ANOVA-GP Modeling for High-Dimensional Bayesian Inverse Problems

doi:10.3390/math12020301

	ANOVA-GP Modeling for High-Dimensional Bayesian Inverse Problems
	Shi, Xiaoyu1 ; Zhang, Hanyu1 ; Wang, Guanjie 2
	2024-01
发表期刊	MATHEMATICS (IF:2.3[JCR-2023],2.2[5-Year])
EISSN	2227-7390
卷号	12 期号:2
发表状态	已发表
DOI	10.3390/math12020301
摘要	Markov chain Monte Carlo (MCMC) stands out as an effective method for tackling Bayesian inverse problems. However, when dealing with computationally expensive forward models and high-dimensional parameter spaces, the challenge of repeated sampling becomes pronounced. A common strategy to address this challenge is to construct an inexpensive surrogate of the forward model, which cuts the computational cost of individual samples. While the Gaussian process (GP) is widely used as a surrogate modeling strategy, its applicability can be limited when dealing with high-dimensional input or output spaces. This paper presents a novel approach that combines the analysis of variance (ANOVA) decomposition method with Gaussian process regression to handle high-dimensional Bayesian inverse problems. Initially, the ANOVA method is employed to reduce the dimension of the parameter space, which decomposes the original high-dimensional problem into several low-dimensional sub-problems. Subsequently, principal component analysis (PCA) is utilized to reduce the dimension of the output space on each sub-problem. Finally, a Gaussian process model with a low-dimensional input and output is constructed for each sub-problem. In addition to this methodology, an adaptive ANOVA-GP-MCMC algorithm is proposed, which further enhances the adaptability and efficiency of the method in the Bayesian inversion setting. The accuracy and computational efficiency of the proposed approach are validated through numerical experiments. This innovative integration of ANOVA and Gaussian processes provides a promising solution to address challenges associated with high-dimensional parameter spaces and computationally expensive forward models in Bayesian inference.
关键词	Bayesian inverse problem uncertainty quantification ANOVA decomposition principle component analysis Gaussian process regression
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收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:001150782400001
出版者	MDPI
文献类型	期刊论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/349929
专题	信息科学与技术学院信息科学与技术学院_硕士生信息科学与技术学院_本科生
通讯作者	Wang, Guanjie
作者单位	1.ShanghaiTech Univ, Sch Informat Sci & Technol, Shanghai 201210, Peoples R China 2.Shanghai Lixin Univ Accounting & Finance, Sch Stat & Math, Shanghai 201209, Peoples R China
第一作者单位	信息科学与技术学院
第一作者的第一单位	信息科学与技术学院
推荐引用方式 GB/T 7714	Shi, Xiaoyu,Zhang, Hanyu,Wang, Guanjie. ANOVA-GP Modeling for High-Dimensional Bayesian Inverse Problems[J]. MATHEMATICS,2024,12(2).
APA	Shi, Xiaoyu,Zhang, Hanyu,&Wang, Guanjie.(2024).ANOVA-GP Modeling for High-Dimensional Bayesian Inverse Problems.MATHEMATICS,12(2).
MLA	Shi, Xiaoyu,et al."ANOVA-GP Modeling for High-Dimensional Bayesian Inverse Problems".MATHEMATICS 12.2(2024).