Computing Leapfrog Regularization Paths with Applications to Large-Scale K-mer Logistic Regression.

High-dimensional statistics deals with statistical inference when the number of parameters or featurespexceeds the number of observationsn(i.e.,p≫n). In this case, the parameter space must be constrained either by regularization or by selecting a small subset ofm≤nfeatures. Feature selection throughl1-regularization combines the benefits of both approaches and has proven to yield good results in practice. However, the functional relation between the regularization strengthλand the number of selected featuresmis difficult to determine. Hence, parameters are typically estimated for all possible regularization strengthsλ. 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 thel1-regularization strengthλiteratively for a fixedm. The algorithm can be used to compute leapfrog regularization paths by subsequently increasingm.