具有复杂后验的贝叶斯模型推断:指数影响的贝叶斯正交

IF 8.9 1区 工程技术 Q1 ENGINEERING, MECHANICAL
Pengfei Wei
{"title":"具有复杂后验的贝叶斯模型推断:指数影响的贝叶斯正交","authors":"Pengfei Wei","doi":"10.1016/j.ymssp.2025.113333","DOIUrl":null,"url":null,"abstract":"<div><div>Estimation of multimodal and sharp posteriors with nonlinear dependencies as well as the associated model evidence remains a critical challenge in many Bayesian model inference tasks such as model parameter calibration, model selection and model averaging. Bayesian Quadrature (BQ) based on approximating the logarithm of likelihood with a Gaussian Process surrogate model has been proven to be a promising scheme for multimodal inference, but the mechanism behind it has not yet been sufficiently investigated. By exploring the mechanism of exponential impact behind this, I first answer the questions “why it works?”, as well as “can it work better, and how?” This mechanism then motivates the development of a simpler but more effective BQ method informed by the exponential impact. This BQ method is equipped with measures of prediction uncertainties and active learning, driven by two new acquisition functions, which have insightful interpretations, closed-form expressions and sound performance. Further, a transitional learning scheme based on adaptive tempering is developed and embedded into the developed BQ method, allowing for adaptive inference of sharp posteriors with desired accuracy. Several specific treatments, including elimination of error accumulation across stages, adaptive specification of tempering parameters, etc., have been developed for achieving the robust and efficient Transitional Bayesian Quadrature (TBQ) algorithm. Ultimately, the performance of TBQ for learning posteriors with multiple disconnected modes, high sharpness and nonlinear dependencies are demonstrated with both numerical cases and dynamics models.</div></div>","PeriodicalId":51124,"journal":{"name":"Mechanical Systems and Signal Processing","volume":"239 ","pages":"Article 113333"},"PeriodicalIF":8.9000,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bayesian model inference with complex posteriors: Exponential-impact-informed Bayesian Quadrature\",\"authors\":\"Pengfei Wei\",\"doi\":\"10.1016/j.ymssp.2025.113333\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Estimation of multimodal and sharp posteriors with nonlinear dependencies as well as the associated model evidence remains a critical challenge in many Bayesian model inference tasks such as model parameter calibration, model selection and model averaging. Bayesian Quadrature (BQ) based on approximating the logarithm of likelihood with a Gaussian Process surrogate model has been proven to be a promising scheme for multimodal inference, but the mechanism behind it has not yet been sufficiently investigated. By exploring the mechanism of exponential impact behind this, I first answer the questions “why it works?”, as well as “can it work better, and how?” This mechanism then motivates the development of a simpler but more effective BQ method informed by the exponential impact. This BQ method is equipped with measures of prediction uncertainties and active learning, driven by two new acquisition functions, which have insightful interpretations, closed-form expressions and sound performance. Further, a transitional learning scheme based on adaptive tempering is developed and embedded into the developed BQ method, allowing for adaptive inference of sharp posteriors with desired accuracy. Several specific treatments, including elimination of error accumulation across stages, adaptive specification of tempering parameters, etc., have been developed for achieving the robust and efficient Transitional Bayesian Quadrature (TBQ) algorithm. Ultimately, the performance of TBQ for learning posteriors with multiple disconnected modes, high sharpness and nonlinear dependencies are demonstrated with both numerical cases and dynamics models.</div></div>\",\"PeriodicalId\":51124,\"journal\":{\"name\":\"Mechanical Systems and Signal Processing\",\"volume\":\"239 \",\"pages\":\"Article 113333\"},\"PeriodicalIF\":8.9000,\"publicationDate\":\"2025-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mechanical Systems and Signal Processing\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0888327025010349\",\"RegionNum\":1,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanical Systems and Signal Processing","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0888327025010349","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0

摘要

具有非线性依赖的多模态和锐后验的估计以及相关的模型证据仍然是许多贝叶斯模型推理任务(如模型参数校准,模型选择和模型平均)中的关键挑战。基于高斯过程代理模型逼近似然对数的贝叶斯正交(BQ)已被证明是一种很有前途的多模态推理方案,但其背后的机制尚未得到充分的研究。通过探索这背后的指数影响机制,我首先回答了“为什么它会起作用?”,以及“它能更好地工作吗?如何更好地工作?”然后,这种机制激发了一种更简单但更有效的BQ方法的发展,这种方法受到指数影响的影响。该BQ方法配备了预测不确定性和主动学习的度量,由两个新的习得函数驱动,具有深刻的解释,封闭的形式表达和良好的性能。此外,开发了一种基于自适应回火的过渡学习方案,并将其嵌入到所开发的BQ方法中,允许以期望的精度自适应推断尖锐后验。为了实现鲁棒高效的过渡贝叶斯正交(TBQ)算法,提出了若干具体的处理方法,包括消除各阶段误差积累、自适应规范回火参数等。最后,通过数值实例和动态模型证明了TBQ在学习具有多个断开模式、高清晰度和非线性依赖的后验方面的性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Bayesian model inference with complex posteriors: Exponential-impact-informed Bayesian Quadrature
Estimation of multimodal and sharp posteriors with nonlinear dependencies as well as the associated model evidence remains a critical challenge in many Bayesian model inference tasks such as model parameter calibration, model selection and model averaging. Bayesian Quadrature (BQ) based on approximating the logarithm of likelihood with a Gaussian Process surrogate model has been proven to be a promising scheme for multimodal inference, but the mechanism behind it has not yet been sufficiently investigated. By exploring the mechanism of exponential impact behind this, I first answer the questions “why it works?”, as well as “can it work better, and how?” This mechanism then motivates the development of a simpler but more effective BQ method informed by the exponential impact. This BQ method is equipped with measures of prediction uncertainties and active learning, driven by two new acquisition functions, which have insightful interpretations, closed-form expressions and sound performance. Further, a transitional learning scheme based on adaptive tempering is developed and embedded into the developed BQ method, allowing for adaptive inference of sharp posteriors with desired accuracy. Several specific treatments, including elimination of error accumulation across stages, adaptive specification of tempering parameters, etc., have been developed for achieving the robust and efficient Transitional Bayesian Quadrature (TBQ) algorithm. Ultimately, the performance of TBQ for learning posteriors with multiple disconnected modes, high sharpness and nonlinear dependencies are demonstrated with both numerical cases and dynamics models.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Mechanical Systems and Signal Processing
Mechanical Systems and Signal Processing 工程技术-工程:机械
CiteScore
14.80
自引率
13.10%
发文量
1183
审稿时长
5.4 months
期刊介绍: Journal Name: Mechanical Systems and Signal Processing (MSSP) Interdisciplinary Focus: Mechanical, Aerospace, and Civil Engineering Purpose:Reporting scientific advancements of the highest quality Arising from new techniques in sensing, instrumentation, signal processing, modelling, and control of dynamic systems
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信