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Abstract

High-dimensional statistics deals with statistical inference when the number of parameters or featurespexceeds the number of observationsn(i.e.,). In this case, the parameter space must be constrained either by regularization or by selecting a small subset offeatures. Feature selection through-regularization combines the benefits of both approaches and has proven to yield good results in practice. However, the functional relation between the regularization strengthand the number of selected featuresmis difficult to determine. Hence, parameters are typically estimated for all possible regularization strengths. These so-called regularization paths can be expensive to compute and most solutions may not even be of interest to the problem at hand. As an alternative, an algorithm is proposed that determines the-regularization strengthiteratively for a fixedm. The algorithm can be used to compute leapfrog regularization paths by subsequently increasingm.