Information Technology Reference
In-Depth Information
(n)
to calculate the error rate
e
i
. The reverse logarithm of
e
i
is
then used as the weight
w
i
for each base hypothesis
h
i
.Since
w
i
is inversely
proportional to the error rate
e
i
of
h
i
, a strong hypothesis automatically gets
higher votes in constituting the final hypothesis
h
final
. One should be cautious in
dealing with the situation when
w
i
is either too small or too large, which would
mean either an obsoleted or an over-fitting
h
i
.
In theory, MuSERA/REA can obtain a smaller error bound than that of “UB”
introduced in Section 7.3.2.
By making the same assumption that the Bayes error rate comes from the
variance η
c
of the base hypothesis
h
i
as for the analysis of UB, as weights
is applied onto
S
{
w
i
}
are inversely proportional to the error rates
{
e
i
}
, they can be approximated by
C
σ
η
c
w
i
=
(7.20)
where
σ
η
c
is the variance of
η
c
and
C
is a constant for all base hypotheses
{
h
i
}
.
On the basis of Equation 7.9,
η
c
is a part of the probability output; thus, the
variance η
C
of the final hypothesis at time stamp
n
is
i
=
1
w
i
η
c
(
x
)
η
C
(
x
)
=
i
=
1
w
i
(7.21)
The variance of
η
C
is
i
=
1
w
i
σ
η
c
i
=
1
w
i
σ
η
C
=
(7.22)
According to Equation 7.20, Equation 7.22 can be simplified into
1
i
=
1
1
/σ
η
i
C
σ
η
C
=
(7.23)
On the other hand, there is Inequation 7.24:
n
n
1
σ
η
i
C
σ
η
i
C
×
≥
n
2
(7.24)
i
=
1
i
=
1
The proof is straightforward, assuming
σ
η
i
C
=
a
i
:
n
n
n
n
1
a
j
=
1
a
j
+
1
a
j
a
i
×
a
i
×
a
i
×
(7.25)
i
=
1
j
=
1
i
=
1
,j
=
1
i
=
1
,j
=
1
i
=
j
i
=
j
Search WWH ::
Custom Search