ملخص: The Minimum Description Length (MDL) principle is solidly based on a provably ideal method of inference using Kolmogorov complexity. We test how the theory behaves in practice on a general problem in model selection: that of learning the best model granularity. The performance of a model depends critically on the granularity, for example the choice of precision of the parameters. Too high precision generally involves modeling of accidental noise and too low precision may lead to confusion of models that should be distinguished. This precision is often determined ad hoc. In MDL the best model is the one that most compresses a two-part code of the data set: this embodies “Occam’s Razor”. In two quite different experimental settings the theoretical value determined using MDL coincides with the best value found experimentally. In the first experiment the task is to recognize isolated handwritten characters in one subject’s handwriting, irrespective of size and orientation. Based on a new modification of elastic matching, using multiple prototypes per character, the optimal prediction rate is predicted for the learned parameter (length of sampling interval) considered most likely byMDL, which is shown to coincide with the best value found experimentally. In the second experiment the task is to model a robot arm with two degrees of freedom using a three layer feed-forward neural network where we need to determine the number of nodes in the hidden layer giving best modeling performance. The optimal model (the one that extrapolizes best on unseen examples) is predicted for the number of nodes in the hidden layer considered most likely by MDL, I Parts of this work were presented at IJCAI, 1989, and at ESANN, 1994.  Corresponding author. Partially supported by the European Union through 4th Framework NeuroCOLT II Working Group EP 27150, the 5th Framework QAIP Project IST-1999-11234, the 5th Framework Network of Excellence QUIPROCONE IST-1999-29064, the COLORETWorking Group, the European Science Foundation, and by an NSERC International Scientific Exchange Award ISE0125663. E-mail addresses: paulv@cwi.nl (P. Vit?nyi), mli@cs.ucsb.edu (M. Li). 1 Supported in part by ONR Grant N00014-85-K-0445 and ARO Grant DAAL03-86-K-0171 at Harvard University, by NSERC operating grant OGP-0036747 at York University, and by NSERC operating grant OGP- 046506 at the University of Waterloo. On leave from the University of Waterloo.

لغة: إنجليزية