Finite Biased Teaching with Infinite Concept Classes

TL;DR

This paper explores how biases in teaching and sampling affect the teaching complexity of infinite concept classes like Turing and finite-state machines, revealing trade-offs and bounds related to complexity measures.

Contribution

It introduces bounds for biased teaching dimensions based on complexity measures and analyzes sampling distributions for infinite concept classes.

Findings

Derived bounds for biased teaching dimension using Kolmogorov complexity and state minimality

Identified sampling distributions that yield finite expected biased teaching dimensions

Highlighted trade-offs between sample representativeness and teaching bounds

Abstract

We investigate the teaching of infinite concept classes through the effect of the learning bias (which is used by the learner to prefer some concepts over others and by the teacher to devise the teaching examples) and the sampling bias (which determines how the concepts are sampled from the class). We analyse two important classes: Turing machines and finite-state machines. We derive bounds for the biased teaching dimension when the learning bias is derived from a complexity measure (Kolmogorov complexity and minimal number of states respectively) and analyse the sampling distributions that lead to finite expected biased teaching dimensions. We highlight the existing trade-off between the bound and the representativeness of the sample, and its implications for the understanding of what teaching rich concepts to machines entails.