Maps for Learning Indexable Classes

TL;DR

This paper explores the theoretical framework of learning indexable classes from positive data, analyzing various restrictions and conditions to map the relationships between different learning criteria.

Contribution

It provides comprehensive maps of relationships among various learning restrictions and criteria, extending previous theoretical results in the field.

Findings

Mapped relations among learning criteria including monotonicity and data presentation restrictions.

Analyzed the impact of consistency assumptions on learning capabilities.

Extended the theoretical understanding of learning indexable classes.

Abstract

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.