Biomedical Engineering Reference
In-Depth Information
-
do not depend on the positions of subwords within the overall input word, but
-
should at least depend on the lengths of the corresponding subwords,
where it is strongly recommended to make sure that as much information on the compo-
sition of the actual input sequence as possible is incorporated into these approximated
terms.
Therefore, we decided to use the following emission terms that incorporate relative
frequencies
rf
em
(
r
i
,i− i
+1)
and
rf
em
(
r
i
r
j
,j− i
+1)
for unpaired bases and base
pairs, respectively, that can be efficiently derived from the actual input sequence:
Pr
em
(1) :=
u∈Σ
G
r
Pr
em
(
u
)
rf
em
(
u,
1)
,
·
(4)
Pr
em
(
d
):=
p
1
p
2
∈Σ
G
r
Pr
em
(
p
1
p
2
)
rf
em
(
p
1
p
2
,d
)
.
·
(5)
3.3
(Improved) Approximated Sampling Probabilities
Fortunately, during the complete sampling process, not only the start and end positions
of the currently considered sequence fragment
R
i,j
,
1
n
, but also the actual
input sequence
r
are always known. Thus, we can in certain cases easily remove some
approximate factors in the corresponding approximated inside and outside probabilities
and replace them with the respective correct terms (depending on
i
,
j
and
r
)inorderto
obtain more reliable values.
Therefore, for any sampling strategy, the sampling probabilities from which the re-
spective (conditional) distributions for possible choices are inferred should be defined
by using such improved inside and outside probabilities (instead of the corresponding
uncorrected precomputed ones). For example, if
X
≤
i,j
≤
∈I
G
s
generates hairpin loops, we
should use
α
X
(
i,j
):=
α
X
(
i,j
)
,
if
(
j
−
i
+1)
≤
W
exact
,
(6)
c
em
(
i,j
)
,
else
,
α
X
(
j
−
i
+1)
·
and
⎧
⎨
β
X
(
i,j
)
,
if
(
j
−
i
+1)
≥
n
−
W
exact
,
β
X
(
i,j
):=
β
X
(
j
−
i
+1)
×
(7)
⎩
c
em
(
i
−
min
hel
,j
+min
hel
,
min
hel
)
,
else
,
where
c
em
(
s, e
):=
k
=
s
Pr
em
(
r
k
)
(8)
Pr
em
(1)
e−s
+1
and
l−
1
k
=0
Pr
em
(
r
i
+
k
r
j−k
)
c
em
(
i,j,l
):=
.
(9)
l−
1
k
=0
Pr
em
((
j
−
k
)
−
(
i
+
k
)+1)
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