Version space learning is a
logical
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
approach to
machine learning
Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence.
Machine ...
, specifically
binary classification
Binary classification is the task of classifying the elements of a set into two groups (each called ''class'') on the basis of a classification rule. Typical binary classification problems include:
* Medical testing to determine if a patient has c ...
. Version space learning algorithms search a predefined space of
hypotheses, viewed as a set of
logical sentences. Formally, the hypothesis space is a
disjunction
In logic, disjunction is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is raining or it is snowing" can be represented in logic using the disjunctive formula R \lor S ...
:
(i.e., either hypothesis 1 is true, or hypothesis 2, or any subset of the hypotheses 1 through ). A version space learning algorithm is presented with examples, which it will use to restrict its hypothesis space; for each example , the hypotheses that are
inconsistent
In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent ...
with are removed from the space.
This iterative refining of the hypothesis space is called the candidate elimination algorithm, the hypothesis space maintained inside the algorithm its ''version space''.
The version space algorithm
In settings where there is a generality-ordering on hypotheses, it is possible to represent the version space by two sets of hypotheses: (1) the most specific consistent hypotheses, and (2) the most general consistent hypotheses, where "consistent" indicates agreement with observed data.
The most specific hypotheses (i.e., the specific boundary SB) cover the observed positive training examples, and as little of the remaining
feature space
In machine learning and pattern recognition, a feature is an individual measurable property or characteristic of a phenomenon. Choosing informative, discriminating and independent features is a crucial element of effective algorithms in pattern r ...
as possible. These hypotheses, if reduced any further, ''exclude'' a ''positive'' training example, and hence become inconsistent. These minimal hypotheses essentially constitute a (pessimistic) claim that the true concept is defined just by the ''positive'' data already observed: Thus, if a novel (never-before-seen) data point is observed, it should be assumed to be negative. (I.e., if data has not previously been ruled in, then it's ruled out.)
The most general hypotheses (i.e., the general boundary GB) cover the observed positive training examples, but also cover as much of the remaining feature space without including any negative training examples. These, if enlarged any further, ''include'' a ''negative'' training example, and hence become inconsistent. These maximal hypotheses essentially constitute a (optimistic) claim that the true concept is defined just by the ''negative'' data already observed: Thus, if a novel (never-before-seen) data point is observed, it should be assumed to be positive. (I.e., if data has not previously been ruled out, then it's ruled in.)
Thus, during learning, the version space (which itself is a set – possibly infinite – containing ''all'' consistent hypotheses) can be represented by just its lower and upper bounds (maximally general and maximally specific hypothesis sets), and learning operations can be performed just on these representative sets.
After learning, classification can be performed on unseen examples by testing the hypothesis learned by the algorithm. If the example is consistent with multiple hypotheses, a majority vote rule can be applied.
Historical background
The notion of version spaces was introduced by Mitchell in the early 1980s as a framework for understanding the basic problem of supervised learning within the context of
solution search. Although the basic "candidate elimination" search method that accompanies the version space framework is not a popular learning algorithm, there are some practical implementations that have been developed (e.g., Sverdlik & Reynolds 1992, Hong & Tsang 1997, Dubois & Quafafou 2002).
A major drawback of version space learning is its inability to deal with noise: any pair of inconsistent examples can cause the version space to ''collapse'', i.e., become empty, so that classification becomes impossible. One solution of this problem is proposed by Dubois and Quafafou that proposed the Rough Version Space,
where rough sets based approximations are used to learn certain and possible hypothesis in the presence of inconsistent data.
See also
*
Formal concept analysis
*
Inductive logic programming
*
Rough set. [The rough set framework focuses on the case where ambiguity is introduced by an impoverished feature set. That is, the target concept cannot be decisively described because the available feature set fails to disambiguate objects belonging to different categories. The version space framework focuses on the (classical induction) case where the ambiguity is introduced by an impoverished data set. That is, the target concept cannot be decisively described because the available data fails to uniquely pick out a hypothesis. Naturally, both types of ambiguity can occur in the same learning problem.]
*Inductive reasoning. [On the general problem of induction.]
References
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]
[
]
*
*
*{{cite conference
, first = W.
, last = Sverdlik
, author2=Reynolds, R.G.
, title = Dynamic version spaces in machine learning
, book-title = Proceedings, Fourth International Conference on Tools with Artificial Intelligence (TAI '92)
, pages = 308–315
, year = 1992
, location = Arlington, VA
Machine learning