Conceptual Complexity and the Bias-Variance Tradeoff
Erica Briscoe, Jacob Feldman · eScholarship (California Digital Library) · 2006
In this paper we propose that the dichotomy between exemplarbased and prototype-based models of concept learning can be regarded as an instance of the tradeoff between complexity and data-fit, often referred to in the statistical learning literature as the bias-variance tradeoff.This continuum reflects differences in models' assumptions about the form of the concepts in their environments: models at one extreme, here exemplified by prototype models, assume a simple conceptual form, entailing high bias; models at the other extreme, exemplified by exemplar models, entertain more complex hypotheses, but tend to overfit the data, with a concomitant loss in generalization performance.To investigate human learners' place on this continuum, we had subjects learn concepts of varying levels of structural complexity.Concepts consisted of mixtures of Gaussian distributions, with the number of mixture components serving as the measure of complexity.We then fit subjects' responses to both a representative exemplar model and a representative prototype model.With moderately complex multimodal categories, the exemplar model generally fit subjects' performance better, due to the prototype models' overly narrow (high-bias) assumption of a unimodal concept.But with high-complexity concepts, the exemplar model's overly flexible (high-variance) assumptions made it overfit concepts relative to subjects, allowing it to outperform subjects on highly complex concepts.We conclude that neither strategy is uniformly optimal as a model of human performance.