Space-Filling Designed Sampling from Databases

Shang, Boyang

doi:https://doi.org/10.21985/n2-btd7-mb27

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Space-Filling Designed Sampling from Databases

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This thesis develops novel methods for generating space-filling designs inside a designspace and subsampling from a data set. It incorporates materials from two papers by the author: Shang and Apley 2021; Shang, Apley, and Mehrotra 2022a. Chapter 1 discusses space-filling designs of computer experiments, which is publishedas Shang and Apley 2021. Fully-sequential (i.e., with design points added one-at-a-time) space-filling designs are useful for global surrogate modeling of expensive computer experiments when the number of design points required to achieve a suitable accuracy is unknown in advance. We develop and investigate three fully-sequential space-filling (FSSF) design algorithms that are conceptually simple and computationally efficient and that achieve much better space-filling properties than alternative methods such as Sobol sequences and more complex batch-sequential methods based on sliced or nested optimal Latin hypercube designs (LHDs). Remarkably, at each design size in the sequence, our FSSF algorithms even achieve much better space filling properties than a one-shot LHD optimized for that specific size. The algorithms we propose also scale well to very large design sizes. We provide the FSSF R package to implement the approaches. Chapter 2 focuses on diversity subsampling from a data set, which is published asShang, Apley, and Mehrotra 2022a. 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 chapter, 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.

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