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Fig. 2.2 Hingle loss as a
function of y j f(x j )
The above optimization problem can be transformed to its dual form, and get
efficiently solved. In addition, the so-called kernel trick can be used to extend
the algorithm to the non-linear case (for more information, please see Chaps. 21
and 22). Experiments on ad-hoc retrieval indicate that the SVM-based algorithm
is comparable with and sometimes slightly better than language models. Accord-
ing to the experimental results, it is claimed that SVM is preferred because of its
ability to learn arbitrary features automatically, fewer assumptions, and expressive-
ness [ 16 ].
Logistic Regression-Based Method In [ 9 ], logistic regression (which is a pop-
ular classification technique although it contains regression in its name) is used to
perform the task of binary classification for ranking. First of all, given the features
of the documents, the logarithm of the odds of relevance for the document x j is
defined as follows,
log
T
P(R
|
x j )
=
c
+
w t x j,t ,
(2.3)
1
P(R
|
x j )
t
=
1
where c is a constant.
Equivalently, the probability of relevance of a document to a query is defined as
below,
1
P(R
|
x j )
=
e c t = 1 w t x j,t .
(2.4)
+
1
Given some training data, the likelihood of the relevant documents can be com-
puted based on the above equation, and the parameter w t can be estimated by max-
imizing the likelihood. Then these parameters can be used to predict odds of rele-
vance for other query-document pairs.
Specifically, six features are used to build the model in [ 9 ], i.e., query absolute
frequency, query relative frequency, document absolute frequency, document rela-
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