Asymptotics of lower dimensional zero-density regions

Luo, Hengrui; MacEachern, Steven N.; Peruggia, Mario

doi:10.1080/02331888.2023.2262665

Statistics

2023

DOI: 10.1080/02331888.2023.2262665

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Asymptotics of lower dimensional zero-density regions

Hengrui Luo,

Steven N. MacEachern,

Mario Peruggia

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2024

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Cited by 2 publications

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“…Notably, for the first of these three steps, we develop a version of the SVE algorithm that alternates between sampling PIPP parameters and sampling auxiliary PDs via RPDG. Interestingly, a recent work [19] could be used to devise a mapping of lower dimensional features, such as the boundaries of the PD windows to the PIPP model. In particular, it might be possible to directly use some topological features to define the spatial component s, i.e., the Voronoi tesselation of joint density in Equation (1).…”

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confidence: 99%

Bayesian random persistence diagram generation: An application to material microstructure analysis

Nasrin,

Papamarkou,

Lawson

et al. 2024

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Data analysis helps identify changes in the microstructure of materials, but is often hindered by the cost and time requirements of experimental data generation. Data augmentation provides an in silico alternative. A recent data augmentation algorithm, known as the random persistence diagram generator (RPDG), samples a sequence of synthetic topological summaries from a possibly limited amount of data. RPDG relies on a parametric model for persistence diagrams, namely a pairwise interacting point process (PIPP). Herein, we develop a Bayesian approach to infer the PIPP parameters and call the resulting pipeline the Bayesian RPDG (BRPDG). We showcase that BRPDG exhibits higher discriminative power than RPDG in the identification of materials structural changes.

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mentioning

confidence: 99%

Bayesian random persistence diagram generation: An application to material microstructure analysis

Nasrin,

Papamarkou,

Lawson

et al. 2024

FoDS

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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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Asymptotics of lower dimensional zero-density regions

Cited by 2 publications

References 23 publications

Bayesian random persistence diagram generation: An application to material microstructure analysis

Bayesian random persistence diagram generation: An application to material microstructure analysis

Non-smooth Bayesian optimization in tuning scientific applications

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