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Regression – Recommendations Improved
This works correctly, but is very slow. A better implementation has more
infrastructure so you can avoid having to loop over all the datasets to get the count
(c_newset). In particular, we keep track of which shopping baskets have which
frequent itemsets. This accelerates the loop but makes the code harder to follow.
Therefore, we will not show it here. As usual, you can find both implementations on
the book's companion website. The code there is also wrapped into a function that
can be applied to other datasets.
The Apriori algorithm returns frequent itemsets, that is, small baskets that are not in
any specific quantity (minsupport in the code).
Association rule mining
Frequent itemsets are not very useful by themselves. The next step is to build
association rules. Because of this final goal, the whole field of basket analysis is
sometimes called association rule mining.
An association rule is a statement of the "if X then Y" form; for example, if a
customer bought War and Peace, they will buy Anna Karenina. Note that the rule is not
deterministic (not all customers who buy X will buy Y), but it is rather cumbersome
to always spell it out. So if a customer bought X, he is more likely to buy Y according
to the baseline; thus, we say if X then Y, but we mean it in a probabilistic sense.
Interestingly, the antecedent and conclusion may contain multiple objects: costumers
who bought X, Y, and Z also bought A, B, and C. Multiple antecedents may allow
you to make more specific predictions than are possible from a single item.
You can get from a frequent set to a rule by just trying all possible combinations of X
implies Y. It is easy to generate many of these rules. However, you only want to have
valuable rules. Therefore, we need to measure the value of a rule. A commonly used
measure is called the lift. The lift is the ratio between the probability obtained by
applying the rule and the baseline:
In the preceding formula, P(Y) is the fraction of all transactions that include Y while
P(Y|X) is the fraction of transactions that include Y and X both. Using the lift helps
you avoid the problem of recommending bestsellers; for a bestseller, both P(Y)
and P(X|Y) will be large. Therefore, the lift will be close to one and the rule will be
deemed not very relevant. In practice, we wish to have at least 10, perhaps even 100,
values of a lift.
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