Differential Description Length for Hyperparameter Selection in Machine Learning

Abstract: This paper introduces a new method for model selection and more generally hyperparameter selection in machine learning. Minimum description length (MDL) is an established method for model selection, which is however not directly aimed at minimizing generalization error, which is often the primary goal in machine learning. The paper demonstrates a relationship between generalization error and a difference of description lengths of the training data; we call this difference differential description length (DDL). This allows prediction of generalization error from the training data alone by performing encoding of the training data. DDL can then be used for model selection by choosing the model with the smallest predicted generalization error. We show how this method can be used for linear regression and neural networks and deep learning. Experimental results show that DDL leads to smaller generalization error than cross-validation and traditional MDL and Bayes methods.