Cost-sensitive Active and Proactive Learning of Decision Trees - Data Mining with Decision Trees: Theory and Applications - page 193

unknown probability p i agrees to the offer, the utility obtained from this
customer is denoted as U i ∈

. If the customer rejects the offer, the utility

is denoted as U i ∈

. Thus, the net acquisition cost of customer i is

defined as:
NAC i = C i −

U i

if customer i accepts the offer

(12.7)

U i

C i − if customer i rejects the offer

Note that all utility values are a function of the customer's attribute
vector (

x i ).
Let the corresponding utility of inaction with respect to customer i be
denoted as Ψ i . In order to maximize the expected profit, the decision-maker
should court customer i if the probability of a positive response is higher
than the cost of approach (Saar-Tsechansky and Provost, 2007). This is
represented in the following equivalent equations:

U i U i −

p i · +(1 − p i ) · C i > Ψ i (12.8)

or:

U i C i +Ψ i − o i

r i

p i >

≡

(12.9)

U i − U i

where o i and r i are merely shorthand for the numerator and denominator
of the decision threshold ratio. The notation p i

represents the classifier's

estimation for p i .
A pseudo code for the active learning framework used for the target
marketing process is presented in Figure 12.1. The received input includes:
a pool of unlabeled instances ( S ), an inducer ( I ), and a stopping criterion
( CRIT ). The first step is to initiate the labeled pool. An initial set of labeled
examples is selected. Once the potential customers are selected, they are
approached with a product offer. According to the customers' response, the
newly labeled examples are added to the labeled pool. The labeled pool
is then used for building the classifier. Based on the classifier, the next
subset from the unlabeled pool is selected. This process is repeated until
triggering some sort of stopping criteria, such as running out of budget. The
final classifier (the output) is used to estimate the probability of positive
response p i of new customers. Customers with an estimated probability
that exceeds the threshold in Eq. (12.9) are contacted.