A Generic Algorithm for Top-Down Induction of Decision Trees - Data Mining with Decision Trees: Theory and Applications - page 26

Table 3.3 An illustration of direct mailing dataset.

Age Gender Last Reaction Buy

35 Male Yes No

26 Female No No

22 Male Yes Yes

63 Male No Yes

47 Female No No

54 Male No No

27 Female Yes Yes

38 Female No Yes

42 Female Yes Yes

19 Male No No

Consider the training set in Table 3.3 containing data about 10 cus-
tomers. Each customer is characterized by three attributes: Age, Gender
and Last Reaction (an indication whether the customer has positively
responded to the last previous direct mailing campaign). The last attribute
(“Buy”) describes whether that customer was willing to purchase a product
in the current campaign. The goal is to induce a classifier that most
accurately classifies a potential customer to “Buyers” and “Non-Buyers”
in the current campaign, given the attributes: Age, Gender, Last Reaction.

3.3 Induction Algorithms

An induction algorithm , or more concisely an inducer (also known as
learner), is an entity that obtains a training set and forms a model that
generalizes the relationship between the input attributes and the target
attribute. For example, an inducer may take as an input specific training
tuples with the corresponding class label, and produce a classifier .
The notation DT represents a decision tree inducer and DT ( S )
represents a classification tree which was induced by performing DT on
a training set S .Using DT ( S ), it is possible to predict the target value of
a tuple x q . This prediction is denoted as DT ( S )( x q ).
Given the long history and recent growth of the machine learning field,
it is not surprising that several mature approaches to induction are now
available to the practitioner.

3.4 Probability Estimation in Decision Trees

The classifier generated by the inducer can be used to classify an unseen
tuple either by explicitly assigning it to a certain class (crisp classifier)
or by providing a vector of probabilities representing the conditional
probability of the given instance to belong to each class (probabilistic