Information Technology Reference
In-Depth Information
With the above feature representations, several learning-to-rank technologies are
applied to optimize the total revenue. One of the models is call RankLogistic. The
model is very similar to RankNet [
3
]: its loss function is also defined as a pairwise
cross entropy. The difference lies in that RankLogisitic also involves a regularization
item in its loss function. Another model is called revenue direct optimization. In this
model, the revenue is first formulated as follows:
m
(i)
n
r
(i)
j
c
(i)
j
=
Rev(w)
I
,
(14.2)
min
k
=
j
f(w,x
(i
j
)
f(w,x
(i
k
)>
0
{
−
}
i
=
1
j
=
1
where
r
(i)
j
is the bid price for the
j
th ad associated with query
q
i
,
c
(i)
j
indi-
cates whether the
j
th ad associated with query
q
i
is clicked by the user, and
I
measures whether the ranking function
f
can rank the
min
k
=
j
f(w,x
(i)
j
)
−
f(w,x
(i)
{
}
k
)>
0
ad on the top position.
Since the revenue defined above is not continuous,
I
is
min
k
=
j
f(w,x
(i)
f(w,x
(i)
{
j
)
−
k
)>
0
}
first replaced with
k
=
j
I
, and then approximated by changing
the indicator function for a Bernoulli log-likelihood function. In this way, a contin-
uous loss function is obtained as follows:
f(w,x
(i
j
)
f(w,x
(i
k
)>
0
{
−
}
m
(i)
n
log
1
+
e
f(w,x
(i
k
)
−
f(w,x
(i
j
)
.
2
r
(i)
j
c
(i)
j
L(w)
=
λ
w
+
(14.3)
i
=
1
j
=
1
k
=
j
The above models have been tested on commercial data, with Ad CTR as the
evaluation measure. The experimental results show that the revenue direct optimiza-
tion method can outperform RankLogisic and several other baselines. This empirical
observation is consistent with what we have observed in document retrieval: direct
optimization of evaluation measures can usually outperform pairwise ranking meth-
ods.
14.6 Summary
In addition to the above applications, learning-to-rank technologies have also been
applied in several other applications, such as collaborative filtering [
11
], expert find-
ing [
6
], and subgroup ranking in database [
12
]. From these examples, we can see
that ranking is the key problem in many different applications, and learning-to-rank
technologies can help improve conventional ranking heuristics by learning the opti-
mal ranking model from training data. This demonstrates well the practical impact
of the various research efforts on learning-to-rank. We hope that learning-to-rank
technologies can be applied in more and more applications, and continuously con-
tribute to the development of information retrieval, natural language processing, and
many other fields.
