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.