In machine-learning problem space can be represented through concept space, instance space version space and hypothesis space. These problem spaces used the conjunctive space and is very restrictive one and also in the above-mentioned representations of problem spaces, it is not sure that the true concept lies within conjunctive space.
The question is, what if we have a bigger search space and want to overcome the restrictive nature of conjunctive space, then how can we represent our problem space. Secondly in a given scenario which algorithm is used for problem space to represent the learning problem.
If we want to overcome the restrictiveness of the conjunctive space and have a bigger search space, we can use a more expressive representation for our problem space. One such representation is the disjunctive space, which allows us to represent hypotheses as a disjunction (logical OR) of literals. This means that we can consider multiple possibilities and combinations for our hypotheses, rather than just the conjunctions (logical AND) allowed in the conjunctive space.
To represent the problem space using the disjunctive space, we can consider all possible combinations and alternatives for the individual literals. This allows us to explore a wider range of hypotheses and makes the search space less restrictive.
Regarding the algorithm to represent the learning problem in such a scenario, a commonly used approach is the Candidate Elimination algorithm. This algorithm operates on the version space, which is the set of all hypotheses in the hypothesis space that are consistent with the observed training data.
The Candidate Elimination algorithm starts with the most general hypothesis and most specific hypothesis in the version space, and gradually refines them based on the observed examples. The algorithm updates the version space by eliminating hypotheses that are inconsistent with the observed data, and keeping the remaining hypotheses that are still consistent.
By using the disjunctive space representation and the Candidate Elimination algorithm, we can overcome the restrictive nature of the conjunctive space and have a more flexible and expressive problem space for machine learning problems.