MAP- and MLE-Based Teaching
Hans Ulrich Simon, Jan Arne Telle

TL;DR
This paper introduces a formal framework for teaching concepts to learners modeled by MAP and MLE methods, analyzing different sampling modes and deriving bounds and computational properties of teaching dimensions.
Contribution
It formalizes MAP and MLE-based teaching models, explores their properties across sampling modes, and characterizes teaching dimensions using graph theory and combinatorial parameters.
Findings
MAP- and MLE-teaching dimensions are related and can be bounded by VC-dimension.
The dimensions are computable in polynomial time.
The model exhibits desirable monotonicity properties.
Abstract
Imagine a learner L who tries to infer a hidden concept from a collection of observations. Building on the work [4] of Ferri et al., we assume the learner to be parameterized by priors P(c) and by c-conditional likelihoods P(z|c) where c ranges over all concepts in a given class C and z ranges over all observations in an observation set Z. L is called a MAP-learner (resp. an MLE-learner) if it thinks of a collection S of observations as a random sample and returns the concept with the maximum a-posteriori probability (resp. the concept which maximizes the c-conditional likelihood of S). Depending on whether L assumes that S is obtained from ordered or unordered sampling resp. from sampling with or without replacement, we can distinguish four different sampling modes. Given a target concept c in C, a teacher for a MAP-learner L aims at finding a smallest collection of observations that…
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Taxonomy
TopicsMachine Learning and Algorithms · Algorithms and Data Compression · Computability, Logic, AI Algorithms
