Diversity Subsampling: Custom Subsamples from Large Data Sets

TL;DR

This paper introduces a diversity subsampling method that efficiently selects representative, space-filling subsamples from large datasets, ensuring near-uniform coverage and outperforming existing algorithms in speed and quality.

Contribution

The paper proposes a novel diversity subsampling algorithm with theoretical guarantees, demonstrating superior performance and efficiency over existing methods, and provides a practical Python implementation.

Findings

The method achieves near-uniform coverage of the data support.

It outperforms competing algorithms in closeness to uniform sampling.

The algorithm is computationally efficient, handling large datasets in minutes.

Abstract

Subsampling from a large data set is useful in many supervised learning contexts to provide a global view of the data based on only a fraction of the observations. Diverse (or space-filling) subsampling is an appealing subsampling approach when no prior knowledge of the data is available. In this paper, we propose a diversity subsampling approach that selects a subsample from the original data such that the subsample is independently and uniformly distributed over the support of distribution from which the data are drawn, to the maximum extent possible. We give an asymptotic performance guarantee of the proposed method and provide experimental results to show that the proposed method performs well for typical finite-size data. We also compare the proposed method with competing diversity subsampling algorithms and demonstrate numerically that subsamples selected by the proposed method are closer to a uniform sample than subsamples selected by other methods. The proposed DS algorithm is shown to be more efficient than known methods and takes only a few minutes to select tens of thousands of subsample points from a data set of size one million. Our DS algorithm easily generalizes to select subsamples following distributions other than uniform. We provide the FADS Python package to implement the proposed methods.