Information Technology Reference
In-Depth Information
and target domains share the same set of features, and their differences only lie in
the different distributions of the data. Denote the source and target distributions by
P
s
and
P
t
, respectively, then we have
arg min
w
t
=
L(w
;
x
,
y
)P
t
(
x
,
y
)d
x
d
y
arg min
P
t
(
x
,
y
)
=
P
s
(
x
,
y
)
L(w
;
x
,
y
)P
s
(
x
,
y
)d
x
d
y
arg min
P
t
(
x
)
P
s
(
x
)
P
t
(
y
|
x
)
=
x
)
L(w
;
x
,
y
)P
s
(
x
,
y
)d
x
d
y
.
(9.2)
P
s
(
y
|
P
t
(
y
|
x
)
P
t
(
x
)
Let
δ
=
and
η
=
P
s
(
x
)
; one obtains
P
s
(
y
|
x
)
w
t
=
arg min
w
δηL(w
;
x
,
y
)P
s
(
x
,
y
)d
x
d
y
.
(9.3)
In other words, with re-weighting factors, the minimization of the loss on the
source domain can also lead to the optimal ranking function on the target domain.
Therefore, in practice,
w
t
can be learned by minimizing the re-weighted empirical
risk on the source-domain data:
n
s
δ
i
η
i
L
w
,
y
(i
s
,
x
(i)
w
t
=
;
arg min
w
(9.4)
s
i
=
1
where the subscript
s
means the source domain, and
n
s
is the number of queries in
the source-domain data.
In [
1
], it is assumed that
η
i
=
1. In other words, there is no difference in the
distribution of
x
for the source and target domains. To set
δ
i
, the following heuristic
method is used. First a ranking model is trained from the target-domain data and
then it is tested on the source-domain data. If a pair of documents in the source-
domain data is ranked correctly, the corresponding pair is retained and assigned
with a weight; else, it is discarded. Since in learning to rank each document pair
is associated with a specific query, the pairwise precision of this query is used to
determine
δ
i
:
# pairs correctly ranked of a query
# total pairs of a query
δ
i
=
.
According to the experimental results in [
1
], the instance-level method only
works well for certain datasets. On some other datasets, its performance is even
worse than only using the target-domain data. This in a sense shows that simple
re-weighting might not effectively bridge the gap between the source and target do-
mains.
