No Free Lunch versus Occam’s Razor in supervised learning

Abstract

The No Free Lunch theorems are often used to argue that domain specific knowledge is required to design successful algorithms. We use algorithmic information theory to argue the case for a universal bias allowing an algorithm to succeed in all interesting problem domains. Additionally, we give a new algorithm for off-line classification, inspired by Solomonoff induction, with good performance on all structured (compressible) problems under reasonable assumptions. This includes a proof of the efficacy of the well-known heuristic of randomly selecting training data in the hope of reducing the misclassification rate. Show more