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and (2) TLinks between events that are co-referenced. To resolve both cases,
we designed three rules for consecutive sentences (R.CS) and one rule for co-
referenced events (R.CR).
R.CS.1:
isEventType
(
e
i
,
“
EV IDENTIAL
)
∧
isEventContain
(
e
i
,
“
report
”)
∧
isEventType
(
e
j
,
“
PROBLEM
)
⃒
TLink
(
e
i
,e
j
.
“
AFTER
)
isEventType
(
e
i
,
“
OCCURRENCE
)
R.CS.2:
∧
isEventContain
(
e
i
,
isEventType
(
e
j
,
“
TREATMENT
)
“
admission
”)
∧
⃒
TLink
(
e
i
,e
j
,
“
AFTER
)
R.CS.3:
isEventType
(
e
i
,etype
)
∧
isEventType
(
e
j
,etype
)
TLink
(
e
i
,e
j
,
“
OV ERLAP
)
R.CR.1:
isCoreference
(
e
i
,e
j
)
⃒
TLink
(
e
i
,e
j
,
“
OV ERLAP
)
where;
isCoreference
(
e
i
,e
j
)means
e
i
and
e
j
have any word in common and
are before/after one sentence with the same event type.
⃒
3.2 CRFs-Based approach
In the rule-based approach, once the event-time or event-event pair are matched
by our rules, and they will be assigned the TLink types. The rules always assign
the TLink type to each pair individually, and the dependency relation between
the similar or near event/time are not considered. However, pairs are not wholly
independent in following cases:
case i. Pair with the same time
case ii. Pair with the same event
We formulate the task of assigning TLink types to a series of pairs as a se-
quence labeling problem and solve it using CRFs. Pair with the same event/time
in the same sentence are treated as a sequence in the order they appears in
sentences. For example, if the order of the time and events in the sentence is
[
e
1
,t
1
,e
2
,e
3
] and we will expand them into
{
(
t
1
,e
1
)
,
(
t
1
,e
2
)
,
(
t
1
,e
3
)
}
; if the order
of the events appear in the sentence is [
a,b,c,d
] and we will expand them into
{
(
a, b
)
,
(
a, c
)
,
(
a, d
)
,
(
b,c
)
,
(
b,d
)
,
(
c, d
)
}
Conditional Random Fields
CRFs are undirected graphical models, in which each node represents a state
that is trained to maximize a conditional probability [3]. A linear-chain CRF
with parameters
ʻ
=
{
ʻ
1
,ʻ
2
, ...
}
defines a conditional probability for a state
sequence
y
=
y
1
...y
n
given a length-
n
input sequence
x
=
{x
1
, ..., x
n
}
as follows:
Z
(
x
)
exp
c∈C
j
ʻ
j
h
j
(
y
c
,x,c
)
1
p
(
y|x
)=
Z
(
x
)=
y
exp
c∈C
j
ʻ
j
h
j
(
y
c
,x,c
)
where
Z
(
x
) is the normalization factor that ensures the probability of all state
sequences sum to one,
C
is the set of all cliques in the target sentence, and
c
is any single clique. A clique is a fully connected subset of nodes. Note that
h
j
(
y
c
,x,c
) is usually a binary-valued feature function and
ʻ
j
is its weight. Large
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