Sparsity-promoting bootstrap method for large-scale data

Performing statistical inference on massive data sets may not be computationally feasible using the conventional statistical inference methodology. In particular, there is a need for methods that are scalable to large volume and variability of data. Moreover, veracity of the inference is crucial. Hence, there is a need to produce quantitative information on the statistical correctness of parameter estimates or decisions. In this paper, we propose a scalable nonparametric bootstrap method that operates with smaller number of distinct data points on multiple disjoint subsets of data. The sampling approach stems from the Bag of Little Bootstraps method and is compatible with distributed storage systems and distributed and parallel processing architectures. Iterative reweighted l₁ method is used for each bootstrap replica to find a sparse solution in the face of high-dimensional signal model. The proposed method finds reliable estimates even if the problem is not overdetermined for full data or distinct data subsets by exploiting sparseness. The performance of the proposed method in identifying sparseness in parameter vector and finding confidence intervals and parameter estimates is studied in simulation.