  Subdata selection is a study of methods that select a small representative
sample of the big data, the analysis of which is fast and statistically
efficient. The existing subdata selection methods assume that the big data can
be reasonably modeled using an underlying model, such as a (multinomial)
logistic regression for classification problems. These methods work extremely
well when the underlying modeling assumption is correct but often yield poor
results otherwise. In this paper, we propose a model-free subdata selection
method for classification problems, and the resulting subdata is called PED
subdata. The PED subdata uses decision trees to find a partition of the data,
followed by selecting an appropriate sample from each component of the
partition. Random forests are used for analyzing the selected subdata. Our
method can be employed for a general number of classes in the response and for
both categorical and continuous predictors. We show analytically that the PED
subdata results in a smaller Gini than a uniform subdata. Further, we
demonstrate that the PED subdata has higher classification accuracy than other
competing methods through extensive simulated and real datasets.
