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Fig. 13.2
The BBM model
[0,1], and a larger value indicates stronger relevance. While this single-number esti-
mate could suffice for many usages, it nevertheless falls short of capacity for broader
applications. For example, it is unspecified how to estimate the probability that doc-
ument d u is preferred to d v for the same query when their relevances are r u and r v
respectively.
Note that many learning-to-rank algorithms, especially the pairwise ranking al-
gorithms, require pairwise preference relationship as the training data. It is desirable
that we can also mine such pairwise information from the click-through data in a
principled way. To tackle this issue, a new click model named Bayesian Browsing
Model (BBM) is proposed in [ 24 ]. By virtue of the Bayesian approach to modeling
the document relevance, the preference probability between multiple documents is
well-defined and can be computed based on document relevance posteriors.
The BBM model can be vividly illustrated using Fig. 13.2 .
From the figure we can see that the model consists of three layers of random vari-
ables. The top layer S = (S 1 ,S 2 ,...,S M ) represents nominal relevance variables
with S i =
R π 1 (i) (here R j is the relevance of document j , and π is the ranked list
of the search result). The other two layers E and C represent examination and click
events, respectively. The full model specification is as follows:
P(E 1 =
1 )
=
β 0 , 1 ,
P(C i =
1
|
E i =
0 ,S i )
=
0 ,
(13.6)
P(C i =
1
|
E i =
1 ,S i )
=
S i ,
P(E i =
1
|
C 1 ,...,C i 1 )
=
β t i ,s i ,
where t i =
t i .
Detailed explanation of the model is given as follows. First, if a document is
not examined by the user, it will not be clicked no matter whether it is relevant or
not. Second, if a document has been examined by the user, the probability that it
is clicked is determined by the relevance of the document. Third, given previous
clicks, the probability of examining the next document is parameterized by β t i ,s i ,
which is dependent on the preceding click position t i and the distance from the
current position to the preceding click s i .
arg max l<t (C l =
1 ) , and s i =
i             Search WWH ::

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