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In-Depth Information
Algorithm 7.3
Uncorrelated bagging with take-in-all accommodation of previ-
ous minority class examples
Inputs:
1: timestamp:
t
2: current training data chunk:
={
(
x
1
,y
1
),...,(
x
m
,y
m
)
}
3: current data set under evaluation:
S
(t)
x
1
,...,
x
n
}
T
(t)
={
4: minority class data queue:
Q
stores all previous minority class examples before the current time
t
.*/
5: soft-typed base classifier:
L
/*
Q
Procedure:
6:
for
t
:1
→
...
do
7:
(t)
(t)
,
N
(t)
S
←{
P
}
(t)
(t)
/* Assume
||
P
|| =
p
and
||
N
|| =
q
*/
P
(t)
(t)
,
Q
(t)
8:
←{
P
}
|| =
p
,and
p
=
K
*/
/* Assume
||
P
(t)
for
k
←
1
...K
do
9:
N
(k)
←
sample without replacement
(
N
(t)
)
10:
||
Q
(k)
|| =
p
*/
/*
h
(t)
k
11:
←
L(
{
Q
(k)
,
P
(k)
}
)
12:
Q
←{
Q
,
P
}
return
Averaged composite hypothesis
h
(t)
final
for predicting class label of any instance
x
j
13:
(t)
:
within
T
K
1
k
×
h
(t)
final
(
x
j
)
=
f
i
(
x
j
)
argmax
c
(7.4)
∈
Y
i
=
1
the best use could be made of the minority class examples, while minimizing
the correlation of different base hypotheses. This is particularly important for
designing a decent composite classifier as
diversity
across base hypotheses plays
a crucial role in lifting the performance of aggregating ensemble of hypotheses
as compared to that of a single one. Finally, the minority class examples within
the current data chunk are pushed back to
Q
to facilitate imbalanced learning on
future data chunks.
The independence across base hypotheses can help reduce the overall error
rate of prediction. Assuming that the estimated
a posteriori
probability of base
hypothesis
h
k
for an instance
x
is
f
k
(
x
)
, the output of the composite classifier
h
final
for
x
is,
K
1
K
f
E
(
x
)
=
f
k
(
x
)
(7.5)
k
=
1
Figure 7.2 shows the error regions introduced by estimating the
true
Bayes
model, in which
P
i/j
and
f
i/j
represent the
a posteriori
probability of the outputs
of classes
i
and
j
by true Bayes model and estimated Bayes model, respectively.
x
∗
and
x
b
are where the true and estimated Bayes models output exactly the
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