  Subsampling is one of the popular methods to balance statistical efficiency
and computational efficiency in the big data era. Most approaches aim at
selecting informative or representative sample points to achieve good overall
information of the full data. The present work takes the view that sampling
techniques are recommended for the region we focus on and summary measures are
enough to collect the information for the rest according to a well-designed
data partitioning. We propose a multi-resolution subsampling strategy that
combines global information described by summary measures and local information
obtained from selected subsample points. We show that the proposed method will
lead to a more efficient subsample-based estimator for general large-scale
classification problems. Some asymptotic properties of the proposed method are
established and connections to existing subsampling procedures are explored.
Finally, we illustrate the proposed subsampling strategy via simulated and
real-world examples.
