A Note on The Comparison of Polynomial Selection Methods

Abstract

Minimum Message Length (MML) and Structural Risk Minimisation (SRM) are two computational learning principles that have achieved wide acclaim in recent years. Whereas the former is based on Bayesian learning and the latter on the classical theory of VC-dimension, they are similar in their attempt to define a trade-off between model complexity and goodness of fit to the data. A recent empirical study by Wallace compared the performance of standard model selection methods in a one-dimensional polynomial regression framework. The results from this study provided strong evidence in support of the MML and SRM based methods over the other standard approaches. In this paper we present a detailed empirical evaluation of three model selection methods which include an MML based approach and two SRM based methods. Results from our analysis and experimental evaluation suggest that the MML-based approach in general has higher predictive accuracy and also raise questions on the inductive capabilities of the Structural Risk Minimization Principle.