Combining Geometric and Topological Information for Boundary Estimation

Luo, Hengrui; Strait, Justin

doi:10.1109/bigdata52589.2021.9672024

Cited by 3 publications

(1 citation statement)

References 28 publications

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“…As is to be expected, when more sample points are available, our covering scheme locates the zero-density region S 0 more accurately. In applied scenarios where the boundaries arise as zero-density regions of certain density functions, our method could help in detection [15].…”

Section: Connections To Existingmentioning

confidence: 99%

Asymptotics of Lower Dimensional Zero-Density Regions

Luo

MacEachern

Peruggia

2020

Preprint

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Topological data analysis (TDA) allows us to explore the topological features of a dataset. Among topological features, lower dimensional ones have recently drawn the attention of practitioners in mathematics and statistics due to their potential to aid the discovery of low dimensional structure in a data set. However, lower dimensional features are usually challenging to detect from a probabilistic perspective.In this paper, lower dimensional topological features occurring as zero-density regions of density functions are introduced and thoroughly investigated. Specifically, we consider sequences of coverings for the support of a density function in which the coverings are comprised of balls with shrinking radii. We show that, when these coverings satisfy certain sufficient conditions as the sample size goes to infinity, we can detect lower dimensional, zero-density regions with increasingly higher probability while guarding against false detection. We supplement the theoretical developments with the discussion of simulated experiments that elucidate the behavior of the methodology for different choices of the tuning parameters that govern the construction of the covering sequences and characterize the asymptotic results.

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Section: Connections To Existingmentioning

confidence: 99%

Asymptotics of Lower Dimensional Zero-Density Regions

Luo

MacEachern

Peruggia

2020

Preprint

Self Cite

View full text Add to dashboard Cite

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Asymptotics of lower dimensional zero-density regions

Luo,

MacEachern,

Peruggia

2023

Statistics

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Non-smooth Bayesian optimization in tuning scientific applications

Luo,

Cho,

Demmel

et al. 2024

The International Journal of High Performance Computing Applica

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Tuning algorithmic parameters to optimize the performance of large, complicated computational codes is an important problem involving finding the optima and identifying regimes defined by non-smooth boundaries in black-box functions. Within the Bayesian optimization framework, the Gaussian process surrogate model produces smooth mean functions, but functions in the tuning problem are often non-smooth, which is exacerbated by the fact that we usually have limited sequential samples from the black-box function. Motivated by these issues encountered in tuning, we propose a novel Gaussian process model called a clustered Gaussian process (cGP), where the components are dynamically updated by clustering. In our studies, the performance of cGP can be better than stationary GPs in nearly 90% of the experiments and better than non-stationary GPs in nearly 70% of the repeated experiments while requiring less computational cost. cGP provides a novel approach for dynamic GP, computes more efficiently than recursive partitioning, and discovers non-smoothness regimes. We provide extensive experiments including high-performance computing (HPC) and industrial simulation functions to show the effectiveness of our methods.

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Combining Geometric and Topological Information for Boundary Estimation

Cited by 3 publications

References 28 publications

Asymptotics of Lower Dimensional Zero-Density Regions

Asymptotics of Lower Dimensional Zero-Density Regions

Asymptotics of lower dimensional zero-density regions

Non-smooth Bayesian optimization in tuning scientific applications

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