A Concept Learning Task
Consider the example task of learning the target concept "days on which my friend enjoys his favorite water sport." The following table describes a set of example days, each represented by a set of attributes. The attribute ‘Enjoy Sport’ indicates whether or not my friend enjoys his favorite water sport on this day. The task is to learn to predict the value of Enjoy Sport for an arbitrary day, based on the values of its other attributes.
Let us begin by considering a simple representation in which each hypothesis consists of a conjunction of constraints on the instance attributes. In particular, let each hypothesis be a vector of six constraints, specifying the values of the six attributes Sky, Air Temp, Humidity, Wind, Water, and Forecast. For each attribute, the hypothesis will either
Indicate by a "?' that any value is acceptable for this attribute,
Specify a single required value (e.g., Warm) for the attribute, or
Indicate by a "0" that no value is acceptable.
If some instance x satisfies all the constraints of hypothesis h, then h classifies x as a positive example (h(x) = 1). To illustrate, the hypothesis that Friend enjoys his favourite sport only on cold days with high humidity (independent of the values of the other attributes) is represented by the expression.
(?, Cold, High, ?, ?, ?)
he most general hypothesis-that every day is a positive example-is represented by (?, ?, ?, ?, ?) and the most specific possible hypothesis that no day is a positive example is represented by (¢,¢,¢,¢,¢).
To summarize, the Enjoy Sport concept learning task requires learning the set of days for which Enjoy Sport = yes, describing this set by a conjunction of constraints over the instance attributes. In general, any concept learning task can be described by the set of instances over which the target function is defined, the target function, the set of candidate hypotheses considered by the learner, and the set of available training examples.