Maps for Learning Indexable Classes
This work addresses foundational learning theory problems for researchers in computational learning, but it is incremental as it extends existing maps and criteria without introducing new methods.
The paper tackles the problem of learning indexable classes from positive data under various learning restrictions, such as consistency and conservativeness, by providing comprehensive maps that depict all pairwise relations among these criteria, building on previous results.
We study learning of indexed families from positive data where a learner can freely choose a hypothesis space (with uniformly decidable membership) comprising at least the languages to be learned. This abstracts a very universal learning task which can be found in many areas, for example learning of (subsets of) regular languages or learning of natural languages. We are interested in various restrictions on learning, such as consistency, conservativeness or set-drivenness, exemplifying various natural learning restrictions. Building on previous results from the literature, we provide several maps (depictions of all pairwise relations) of various groups of learning criteria, including a map for monotonicity restrictions and similar criteria and a map for restrictions on data presentation. Furthermore, we consider, for various learning criteria, whether learners can be assumed consistent.