Goal of Concept Learning

The goal of concept learning is to infer a boolean-valued function, known as a concept, from a set of training examples that have been classified as either positive or negative instances of that concept.

Equivalently, the goal is to identify a specific subset of items from a larger set. It is a fundamental task in supervised classification.

The learning scenario is formalized with the following components:

• Instance Space ($X$): The set of all possible instances or objects that can be classified.
• Target Concept ($c$): The specific function to be learned. It is a subset of the instance space ($c\subseteq X$) and can be represented as an indicator function $c:X\to \{0,1\}$.
• Training Examples ($D$): A set of instances from $X$, each paired with its correct classification given by the target concept, i.e., $D=\{(x_1,c(x_1)),(x_2,c(x_2)),...\}$.
• Hypothesis Space ($H$): The set of all possible concepts that the learning algorithm is allowed to consider. The output of the learner is a hypothesis $h\in H$, where $h:X\to \{0,1\}$, which is intended to be the best approximation of the target concept $c$.

Example

Month	Temp	Humidity	Wind	Go Surfing? (c(x))
July	Cold	Low	Strong	Yes
August	Hot	Low	Strong	Yes
July	Hot	Low	Weak	No
Sept.	Cold	High	Weak	No
Target Concept $(c)$: A true rule that defines a good day for surfing.
Assume that the unknown rule is simple “any day with strong wind”