Information Technology Reference
InDepth Information
Similar to the DCM model, the parameters in the above BBM model can also be
learned by maximizing a loglikelihood of the observed clicks:
m
C
i
1
C
i
log
(
1
β
t
i
,s
i
/
2
)
,
L
BBM
=
log
(β
t
i
,s
i
/
2
)
+
−
−
(13.7)
k
=
1
i
=
1
where
k
indexes the sessions in the log data.
After the parameters are learned, according to the graphical model as shown in
Fig.
13.2
, it is not difficult to obtain the posterior probability of variables
R
j
:
m(m
+
1
)/
2
R
e
0
j
γ
j
R
i
)
e
j
,
p(R
i

C
1
,...,C
N
)
∝
(
1
−
(13.8)
j
=
1
where
γ
t(
2
m
−
t
+
1
)
2
+
s
=
β
t,s
m
e
0
=
I
(13.9)
{
(C
i
=
1
)
∧
(π
−
1
(i)
=
j)
}
k
=
1
i
=
1
m
e
t(
2
m
−
t
+
1
)
2
s
=
I
.
(C
i
=
(π
−
1
(i)
(t
i
=
(s
i
=
{
0
)
∧
=
j)
∧
t)
∧
s)
}
+
k
=
1
i
=
1
With this probability, one can easily get the pairwise preference probability:
p(d
j
d
i
)
=
P(R
j
>R
i
)
=
p
j
(R
j
)p
i
(R
i
)dR
j
dR
i
.
(13.10)
R
j
>R
i
This preference probability can be used in the pairwise ranking methods.
13.2.1.3 Dynamic Bayesian Network Click Model
To better model the perceived relevance and actual relevance, a Dynamic Bayesian
Network (DBN) model is proposed in [
7
]. In this model, a click is assumed to occur
if and only if the user has examined the URL and deemed it relevant. Furthermore,
the DBN model assumes that users make a linear transversal through the results
and decide whether to click based on the perceived relevance of the document. The
user chooses to examine the next URL if he/she is unsatisfied with the clicked URL
(based on actual relevance). The DBN model can be represented by Fig.
13.3
.
For simplicity, suppose we are only interested in the top 10 documents appearing
in the first page of the search results, which means that the sequence in Fig.
13.3
goes from 1 to 10. The variables inside the box are defined at the session level, while
those out of the box are defined at the query level.