MML invariant linear regression

Abstract

This paper derives two new information theoretic linear regression criteria based on the minimum message length principle. Both criteria are invariant to full rank affine transformations of the design matrix and yield estimates that are minimax with respect to squared error loss. The new criteria are compared against state of the art information theoretic model selection criteria on both real and synthetic data and show good performance in all cases. © Springer-Verlag Berlin Heidelberg 2009.