Database Reference
In-Depth Information
5.4.1 Verification of the Environment Model
We consider the following example.
Example 5.2
We use the data of an online furniture shop We start with the off-line
test method of Sect.
4.4
. The shop contains approximately 1,900 products. We use
the data of one day as training set; it contains 9,736 sessions with 31,349 trans-
actions. The test set consists of the data of the following day; it has 7,430 sessions
with 24,161 transactions. Up to removing multiple clicks, we did not change
the data.
We want to check the plausibility of Assumption 5.2. In the shop of our test
data, no control sessions exist, and all sessions get recommendations of the
prudsys RDE. In order to check the influence of the recommendations on the
browsing behavior of the shop visitors as good as possible, the RDE varies
the recommendations strongly. This was achieved by applying the softmax policy
50 % of all recommendations as “greedy,” i.e., corresponding to the strongest
action values, and the remaining 50 % explorative. There are always 4 recommen-
dations displayed for each product.
We use the training data set to determine both the conditional transition
probabilities
p
ss
a
and the unconditional ones
p
ss
a
by means of the adaptive algorithms
5.1 and 5.2.
We now consider all product views
s
that actually received at least one recom-
mendation
a and
where at least one rule
s ! s
a
exists that was learned on the
training set. We call this set of product views
recommendation relevant
.
We now follow the notation of Sect.
5.3
.Let
n
be the number of updates of
conditional probabilities
n
p
ss
0
and
m
the number of updates of unconditional
probabilities
m
p
ss
0
of the rule
s ! s
0
on the training data. We define
k
min
¼
min
n
ð
;
m
Þ
ð
5
:
28
Þ
as minimum of both updates. The higher
k
min
, the better the conditional probability
n
p
ss
0
can be compared with the unconditional
m
p
ss
0
because for
s
the recommenda-
tion
a
was sufficiently often delivered (high
n
) and at the same time also sufficiently
often not delivered (high
m
).
We want to compare the probability types
p
ss
a
¼
m
p
ss
a
depending
on
k
min
in order to see how the recommendation of
a
increases the transition to
s
a
.So
we calculate the mean values of the transition probabilities over all product recom-
mendation pairs
s
n
p
ss
a
and
p
ss
a
¼
ð
k
min
whose update number is not smaller than
k
min
,i.e.,
;
X
X
1
1
n
p
ss
a
,
m
p
ss
a
p
a
¼
p ¼
ð
k
min
s
;
ð
k
min
s
;
s;ð
k
min
s;ð
k
min
and their coefficient:
