Cost-sensitive Active and Proactive Learning of Decision Trees - Data Mining with Decision Trees: Theory and Applications - page 192

customers in question, and helps the decision-maker assess the profitability
of the different customers. Predictive models assist a target marketing
strategy: offering the right product to the right customer at the right time
using the proper distribution channel. The firm approaches the customers
estimated as the most interested and proposes a marketing offer. A customer
that accepts the offer and conducts a purchase adds to the firms' profits.
This strategy affords better eciency than a mass marketing strategy, in
which a firm offers a product to all known potential customers, usually
resulting in low positive response rates. For example, a mail marketing
response rate of 2% or a phone marketing response of 10% are considered
good.
The main objective of a marketing campaign is to select which potential
customers a firm should approach with a new product offer, in order to
maximize the net profit. In the marketing problem presented in this paper,
we assume that the firm holds an initial dataset of potential customers
that can be used during the exploration phase. This initial dataset does
not, however, cover all potential customers. We also assume that, while
acquiring the customers' response is costly, some of the courted customers
will respond positively to the offer and the income from their purchase will
offset the cost. We propose to refer to the net acquisition cost, which is the
total cost of acquiring customer response, less the income generated if the
courted customers purchase the products.
We also assume that during a marketing campaign, a firm will not
approach its customers one by one, but it will rather approach a batch of
customers simultaneously, so that the firm can concentrate its exploitation
of resources, such as marketing personnel and equipment. After a campaign
session is over and a batch of customers has been courted, the firm can
analyze the results and proceed to the next stage of the campaign. We
assume a fixed batch size.
In our targeted marketing context, an instance x i X is defined

as the set of attributes, such as age and gender, of a unique potential
customer i . For the sake of clarity, we will assume a binary outcome for
the target attribute y, specifically y=

∈

. Unlabeled
instances are defined as instances with an unknown target attribute. A set
S of M unlabeled instances from the set X is obtained. The instances in
S are independent and behave according to some fixed and unknown joint
probability distribution D of X and Y . The cost of approaching customer
i with an offer is denoted as C i ∈

{ “accept”, “reject” }

. The probability that customer i will
respond positively to the offer is denoted as p i .Ifcustomer i with some