Editing Association rule learning (section)

=== Conviction ===
The ''conviction'' of a rule is defined as <math> \mathrm{conv}(X\Rightarrow Y) =\frac{ 1 - \mathrm{supp}(Y) }{ 1 - \mathrm{conf}(X\Rightarrow Y)}</math>.<ref name="brin-dynamic-itemset1">{{cite book |doi=10.1145/253260.253325 |chapter=Dynamic itemset counting and implication rules for market basket data |title=Proceedings of the 1997 ACM SIGMOD international conference on Management of data - SIGMOD '97 |pages=255–264 |year=1997 |last1=Brin |first1=Sergey |last2=Motwani |first2=Rajeev |last3=Ullman |first3=Jeffrey D. |last4=Tsur |first4=Shalom |isbn=978-0897919111 |citeseerx=10.1.1.41.6476 |s2cid=15385590 }}</ref>

For example, the rule <math>\{\mathrm{milk, bread}\} \Rightarrow \{\mathrm{butter}\}</math> has a conviction of <math>\frac{1 - 0.4}{1 - 0.5} = 1.2 </math>, and can be interpreted as the ratio of the expected frequency that X occurs without Y (that is to say, the frequency that the rule makes an incorrect prediction) if X and Y were independent divided by the observed frequency of incorrect predictions. In this example, the conviction value of 1.2 shows that the rule <math>\{\mathrm{milk, bread}\} \Rightarrow \{\mathrm{butter}\}</math> would be incorrect 20% more often (1.2 times as often) if the association between X and Y was purely random chance.