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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-
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