## Predictive Rules

We will use the word rule here to denote patterns of the form 'IF Conjunction of conditions THEN Conclusion'. The individual conditions in the conjunction will be tests concerning the values of individual attributes, such as 'Income < 108 000' or 'Gender = Male'. For predictive rules, the conclusion gives a prediction for the value of the target (class) variable.

If we are dealing with a classification problem, the conclusion assigns one of the possible discrete values to the class, for example, 'BigSpender = No'. A rule applies to an example if the conjunction of conditions on the attributes is satisfied by the particular values of the attributes in the given example. Each rule corresponds to a hyper-rectangle in the data space, as illustrated in Figure 4.

Predictive rules can be ordered or unordered. Unordered rules are considered independently and several of them may apply to a new example that we need to classify. A conflict resolution mechanism is needed if two rules which recommend different classes apply to the same example. A default rule typically exists, whose recommendation is taken if no other rule applies.

Ordered rules form a so-called decision list. Rules in the list are considered from the top to the bottom of the list. The first rule that applies to a given example is used to predict its class value. Again, a default rule with an empty precondition is typically found as the last rule in the decision list and is applied to an example when no other rule applies.

An ordered list and an unordered list of rules are given in Table 2. Both have been derived using a covering algorithm (see the section titled 'The covering algorithm for rule induction'). The ordered list of rules in Figure 4, on the other hand, has been generated from the decision tree in the left-hand side of Figure 2. Note that each of the leaves of a classification tree corresponds to a classification rule. Although less common in practice, regression rules also exist, and can be derived, for example, by transcribing regression trees into rules.

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