Biology Reference
In-Depth Information
arcs:
10
undirected arcs:
0
directed arcs:
10
average markov blanket size:
1.82
average neighbourhood size:
1.82
average branching factor:
0.91
generation algorithm:
Model Averaging
significance threshold: 0.374
The value of the threshold is computed as follows. If we denote the arc strengths
stored in
boot
as
p
=
{
p
i
,
i
=
1
,...,
k
}
and
p
(
·
)
is
p
(
·
)
=
{
0
p
(
1
)
p
(
2
)
...
p
(
k
)
1
},
(2.16)
then we can define the corresponding arc strengths in the (unknown) averaged net-
work
G
=(
V
,
A
0
)
as
1 f
a
(
i
)
∈
A
0
0o h rw e
p
(
i
)
=
,
(2.17)
that is, the set of strengths that characterizes any arc as either significant or non-
significant without any uncertainty. In other words,
p
(
·
)
=
{
0
,...,
0
,
1
,...,
1
}.
(2.18)
The proportion
t
of elements of
p
(
·
)
that are equal to 1 determines the number of
arcs in the averaged network and is a function of the significance threshold we want
to estimate. One way to do that is to find the value
t
that minimizes the
L
1
norm
L
1
t
;
p
(
·
)
=
F
p
(
·
)
(
x
)
−
F
p
(
·
)
(
x
;
t
)
dx
(2.19)
between the cumulative distribution functions of
p
(
·
)
and
p
(
·
)
and then to include
every arc that satisfies
F
−
1
p
t
a
(
i
)
∈
A
0
⇐⇒
p
(
i
)
>
(
·
)
(
)
(2.20)
in the average network. This amounts to finding the averaged network whose arc set
is “closest” to the arc strength computed from the data, with
F
−
1
p
t
(
·
)
(
)
acting as the
significance threshold.
For the
dsachs
data, the estimated value for the threshold is 0
374; so, any arc
with a
strength
value strictly greater than that is considered significant. Again,
the resulting averaged network is the same as the one obtained with the original
threshold in
Sachs et al.
(
2005
).
.
> all.equal(avg.boot, averaged.network(boot))
[1] TRUE
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