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Second we observe that with increasing
k
min
the prediction quality of
p
ss
0
improves, and for higher
k
min
it even outperforms
p
ss
0
. This is because Assumption
5.2 requires a more complex treatment of the data, including a partition of the
transactions and their different handling for the two probability types. On the
contrary, Assumption 5.1 makes use of all data for unified learning, and hence its
algorithms achieve good prediction results even for small statistical volumes. The
higher the statistical mass, however, algorithms based on Assumption 5.2 increas-
ingly benefit from their structural advantage and finally outperform the simple ones.
Of course, this only applies if Assumption 5.2 is actually realistic! But Table
5.4
seems to confirm that and that's another good news. Finally, we emphasize that
Assumption 5.1 used in conjunction with simple update schemas like Algorithm
4.1, though quite simple, exhibits a good overall prediction rate that is really hard to
top. We will see this, for example, in Sect.
8.4.4
where we will continue this
discussion.
■
So first experience supports Assumption 5.2. The presented results are also
confirmed by similar tests on other data sets. Nevertheless, it is too early to speak
about a full improvement. Yet our methodology may be subject to another critical
objection: despite all random variations by the softmax policy, our recommenda-
tions are still the result of previous analyses and thus not fully statistically inde-
pendent. This raises the question whether the presented results are indeed based on
the effect of recommendations rather than their analytical selection.
Luckily the effect can be studied by comparison with the control group.
We remember that in the control group no recommendations of the RE algorithm
are displayed. In the transaction log files described in Sect.
4.4
(column
itemsAction
), the RDE also stores the products
that it would recommend
if it
would be allowed to do that. Since recommendation and control sessions are always
mixed in time, these recommendations represent that current one of the RE algo-
rithm. By treating these would-like recommendations in the same way as “real”
recommendations, we can repeat all tests and compare them for both recommen-
dation and control group.
Example 5.3
We again used data from a real-world web shop; this time it was a
fashion shop. We have analyzed data from two days with (in total) about 12,500
different products and 1.6 Mio. transactions. The procedure was exactly like that of
Example 5.2 but now separately for the recommendation and the control group.
Although the recommendations have been less explorative than that of Example 5.2,
we obtained similar results.
Figure
5.4
shows the quotient of conditional and unconditional probabilities for
both groups in the same setting as Fig.
5.3
.
Not surprising the control group coefficient
rs
C
_
ctrl
is about 1, whereas the one of
the recommendation group is higher, between 2 and 3. As in Fig.
5.3
it clearly
increases at
k
min
¼
20 but then only slightly. The recommendation coefficient
rs
C
is about twice as high as that of Example 5.2 - this also corresponds to reality
(recommendations in the fashion shop are more accepted) and confirmed by click
statistics.
■
