Principal-component-based observation identification for PTS

Determine whether informative observations for the Prescreen, Then Subsample (PTS) framework can be identified using a small number of derived variables, such as principal components, instead of the prescreened covariates.

Background

The PTS framework first prescreens covariates and then applies informative subsampling, specifically IBOSS in the paper’s numerical evaluation, within the retained covariate space. The paper notes that the effectiveness of this procedure depends on the dimension of that space, because the standard IBOSS allocation requires the target subsample size to satisfy k ≥ 2q, where q is the number of retained covariates.

As a possible way to address this dimensionality constraint, the authors raise the unresolved possibility of selecting observations using a small number of derived variables rather than the full prescreened covariate set. Principal components are given as a concrete example, but the paper does not determine whether this alternative preserves the predictive and computational advantages of PTS.