An Optimal Transport Approach for Selecting a Representative Subsample with Application in Efficient Kernel Density Estimation

Subsampling methods aim to select a subsample as a surrogate for the observed sample. Such methods have been used pervasively in large-scale data analytics, active learning, and privacy-preserving analysis in recent decades. Instead of model-based methods, in this article, we study model-free subsam...

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Vydáno v:Journal of computational and graphical statistics Ročník 32; číslo 1; s. 329 - 339
Hlavní autoři: Zhang, Jingyi, Meng, Cheng, Yu, Jun, Zhang, Mengrui, Zhong, Wenxuan, Ma, Ping
Médium: Journal Article
Jazyk:angličtina
Vydáno: Alexandria Taylor & Francis 02.01.2023
Taylor & Francis Ltd
Témata:
Adaptive algorithms
Clustering
Convergence
Density estimation
Empirical analysis
Inverse transform sampling
Kernels
Optimal transport
Population distribution
Probability density functions
Star discrepancy
Subsampling
ISSN:1061-8600, 1537-2715
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Shrnutí:Subsampling methods aim to select a subsample as a surrogate for the observed sample. Such methods have been used pervasively in large-scale data analytics, active learning, and privacy-preserving analysis in recent decades. Instead of model-based methods, in this article, we study model-free subsampling methods, which aim to identify a subsample, that is, not confined by model assumptions. Existing model-free subsampling methods are usually built upon clustering techniques or kernel tricks. Most of these methods suffer from either a large computational burden or a theoretical weakness. In particular, the theoretical weakness is that the empirical distribution of the selected subsample may not necessarily converge to the population distribution. Such computational and theoretical limitations hinder the broad applicability of model-free subsampling methods in practice. We propose a novel model-free subsampling method by using optimal transport techniques. Moreover, we develop an efficient subsampling algorithm, that is, adaptive to the unknown probability density function. Theoretically, we show the selected subsample can be used for efficient density estimation by deriving the convergence rate for the proposed subsample kernel density estimator. We also provide the optimal bandwidth for the proposed estimator. Numerical studies on synthetic and real-world datasets demonstrate the performance of the proposed method is superior.
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ISSN:1061-8600
1537-2715
DOI:10.1080/10618600.2022.2084404