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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 >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 </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"><<a moz-do-not-send="true"
href="mailto:irezazadeh@ucdavis.edu" target="_blank">irezazadeh@ucdavis.edu</a>></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:
"Calibri","sans-serif"; 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:
"Calibri","sans-serif"; color:
rgb(31, 73, 125);"> </span></p>
<p class="MsoNormal"><a moz-do-not-send="true"
name="144495a6d99af755__MailEndCompose"><span
style="font-size: 11pt; font-family:
"Calibri","sans-serif"; 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 McKeown, et
al. (1998)</span></a></p>
<p class="MsoNormal"><span style="font-size: 11pt;
font-family:
"Calibri","sans-serif"; color:
rgb(31, 73, 125);"> </span></p>
<p class="MsoNormal"><span style="font-size: 11pt;
font-family:
"Calibri","sans-serif"; color:
rgb(31, 73, 125);">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<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>… 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.” 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:
"Calibri","sans-serif"; color:
rgb(31, 73, 125);"> </span></p>
<p class="MsoNormal"><span style="font-size: 11pt;
font-family:
"Calibri","sans-serif"; 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 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:
"Calibri","sans-serif"; color:
rgb(31, 73, 125);"> </span></p>
<p class="MsoNormal"><span style="font-size: 11pt;
font-family:
"Calibri","sans-serif"; color:
rgb(31, 73, 125);">Best</span></p>
<p class="MsoNormal"><span style="font-size: 11pt;
font-family:
"Calibri","sans-serif"; color:
rgb(31, 73, 125);">Iman </span></p>
<p class="MsoNormal"><span style="font-size: 11pt;
font-family:
"Calibri","sans-serif"; color:
rgb(31, 73, 125);"> </span></p>
<p class="MsoNormal"><b><span style="font-size: 11pt;
font-family:
"Calibri","sans-serif"; color:
rgb(31, 73, 125);">-------------------------------------------------------------</span></b></p>
<p class="MsoNormal">
<b><span style="font-size: 11pt; font-family:
"Calibri","sans-serif"; color:
rgb(31, 73, 125);">Iman M.Rezazadeh, Ph.D</span></b></p>
<p class="MsoNormal"><span style="font-size: 11pt;
font-family:
"Calibri","sans-serif"; color:
rgb(31, 73, 125);">Research Fellow</span></p>
<p class="MsoNormal"><span style="font-size: 11pt;
font-family:
"Calibri","sans-serif"; color:
rgb(31, 73, 125);">Semel Intitute, UCLA , Los
Angeles</span></p>
<p class="MsoNormal"><span style="font-size: 11pt;
font-family:
"Calibri","sans-serif"; color:
rgb(31, 73, 125);">& Center for Mind and Brain,
UC DAVIS, Davis</span></p>
<p class="MsoNormal"><span style="font-size: 11pt;
font-family:
"Calibri","sans-serif"; color:
rgb(31, 73, 125);"> </span></p>
<p class="MsoNormal"><span style="font-size: 11pt;
font-family:
"Calibri","sans-serif"; color:
rgb(31, 73, 125);"> </span></p>
<p class="MsoNormal"><b><span style="font-size: 11pt;
font-family:
"Calibri","sans-serif";">From:</span></b><span
style="font-size: 11pt; font-family:
"Calibri","sans-serif";"> <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"> </p>
<div>
<p class="MsoNormal">Dear Tim,</p>
<div>
<p class="MsoNormal"> </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"> </p>
</div>
<div>
<p class="MsoNormal">Dear Joe,</p>
</div>
<div>
<p class="MsoNormal"> </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"> </p>
</div>
<div>
<p class="MsoNormal">Makoto</p>
</div>
</div>
<div>
<p class="MsoNormal" style="margin-bottom: 12pt;"> </p>
<div>
<p class="MsoNormal">2014-02-18 15:46 GMT-08:00
Makoto Miyakoshi <<a moz-do-not-send="true"
href="mailto:mmiyakoshi@ucsd.edu"
target="_blank">mmiyakoshi@ucsd.edu</a>>:</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;
margin-left: 4.8pt; margin-right: 0in;">
<div>
<p class="MsoNormal">Dear Bethel,</p>
<div>
<div>
<p class="MsoNormal"> </p>
</div>
<div>
<p class="MsoNormal">> say A=sunrise
and B=ice-cream-sale, then the ICA in
EEGLAB should find that A is maximally
temporaly independent from B.</p>
</div>
<div>
<p class="MsoNormal"> </p>
</div>
</div>
<div>
<p class="MsoNormal">ICA would find a
correlation between sunrise and
ice-cream-sale.</p>
</div>
<div>
<p class="MsoNormal"> </p>
</div>
<div>
<p class="MsoNormal">Makoto</p>
</div>
<div>
<p class="MsoNormal"> </p>
<div>
<p class="MsoNormal">2014-02-10 4:57
GMT-08:00 Bethel Osuagwu <<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>>:</p>
<div>
<div>
<p class="MsoNormal"> </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;
margin-left: 4.8pt; margin-right:
0in;">
<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 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.<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 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
–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>
“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
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 ].
“<br>
<br>
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.<br>
<br>
<br>
· 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>
· 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?<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>
</div>
<p class="MsoNormal">Email: <a
moz-do-not-send="true"
href="mailto:ith@deakin.edu.au"
target="_blank">ith@deakin.edu.au</a><mailto:<a
moz-do-not-send="true"
href="mailto:ith@deakin.edu.au"
target="_blank">ith@deakin.edu.au</a>><br>
Web :<a moz-do-not-send="true"
href="http://www.deakin.edu.au/cisr"
target="_blank">www.deakin.edu.au/cisr</a><<a
moz-do-not-send="true"
href="http://www.deakin.edu.au/cisr"
target="_blank">http://www.deakin.edu.au/cisr</a>><br>
<br>
[<a moz-do-not-send="true">cid:image001.jpg@01CF23FF.F8259940</a>]<br>
<br>
<br>
<br>
<br>
<br>
<br>
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</blockquote>
</div>
</div>
</div>
<p class="MsoNormal"><span style="color:
rgb(136, 136, 136);"><br>
<br clear="all">
<span></span></span></p>
<div>
<p class="MsoNormal"> </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>
</div>
</div>
</blockquote>
</div>
<p class="MsoNormal"><br>
<br clear="all">
</p>
<div>
<p class="MsoNormal"> </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>
</div>
</div>
</div>
</div>
</div>
</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>
</div>
</div>
<pre wrap="">
<fieldset class="mimeAttachmentHeader"></fieldset>
_______________________________________________
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</blockquote>
<br>
<pre class="moz-signature" cols="72">
</pre>
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