Information Technology Reference
In-Depth Information
where
e
d
i
,i
is the examination probability for document
d
i
,
c
d
i
,i
is the click prob-
ability for document
d
i
,
r
d
i
represents the relevance of document
d
i
, and
λ
i
is the
aforementioned user behavior parameter.
The model can be explained as follows. First, after the user examines a document,
the probability of clicking on it is determined by its relevance. Second, after clicking
on a document, the probability of examining the next document is determined by the
parameter
λ
i
.
From the above formulas, one can derive the closed-form equations
i
−
1
e
d
i
,i
=
(
1
−
r
d
j
+
λ
j
r
d
j
),
j
=
1
(13.2)
i
−
1
c
d
i
,i
=
r
d
i
(
1
−
r
d
j
+
λ
j
r
d
j
).
j
=
1
Given the actual click events
{
C
i
}
in a query session and the document impres-
sion
{
d
i
}
, a lower bound of its log-likelihood before position
k
can be obtained as
k
−
1
C
i
log
r
d
i
+
r
d
i
)
L
DCM
≥
−
−
(
1
C
i
)
log
(
1
i
=
1
k
−
1
+
C
i
log
λ
i
+
log
(
1
−
λ
k
).
(13.3)
i
=
1
By maximizing the above lower bound of the log-likelihood, one can get the best
estimates for the relevance and user behavior parameters:
# Clicks on
d
Impressions of
d
before position
k
,
r
d
=
(13.4)
# Query sessions when last clicked position is
i
# Query sessions when position
i
is clicked
λ
i
=
1
−
.
(13.5)
Experimental results on the click-through logs of a commercial search engine
have shown that the DCM model can perform effectively. The model is further en-
hanced in a follow-up work, referred to as the Click Chain Model [
18
]. The new
model removes some unrealistic assumptions in DCM (e.g., users would scan the
entire list of the search results), and thus performs better on tail queries and can
work in a more efficient manner.
13.2.1.2 Bayesian Browsing Model
As can be seen, both the DCM model and the cascaded model, despite of their
different user behavior assumptions, follow the point-estimation philosophy: the es-
timated relevance for each query-document pair is a single number normalized to
