Information Technology Reference
InDepth Information
The idea is to replace the loss term
(y
(i)
j
f(x
(i)
j
))
2
with the difference between
the ground truth label
y
(i
j
and a querydependent linear transformation of the rank
ing function, i.e.,
g
(i)
(f (x))
−
α
(i)
f(x
(i)
j
β
(i)
, where
α
(i)
and
β
(i)
are parameters
for query
q
i
. Accordingly, the loss function becomes
=
)
+
m
(i)
n
y
(i)
j
α
(i)
f
x
(i)
j
2
β
(i)
L(f
;
α, β)
=
−
−
i
=
j
=
1
1
2
2
2
,
+
λ
β
β
+
λ
α
α
+
λ
f
f
(7.2)
where
β
=[
β
(i)
n
i
α
(i)
n
i
1
, and
λ
α
,
λ
β
,
λ
f
are regularization parameters.
By minimizing this loss function on the training data, one will get the optimal
parameters
]
1
,
α
=[
]
=
=
. Note that in the test phase, only
f
is used. There are two
reasons for doing so: (i) for new queries it is impossible to obtain parameter
α
and
β
; (ii) as long as the (unknown) parameter
α
is positive, the corresponding linear
transformation on the ranking function will not change the ranking order of the
documents.
In [
2
], a framework is proposed to better describe how to use querydependent
loss function. In particular, the loss function in training is formulated in the follow
ing general form:
{
f, α, β
}
L(f )
=
L(f
;
q),
(7.3)
q
where
L(f
q)
is the querylevel loss function defined on both query
q
and ranking
function
f
, and each query has its own form of loss function.
Since it is infeasible to really give each individual query a different loss function,
for practical consideration, the following query categorybased realization of the
above querydependent loss function is proposed:
;
q,c)
,
=
L(f )
L(f
;
q)
=
P(c

q)L(f
;
(7.4)
q
q
c
where
L(f
;
q,c)
denotes a categorylevel loss function defined on query
q
, ranking
function
f
and
q
's category
c
.
The categorization of queries can be given according to the search intentions
behind queries. For example, queries can be classified into three major categories
according to Broder's taxonomy [
3
]: navigational, informational, and transactional.
Under this taxonomy, a navigational query is intended to locate a specific Web page,
which is often the official homepage or subpage of a site; an informational query
seeks information on the query topic; and a transactional query seeks to complete
a transaction on the Web. According to the definition of the above categories, for
the navigational and transactional queries, the ranking model should aim to retrieve
the exact relevant Web page for the top position in the ranking result; while for the
informational query, the ranking model should target to rank more relevant Web
pages on a set of top positions in the ranking result.