The correlation mechanism is more complicated here. Basically
(NOTXOR) except when
X
=
f, Y
=
t
then
with high probability.
Now, if, knowing
Y
=
t
should not change the
probability of
X
, however
the exceptional case increases the probability that
X
is false. Also,
we have
is extremely high as, if
Y
are true,
X
should be
true to allow
Y
to be true as
.
2.1
.
Order
:
2.2
.
Fix an ordering of the
variables
:
for each
select its parents to be minimal subset of such that
this will yield a minimal imap
3
.
3.1
.
To construct a minimal Imap for a marginalized network, we should
preserve all independencies that exist in G when the variable being
marginalized, A, is unobserved. We will see what active trails pass though A
and try to preserve them. For B there is an active trail from it to J, , so we must
add an edge
in , otherwise we are asserting an independence
that does not
exist in G. similarly, we need to add an edge from each parent to each parent
to each child of A. There is also an active trail in G between J and M, ,
therefore
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we must add an edge between J and M(either direction is ok), but we will choose .
Moreover,
observing
J
, there is an active trail from
T
to
M
that passes through
A
, , however, in , this trail will
be blocked when
J
is observed. Moreover, while there exists an alternative trail in
that utilizes the
new added vstructure between
T,B
via
or the other vstructure
T,E
via , observing both B and E, in
addition to
J
, will block these trails in
but not in
G
. Therefore, we must add an edge between
T
and
M
, otherwise, we are asserting an independence that does not exist in
G
. Moreover, the active trail
in
G
between
N
and
J
, when
M
is observed, is still active in
due to the new vstructure between
N
and
J
. No other edges are needed. (It should be noted that if we had chosen to direct the edge
between
J
and
M
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 Spring '13
 Dr.ZAre
 Probability theory, Pearson productmoment correlation coefficient, active trail, G. Therefore, G. Moreover, Soheila Molaei

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