Efficient subsampling for exponential family models

A novel two-stage subsampling algorithm is proposed which is based on optimal design principles. In the first stage, a density-based clustering algorithm is used to identify an approximating design space for the predictors from an initial subsample. Next, an optimal approximate design is determined on this design space. Finally, the remaining points of the subsample are defined as those that are closest to the support points of the optimal design, where closeness is measured using matrix distances such as the Procrustes, Frobenius, or square-root distance. The new subsampling approach reflects the specific nature of the information matrix as a weighted sum of non-negative definite Fisher information matrices evaluated at the design points and applies to a large class of regression models including models where the Fisher information is of rank larger than 1.