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positive
ʻ
j
values indicate a preference for such an event, while large negative
values make the event unlikely. The size of
c
determines which states
h
j
can refer
to. If
c
contains only the current state, then
h
j
can only refer to the current state.
However, if
c
contains the current and the previous states, then
h
j
can refer to
all of them. We use the linear chain CRFs. Set
C
contains only current-state
and current-and-previous state types. Given
x
, the conditional probability of
y
is equal to the exponential sum of
ʻ
j
h
j
in all cliques. The most probable label
sequence for x,
y
∗
=
argmax
y
P
ʻ
(
y
x
)
can be eciently determined using the Viterbi algorithm [9]. The parameters
can be estimated by maximizing the conditional probability of a set of label se-
quences, given each of their corresponding input sequences. The log-likelihood of
a training set
|
(
x
(
i
)
,y
(
i
)
):
i
=1
, ..., M
is written as: To optimize the parameters
in CRFs, we use a quasi-Newton gradient-climber BFGS [5].
{
}
Features
We transform all rules used in the rule-based approach to CRF features. Feature
set
i
corresponds to Rule set
i
.
Feature set 1
:
Section-event Features
The following are two examples of section-event features. The first feature is a
unigram feature and refers to the pair
y
i
. The second one is a bigram feature and
refers to
y
i
and
y
i−
1
. For the admission and discharge times, we train different
classifiers.
1
,i
]) =
1
,
if
R.SE.
1(
s
a
,e
b
,t
admission
)and
y
i
=
B
−
AFTER
h
i
(
y
c
,x,
[
i
−
0
,
otherwise
⊧
⊨
1
,
if
R.SE.
1(
s
a
,e
b
,t
admission
)and
y
i−
1
=
B
−
AFTER
h
i
(
y
c
,x,
[
i
−
1
,i
]) =
and
y
i
=
I
−
AFTER
⊩
0
,
otherwise
Feature set 2
:
Within-sentence Features
The following are two examples of within-sentence features. The first refers
to the pair
y
i
and the second refers to
y
i
and
y
i−
1
:
1
,i
]) =
1
,
if
R.WS.
1(
e
a
,e
b
)and
y
i
=
B
−
AFTER
h
i
(
y
c
,x,
[
i
−
0
,
otherwise
⊧
⊨
1
,
if
R.WS.
1(
e
a
,e
b
)and
y
i−
1
=
B
−
AFTER
h
i
(
y
c
,x,
[
i
−
1
,i
]) =
and
y
i
=
I
−
AFTER
⊩
0
,
otherwise
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