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The Minimum Description Length (MDL) principle states that the optimal modelfor a given data set is that which compresses it best. Due to practiallimitations the model can be restricted to a class such as linear regressionmodels, which we address in this study. As in other formulations such as theLASSO and forward step-wise regression we are interested in sparsifying thefeature set while preserving generalization ability. We derive awell-principled set of codes for both parameters and error residuals along withsmooth approximations to lengths of these codes as to allow gradient descentoptimization of description length, and go on to show that sparsification andfeature selection using our approach is faster than the LASSO on severaldatasets from the UCI and StatLib repositories, with favorable generalizationaccuracy, while being fully automatic, requiring neither cross-validation nortuning of regularization hyper-parameters, allowing even for a nonlinearexpansion of the feature set followed by sparsification.

Sparsification and feature selection by compressive linear regression