Concept class

In <a href="/facts/Computational_learning_theory/DKMoukIr">computational learning theory</a> in <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a concept over a domain X is a total <a href="/facts/Boolean_function/uT7E8pqC">Boolean function</a> over X. A concept class is a class of concepts. Concept classes are a subject of <a href="/facts/Computational_learning_theory/DKMoukIr">computational learning theory</a>.
Concept class terminology frequently appears in <a href="/facts/Model_theory/vLWVV8sQ">model theory</a> associated with <a href="/facts/Probably_approximately_correct/vBQlvDV1">probably approximately correct</a> (PAC) learning. In this setting, if one takes a set Y as a set of (classifier output) labels, and X is a set of examples, the map 
 
 
 
 c
 :
 X
 →
 Y
 
 
 {\displaystyle c:X\to Y}
 
, i.e. from examples to classifier labels (where 
 
 
 
 Y
 =
 {
 0
 ,
 1
 }
 
 
 {\displaystyle Y=\{0,1\}}
 
 and where c is a subset of X), c is then said to be a concept. A concept class 
 
 
 
 C
 
 
 {\displaystyle C}
 
 is then a collection of such concepts.
Given a class of concepts C, a subclass D is reachable if there exists a sample s such that D contains exactly those concepts in C that are extensions to s. Not every subclass is reachable.[why?]

Concept class open-in-new

Concept class