The New England Journal of Statistics in Data Science

Estimating a prediction function is a fundamental component of many data analyses. The super learner ensemble, a particular implementation of stacking, has desirable theoretical properties and has been used successfully in many applications. Dimension reduction can be accomplished by using variable screening algorithms (screeners), including the lasso, within the ensemble prior to fitting other prediction algorithms. However, the performance of a super learner using the lasso for dimension reduction has not been fully explored in cases where the lasso is known to perform poorly. We provide empirical results that suggest that a diverse set of candidate screeners should be used to protect against poor performance of any one screener, similar to the guidance for choosing a library of prediction algorithms for the super learner. These results are further illustrated through the analysis of HIV-1 antibody data.

Subdata selection from big data is an active area of research that facilitates inferences based on big data with limited computational expense. For linear regression models, the optimal design-inspired Information-Based Optimal Subdata Selection (IBOSS) method is a computationally efficient method for selecting subdata that has excellent statistical properties. But the method can only be used if the subdata size, k, is at last twice the number of regression variables, p. In addition, even when $k\ge 2p$, under the assumption of effect sparsity, one can expect to obtain subdata with better statistical properties by trying to focus on active variables. Inspired by recent efforts to extend the IBOSS method to situations with a large number of variables p, we introduce a method called Combining Lasso And Subdata Selection (CLASS) that, as shown, improves on other proposed methods in terms of variable selection and building a predictive model based on subdata when the full data size n is very large and the number of variables p is large. In terms of computational expense, CLASS is more expensive than recent competitors for moderately large values of n, but the roles reverse under effect sparsity for extremely large values of n.