# Current Best Hypothesis Search

The idea behind the current best hypothesis search is to maintain a single hypothesis and to adjust it as a new example arise in order to maintain consistency.

The hypothesis space **H **is a set of hypothesis that learning algorithm is designed to entertain. The learning algorithm believes that one hypothesis is correct, that is, it believes the sentence:

h_{1 }V_{ }h_{2 }V h_{3 }V_{.... }V h_{n}

Hypothesis that are not consistent with the example can be ruled out.

There are two possible ways to be inconsistent with an example:

- False negative: In this hypothesis, the example should be negative but in fact it is positive.
- False positive: In this type of hypothesis, the example should be positive but in fact it is negative.

if the example is consistent with the hypothesis then do not change it. If the example is false negative then, generalize the hypothesis and if the example is false positive then specialize the hypothesis.

function CURRENT-BEST-LEARNING(examples) return a hypothesis H<- any hypothesis consistent with the first example in examples for each remaining example in examples do if e is a false positive for H then H<- choose a specialization of H is consistent with examples else if e is a false negative for H then H<- choose a generalization of H is consistent with examples if no consistent specialization/generalization can be found then fail return H

The current best hypothesis learning algorithm searches for a consistent hypothesis and backtracks the algorithm when no solution is found .

Notice that each time, we consider generalizing or specializing the hypothesis, we must check for consistency with other examples, because an arbitrary increase or decrease in the extension might include or exclude previously seen negative or positive examples.

Generalization and specialization are defined as operations that change the extension of hypothesis .

The current best hypothesis algorithm and its variants have been used in many learning systems.

#### Disadvantages:

- checking all the previous instances over again for each modification is very expensive.
- the search process may involve a great deal of backtracking. Hypothesis space can be a doubly exponentially large place.

The more general than and “more specific than” relations between hypothesis provide logical structure on hypothesis space that makes efficient search possible.