;Calibri&quot;,&quot;sans-serif&quot;;">From:</span></b><span
                    style="font-size: 11pt; font-family:
                    &quot;Calibri&quot;,&quot;sans-serif&quot;;"> <a
                      moz-do-not-send="true"
                      href="mailto:eeglablist-bounces@sccn.ucsd.edu"
                      target="_blank">eeglablist-bounces@sccn.ucsd.edu</a>
                    [mailto:<a moz-do-not-send="true"
                      href="mailto:eeglablist-bounces@sccn.ucsd.edu"
                      target="_blank">eeglablist-bounces@sccn.ucsd.edu</a>]
                    <b>On Behalf Of </b>Makoto Miyakoshi<br>
                    <b>Sent:</b> Tuesday, February 18, 2014 3:54 PM<br>
                    <b>To:</b> <a moz-do-not-send="true"
                      href="mailto:mullen.tim@gmail.com" target="_blank">mullen.tim@gmail.com</a><br>
                    <b>Cc:</b> <a moz-do-not-send="true"
                      href="mailto:eeglablist@sccn.ucsd.edu"
                      target="_blank">eeglablist@sccn.ucsd.edu</a><br>
                    <b>Subject:</b> Re: [Eeglablist] Two step source
                    connectivity analysis (as implemented in SIFT)</span></p>
                <div>
                  <div class="h5">
                    <p class="MsoNormal">&nbsp;</p>
                    <div>
                      <p class="MsoNormal">Dear Tim,</p>
                      <div>
                        <p class="MsoNormal">&nbsp;</p>
                      </div>
                      <div>
                        <p class="MsoNormal">Why don't you comment on
                          the following question: If independent
                          components are truly independent, how do
                          causality analyses work?</p>
                      </div>
                      <div>
                        <p class="MsoNormal">&nbsp;</p>
                      </div>
                      <div>
                        <p class="MsoNormal">Dear Joe,</p>
                      </div>
                      <div>
                        <p class="MsoNormal">&nbsp;</p>
                      </div>
                      <div>
                        <p class="MsoNormal">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?</p>
                      </div>
                      <div>
                        <p class="MsoNormal">&nbsp;</p>
                      </div>
                      <div>
                        <p class="MsoNormal">Makoto</p>
                      </div>
                    </div>
                    <div>
                      <p class="MsoNormal" style="margin-bottom: 12pt;">&nbsp;</p>
                      <div>
                        <p class="MsoNormal">2014-02-18 15:46 GMT-08:00
                          Makoto Miyakoshi &lt;<a moz-do-not-send="true"
                            href="mailto:mmiyakoshi@ucsd.edu"
                            target="_blank">mmiyakoshi@ucsd.edu</a>&gt;:</p>
                        <blockquote style="border-width: medium medium
                          medium 1pt; border-style: none none none
                          solid; border-color: -moz-use-text-color
                          -moz-use-text-color -moz-use-text-color
                          rgb(204, 204, 204); padding: 0in 0in 0in 6pt;
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                          <div>
                            <p class="MsoNormal">Dear Bethel,</p>
                            <div>
                              <div>
                                <p class="MsoNormal">&nbsp;</p>
                              </div>
                              <div>
                                <p class="MsoNormal">&gt; say A=sunrise
                                  and B=ice-cream-sale, then the ICA in
                                  EEGLAB should find that A is maximally
                                  &nbsp;temporaly independent from B.</p>
                              </div>
                              <div>
                                <p class="MsoNormal">&nbsp;</p>
                              </div>
                            </div>
                            <div>
                              <p class="MsoNormal">ICA would find a
                                correlation between sunrise and
                                ice-cream-sale.</p>
                            </div>
                            <div>
                              <p class="MsoNormal">&nbsp;</p>
                            </div>
                            <div>
                              <p class="MsoNormal">Makoto</p>
                            </div>
                            <div>
                              <p class="MsoNormal">&nbsp;</p>
                              <div>
                                <p class="MsoNormal">2014-02-10 4:57
                                  GMT-08:00 Bethel Osuagwu &lt;<a
                                    moz-do-not-send="true"
                                    href="mailto:b.osuagwu.1@research.gla.ac.uk"
                                    target="_blank">b.osuagwu.1@research.gla.ac.uk</a>&gt;:</p>
                                <div>
                                  <div>
                                    <p class="MsoNormal">&nbsp;</p>
                                    <blockquote style="border-width:
