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In the signal processing and statistics literature, the minimum descriptionlength (MDL) principle is a popular tool for choosing model complexity.Successful examples include signal denoising and variable selection in linearregression, for which the corresponding MDL solutions often enjoy consistentproperties and produce very promising empirical results. This paperdemonstrates that MDL can be extended naturally to the high-dimensionalsetting, where the number of predictors $p$ is larger than the number ofobservations $n$. It first considers the case of linear regression, then allowsfor outliers in the data, and lastly extends to the robust fitting ofnonparametric additive models. Results from numerical experiments are presentedto demonstrate the efficiency and effectiveness of the MDL approach.

Extending the Use of MDL for High-Dimensional Problems: Variable Selection, Robust Fitting, and Additive Modeling