Nonmonotonic Extrapolation

Margery J. Doyle

Institute of Cognitive Science

University of Louisiana at Lafayette

 

Abstract

Common everyday tasks like learning how to brake and accelerate in traffic require function learning where a continuous stimulus variable (e.g. speed) must be associated with another continuous variable (e.g. distance). A contrast exists between parametric and nonparametric models of function learning. Under a parametric theory, an nth-order polynomial is optimized during training. In contrast, nonparametric models rely on the association between individual input-output pairs. It is known thus far that nonparametric and mixture models lead to greater flexibly and have had fair success in modeling human performance. However, these models still extrapolate linearly. In light of these claims, L. Bott and E. Heit (2004) trained participants on a nonmonotonic cyclic cosine function and modeled their nonlinear extrapolation. In this talk, I present the results of an attempt to replicate the work of Bott and Heit. The replication failed to support the critical finding of nonlinear extrapolation. I report additional experiments aimed at resolving the apparent contradiction between Bott and Heitā's results and those in our lab.