                                      medium medium medium 1pt;
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                                      solid; border-color:
                                      -moz-use-text-color
                                      -moz-use-text-color
                                      -moz-use-text-color rgb(204, 204,
                                      204); padding: 0in 0in 0in 6pt;
                                      margin-left: 4.8pt; margin-right:
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                                      <p class="MsoNormal">Hi<br>
                                        I am not an expert but I just
                                        want to give my own opinion!<br>
                                        <br>
                                        I do not think that temporal
                                        independence of two variables (A
                                        and B) violets causality between
                                        them as implemented in SIFT. In
                                        fact if &nbsp;say A=sunrise and
                                        B=ice-cream-sale, then the ICA
                                        in EEGLAB should find that A is
                                        maximally &nbsp;temporaly independent
                                        from B. However we know there is
                                        causal flow from A to B.<br>
                                        <br>
                                        This is what I think, but I wait
                                        to be corrected so that I can
                                        learn!<br>
                                        <br>
                                        Thanks<br>
                                        Bethel<br>
________________________________________<br>
                                        From: <a moz-do-not-send="true"
href="mailto:eeglablist-bounces@sccn.ucsd.edu" target="_blank">eeglablist-bounces@sccn.ucsd.edu</a>
                                        [<a moz-do-not-send="true"
                                          href="mailto:eeglablist-bounces@sccn.ucsd.edu"
                                          target="_blank">eeglablist-bounces@sccn.ucsd.edu</a>]
                                        On Behalf Of IMALI THANUJA
                                        HETTIARACHCHI [<a
                                          moz-do-not-send="true"
                                          href="mailto:ith@deakin.edu.au"
                                          target="_blank">ith@deakin.edu.au</a>]<br>
                                        Sent: 07 February 2014 01:27<br>
                                        To: <a moz-do-not-send="true"
                                          href="mailto:mullen.tim@gmail.com"
                                          target="_blank">mullen.tim@gmail.com</a><br>
                                        Cc: <a moz-do-not-send="true"
                                          href="mailto:eeglablist@sccn.ucsd.edu"
                                          target="_blank">eeglablist@sccn.ucsd.edu</a><br>
                                        Subject: [Eeglablist] Two step
                                        source connectivity analysis (as
                                        implemented &nbsp; &nbsp; in SIFT)</p>
                                      <div>
                                        <div>
                                          <p class="MsoNormal"><br>
                                            Hi Tim and the list,<br>
                                            <br>
                                            I am just in need of a
                                            clarification regarding the
                                            ICA source reconstruction
                                            and the subsequent MVAR
                                            &#8211;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.<br>
                                            <br>
                                            &#8220;When using independent
                                            component analysis (ICA), we
                                            assume the mutual
                                            independence<br>
                                            of underlying sources,
                                            however when we try to
                                            estimate connectivity
                                            between EEG sources,<br>
                                            we implicitly assume that
                                            the sources may be
                                            &nbsp;influenced by each other.
                                            This contradicts the<br>
                                            fundamental assumption of
                                            mutual independence between
                                            sources in ICA [Cheung et
                                            al., 2010, Chiang et al.,
                                            2012, Haufe et al., 2009 ].
