Learning to Learn Functions

Abstract

Humans can learn complex functional relationships between variables from small amounts of data. In doing so, they draw on prior expectations about the form of these relationships. In three experiments, we show that people learn to adjust these expectations through experience, learning about the likely forms of the functions they will encounter. Previous work has used Gaussian processes-a statistical framework that extends Bayesian nonparametric approaches to regression-to model human function learning. We build on this work, modeling the process of learning to learn functions as a form of hierarchical Bayesian inference about the Gaussian process hyperparameters.

Keywords: Bayesian nonparametrics; Function learning; Gaussian process; Hierarchical Bayesian models; Learning-to-learn.