Modularity in Query-Based Concept Learning

TL;DR

This paper explores modular concept learning, where complex concepts are composed of simpler components, and analyzes how different oracle query types affect the learnability of such concepts.

Contribution

It introduces the formal problem of modular concept learning and analyzes the impact of various oracle interfaces on the complexity of learning composite concepts.

Findings

Learning from superset queries is straightforward.

Membership, equivalence, or subset queries are more challenging.

Providing positive examples and membership queries makes learning tractable.

Abstract

We define and study the problem of modular concept learning, that is, learning a concept that is a cross product of component concepts. If an element's membership in a concept depends solely on it's membership in the components, learning the concept as a whole can be reduced to learning the components. We analyze this problem with respect to different types of oracle interfaces, defining different sets of queries. If a given oracle interface cannot answer questions about the components, learning can be difficult, even when the components are easy to learn with the same type of oracle queries. While learning from superset queries is easy, learning from membership, equivalence, or subset queries is harder. However, we show that these problems become tractable when oracles are given a positive example and are allowed to ask membership queries.