                                            &#8220;<br>
                                            <br>
                                            So due to this reason
                                            different approaches such as
                                            MVARICA, CICAAR(convolution
                                            ICA+MVAR), &nbsp;SCSA and state
                                            space-based methods have
                                            been proposed as ICA+MVAR
                                            based source connectivity
                                            analysis techniques.<br>
                                            <br>
                                            <br>
                                            &middot; &nbsp; &nbsp; &nbsp; &nbsp; So, how would you
                                            support the valid use of
                                            SIFT ( ICA+MVAR as a
                                            two-step procedure) for the
                                            source connectivity
                                            analysis?<br>
                                            <br>
                                            <br>
                                            &middot; &nbsp; &nbsp; &nbsp; &nbsp; If I argue that I
                                            do not assume independent
                                            sources but rely on the fact
                                            that ICA will decompose the
                                            EEG signals and output
                                            &#8216;maximally independent&#8217;
                                            sources and then, I
                                            subsequently model for the
                                            dependency, will you agree
                                            with me? How valid would my
                                            argument be?<br>
                                            <br>
                                            It would be really great to
                                            see different thoughts and
                                            opinions.<br>
                                            <br>
                                            Kind regards<br>
                                            <br>
                                            Imali<br>
                                            <br>
                                            <br>
                                            Dr. Imali Thanuja
                                            Hettiarachchi<br>
                                            Researcher<br>
                                            Centre for Intelligent
                                            Systems research<br>
                                            Deakin University, Geelong
                                            3217, Australia.<br>
                                            <br>
                                            Mobile : <a
                                              moz-do-not-send="true"
                                              href="tel:%2B61430321972"
                                              target="_blank">+61430321972</a></p>
                                        </div>
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                                      <p class="MsoNormal">Email: <a
                                          moz-do-not-send="true"
                                          href="mailto:ith@deakin.edu.au"
                                          target="_blank">ith@deakin.edu.au</a>&lt;mailto:<a
                                          moz-do-not-send="true"
                                          href="mailto:ith@deakin.edu.au"
                                          target="_blank">ith@deakin.edu.au</a>&gt;<br>
                                        Web :<a moz-do-not-send="true"
                                          href="http://www.deakin.edu.au/cisr"
                                          target="_blank">www.deakin.edu.au/cisr</a>&lt;<a
                                          moz-do-not-send="true"
                                          href="http://www.deakin.edu.au/cisr"
                                          target="_blank">http://www.deakin.edu.au/cisr</a>&gt;<br>
                                        <br>
                                        [<a moz-do-not-send="true">cid:image001.jpg@01CF23FF.F8259940</a>]<br>
                                        <br>
                                        <br>
                                        <br>
                                        <br>
                                        <br>
                                        <br>
_______________________________________________<br>
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                                    </blockquote>
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                              <p class="MsoNormal"><span style="color:
                                  rgb(136, 136, 136);"><br>
                                  <br clear="all">
                                  <span></span></span></p>
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                                <p class="MsoNormal">&nbsp;</p>
                              </div>
                              <p class="MsoNormal"><span><span
                                    style="color: rgb(136, 136, 136);">--
                                  </span></span></p>
                              <div>
                                <p class="MsoNormal"><span style="color:
                                    rgb(136, 136, 136);">Makoto
                                    Miyakoshi<br>
                                    Swartz Center for Computational
                                    Neuroscience<br>
                                    Institute for Neural Computation,
                                    University of California San Diego</span></p>
                              </div>
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                      </div>
                      <p class="MsoNormal"><br>
                        <br clear="all">
                      </p>
                      <div>
                        <p class="MsoNormal">&nbsp;</p>
                      </div>
                      <p class="MsoNormal">-- </p>
                      <div>
                        <p class="MsoNormal">Makoto Miyakoshi<br>
                          Swartz Center for Computational Neuroscience<br>
                          Institute for Neural Computation, University
                          of California San Diego</p>
                      </div>
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          </blockquote>
        </div>
        <br>
        <br clear="all">
        <div><br>
        </div>
        -- <br>
        <div dir="ltr">Makoto Miyakoshi<br>
          Swartz Center for Computational Neuroscience<br>
          Institute for Neural Computation, University of California San
          Diego<br>
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